Torque loss in a planetary multiplier gearbox: Influence of operating conditions and gear oil formulation
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Faculdade Engenharia da Universidade do Porto Departamento de Engenharia Mecânica e Gestão Industrial Torque Loss in a Planetary Multiplier Gearbox: Inuence of Operating Conditions and Gear Oil Formulation Raquel Camacho Simões Dias Master's Degree Dissertation presented to Faculdade de Engenharia da Universidade do Porto Dissertation supervised by Dr. Ramiro Carneiro Martins Dr. Jorge Humberto O. Seabra Auxiliary researcher of INEGI Full Professor of FEUP Porto, July 2014
L A TEX FEUP-U.PORTO r.camacho 2014 ii
to Eng. Manuel Camacho Simões, my grandfather and greatest teacher iii
Acknowledgements I would like to express my gratitude to a few people who have helped and supported me throughout my Master's Degree Thesis. First of all, I would like to express my very great appreciation to my supervisors, Prof. Jorge H. O. Seabra, Dr. Ramiro C. Martins and Eng. Pedro M. T. Marques, for their support, availability, guidance and for all the transmitted knowledge. I would like to oer my special thanks to CETRIB (Unidade de Tribologia, Vibrações e Manutenção Industrial) for having given me the opportunity of doing this work in an outstanding laboratory. To my CETRIB colleagues: Armando Campos, Beatriz Graça, Carlos Fernandes, David Gonçalves, João Nogueira, Jorge Castro, José Brandão and Samuel Pinho, I would like to give my sincere thanks not only for all the help and support, but also for the warm welcome and the good moments we shared. I wish to acknowledge Fundação para a Ciência e Tecnologia for the nancial support given through the project Transmissões por engrenagem de elevada eciência e abilidade tribológica , with research contract EXCL/EMS-PRO/0103/2012. I would also like to acknowledge Faculdade de Engenharia da Universidade do Porto for the time and resources spent on my Master's degree in Mechanical Engineering. This thesis represents the end of a ve years journey. To the strangers I met as a freshman and to whom I have the honor to call friends, thank you. College life wouldn't be the same without you. You are unbeatable. Last, but for sure not the least, I would like to give my biggest thank you to my family, for being always there. You are three powerful guardian angels. v
Keywords Wind Turbine gear oils Power loss Eciency Planetary gearbox Multiplier gearbox Coecient of Friction Gears friction loss Rolling bearings power loss Wear Palavras Chave Lubricantes para engrenagens de turbinas eólicas Perdas de Potência Eciência Engrenagens planetárias Caixa de engrenagens multiplicadora Coeciente de fricção Perdas de potência por atrito nos engrenamentos Perdas de potência nos rolamentos Desgaste vi
Abstract In the past few years, sustainability issues have acquired major importance, as the environmental toxicity and the ozone layer destruction indicators reach worrying levels. Worldwide eort have been made aiming to increase renewable energy production and to diminish the usage of energy produced with fossil fuels. One of the most relevant renewable energy is the wind power, which represents the second greatest renewable energy source worldwide. Wind power is obtained through wind turbines, converting the kinetic power of the wind to mechanical energy. One of the most important components in a wind turbines is the gearbox, where the rotational speed of the rotor is multiplied in order to match the working conditions of the generator. Despite the wind energy industry development, wind turbine are still experiencing several breakdowns in the gearboxes and in the roller bearings due to the high loads and variable working conditions, requiring regular maintenance interventions. Optimizing the gearbox eciency represents not only an increase of the amount energy produced per wind turbine, but also leads to lower operating temperatures which benets the working life of all components. Lower operating temperatures lead to a lower failure probability, therefore lowering the maintenance costs. The purpose of this work is to continue the studies already done by Gonçalves [1], Marques [2] and Pereira [3], in an eort to clarify the inuence of the oil formulation on a gearbox eciency. Gonçalves and Marques [1, 2] carried out tests in parallel shaft helical gears, although with dierent working conditions. Pereira [3] has done tests in planetary gears at low loads. The work that is presented in this document consisted in tests with planetary gears, with the care that the operating conditions matched the rst stage of a wind turbine gearbox in terms of tangential speed and Hertz pressure. Four lubricants were tested: two of them being mineral based, and two of them being synthetic. Several working parameters indicators of the oil performance were measured and analyzed. Also, oil samples were collected and the wear indexes were calculated, and the wear particles were analyzed, using Direct Reading Ferrography (DRIII) and Analytical Ferrography (FRIII). A power loss numerical model was implemented aiming to understand the inuence of each component in the power loss of the tested gearbox . vii
Resumo Nos últimos anos a questão da sustentabilidade tem ganho particular relevância, à medida que os vários indicadores de toxicidade ambiental e de destruição da camada de ozono atingem valores preocupantes. Um pouco por todo o mundo estão a ser feitos esforços no sentido de se aumentar a produção de energia através de fontes renováveis e no sentido de se diminuir a quantidade de energia produzida a partir da queima de combustiveis fósseis. Uma das energias renovaveis de maior importânica é a energia eólica, representando a segunda maior fonte de energia renovavel à escala mundial. A energia eólica é obtida através de turbinas eólicas que convertem a energia cinética do vento em energia mecânica. Um dos componentes mais relevantes de uma turbina eólica é a caixa de engrenagens, onde a velocidade de rotação do rotor é multiplicada de forma a atingir as condições de funcionamento do gerador. Apesar do desenvolvimento da indústria de energia eólica, as turbinas eólicas continuam a apresentar inúmeras falhas ao nivel das engrenagens e dos rolamentos, devido às elevadas cargas a que estão sujeitos e às condições de funciomento variavel, obrigando a intervenções de manutenção regulares. A optimização da eciência da caixa de engrenagens representa não só um aumento na quantidade de energia gerada por cada turbina eólica, como conduz a temperaturas de funcionamento mais baixas, o que benecia a vida geral de todos os componentes em funcionamento. Temperaturas de funcionamento mais baixas conduzem a uma menor probabilidade de avaria, reduzindo também os custos de manutenção. O objectivo deste trabalho é dar continuação aos estudos realizados por Gonçalves [1], Marques [2] e Pereira [3], no sentido de claricar a inuência da formulação de lubricação na eciência de uma caixa de engrenagens. Gonçalves e Marques [1, 2] levaram a cabo testes em caixas de engrenagens helicoidais, embora com condições de funcionamento diferentes. Pereira [3] realizou testes em caixas planetárias com um nivel de carga reduzido. O trabalho levado a cabo consistiu na realização de testes em caixas planetárias, com o cuidado de que as condições de funcionamento fossem equiparadas ao primeiro andar da caixa de engrenagens de uma turbina eólica em termos de velocidade tangencial e de pressão de Hertz. Foram testados quatro lubricantes diferentes: dois de base mineral e dois sintéticos. Foram avaliados vários parâmetros de funcionamento indicadores da performance de cada óleo. Foram também retiradas amostras de lubricante de forma a determinar os indices de desgaste e a analisar as particulas de desgaste, através de Ferrometria de Leitura Directa (DRIII) e Ferrometria Analítica (FRIII). ix
Contents 5.6. Needle roller bearing losses . . . . . . . . . . . . . . . . . . . . . . . . 50 5.7. Sealspowerloss.............................. 51 5.8. Heatbalance ............................... 52 III. Experimental and Numerical Results 55 6. Sixteen Test Grid (PAOR) 57 6.1. Overallanalysis.............................. 57 6.2. Numerical predictions:part by part . . . . . . . . . . . . . . . . . . . 62 7. Five Test Grid 65 7.1. PAOR ................................... 65 7.2. MINR ................................... 67 7.3. MINE ................................... 69 7.4. PAGD................................... 70 7.5. OilComparison.............................. 73 7.5.1. Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 73 7.5.2. Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . 81 8. Additional tests 85 IV. Conclusions and Future Work 89 9. Conclusions 91 9.1. Conclusions based on experimental results . . . . . . . . . . . . . . . 91 9.2. Conclusions based on numerical results . . . . . . . . . . . . . . . . . 92 10.Future Works 93 A. Ring surface temperature tests 101 B. Test Reports 103 B.1. PAOR Oil: 16 Test Grid . . . . . . . . . . . . . . . . . . . . . . . . . 105 B.2. PAOR Oil: 5 Test Grid . . . . . . . . . . . . . . . . . . . . . . . . . . 123 B.3. PAOR: comparison between test grids . . . . . . . . . . . . . . . . . . 129 B.4. MINR Oil: 5 Test Grid . . . . . . . . . . . . . . . . . . . . . . . . . . 131 B.5. MINE Oil: 5 Test Grid . . . . . . . . . . . . . . . . . . . . . . . . . . 137 B.6. PAGD Oil: 5 Test Grid . . . . . . . . . . . . . . . . . . . . . . . . . . 143 C. Lubrican Analysis Report 149 D. KISSsoft analysis of the planetary gearbox 161 xvi
List of Figures 1.1. Global cumulative wind installed wind capacity 1996 −2013 . . . . . . 1 1.2. Size and capacity of wind turbines: evolution and prediction. . . . . . 2 2.1. Devicesused. ............................... 8 2.2. Tested oils' viscosity variation with temperature. . . . . . . . . . . . . 9 2.3. Tested oils' density variation with temperature. . . . . . . . . . . . . 9 3.1. Top view diagram of the gearbox test rig. . . . . . . . . . . . . . . . . 11 3.2. Photographs of the test rig. . . . . . . . . . . . . . . . . . . . . . . . 12 3.3. Centralcontrol............................... 12 3.4. Temperature sensors' positioning in the tested gearbox. . . . . . . . . 13 3.5. Photographs of the tested gearbox. . . . . . . . . . . . . . . . . . . . 14 3.6. Scheme of the planetary gearbox. . . . . . . . . . . . . . . . . . . . . 14 3.7. Vacuum pump and oil samples. . . . . . . . . . . . . . . . . . . . . . 19 4.1. Direct reading ferrograph by Predict Technologies ............ 21 4.2. Sedimentation process of the particles in the ferrogram . . . . . . . . 22 4.3. Devices used in analytic ferrography, both by Predict Technologies . . 23 5.1. Schematic representation of the planetary gear (side view). . . . . . . 27 5.2. Free body diagram of the planet carrier. . . . . . . . . . . . . . . . . 28 5.3. Free body diagram of the planet. . . . . . . . . . . . . . . . . . . . . 28 5.4. Free body diagram of the sun. . . . . . . . . . . . . . . . . . . . . . . 29 5.5. Schematic representation of the planetary gear (front view). . . . . . 32 5.6. Dierent power loss components in a gearbox. . . . . . . . . . . . . . 34 5.7. Example of a Stribeck curve. . . . . . . . . . . . . . . . . . . . . . . . 36 5.8. Linear elastohydrodynamic contact. . . . . . . . . . . . . . . . . . . . 37 5.9. Reverse ow in a ball bearing. . . . . . . . . . . . . . . . . . . . . . . 44 5.10. Oil level measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.11. Drag loss factor graph. . . . . . . . . . . . . . . . . . . . . . . . . . . 48 6.1. PAOR:PowerLoss............................. 57 6.2. PAOR:Eciency.............................. 58 6.3. Eciency dierences between both operating directions. . . . . . . . 59 6.4. PAOR: Oil temperature and Stabilization temperature. . . . . . . . . 60 6.5. PAOR: Heat transfer coecient. . . . . . . . . . . . . . . . . . . . . . 60 6.6. PAOR: Specic Film Thickness. . . . . . . . . . . . . . . . . . . . . . 61 6.7. Power Loss: Part by Part. . . . . . . . . . . . . . . . . . . . . . . . . 62 6.8. Percentages of Power Loss Contributions. . . . . . . . . . . . . . . . . 63 xvii
List of Figures 7.1. PAOR:PowerLoss............................. 65 7.2. PAOR:Eciency.............................. 66 7.3. PAOR: Oil and Stabilization temperatures. . . . . . . . . . . . . . . . 67 7.4. MINR:PowerLoss............................. 67 7.5. MINR:Eciency.............................. 68 7.6. MINR: Oil and Stabilization temperatures. . . . . . . . . . . . . . . . 68 7.7. MINE:PowerLoss............................. 69 7.8. MINE:Eciency.............................. 69 7.9. MINE: Oil and Stabilization temperatures. . . . . . . . . . . . . . . . 70 7.10.PAGD:PowerLoss............................. 71 7.11.PAGD:Eciency.............................. 71 7.12. PAGD: Oil and Stabilization temperatures. . . . . . . . . . . . . . . . 72 7.13. Oil comparison: Stabilization Temperature. . . . . . . . . . . . . . . . 73 7.14. Oil comparison: Operating Temperature. . . . . . . . . . . . . . . . . 74 7.15. Oil comparison: Kinematic Viscosity. . . . . . . . . . . . . . . . . . . 75 7.16. Oil comparison: Dynamic Viscosity. . . . . . . . . . . . . . . . . . . . 75 7.17. Oil comparison: Specic Film Thickness. . . . . . . . . . . . . . . . . 76 7.18. Ferrography images: PAOR. . . . . . . . . . . . . . . . . . . . . . . . 77 7.19. Ferrography images: MINE. . . . . . . . . . . . . . . . . . . . . . . . 78 7.20. Ferrography images: MINR. . . . . . . . . . . . . . . . . . . . . . . . 79 7.21. Ferrography images: PAGD. . . . . . . . . . . . . . . . . . . . . . . . 79 7.22. Percentages of Power Loss Contributions. . . . . . . . . . . . . . . . . 81 7.23. Oil comparison: Coecient of friction. . . . . . . . . . . . . . . . . . 82 7.24. Heat transfer coecient: numerical values. . . . . . . . . . . . . . . . 83 8.1. Temperatures evolution at the 100rpm test. . . . . . . . . . . . . . . 85 8.2. Temperatures evolution at the 150rpm test. . . . . . . . . . . . . . . 86 8.3. Wall and Oil temperature evolution. . . . . . . . . . . . . . . . . . . 87 A.1. Thermocouples' positioning. . . . . . . . . . . . . . . . . . . . . . . . 101 A.2. Surface temperatures in the area exterior to the ring (test: 1). . . . . 102 A.3. Surface temperatures in the area exterior to the ring (test: 2). . . . . 102 A.4. Surface temperatures in the area exterior to the ring (test: 3). . . . . 102 xviii
List of Tables 2.1. Chemical composition and physical properties of the tested lubricants. 10 3.1. Geometrical characteristics of the planetary gearbox. . . . . . . . . . 15 3.2. Rolling bearings and seals in the planetary gearbox. . . . . . . . . . . 15 3.3. Tangential speed and Hertz Pressure in the test gearbox. . . . . . . . 16 3.4. Tangential speed and Hertz Pressure in gearboxes used in wind turbines. 16 3.5. Experimental test plan. . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.6. Oil samples collected. . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.1. Forces at nominal working conditions. . . . . . . . . . . . . . . . . . . 31 5.2. Gear ratio and rotational speed of the gearbox components. . . . . . 33 5.3. Formulation of the coecients ai , ( i= 1 : 4 )............... 35 5.4. HV values derived from KISSsoft. . . . . . . . . . . . . . . . . . . . . 36 5.5. EHD lubrication regimes. . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.6. XL factor for the selected oils. . . . . . . . . . . . . . . . . . . . . . . 41 5.7. Example for the bearings losses for the nominal operating conditions. 50 5.8. Example for the needle roller bearing losses. . . . . . . . . . . . . . . 51 5.9. Seals power losses for gearbox nominal working conditions. . . . . . . 52 6.1. Example of input power vs. power loss. . . . . . . . . . . . . . . . . . 58 7.1. Direct Reading Ferrography Results. . . . . . . . . . . . . . . . . . . 80 7.2. Trendline coecients and norm of residuals. . . . . . . . . . . . . . . 83 xix
1. Introduction Modern energy enables quality of life. From lighting and heating to powering cutting-edged technology, modern energy is one of the foundations of mankind as we know it today. Yet, over one billion people lack access to modern energy and as world population increases so increases world's energy demand [4]. Global warming and environmental issues are major concerns that push us toward renewable energy and eciency improvements in energy generation and consumption. Eciency is expected to be the most important factor in the near term, whereas renewables will become increasingly important over time [4]. By 2035 , it is expected that renewables will be generating more than 25 % of world's electricity, with a quarter of this coming from wind. Over the last 18 years, the global wind installed capacity has grown from 6 GW in 1996 to nearly 320 GW in 2013 [5], as shown in gure 1.1. Figure 1.1.: Global cumulative wind installed wind capacity 1996 −2013 [5]. Wind turbines are used to generate electricity from the kinetic power of the wind. The blades are aerodynamically designed to spin as the air ows through them, converting the kinematic energy of the wind into mechanical energy - torque - which is transmitted along the main shaft to the generator. The rotor rotational speed and torque are transformed by the gearbox in order to match the necessary operating conditions of the generator. Global wind capacity owns its growth not only to the number of installed turbines but also to the growing capacity of each unit. Figure 1.2 shows the average diameter and capacity of wind turbines in 1985 and today, as well as the expectation for the future. As the rated power increases, the drive train concept evolves. Research on directdrive systems and torque splitting mechanism is being done in order to keep up the 1
1. Introduction Figure 1.2.: Size and capacity of wind turbines: evolution and prediction [6]. growing capacity of wind turbines, but the current drive train standard option for the 1.5−3 MW wind turbines is the planetary gearbox [7]. The most common planetary gearbox oset for wind turbines is one or two planetary stages with a helical stage at the end of the drive train. Planetary gearing systems exhibit higher power densities than parallel axis gears and oer a multitude of gearing options that allow signicant changes in rotational speed with a small volume [8]. Dierent operating and lubrication conditions are to be found between the dierent stages of the gearbox and their weight on the torque loss of a planetary multiplier gearbox is not yet fully understood. Mechanical energy is transmitted with high eciencies when compared with other forms. In the overall power losses of a wind turbine the losses related to the gearbox represent a minor role. As so, the war on gear eciency improvement is seen by many as a war that is no longer worth ghting for. Nevertheless, in a three stage gearbox used in a 1MW wind turbine, an improvement of 0.33% per gear stage leads to an overall eciency improvement of 1% which represents an energy gain of 10kW. The average household energy consumption world wide for 2011 was 3338kWh, [9], representing 0.93kW per household. This means that such a slight improvement as 0.33% would allow each wind turbine to supply ten extra households. As little as it may seem, taking into account all the already existent wind farms with wind turbines usually with a capacity ranging 1.5−3 MW, the slight improvements on a the eciency of a gearbox should not be neglected. In a gearbox operating at or near nominal operating conditions the main energy dissipation sources are the gears and the rolling bearings [10, 11]. In order to improve gearbox eciency one can then act to improve the gears and rolling bearings eciency. This can be achieved by simply changing to a more ecient gear design [12] or changing the rolling bearings type [11]. Despite being an eective way to improve the eciency of a gearbox, changing the components is usually only a viable option at the design stage. Nevertheless, for gearbox units that are already installed there's still an option which is changing to a lubricating uid that promotes less friction between the contacting bodies. Fernandes et al. [13, 14, 15, 16] and Marques et al. [17] have already shown that is possible to obtain important eciency gains in gears and rolling bearings by changing between dierent formulations of wind turbine gear oils. The work presented in this dissertation comes as a follow up of previous works that aimed to study the inuence of wind turbine gear oils in gearbox eciency. 2
1.1. Thesis Outline Gonçalves [1] and Marques [2] have done their studies in a parallel axis gearbox with helical gears (3rd stage in a wind turbine gearbox) and more recently Pereira [3] has done a similar work in a planetary gearbox with helical gears at low loads. The aim of this work is then to study the inuence of dierent wind turbine gear oil formulations in the eciency of a planetary gearbox with helical gears at high loads and low speeds (1st and 2nd stages in a wind turbine gearbox). 1.1. Thesis Outline This dissertation is divided in ve parts. The rst part deals with the presentation and measurement of some of the properties of the wind turbine gear oils properties and techniques that were used. The gearbox test rig and tested planetary gearbox are also presented as well as the planing of the eciency tests and the experimental procedure. The ferrography techniques that were used to verify the gear oils wear performance are also presented. The second part is dedicated to describe and present the power loss model for planetary gearboxes. The derivation of the static loads and kinematics is shown. Some considerations regarding the power loss and dissipated heat at stabilized operating conditions are also done. The third part introduces the experimental results that were obtained. These results are analysed in detail and comparisons with the numerical predictions are done. This part also introduces the results that were obtained after some additional tests were done in order ascertain certain specics of the experimental results. The forth and last Part of the main text is dedicated to the nal conclusions of this work and future work suggestions. The last section of this dissertation consist of a compilation of the test sheets with the results of the eciency tests and some numerical and experimental results that were not in the main text. 3
Part I. Materials and Methods 5
3. Testing gearbox eciency (a) Test rig. (b) Back-to-back conguration. Figure 3.2.: Photographs of the test rig. Figure 3.3.: Central control. 12
3.1. Test rig On it's current conguration, the test rig has the highest torque in between the gearboxes, which allows smoother working conditions for all the test rig. The working conditions of the test rig are the following: • Rotational speed: 100 −1900 rpm; • Torque: 100 −1300 Nm. The torque control is done in the torque transducer (5) which is located between both gearboxes. The gearboxes setup is so that the highest torque only happen in between gearboxes, allowing to test higher loads without submitting the rest of the test rig to those loads. Therefore, the rest of the test rig operates at lower loads, but higher speeds, which is also benecial for the motor speed control. In order to assess the working temperatures, the test rig is equipped with several sensors, some of which were installed in the test gearbox. The sensors are measuring: • The oil temperature in two dierent zones (industrial grade PT100 RTD's); • The wall temperature (industrial grade PT100 RTD's); • The ambient temperature; • The room temperature. A photograph of the gearbox instrumented with the three temperature sensors is shown in gure 3.4 (a) Oil temperature sensors. (b) Wall temperature sensor. Figure 3.4.: Temperature sensors' positioning in the tested gearbox. The input and output torque as well as rotating speeds were also constantly measured and recorded overtime. 13
3. Testing gearbox eciency 3.2. Planetary gearbox The selected gearbox is a planetary multiplier with a transmission ratio of 4 and with a nominal input speed of 1000rpm and a nominal output torque of 2500Nm. The tested planetary gearbox was partially disassembled (details shown in gures 3.5a, 3.5b and 3.5c) and therefore some of the components of the gearbox could be listed. The access to other components, such as the needle and the tapered bearings, was not possible and so this components are estimated based on the size and dimension of the gearbox, the shaft diameter and on the scheme presented in the manufacturer's catalog, gure 3.6. (a) Sun gear. (b) Planet carrier assemble. (c) Detail of the planet. Figure 3.5.: Photographs of the tested gearbox. Figure 3.6.: Scheme of the planetary gearbox. 14
3.2. Planetary gearbox The geometrical characteristics of the gears are listed in table 3.1. The gearbox rolling bearings are listed in table 3.2. While disassembled it was possible to see that the deep grove ball bearing is shielded and contains it's own lubricant. Although the tapered rolling bearings were not visible, it was assumed that they are equally shielded and contain their own lubricant as well. Table 3.1.: Geometrical characteristics of the planetary gearbox. Sun Planet Ring Number of teeth [/] 36 36 -108 Prole shit coecient [mm] -0.0189 -0.0189 0.0566 Reference diameter [mm] 73.1101 73.1101 -219.332 Base diameter [mm] 68.577 68.577 -205.731 Tip diameter [mm] 77.035 77.035 -215.106 Width [mm] 42 Pressure angle [ ◦ ] 20 Working transverse pressure angle [ ◦ ] 20.122 Helix angle [ ◦ ] 10 Normal module [mm] 2 Center distance [mm] 73.111 Working center distance [mm] 73.035 Table 3.2.: Rolling bearings and seals in the planetary gearbox. Component Quantity Designation Tapered roller bearings 2 32022 X/Q * Deep groove ball bearing 1 6217-2Z Input and output seal 2BAUM6 SLX7 140170-13/12 CFW A1 Needle roller bearing 6 K 40x48x20* ∗ − Estimated 15
3. Testing gearbox eciency 3.3. Tests planning In order to fully understand the inuence of the operating conditions on the torque loss behavior of the gearbox, a 16 test grid was planned, comprising 4 dierent loads (1600/2000/2400/2800Nm) and 4 dierent speeds (100/150/200/250rpm). The operating conditions of the 16 test grid were selected according to the working conditions allowed by the test rig and according to the planetary gearbox specications. From that grid, 5 tests were selected trying to meet the working conditions of one the stages of a gearbox used in wind turbines in terms of Hertz pressure and tangential speed. The Hertz pressure is essentially function of the load while the tangential speed is function of the rotational speed. The contact pressure and the tangential speed resulting from the imposed working conditions on the test gearbox are represented in table 3.3, and the contact pressure and the tangential speed of the gearboxes used in wind turbine are represented in table 3.4. The full planning of tests is shown in table 3.5. The speed and torque mentioned are the ones measured in between gearboxes, see gure 3.1. Table 3.3.: Tangential speed and Hertz Pressure in the test gearbox. Imposed rotational Tangential speed Imposed torque Hertz pressure speed [rpm] [m/s] [Nm] [N/mm 2] 100 1.15 1600 955.0738 (SP) 646.1703 (PR) 150 1.72 2000 1063.6336 (SP) 719.9055 (PR) 200 2.30 2400 1165.3512 (SP) 785.9340 (PR) 250 2.87 2800 1249.1650 (SP) 846.1466 (PR) SP − Sun-Planet contact PR − Planet-Ring contact Table 3.4.: Tangential speed and Hertz Pressure in gearboxes used in wind turbines. Gear Stage Tangential Speed Hertz pressure [m/s] [N/mm 2] 1 st Stage 1.63 1381.769 (SP) 987.743 (PR) 2 nd Stage 5.49 2873.516 (SP) 2029.198 (PR) SP − Sun-Planet contact PR − Planet-Ring contact 16
3.3. Tests planning Table 3.5.: Experimental test plan. Oil Speed Torque Power Test time [rpm] [Nm] [W] [min] PAOR 100 1600 16755.2 240 + 90 2000 20944.0 240 + 90 2400 25132.7 240 + 90 2800 29321.5 240 + 90 150 1600 25132.7 240 + 90 2000 31415.9 240 + 90 2400 37699.1 240 + 90 2800 43982.3 240 + 90 200 1600 33510.3 240 + 90 2000 41887.9 240 + 90 2400 50265.5 240 + 90 2800 58643.1 240 + 90 250 1600 41887.9 240 + 90 2000 52359.9 240 + 90 2400 62831.9 240 + 90 2800 73303.8 240 + 90 PAOR/MINR/MINE/PAGD 100 2800 29321.5 240 + 90 150 2000 31415.9 240 + 90 2400 37699.1 240 + 90 2800 43982.3 240 + 90 200 2800 58643.1 240 + 90 17
3. Testing gearbox eciency 3.4. Experimental procedure The duration of each test was ve hours and thirty minutes. During the rst four hours the test gearbox worked as a multiplier, and in the other one and a half hour worked as a reducer. The duration of both parts of the test was set in order to achieve stabilized operating conditions: load, speed and temperatures. The ventilation of the room where the test rig works doesn't have enough power to guarantee a stabilized room temperature. Nevertheless, the power losses are function of a temperature dierence, which achieved reasonably stable values. The values read by the sensors were automatically recorded by the central control with a frequency of 0.5Hz. The calibration of the torque transducers was checked periodically in order to assure proper function. The behavior of various metrics, such as torque, speed and temperature, were displayed in the central control over time, to allow a fast detection and intervention of any abnormal variation on the behavior of the test rig. An oil sample was collected from the test gearbox when appropriate, being collected a total of 8 samples. The samples are shown in gure 3.7b and the working conditions that preceded the sample collection are represented in table 3.6. Table 3.6.: Oil samples collected. Test Grid Oil Sample Tests performed 16 PAOR PAOR_100 100rpm; 1600/2000/2400Nm; PAOR_150 150rpm; 1600/2000/2400Nm; PAOR_200 200rpm; 1600/2000/2400Nm; PAOR_250 250rpm; 1600/2000/2400Nm; PAOR_2800 100/150/200/250rpm; 2800Nm; 5 Test Grid MINR_5 Full test grid MINE_5 Full test grid PAGD_5 Full test grid Each oil sample was collected through the top gearbox plug's hole, using a vacuum pump, gure 3.7a. All oil samples were collected immediately at the end of a given test, in the interest of avoiding particle deposition at the bottom of the gearbox and to guarantee that the sample is representative of the oil's condition. There was no fresh MINE oil available, so it was also taken an oil sample of MINE oil before it was introduced in the gearbox, to serve as a point of comparison. The last test in the 16 PAOR test grid (250rpm; 2800Nm) showed an abnormal increase of the oil temperature and the test was aborted at 15min to it's end. Therefore, the tested gearbox was open and it was found that one of the seals was no longer sealing. The ball bearing of the tested gearbox was therefore being lubricated with oil instead of grease. The test and slave gearbox changed places, and several 18
3.4. Experimental procedure (a) Vacuum pump. (b) Oil samples. Figure 3.7.: Vacuum pump and oil samples. tests were conducted. The repeatability of the test was assured, and the remaining planned tests were performed. The gearboxes' oil was always changed at the same time. The oil was drained through a plug in the bottom and then the gearboxes were lled with petroleum ether, except for PAGD which was rst ushed with an ISO VG320 ester oil and with a special solvent afterward. While the gearboxes were lled with solvent, the test rig was manually rotated for several minutes aiming to remove the maximum amount of remaining oil and wear particles. The solvent was removed the same way as the oil, and then the gearboxes were left to dry for 12h and then lled with 1litre of fresh lubricant. 19
4. Analysis techniques The oil samples were analyzed using a set of techniques called ferrography which are normally used to monitor the wear evolution over time and diagnose the causes of certain failures in mechanical components lubricated with oil or grease. Using this technique the quantity and the morphology of the wear particles suspended in the oil sample can be analyzed allowing an evaluation of the wear performance of a lubricant. It can also be used to perform preventive maintenance and to predict the failure of a component in a mechanism. Two dierent methods were used: direct reading ferrography (DRIII) and analytic ferrography (FMIII). 4.1. Direct Reading Ferrography (DRIII) A direct reading ferrograph (gure 4.1) allows a rapid and objective quantication of large and small particles in an oil sample. Figure 4.1.: Direct reading ferrograph by Predict Technologies . One milliliter of oil circulates through a capillary tube which has a section submitted to a strong magnetic eld and two beams of light. The solid particles lodge along the tube due to the magnetic eld or simply by sedimentation. The larger will deposit rst, as they are heavier and suer greater inuence of the magnetic eld, followed by those of smaller dimension. 21
5. Planetary gearbox: Loads, Kinematics and Power Loss Figure 5.2.: Free body diagram of the planet carrier. Figure 5.3.: Free body diagram of the planet. Where N is the number of planets of the gearbox and a is the center distance, which is the same for the sun/planet gears and the planet/ring gears. Since the gearbox in study has 3 planets, N= 3 will be assumed. The free body diagram of a planet is represented in gure 5.3. The force balance equation of the planet is written as following: X#» F= # » F42 + # » F32 + # » F12 (5.1.3) Where: # » F12 = # » Ft12 + # » Fr12 (5.1.4) # » F32 = # » Ft32 + # » Fr32 (5.1.5) 28
5.1. Load analysis Figure 5.4.: Free body diagram of the sun. Considering the Cx axis it is possible to write that: XFx= 0 ⇔ (5.1.6) ⇔F42 =Ft12 +Ft32 (5.1.7) And on the Cy axis: XFy= 0 ⇔ (5.1.8) ⇔Fr12 =Fr32 (5.1.9) Therefore: Ft12 =Ft32 =−F42 2 (5.1.10) |Fr12|=|Fr32|=|Ft12 ·tan(αt)| (5.1.11) The free body diagram of the sun gear is represented in gure 5.4. The moment balance regarding A is established according to equation (5.1.12). X# » MA=AB1· # » F1 t21 +AB2· # » F2 t21 +AB3· # » F3 t21 + # » Mext =#» 0 (5.1.12) Due to the symmetry of the sun/planet system, the equalities written in equations 29
5. Planetary gearbox: Loads, Kinematics and Power Loss (5.1.15) and (5.1.13) can be established: AB1=AB2=AB3 (5.1.13) |F1 t21|=|F2 t21|=|F3 t21| (5.1.14) |F1 r21|=|F2 r21|=|F3 r21| (5.1.15) The radial forces are equal, and due to their spatial position they cancel each other out. Since ABi=d1 2 , # » Mext = 3 · # » Ft21 ·d1 2 (5.1.16) The reaction in A can be obtained through equation (5.1.17). X#» F= # » F1 21 + # » F2 21 + # » F3 21 + # » F01 =#» 0 (5.1.17) On the Ax axis, Fx 01 −F1 t21 +| # » F2 t21| · sin(30◦) + | # » F3 t21| · sin(30◦) = 0 (5.1.18) Fx 01 = 0 (5.1.19) And on the Ay axis, Fy 01 − | # » F2 t21| · cos(30◦) + | # » F3 t21| · cos(30◦)=0 (5.1.20) Fy 01 = 0 (5.1.21) The axial forces can be obtained using equations (5.1.22) and (5.1.23). | # » Fa12|=| # » Ft12| · tan(β) (5.1.22) | # » Fa32|=| # » Ft32| · tan(β) (5.1.23) The results for the forces at nominal working conditions (2500Nm and 250rpm) is presented in table 5.1. 30
5.2. Kinematic analysis Table 5.1.: Forces at nominal working conditions. Variables Results Tangential force [N] F1 t21, F2 t21, F3 t21, Ft32 5699.1 Radial force [N] F1 r21, F2 r21, F3 r21, Fr32 2106.3 Axial force [N] Fa12, Fa32 1004.9 5.2. Kinematic analysis The power losses of all the components in the gearbox are dependent of the speed at which they operate. Therefore, it is necessary a kinematic analysis in order to determine the velocities involved. In the following paragraphs the calculation method adopted is presented. The numbers and letters used in the kinematic analysis follow the labeling presented in section 5.1. A dierent schematic representation of the planetary gear is show in gure 5.5. As the gearbox will be working as a multiplier, the power input will be in the planet carrier (4). Point C belongs to the planet carrier as well as it is the geometric center of the planets. Thus, the velocity of point C calculated from one object or another must match, equation (5.2.1). # » vC40 =# » vC20 (5.2.1) In equations (5.2.2) and (5.2.3), Mozzi's equations are used to determine the rotational speed of the planet: # » vA40 +# » ω40 × # » AC =# » vD20 +# » ω20 × # » DC (5.2.2) Let ri be the radius of body i . As the velocities of point A and D are null, 0 0 ω40 × 0 r1+r2 0 = 0 0 ω20 × 0 −r2 0 (5.2.3) The planet's rotational speed is given by equation (5.2.4) ω20 =−ω40 ·r1+r2 r2 (5.2.4) Point B is the contact point between the sun and the planet, and therefore can be used to relate the sun velocity with the planet velocity considering that point B velocity is the same for both the planet and the sun, equation (5.2.5). 31
5. Planetary gearbox: Loads, Kinematics and Power Loss Figure 5.5.: Schematic representation of the planetary gear (front view). # » vB10 =# » vB20 (5.2.5) In equations (5.2.6) and (5.2.7), Mozzi's equations are used to determine the rotational speed of the sun: # » vA10 +# » ω10 × # » AB =# » vD20 +# » ω20 × # » DB (5.2.6) 0 0 ω10 × 0 r1 0 = 0 0 ω20 × 0 −2r2 0 (5.2.7) The sun rotational speed is given by equation (5.2.8), ω10 =−ω20 ·2r2 r1 (5.2.8) Or, in terms of the carrier rotational speed: ω10 =−ω40 ·2(r1+r2) r1 (5.2.9) Considering the denition of gear normal module, equation (5.2.10): m=d z (5.2.10) 32
5.3. Introduction to the power loss in a gearbox and the geometric relations in a planetary gear, equation (5.2.11) r1+ 2r2=r3 (5.2.11) it is possible to write the sun and planet rotational speed as a function of the number of teeth and the rotational speed of the carrier, equation (5.2.12) and (5.2.13): ω10 =ω40 ·2·1 + z2 z1=ω40 ·1 + z3 z1 (5.2.12) ω20 =−ω40 ·1 + z1 z2 (5.2.13) Therefore, the gear ration, i , can be written as in equation (5.2.14) or in equation (5.2.15). i= 1 + z3 z1 (5.2.14) i= 2 + 2·z2 z1 (5.2.15) Equation (5.2.11) does not take into account the shift prole coecents, and as a consequence, equation (5.2.14) is not valid for all cases. The gear ratio of the test gearbox is presented in table 5.2 as well as an example of the rotational speed of the several components for the nominal working conditions (2500Nm and 250rpm). Table 5.2.: Gear ratio and rotational speed of the gearbox components. Variables Results Gear ratio [-] i 4 Carrier rotational speed [rpm] ω40 250 Planet rotational speed [rpm] ω20 -500 Sun rotational speed [rpm] ω10 1000 5.3. Introduction to the power loss in a gearbox According to Höhn et al. [10], the total power loss in a gearbox is the sum of gears, bearings, seals and auxiliary losses, gure 5.6. The gear and the roller bearing losses can be divided in load losses, associated to the transmitted power, and the no-load losses which are independent of the transmitted torque. 33
5. Planetary gearbox: Loads, Kinematics and Power Loss Figure 5.6.: Dierent power loss components in a gearbox [10]. The load losses are function of the transmitted torque, the coecient of friction and the sliding velocity in the contact areas. No-load losses are dependent upon the operating speed, the internal housing design, the lubricant viscosity and density, as well as the immersion depth of the gearbox components in the oil sump. Usually, for nominal operating conditions, the dominant power losses of a gearbox are the load losses. When working at high speeds and with low or moderate loads, no-load losses can overcome the load losses. In behalf of improving a gearbox eciency, it is fundamental to understand how each component contributes to the total power loss and how the operating conditions and the lubricant formulation can inuence each energy dissipation source. 5.4. Gears power loss Gear losses are dependent on the transmitted power, the mean coecient of friction and a gear loss factor. The average gear power loss is given by equation (5.4.1). PV ZP =Pa·µm·HV (5.4.1) Where: •Pa is the transmitted power; •µm is the mean coecient of friction (determined in section 5.4.1). •HV is a gear loss factor. The transmitted power can be calculated using equation (5.4.2). Pa=Fbt·ω·rb (5.4.2) The gear loss factor, HV is dependent of the gear geometry and it's an indicator of the eciency associated to a certain gear, despite the working conditions, the transmitted power and the lubricant used. Originally, HV was obtained on the 34
5.4. Gears power loss assumption that the coecient of friction is constant along the line of action, and can be calculated according to equation (5.4.3). HV=π(i+ 1) z1·i·cos(βb)(a0+a1· |1|+a2· |2|+a3· |1| · 1+a4· |2| · 2) (5.4.3) Where: •i is the gear ratio; •z1 os the number of teeth of the pinion; •βb is the helix angle at the base; •α is the prole contact ratio; •1,2 are the tip contact ratios: pinion(1) and wheel(2); •a0,1,2,3,4 are the coecient dependent on the tip contact ratios. Based on 1 , 2 and α three parameters are dened: •1∈]lg−1 : lg[ •2∈]mg−1 : mg[ •α∈]ng−1 : ng[ And the a0,1,2,3,4 can be calculated according to table 5.3. Table 5.3.: Formulation of the coecients ai , ( i= 1 : 4 ). α<1α>1α>1α>1 1<0∨2<01, 2>01, 2>0 l+m=n l +m=n+ 1 a00 0 2lm n 2(lm−n) n−1 a10 1 l(l−1)−m(m−1)−2lm n(n−1) l(l−1)+m(m−1)−2(m−1)n n(n−1) a20 1 −l(l−1)+m(m−1)−2lm n(n−1) l(l−1)+m(m−1)−2(m−1)n n(n−1) a31 α02m n(n−1) 2(m−1) n(n−1) a41 α02l n(n−1) 2(l−1) n(n−1) Equation (5.4.3) was derived for spur gears and for a single gear pair. Despite considering the base helix angle, this equation is not suited to helical gears and the elasticity of the meshing tooth is disregarded. KISSsoft [8] is a software that allows the calculations of a multitude of gears (including planetary gears) considering imposed operating conditions such as input torque, speed and coecient of friction. The contact analysis module allows the study of the gear contacts considering elastic eects. The average power loss in one of the metrics that can be calculated, therefore 35
5. Planetary gearbox: Loads, Kinematics and Power Loss once the friction coecient is imposed, equation (5.4.1) can be used to derive more accurate gear loss factors. Table 5.4 displays the HV values used. Table 5.4.: HV values derived from KISSsoft. Contact HV factor Sun-Planet 0.167709 Planet-Ring 0.062473 5.4.1. Friction and lm thickness between gear teeth The average coecient of friction has a great inuence in the gear mesh power loss, as can be seen in equation (5.4.1), and therefore is a major factor in what concerns to eciency. Besides, the coecient of friction has a direct inuence on the contact temperature and failure probability. To assess the coecient of friction in a lubricated contact, it is necessary to begin with the calculation of the specic lm thickness, which has a strong correlation with the coecient of friction, as shown by the Stribeck curve, gure 5.7. Figure 5.7.: Example of a Stribeck curve [23]. The gear teeth contact is considered to be an elastohydrodynamic (EHD) contact which, according to Dowson and Higginson [24], can be represented as in gure 5.8. 36
5.4. Gears power loss Figure 5.8.: Linear elastohydrodynamic contact [25]. The lm thickness depends on: • Viscosity of the lubricant (which depends on the temperature); • Rolling speed; • Piezoviscosity coecient; • Equivalent radius; • Normal load; • Width of the gear. Classic EHD theory was derived assuming that the lubricant ow inside the contact zone is isothermal and so, the viscosity of the lubricant depends only in the contact pressure. However, this hypothesis is not valid for gears due to the high sliding along the contact line. In the inlet zone, the lubricant suers a high shear rate strain as a result of the pressure gradient as well as the rolling and sliding speed. The shear strain causes inlet shear heating, and the lubricant ow can't be assumed as isothermal. The inlet shear heating causes an increase of the lubricant temperature, followed by a decrease in the lubricant viscosity and lm thickness. To take into account the inlet shear heating, the lm thickness is multiplied by a heating correction factor, φT which depends on the lubricant thermoviscosity and thermal conductivity as well as the surface's speed. Even so, the EHD lm thickness can't be used directly as it considers the surfaces as perfectly smooth and doesn't account the surface's roughness. The ratio between 37
5. Planetary gearbox: Loads, Kinematics and Power Loss •Y is the axial load factor for single row bearings; •dm is the mean diameter; •Fr is the radial load; •Fa is the axial load; •αSKF =Fa C00.24 5.5.2. Inlet shear heating factor The amount of lubricant used to form a hydrodynamic lm is very small. Thus, part of the oil near the contact area is rejected and forms a reverse ow, as show in gure 5.9. Figure 5.9.: Reverse ow in a ball bearing [36]. The reverse ow shears the lubricant generating heat. Therefore, the viscosity lowers, the lm thickness is reduced and the the rolling friction decreases. The inlet shear heating reduction factor was estimated using equation (5.5.6). φish =1 1+1.84 ·10−9·(n·dm)1.28 ·υ0.64 (5.5.6) 5.5.3. Kinematic replenishment/starvation reduction factor When high speeds or high viscosity are involved, the lubricant may not have enough time to replenish the raceways, causing a "kinematic starvation" eect, which reduces the lm thickness and rolling friction. The kinematic replenishment/starvation factor was estimated using equation (5.5.7). φrs =1 eKrs·υ·(d+D)·qKz 2·(D−d) (5.5.7) 44
5.5. Rolling bearings power loss Where: •φrs is the kinematic replenishment/starvation reduction factor; •Krs is the kinematic replenishment/starvation constant: for low level oil bath and oil jet lubrication Krs = 3 ·10−8 and for grease and oil-air lubrication Krs = 6 ·10−8 ; •Kz is a geometric constant related to bearing type; •υ is the kinematic viscosity at operating temperature of the oil or the base oil viscosity of the grease (cSt). •n is the rotational speed (rpm); •d is the bearing bore diameter; •D is the bearing outside diameter. According to the online SKF bearing calculator (REF1), for a tapered roller bearing 32022X/Q, equation (5.5.7) is only valid for a oil level bellow 7.525mm. If this does not verify, φrs = 1 . 5.5.4. Sliding frictional moment The sliding frictional moment was given by equation (5.5.8). Msl =Gsl ·µsl (5.5.8) Where: •Msl is the sliding frictional moment; •Gsl is a variable dependent on the bearing type, mean diameter, radial and axial load. •µsl is the sliding friction coecient. Gsl was calculated dierently for deep groove ball bearing and for tapered bearings, equation (5.5.9) and (5.5.10). Deep groove ball bearing Gsl = S1·d−0.26 m·F 5 3 r if Fa= 0 S1·d−0.145 m·F5 r+S2·d1.5 m sin(αF)·F4 a1 3 if Fa>0 (5.5.9) Tapered roller bearing Gsl =S1·d0.82 m·(Fr+S2·Y·Fa) (5.5.10) 45
5. Planetary gearbox: Loads, Kinematics and Power Loss Where S1,2 are geometric constants for sliding frictional moments. The sliding friction coecient for full-lm and mixed lubrication conditions can be estimated using equation (5.5.11). µsl =φbl ·µbl + (1 −φbl)·µEHL (5.5.11) Where: •φbl is a weighting factor for the sliding friction coecient; •µsl is the sliding friction coecient; •µbl is a friction coecient dependent on the additive package of the lubricant, generally µbl = 0.15 . •µEHL is the sliding frictional coecient in full-lm conditions: 0.02 for cylindrical roller bearings; 0.002 for tapered roller bearings; other bearings: 0.05 for mineral oils and 0.04 for synthetic oils. The weighting factor, φbl , can be estimated using equation (5.5.12). φbl =1 e2.6·10−8·(υ·n)1.4·dm (5.5.12) 5.5.5. Drag Losses Drag losses occur when a bearing is rotating in an oil bath and, in most cases, their contribution to the total power loss is representative enough to not be neglected. Drag losses are dependent on several factors: bearing operating speed, oil viscosity, oil level, size and geometry of the oil sump and external oil agitation caused by surrounding mechanic elements. The SKF model calculates the drag losses of rolling bearings following the equations (5.5.13) to (5.5.16). Deep groove ball bearing Mdrag = 0.4·VM·Kball ·d5 m·n2+1.093·10−7·n2·d3 m·n·d2 m·ft υ−1.379 ·Rs (5.5.13) Kball =irw ·Kz·(d+D) D−d·10−12 (5.5.14) 46
5.5. Rolling bearings power loss Roller bearing Mdrag = 4·VM·Kroll·CW·B·d4 m·n2+1.093·10−7·n2·d3 m·n·d2 m·ft υ−1.379 ·Rs (5.5.15) Kroll =KL·Kz·(d+D) D−d·10−12 (5.5.16) The remaining variables, common for ball and roller bearings are stated in equation (5.5.17) to (5.5.22). CW= 2.789 ·10−10 ·l3 D−2.786 ·10−4·l2 D+ 0.0195 ·lD+ 0.6439 (5.5.17) lD= 5 ·KL·B dm (5.5.18) ft=sin (0.5·t) when 0≤t≤π 1 when π < t < 2π (5.5.19) RS= 0.36 ·d2 m·(t−sin (t)) ·fA (5.5.20) t= 2 ·cos−10.6·dm−H 0.6·dm , when H≥dm use H=dm (5.5.21) fA= 0.05 ·Kz·(D+d) D−d (5.5.22) Where: •Mdrag is the frictional moment of drag losses [N · mm]; •VM is the drag loss factor; •B is the bearing width [mm]; •H is the oil level (gure 5.10); •irw is the number of ball rows; •KL is a geometric constant related to the bearing type; To determine the oil level, for tapered roller bearings the lowest point should be considered the outside diameter (D), and for all the other bearings should be the outer ring mean diameter ( 0.5·(D+D1) ). The drag loss factor, VM can be determined using gure 5.11. 47
5. Planetary gearbox: Loads, Kinematics and Power Loss Figure 5.10.: Oil level measurement [36]. Figure 5.11.: Drag loss factor graph [36]. 48
5.5. Rolling bearings power loss 5.5.6. Preload (tapered roller bearings) The tapered roller bearings are assumed to be in a back-to-back conguration and when an axial force acts in one of the bearings, the second bearing has to be subjected to a preload in order to diminish the axial displacement of the rst bearing. The preload force F0 that prevents the second bearing (bearing B) of becoming unloaded in the presence of an axial force KA in the rst bearing (bearing A) is given by equation (5.5.23). F0=Ka·cB cA+cB (5.5.23) Where cA and cB are the spring constants of the bearings. As in the studied gearbox the bearings are equal, cA=cB and equation (5.5.23) can be rewritten as: F0=1 2·Ka (5.5.24) The Ka value was determined based on the gearbox manufacturer's catalog for the maximum axial force allowed on the output shaft of the planetary gearbox and the axial force caused by the maximum input torque for each test. An example of the power losses for the tapered roller bearing (TRB) and the deep groove ball bearing (DGB) is given in table 5.7, considering the nominal operating conditions of the tested gearbox, running with PAOR at 85◦ C. 49
5. Planetary gearbox: Loads, Kinematics and Power Loss Table 5.7.: Example for the bearings losses for the nominal operating conditions. Variables Results TRB DGB Rolling frictional moment [N · mm] Mrr 2064.5 330.87 Variable of the rolling frictional moment Grr 14.756 1.0556 Inlet shear heating reduction factor φish 0.9932 0.9685 Kinematic replenishment/starvation φrs 1 1 reduction factor Sliding friction moment [N · mm] Msl 2995.1 85.988 Variable of the sliding frictional moment Gsl 43223 4299.4 Sliding frictional coecient µsl 0.1 0.1 Weighting factor for the φbl 0.6867 0 sliding coecient Frictional moment of drag losses [N · m] Mdrag 38.499 0 ∗ Preload F0 33000 − Total frictional moment [N · m] M 5098.2 416.86 Total power loss [W] PV L 133.47 43.65 ( ∗ ) − For grease lubricated rolling bearings the SKF model considers Mdrag = 0 which is the case in study. 5.6. Needle roller bearing losses The rolling bearing power loss model that was previously presented lacks the support for needle roller bearings. The frictional moment of a needle roller bearing, equation (5.6.1), was calculated according to both Höhn et al. [10] and Eschmann et al. [37] models. TV L =TV L0+TV L1 (5.6.1) The no-load component is calculated according to equation (5.6.2). TV L0=1.6·10−8·f0·d3 m when υ·n < 2000 10−10 ·f0·(υ·n)2 3·d3 m when υ·n≥2000 (5.6.2) Where: •TV L0 is the no-load frictional moment [N · m]; •f0 is a coecient dependent on the bearing design and lubrication method ( f0= 12 ); 50
5.7. Seals power loss The load component, TV LP 1 , can be calculated using equation (5.6.3). TV LP 1= 10−3·f1·P1·dm (5.6.3) Where: •P1 is the equivalent bearing load; •f1 is a coecient which takes into account the direction of load application ( f1= 0.002 ) An example of the power losses for the needle roller bearing is given in table 5.8, considering the nominal operating conditions of the tested gearbox, running with PAOR at 85◦ C. Table 5.8.: Example for the needle roller bearing losses. Variables Results No-load component [N · m] TV L0 0.0303 Load component [N · m] TV L1 0.0588 Equivalent bearing load [N] P1 6687.3 Total frictional moment [N · m] TV L 0.0890 Total power loss [W] PV L 6.9937 5.7. Seals power loss In most applications, seal power losses represent a minor fraction of the total power loss of a gearbox, and are almost negligible when compared to the losses of other components. Nevertheless, in order to obtain a model as realistic as possible, the seals losses were also taken into account. An approximation is given in equation (5.7.1) [10]. PV D = 7.69 ×10−6×d2 sh ×n (5.7.1) Where: •dsh is the shaft diameter [mm]; •n is the shaft rotational speed [rpm]. The seals power loss is independent of the transmitted torque, being the major inuences the operating speed and the shaft diameter. It is possible that equation (5.7.1) needs small adjustments as dierent seal materials may inuence the seals power loss [10]. 51
5. Planetary gearbox: Loads, Kinematics and Power Loss Table 5.9.: Seals power losses for gearbox nominal working conditions. Variables Results Input Seal Power Loss [W] PV Din 37.681 Output Seal Power Loss [W] PV Dout 55.560 For the nominal operating conditions of the test gearbox, table 5.9 shows the seal power losses in both input and output seals. 5.8. Heat balance While a gearbox is operating heat is generated, which will be dissipated to the surrounding environment. According to thermodynamics, the mechanical energy that is dissipated by the gearbox must be equal to the thermal energy that the surrounding environment receives, equation (5.8.1). PV=˙ Qtotal (5.8.1) The main heat transfer mechanisms are conduction, convection and radiation, equation (5.8.2). ˙ Qtotal =˙ Qcd +˙ Qcv +˙ Qrad (5.8.2) Thermal conduction reect the small amount of heat that is transferred to the shafts, couplings and foundations of the gearbox. Convection and radiation comprise the heat transfer that occurs through the external surface of the gearbox. Höhn et al. [10] suggested that the total heat ow rate can be calculated according to the equation (5.8.3). ˙ Qtotal =αHeat ·A·(TOil −TRoom) (5.8.3) Where: •αHeat is the heat transfer coecient (which takes into account the heat transfer due to conduction, convection and radiation); •A is the external area of the gearbox; •TOil is the oil temperature; •TRoom is the room temperature. To be noticed, is the fact that equation (5.8.3) does not take into account other relevant characteristics of the air in the room, such as relative humidity. Bearing in 52
5.8. Heat balance mind that the specic heat of dry air and water vapor are, at atmospheric pressure: •cpdry air = 1.01kJ/kg◦C •cpwater vapour = 1.84kJ/kg◦C it is not dicult to understand that the relative humidity might be a relevant factor in the relation between the stabilization temperature ( TOil −TRoom ) and the total heat ow rate, therefore equation 5.8.3 can only be applied in very controlled environments. 53
6. Sixteen Test Grid (PAOR) 1600 2000 2400 2800 1600 2000 2400 2800 1600 2000 2400 2800 1600 2000 2400 2800 10 20 30 40 50 60 70 80 90 100 Oil Temperature and Stabilization Temperature vs. Operating Conditions Torque [Nm] Temperature [ºC] TOil S1 TOil S2 ∆T S1 ∆T S2 250 rpm 200 rpm 150 rpm 100 rpm Figure 6.4.: PAOR: Oil temperature and Stabilization temperature. 15 20 25 30 35 40 45 50 55 60 5 10 15 20 25 Experimental αA ∆T [ºC] αA [W/ºC] 15 20 25 30 35 40 45 50 55 60 5 10 15 20 25 Numerical αA ∆T [ºC] αA [W/ºC] S1 S2 S1 S2 y=0.0735x+13.5 Norm of Residuals: 11.8 y=−0.0335x+15.9 Norm of Residuals: 4.02 Figure 6.5.: PAOR: Heat transfer coecient. 60
6.1. Overall analysis diered considerably between tests and therefore the stabilized room temperature is not enough to ascertain the heat dissipated by the gearbox. As referred in section 5.8, the relative humidity of the air in the room is a relevant factor in the estimation of the dissipated heat. The numerical values, although presenting a lower dispersion, follow a slightly decreasing trend line, which is not consistent with previous works [3]. Nevertheless, this can be explained by the fact that the model is not considering the churning losses. The highest temperatures occur at higher speeds, where the churning losses are more relevant. If the churning losses were considered, the amount of power loss found with higher operating temperatures would have led to an increasing trend line in the numerical values. In order to understand in which range of lubrication regime the tests were performed the specic lm thickness was calculated. The results are presented in gure 6.6. 1600 2000 2400 2800 1600 2000 2400 2800 1600 2000 2400 2800 1600 2000 2400 2800 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Torque [Nm] Λ [−] Specific Film Thickness vs. Operating Conditions Sun−Planet S1 Sun−Planet S2 Planet−Ring S1 Planet−Ring S2 100 rpm 150 rpm 200 rpm 250 rpm Figure 6.6.: PAOR: Specic Film Thickness. The specic lm thickness follows a decreasing trend with increasing torque and/or speed. For lower speeds, the specic lm thickness is very sensitive to an increase of torque while at higher speeds the decrease of the specic lm thickness with increasing torque is not so marked. The lm thickness depends on the oil operating dynamic viscosity, which in turn depends on the operating temperature. Comparing both temperature and lm thickness results, it is clear that the lm thickness lowers with increasing oil temperature, as a consequence of lower dynamic viscosity. The Planet-Ring contact has always higher specic lm thickness than the SunPlanet contact, mainly due to the higher equivalent radius and its lower load line. The Sun-Planet contact presented specic lm values lower than 0.7, meaning it is operating in a boundary lm lubrication regime. As for the Planet-Ring contact, the 61
6. Sixteen Test Grid (PAOR) lubrication regime is also boundary lm, except for the tests 100rpm/1600Nm and 100rpm/2000Nm. It was also found that the specic lm thickness of direction S1 was always higher than the ones for direction S2. This occurs because the specic lm thickness has a direct correlation with the operating viscosity which in turn depend on the oil temperatures which were always higher for direction S2, explaining the lower specic lm thickness values. 6.2. Numerical predictions:part by part In gure 6.7, the numerical power loss results were plotted discerning the contribution of each component of the gearbox in the total power loss. 1600 2000 2400 2800 1600 2000 2400 2800 1600 2000 2400 2800 1600 2000 2400 2800 0 100 200 300 400 500 600 700 800 900 1000 Model Prediction: Power Loss (Part by Part) Power Loss [W] Torque [Nm] Gears Ball Bearings Tapered Bearings Needle Bearings Seals 250 rpm 200 rpm 100 rpm 150 rpm Figure 6.7.: Power Loss: Part by Part. The two main sources of power loss were the gears and the tapered rolling bearings. The tapered rolling bearings losses only overcame the gear losses in the tests with the lowest torque (1600Nm). For all the other torques, the gears were the main source of power loss. The gear losses seem to be equally dependent on the speed and torque. The tapered rolling bearing losses were roughly constant with increasing torque, but showed to be quite sensitive to the operating speed. The studied gearbox is a planetary speed multiplier capable of supporting very high radial and axial loads in the output shaft, meaning that the tapered roller bearings have a fairly high preload. Since the helical angle of the planetary gear is quite low, the axial forces applied in the tapered will be considerably low when compared to the preload, therefore the power loss in the tapered roller bearings is almost independent of the input torque. 62
6.2. Numerical predictions:part by part The third source of power loss were the seals. According to equation (5.7.1), the seals' losses are exclusively dependent on the operating speed. The ball and the needle roller bearing losses had the least signicant contribution to the total power loss. It is evident that both ball and needle roller bearings react to an increase of speed. For the lowest speed (100rpm), the mentioned bearings react poorly to the torque increases, but for the others speeds, it seems that the ball and needle bearing losses gain sensitivity to the torque increases too. Considering the two extreme values of speed and torque, the power loss of each component was plotted as percentages relative to the input power, shown in gure 6.8. 1600 2800 1600 2800 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Torque [Nm] Power Loss Contributions [%] Percentages of Power Loss Contributions Gear Ball Bearing Tap Bearing Needle Bearing Seals 0.67 0.53 0.60 0.06 0.61 0.36 0.36 0.10 0.07 0.07 0.09 0.63 0.08 0.06 0.58 0.23 0.23 0.13 0.13 0.13 100rpm 250rpm 1.64 1.30 1.55 1.21 Figure 6.8.: Percentages of Power Loss Contributions. The weight of each dissipation source in the total power loss does not vary much with the speed, but it's highly sensitive to torque variations. The gears are responsible for a power loss between 0.53% and 0.67% of the input power. Their relevance increases with torque and decreases with speed. The tapered roller bearings are responsible for a power loss of 0.61% and 0.63% at the lowest torque, but decrease to 0.36% at the highest load. Their importance is roughly constant with speed but greatly decreases as torque increases. The importance of the seals is strictly dependent on the torque and decreases when the torque increases. The seals are responsible for losses from 0.13% to 0.23% 63
6. Sixteen Test Grid (PAOR) of the input power. Both ball and needle roller bearings are minor power loss sources. They both decrease their relevance with increasing speed and/or increasing torque. The power losses associated to the ball and needle rolling bearings vary form 0.06% to 0.13% of the input power. 64
7. Five Test Grid 7.1. PAOR After the sixteen test grid the test and slave gearboxes changed places. To assess the repeatability of the tests, the ve grid test was repeated with fresh PAOR oil. The power loss results are shown in gure 7.1. 2000 2400 2800 300 400 500 600 700 800 900 1000 Power Loss at 150rpm Torque [Nm] Power Loss [W] Experimental S1 Model S1 Experimental S2 Model S2 100 150 200 300 400 500 600 700 800 900 1000 Power Loss at 2800Nm Speed [rpm] Power Loss [W] Experimental S1 Model S1 Experimental S2 Model S2 Figure 7.1.: PAOR: Power Loss. For the ve tests carried out, the power loss was always higher when the gearbox worked as reducer, except for the test at 100rpm and 2800Nm, which had very similar values in both operating directions. The numerical results for the power loss values stood in the middle of the experimental values, once again. In terms of eciency, the results are presented in gure 7.2. Despite all the ve tests being carried out above 27kW of nominal input power, the eciency obtained for this tests does not match the results obtained for the sixteen grid test, were above 27kW the eciency in S2 were always higher (see gure 6.3). The two tests carried at a nominal input power lower than 35kW (100rpm/2800Nm and 150rpm/2000Nm) had a higher eciency with the gearbox working as a reducer. For the rest of the tests, with a nominal input power above 35kW, the eciency as multiplier overcame the eciency as reducer. 65
7. Five Test Grid 2000 2400 2800 97 97.5 98 98.5 99 99.5 100 Efficiency at 150rpm Torque [Nm] Efficiency [%] Experimental S1 Model S1 Experimental S2 Model S2 100 150 200 97 97.5 98 98.5 99 99.5 100 Efficiency at 2800Nm Speed [rpm] Efficiency [%] Experimental S1 Model S1 Experimental S2 Model S2 Figure 7.2.: PAOR: Eciency. In both PAOR grids, there is a correlation between the nominal input power and the direction with higher eciency. Nevertheless, this correlation is not clear: in the rst grid, the power level at which the higher eciency changed from one direction to another was at 27kW, and in the second grid was at 35kW. Furthermore, in the rst grid the highest eciency evolves from S1 at lower input power to S2 at higher power and in the second grid, it happens the other way around: the highest eciency belongs to S2 at lower input power, and evolves to S1 at higher power levels. It is worth noting that not all the tests carried for the second time presented the same results. The results obtained for the 100rpm/2800Nm and 150rpm/2000Nm tests were very similar in power loss, eciency and operating and stabilized temperatures. For the rest of the tests, the values presented relevant dierences. A detailed comparison between the sixteen and ve grid tests can be consulted in appendix (consult section B.3). The operating and stabilized temperatures are presented in gure 7.3. In this grid, the operating and stabilized temperatures associated to S2 were always higher. The higher stabilized temperature associated to S2 indicates higher power loss when the gearbox works as a reducer, even that the measured power loss values (see gure 7.1) do not always follow the temperature readings. Comparing with the sixteen test grid, the operating temperatures follow the same trend (S2 higher than S1), although some values do not match. This happens because the power loss is related to the stabilized temperature, which in turn depends of the room temperature. Nevertheless, while the stabilized temperature of the sixteen tests presented very similar values for both operating directions, in the ve test grid these dierences can't be disregarded. 66
7.2. MINR 2000 2400 2800 20 30 40 50 60 70 80 90Oil and Stabilization Temperature at 150 rpm Torque [Nm] Temperature [ºC] TOil S1 TOil S2 ∆T S1 ∆T S2 100 150 200 20 30 40 50 60 70 80 90Oil and Stabilization Temperature at 2800Nm Speed [rpm] Temperature [ºC] TOil S1 TOil S2 ∆T S1 ∆T S2 Figure 7.3.: PAOR: Oil and Stabilization temperatures. 7.2. MINR After the PAOR, the MINR was tested. The power loss values obtained are presented in gure 7.4. 2000 2400 2800 300 400 500 600 700 800 900 1000 Power Loss at 150rpm Torque [Nm] Power Loss [W] Experimental S1 Model S1 Experimental S2 Model S2 100 150 200 300 400 500 600 700 800 900 1000 Power Loss at 2800Nm Speed [rpm] Power Loss [W] Experimental S1 Model S1 Experimental S2 Model S2 Figure 7.4.: MINR: Power Loss. For the test at lowest nominal input power, the numerical predictions were lower than the experimental values in both operating directions, and the power loss in S1 was higher than in S2. For all the other tests, S1 presented lower losses than S2 and the numerical predictions stood between the experimental readings. In what regards to the eciency, the results obtained are shown in gure 7.5. 67
7. Five Test Grid 2000 2400 2800 97 97.5 98 98.5 99 99.5 100 Efficiency at 150rpm Torque [Nm] Efficiency [%] Experimental S1 Model S1 Experimental S2 Model S2 100 150 200 97 97.5 98 98.5 99 99.5 100 Efficiency at 2800Nm Speed [rpm] Efficiency [%] Experimental S1 Model S1 Experimental S2 Model S2 Figure 7.5.: MINR: Eciency. The eciency was always higher when the gearbox worked as a multiplier, and the numerical results stood between the experimental reading or slightly bellow. For the 150rpm set of tests, the eciency of direction S1 showed a decreasing trend with increasing torque, although this values are not supported by any abnormal behavior in the operating or stabilized temperatures, see gure 7.6. 2000 2400 2800 20 30 40 50 60 70 80 90 100 Oil and Stabilization Temperature at 150 rpm Torque [Nm] Temperature [ºC] TOil S1 TOil S2 ∆T S1 ∆T S2 100 150 200 20 30 40 50 60 70 80 90 100 Oil and Stabilization Temperature at 2800Nm Speed [rpm] Temperature [ºC] TOil S1 TOil S2 ∆T S1 ∆T S2 Figure 7.6.: MINR: Oil and Stabilization temperatures. In similarity to what happened with the PAOR, the operating and stabilized temperatures associated to S2 were always higher than S1. Therefore, the temperature readings indicate dierent eciencies for both directions, and independent of the nominal input power. 68
7.3. MINE 7.3. MINE The third oil to be tested was the MINE. The power loss results are presented in gure 7.7. 2000 2400 2800 300 400 500 600 700 800 900 1000 Power Loss at 150rpm Torque [Nm] Power Loss [W] Experimental S1 Model S1 Experimental S2 Model S2 100 150 200 300 400 500 600 700 800 900 1000 Power Loss at 2800Nm Speed [rpm] Power Loss [W] Experimental S1 Model S1 Experimental S2 Model S2 Figure 7.7.: MINE: Power Loss. For the MINE power loss results, the direction S2 had always higher losses than S1 and the numerical results stood between the experimental values for both operating directions. Figure 7.8 presents the eciencies at stabilized operating conditions. 2000 2400 2800 97 97.5 98 98.5 99 99.5 100 Efficiency at 150rpm Torque [Nm] Efficiency [%] Experimental S1 Model S1 Experimental S2 Model S2 100 150 200 97 97.5 98 98.5 99 99.5 100 Efficiency at 2800Nm Speed [rpm] Efficiency [%] Experimental S1 Model S1 Experimental S2 Model S2 Figure 7.8.: MINE: Eciency. As well as the power loss results, the eciency values were quite consistent. S1 69
7. Five Test Grid The specic lm thickness depends on a multitude of factors. In what regards the oil properties, the specic lm thickness depends on the dynamic viscosity and both thermoviscosity and piezoviscosity coecients. Therefore, the specic lm thickness depends of the operating temperature. The specic lm thickness for the Sun-Planet contact and for the Planet-Ring contact is presented in gure 7.17. 2000 2400 2800 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Sun−Planet Contact: Specific Film Thickness at 150rpm Torque [Nm] Λ [−] PAOR MINR MINE PAGD 100 150 200 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Sun−Planet Contact: Specific Film Thickness at 2800Nm Λ [−] Speed [rpm] PAOR MINR MINE PAGD (a) Sun-Planet Contact. 2000 2400 2800 0.3 0.4 0.5 0.6 0.7 0.8 Planet−Ring Contact: Specific Film Thickness at 150rpm Torque [Nm] Λ [−] PAOR MINR MINE PAGD 100 150 200 0.3 0.4 0.5 0.6 0.7 0.8 Planet−Ring Contact: Specific Film Thickness at 2800Nm Λ [−] Speed [rpm] PAOR MINR MINE PAGD (b) Planet-Ring Contact. Figure 7.17.: Oil comparison: Specic Film Thickness. Although with dierent values, all the oils show the similar trends regarding both contacts. The specic lm thickness stood bellow 0.7 for all oils, indicating a boundary lm lubrication regime in both contacts. The only exception was the test 150rpm/2000Nm performed with MINE, were the Planet-Ring contact has a specic lm thickness higher than 0.7. 76
7.5. Oil Comparison MINE showed the highest specic lm thickness for the ranged working conditions, while MINR showed the lowest. According to the American Gear Manufacturers Association [38] the specic lm thickness has a direct relation to the gear failure probability. Such low specic lm thickness as the ones found in MINR lead to a higher breakdown probability than the other oils for the performed tests. PAGD overcame the specic lm thickness of PAOR in the two tests with the highest power level: 150rpm/2800Nm and 200rpm/2800Nm. PAOR showed a decreasing trend with increasing power or with increasing torque while PAGD at constant speed showed a tendency to stabilize with increasing torque and at constant torque showed its best results at 150rpm. Ferrography results The ferrography results for PAOR are present in gure 7.18. The sample analyzed was taken in the end of the sixteen test grid. (a) Dilution: 0.1; Location: Core. (b) Dilution: 0.1; Location: Core. (c) Dilution: 0.1; Location: Core. (d) Dilution: 0.1; Location: Core. Figure 7.18.: Ferrography images: PAOR. In photograph 7.18a is visible the presence of ferrous particles, some of big dimension. Photographs 7.18b, 7.18c and 7.18d are magnications of photgraph 7.18a. Photograph 7.18b and 7.18d show ferrous particles resultant of fatigue wear. In photograph 7.18c is visible a high density friction polymer. 77
7. Five Test Grid The ferrography results for the MINE oil showed a signicant presence of both small and big ferrous particles, see photograph 7.19a. In photograph 7.19b and 7.19c is visible ferrous particles of big dimensions, typical of severe fatigue wear. (a) Dilution: 1; Location: Core. (b) Dilution: 1; Location: Core. (c) Dilution: 1; Location: Core. Figure 7.19.: Ferrography images: MINE. The MINR results are presented in gure 7.20. In photograph 7.20a is visible some wear ferrous particles and thermal oxides. Photographs 7.20b, 7.20d and 7.20c are magnications of the rst photograph. In 7.20b is visible a ferrous particle of big dimensions slightly oxidized; gures 7.20c and 7.20d show ferrous particles of both big and small dimensions as well as particles from varnishes. As for the PAGD, the ferrography results are shown in gure 7.21. Photograph 7.21a shows several particles of big dimensions. Figure 7.21b revels a ferrous particles of large dimensions, typical of adhesive wear. Figures 7.21c and 7.21d show ferrous particles of large and medium sizes typical of fatigue wear and thermal oxides. As for the direct reading ferrography results, the values are presented in table 7.1. The CPUC and ISUC represent, respectively, the wear particles index and the wear severity index. 78
7.5. Oil Comparison (a) Dilution: 0.1; Location: Core. (b) Dilution: 0.1; Location: Core. (c) Dilution: 0.1; Location: Core. (d) Dilution: 0.1; Location: Middle. Figure 7.20.: Ferrography images: MINR. (a) Dilution: 1; Location: Core. (b) Dilution: 1; Location: Core. (c) Dilution: 1; Location: Core. (d) Dilution: 1; Location: Core. Figure 7.21.: Ferrography images: PAGD. 79
7. Five Test Grid Table 7.1.: Direct Reading Ferrography Results. Oil Cycles d DSDL CPUC ISUC PAOR 924000 0.1 3.4 25.9 293.0 6.6E+04 MINR 247500 0.1 13.4 45.8 592.0 1.9E+05 MINE 247500 1.0 27.0 88.9 115.9 7.2E+03 PAGD 247500 1.0 9.2 17.0 26.2 2.0E+02 For both wear indexes, PAGD showed to be the best oil, followed by MINE. The PAOR sample analyzed was the one collected after the sixteen test grid and therefore had more than three times the number of cycles and even so, it showed better wear indexes than MINR. In terms of gear wear and oil degradation, the PAGD showed the lowest wear indexes, even though it showed some premature thermal oxide formation. MINE had good results in the direct reading ferrography, but the analytical ferrography indicates relevant fatigue wear particles. MINR had the worst values in the wear indexes and the analytical ferrography showed a premature oil degradation. PAOR results are not directly comparable to the rest of the oils, but considering the amount of cycles and the working conditions it has supported, the results are satisfactory. 80
7.5. Oil Comparison 7.5.2. Numerical Results Using the numerical results, one operating condition was selected to plot the power losses of each gearbox component, in order to evaluate each oil performance in what regards gears, roller bearings and seals. The selected operating condition was the 150rpm/2800Nm (S1), for being the key point of the 5 test grids and for being the closest comparison in terms of tangential speed and Hertz pressure (see table 3.3). The percentages of each component in terms of power loss are represented in gure 7.22. These percentages are towards the operating power input. PAOR MINR MINE PAGD 0 0,2 0,4 0,6 0,8 1 1,2 1.5 1,6 Percentages of Power Loss Contribuitions Tested Oils Power Loss Contibuitions [%] Gears Ball Bearings Tapered Bearings Needle Bearings Seals 0.63 0.83 0.70 0.53 0.13 0.13 0.13 0.07 0.13 0.36 0.36 0.36 0.35 0.07 0.06 1.26 1.46 1.34 1.15 0.07 0.07 0.08 0.07 0.07 Figure 7.22.: Percentages of Power Loss Contributions. In terms of total power loss, the numeric results indicate that PAGD is the most ecient oil. Nevertheless, it was already concluded that the numerical values of PAGD deviate more from the experimental then the other oils, as the model does not consider the churning losses. For the rest of the oils, the total power loss follows the stabilization temperature tendency: PAOR is better than MINE, which in turn outperforms than MINR (see gure 7.14). In what concerns the power losses of each component, the comparison between oils indicates that at the selected operating conditions, the eciency dierences found are almost exclusively related to the gear losses. PAGD showed the lowest values on gear losses, followed by PAOR and MINE. MINR is the oil which leads to the highest values of gear losses. The roller bearing losses do not vary from one oil to another. Although there are slight dierences, they are always about 0.01%, and therefore the dierences can be neglected. The seals show a perfectly constant value, which was expected since according 81
7. Five Test Grid to equation (5.7.1) the seals only depend on the shaft diameter and the rotational speed. It was also possible to compare the coecient of friction in the meshing line of both Sun-Planet and Planet-Ring contacts, which are presented in gure 7.23. 2000 2400 2800 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 Sun−Planet Contact: Coefficient of Friction at 150rpm Torque [Nm] µ [−] PAOR MINR MINE PAGD 100 150 200 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 Sun−Planet Contact: Coefficient of Friction at 2800Nm µ [−] Speed [rpm] PAOR MINR MINE PAGD (a) Sun-Planet Contact. 2000 2400 2800 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Planet−Ring Contact: Coefficient of Friction at 150rpm Torque [Nm] µ [−] PAOR MINR MINE PAGD 100 150 200 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Planet−Ring Contact: Coefficient of Friction at 2800Nm µ [−] Speed [rpm] PAOR MINR MINE PAGD (b) Planet-Ring Contact. Figure 7.23.: Oil comparison: Coecient of friction. The coecient of friction comparison between oils is very clear: PAGD leads to the lowest coecient of friction, followed by PAOR and MINE, respectively, while MINR lead to the highest value. This explains the dierences found in the gears losses represented in gure 7.22. In the other hand, it is possible to conclude that when using PAGD, the reduction in gear losses due to the lower friction coecient is not enough to compensate the higher churning losses, as the PAGD stabilization temperature is higher than PAOR and MINE. 82
7.5. Oil Comparison The coecient of friction has a inverted relation to the operating dynamic viscosity (gure 7.16). It is possible to verify that the oils with the highest dynamic viscosity lead to the lowest coecient of friction. The Sun-Planet contact and the Planet-Ring contact present the same tendencies in what regards the coecient of friction: it increases with increasing torque, and decreases with increasing speed. Although presenting the same tendencies, the coef- cient of friction in the Planet-Ring contact was always lower than in the Sun-Planet contact, due to its higher equivalent radius and lower line load. The numerical values of αA for the tested oils were plotted in gure 7.24. The values considered were for the operating direction S1. 20 25 30 35 40 45 50 10 11 12 13 14 15 16 17 18 19 20 ∆T [ºC] α A [W/ºC] Numerical αA PAOR MINR MINE PAGD trendline: PAOR trendline: MINR trendline: MINE trendline: PAGD Figure 7.24.: Heat transfer coecient: numerical values. The trendlines were considered to be linear ( y=p1x+p2 ). The values of the coecients p1 and p2 are represented in table 7.2, as well as the norm of residuals. Table 7.2.: Trendline coecients and norm of residuals. Oil p1p2 Norm of Residuals PAOR 0.1742 10.4038 1.1373 MINE 0.1531 10.6973 0.3881 MINR 0.3199 5.0972 2.0643 PAGD 0.1554 7.9502 1.5177 In what concerns the trends of each oil values, it is possible to observe that PAOR and MINE have very close trends, which slightly diverge with increasing stabilization temperature. PAGD showed a similar slope ( p1 ), although the starting point ( p2 ) is nearly half when compared to PAOR and MINE. This is due to the fact that the churning losses are not considered in the numerical results, and they are specially relevant for PAGD. MINR showed a completely dierent trend compared to the other 83
7. Five Test Grid three oils: it has a more accentuated slope, roughly twice, and a starting point that stands in the middle of PAGD and MINE. Regarding the scattering of each oil plot, it is visible that MINR had the worst correlation, followed by PAGD, each one with a norm of residuals higher than 1.5. PAOR had a good correlation, with a norm of residuals of 1.1, while MINE had the best correlation with a norm of residual of 0.4. 84
8. Additional tests The power loss dierences found between the directions S1 and S2, which were followed by an increase of the operating temperature raised some doubts in the analysis of the results. At rst, the increase of the operating temperature was assigned to be a consequence of having another 90min of test after the 240min test was carried out. After that, it was found that the stabilization temperature also suered an increase. At this point, two hypothesis were available to explain the dierences in both power loss and stabilization temperature: • The gearbox could have dierent eciencies for each direction, implying dierent values of power loss and stabilization temperature; • The increase of the stabilization temperature could be a consequence of a malfunction in the data acquisition when the test rig was restarted. In order to clarify these behaviors, PAOR was reintroduced in the gearbox and two tests (100rpm/2800Nm and 150rpm/2800Nm) were carried out but with switched operating directions: at rst the gearbox worked as a reducer (S2) and after as multiplier (S1). The new tests were compared with the tests performed for the sixteen and ve test grid. The evolution of the operating temperature and the dierence between oil and room temperature were plotted through all the 330min and are represented in gure 8.1 and 8.2. 0 50 100 150 200 250 300 40 45 50 55 60 Oil Temperature at 100rpm Time [min] Temperature [ºC] 16Grid 5Grid S2/S1 0 50 100 150 200 250 300 10 15 20 25 30 Difference between Oil and Room Temperature at 100rpm Time [min] ∆ T [ºC] 16Grid 5Grid S2/S1 Figure 8.1.: Temperatures evolution at the 100rpm test. 85
9. Conclusions 9.2. Conclusions based on numerical results The numerical values for power loss and eciency stood between the two experimental readings in most cases. The only signicant exception was PAGD and the high speed tests (200 and 250rpm) for the sixteen test grid. The dierences found between the experimental readings and the numerical values are explained by the churning losses, which the numerical model doesn't take into account. The churning losses are particularly relevant for high operating speeds and for PAGD, as it is denser than the other oils. The numerical values showed that the power loss is more sensitive to speed than to the torque, and the experimental results validate this prediction. In terms of component losses, the numerical model showed that at the ranged working conditions, the gears are the most signicant power loss source, except for the lowest torque applied (1600Nm), where the tapered roller bearings are the main power loss source. For the same working conditions, the numerical results indicate that PAGD had the lowest power loss. The lowest value of PAGD power loss is due to its lowest gear losses which are justied by the experimental results for the gear coecient of friction of PAGD. The rest of the components have nearly the same losses for the tested oils. The gears losses vary accordingly to the coecient of friction obtained for each oil. The churning losses seem to be quite relevant, specially for PAGD which despite showing the lowest coecient of friction in the gears (most important source of power loss) it did not present the best power loss performance. The reduction of the friction in the gears is not big enough to overcome the increase in the churning losses relatively to the other lubricants. For the sixteen test grid, the experimental values of the heat transfer coecient showed a high dispersion of results, when compared to the numerical ones. The scattering indicates a measurement uncertainty in the torque sensors or indicates that the stabilization temperature, by it self, is not enough to ascertain the power loss. 92
10. Future Works The repeatability of the tests could not be assured, specially in terms of torque measurements. The torque sensors accuracy should be checked and the tests carried out should be repeated with higher reliability in the results. The scattering visible on the heat transfer coecients determined with the experimental power loss results is big enough to justify the introduction of a relative humidity sensor in the test rig. The thermal conductibility of the air signicantly changes with the water vapor presence and therefore, two temperature readings are not enough to accurately ascertain the power loss of a gear box. Additional tests should be carried out in order to obtain a more realistic equation regarding other air properties, as relative humidity. The power loss model should be re-built in order to consider successive power losses as the power ows through the gearbox. The eciency dierences found experimentally should be compared to that new version of the model, attempting to comprehend why the gearbox shows dierent eciency for both operating directions. The churning losses and the uid ow seem to be a relevant part of the gearbox losses. A computational uid dynamic (CFD) analysis should be carried out in order to predict the uid motion and the churning losses. The CFD results could be partially validated by lming several tests with a thermographic camera, assuming that the uid motion and temperature would be represented as a gradient temperature at the surface of the gearbox. 93
Bibliography [1] D. Gonçalves. Eciency of a gearbox lubricated with wind mill gear oils. Master's thesis, Faculdade de Engenharia da Universidade do Porto, 2011. [2] P. Marques. Eciency of a gearbox lubricated with wind mill gear oils. Master's thesis, Faculdade de Engenharia da Universidade do Porto, 2012. [3] D. Pereira. Torque loss in a planetary multiplier gearbox: Inuence of operating conditions and gear oil formulation. Master's thesis, Faculdade de Engenharia da Universidade do Porto, 2013. [4] REN21. Renewables 2013 global status report, 2013. [5] GWEC. Global wind report annual market update 2013, 2013. [6] EWEA European Wind Energy Association. Wind energy factsheets, 2013. [7] Magdi Ragheb Adam M. Ragheb. Fundamental and advanced topics in wind power. 2011-06-20. [8] Hanspeter Dinner. KISSsoft:-Wind Turbine Gearbox Calculation, April 2010. [9] World Energy Council. Energy eciency indicators, 2011. [10] B.-R. Höhn, K. Michaelis, and T. Vollmer. Thermal rating of gear drives: Balance between power loss and heat dissipation. AGMA Technical Paper , 1996. [11] B.-R. Höhn, K. Michaelis, and M. Hinterstoiÿer. Optimization of gearbox e- ciency. goriva i maziva , 48(4):462480, 2009. [12] Luís Magalhães, Ramiro Martins, Cristiano Locateli, and Jorge Seabra. Inuence of tooth prole and oil formulation on gear power loss. Tribology International , 43(10):18611871, 2010. 36th Leeds-Lyon Symposium Special Issue: Multi-facets of Tribology. [13] Carlos M.C.G. Fernandes, Pedro M. P. Amaro, Ramiro C. Martins, and Jorge H.O. Seabra. Torque loss in cylindrical roller thrust bearings lubricated with wind turbine gear oils at constant temperature. Tribology International , (0):under review, 2013. [14] Carlos M.C.G. Fernandes, Ramiro C. Martins, and Jorge H.O. Seabra. Friction torque of thrust ball bearings lubricated with wind turbine gear oils. Tribology International , 58(0):47 54, 2013. [15] Carlos M.C.G. Fernandes, Pedro M.P. Amaro, Ramiro C. Martins, and Jorge H.O. Seabra. Torque loss in thrust ball bearings lubricated with wind 95
Bibliography turbine gear oils at constant temperature. Tribology International , 66(0):194 202, 2013. [16] Carlos M.C.G. Fernandes, Ramiro C. Martins, and Jorge H.O. Seabra. Torque loss of type C40 FZG gears lubricated with wind turbine gear oils. Tribology International , (0):, 2013. [17] Pedro M.T. Marques, Carlos M.C.G. Fernandes, Ramiro C. Martins, and Jorge H.O. Seabra. Power losses at low speed in a gearbox lubricated with wind turbine gear oils with special focus on churning losses. Tribology International , 62(0):186 197, 2013. [18] Deirdra Barr. Modern wind turbines: A lubrication challenge, Septmeber 2002. [19] Determination of viscosity of bitumen emulsions - engler method. [20] Astm d341 - 09, standard practice for viscosity - temperature charts for liquid petroleum products. [21] J. Denis, J. Briant, and J.-C. Hipeaux. Physico-Chimie des Lubriants - Analyses et Essais . Éditions Technip, 1997. [22] Matt McMahon Michael Barret. Analytical ferrography, October 2000. [23] José A. Brandão, Mathilde Meheux, Fabrice Ville, Jorge H.O. Seabra, and Jorge Castro. Comparative overview of ve gear oils in mixed and boundary lm lubrication. Tribology International , 47(0):50 61, 2012. [24] D. Dowson and G. R. Higginson. Elasto-hydrodynamic Lubrication . Pergamon Press, SI edition edition, 1977. [25] D. Simner. Quantifying the potential fuel economy benet of transmission lubricants. Industrial and Automotive Lubrication , 2:8, 1998. [26] F. Roux. Notion de tribologie, em La Lubrication Industrielle - Tome 1 - Transmissions Compresseurs, Turbines . Publications de l'Institue Français du Pétrole, 1984. [27] JP. W. Gold, A. Schmidt, H. dicke, H. Loos, and C. Aÿmann. Viscosity-pressuretemperature behaviour of mineral and synthetic oils. Journal of Synthetic Lubrication , 18(1), 2001. [28] L. Schlenk. Unterscuchungen zur Fresstragfähigkeit von Grozahnrädern . PhD thesis, Dissertation TU München, 1994. [29] C. Changenet, G. Leprince, F. Ville, and P. Velex. A note on ow regimes and churning loss modeling. Journal of Mechanical Design , 133(12):121009, 2011. [30] C. Changenet and P. Velex. Housing Inuence on Churning Losses in Geared Transmissions. Journal of Mechanical Design , 130(6):062603, 2008. [31] A. S. Terekhov. Hydraulic losses in gearboxes with oil immersion. Vestn. Mashinostroeniya , 55(5):1317, 1975. 96
Bibliography [32] R. J. Boness. Churning losses of discs and gears running partially submerged in oil. Procedings of ASME International Power Transmission Gearing Conference , 1:355359, 1989. [33] S. Seetharaman and A. Kahraman. Load-independent spin power losses of a spur gear pair: Model formulation. Journal of Tribology , 131(2):022201, 2009. [34] Gauthier LePrince, Christophe Changenet, Fabrice Ville, Philippe Velex, Christophe Dufau, and Frédéric Jarnias. Inuence of Aerated Lubricants on Gear Churning Losses - An Engineering model. Tribology Transactions , 54(6):929 938, 2011. [35] F Concli and C Gorla. Computational and experimental analysis of the churning power losses in an industrial planetary speed reducer. In 9th International Conference on Advances in Fluid Mechanics-Advances in Fluid Mechanics IX, WIT Transactions on Engineering Sciences , volume 74, pages 287298, 2012. [36] SKF General Catalogue 6000 EN . SKF, 2013. [37] Eschmann Hasbargen Weigand. Ball and Roller Bearings - Theory, Design, and Application . Wiley, 1985. [38] American Gear Manufacturers Association. Eect of lubrication on gear surface distress, agma 925-a03. AGMA Information sheet . 97
Appendix 99
A. Ring surface temperature tests The temperatures readings of the additional tests have proven that the uid ow inside the gearbox has a relevant inuence in the temperatures measured in the oil sump and in the wall. Therefore, the gearbox was equipped with four thermocouples placed on the area exterior to the ring (see gure A.1) in an attempt to ascertain the ring temperatures, considering that part of the ring is immersed in the oil sump, an the other is not. Figure A.1.: Thermocouples' positioning. Three tests were performed at 150rpm/2800Nm. In two of them, the rst working direction was S2 (reducer), and in the last one, the rst operating direction was S1 (multiplier). The thermocouples' readings were recorded by two thermologgers; in dierent tests, the combination between thermocouples and thermologgers was changed, in order to verify the results repeatability. The results are shown in gure A.2, A.3 and A.4. The repeatability of the temperature's readings was not veried: Between the rst and the second tests (gures A.2 and A.3), the maximum and minimum temperature points switched positions; in the third test (gure A.4) is visible that in the second part of the test point A and C have dierent trends from point B and D. In this test, the thermocouples measuring point A and C were recorded by one thermologger, while thermocouples measuring point B and D were recorded by the other. The readings might be aected by a "thermologger factor", as there is no plausible explanation for the diagonal dierences found. Nevertheless, the temperature dierence found between two points was higher than 10 ◦C in two out of three cases, reinforcing the need to run additional tests aiming to clarify the uid ow inuence in the oil, wall and surface temperatures' behavior. 101
B. Test Reports Test Number:3 Date:07/03/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 100 rpm TQin 2400 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n199.7rpm TQ12321.5Nm TQ2573.6Nm Temperature readings : Units TOil M547.58 ◦C TOil M12 48.38 ◦C TW all 47.02 ◦C TAmb 26.96 ◦C Additional Information: Units TOil M5−TAmb 20.62 ◦C Efficiency 98.83 % TQLoss 27.2Nm S2: Reducer Gearbox Actual Working Conditions: Units n199.7rpm TQ12320.6Nm TQ2588.5Nm Temperature readings: Units TOil M551.03 ◦C TOil M12 50.11 ◦C TW all 48.80 ◦C TAmb 29.79 ◦C Additional Information: Units TOil M5−TAmb 21.24 ◦C Efficiency 98.58 % TQLoss 33.4Nm 108
B.1. PAOR Oil: 16 Test Grid Test Number:4 Date:10/03/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 150 rpm TQin 1600 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1149.9rpm TQ11549.8Nm TQ2381.6Nm Temperature readings : Units TOil M555.59 ◦C TOil M12 57.79 ◦C TW all 56.74 ◦C TAmb 31.12 ◦C Additional Information: Units TOil M5−TAmb 24.47 ◦C Efficiency 98.48 % TQLoss 23.5Nm S2: Reducer Gearbox Actual Working Conditions: Units n1149.9rpm TQ11549.0Nm TQ2393.5Nm Temperature readings: Units TOil M558.59 ◦C TOil M12 58.77 ◦C TW all 57.73 ◦C TAmb 33.73 ◦C Additional Information: Units TOil M5−TAmb 24.85 ◦C Efficiency 98.40 % TQLoss 25.2Nm 109
B. Test Reports Test Number:5 Date:11/03/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 150 rpm TQin 2000 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1149.9rpm TQ11936.4Nm TQ2475.7Nm Temperature readings : Units TOil M561.00 ◦C TOil M12 62.31 ◦C TW all 61.11 ◦C TAmb 31.07 ◦C Additional Information: Units TOil M5−TAmb 29.93 ◦C Efficiency 98.26 % TQLoss 33.6Nm S2: Reducer Gearbox Actual Working Conditions: Units n1150.6rpm TQ11935.8Nm TQ2490.7Nm Temperature readings: Units TOil M564.04 ◦C TOil M12 64.06 ◦C TW all 62.75 ◦C TAmb 34.49 ◦C Additional Information: Units TOil M5−TAmb 29.55 ◦C Efficiency 98.62 % TQLoss 27.0Nm 110
B.1. PAOR Oil: 16 Test Grid Test Number:6 Date:12/03/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 150 rpm TQin 2400 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1149.9rpm TQ12322.3Nm TQ2571.7Nm Temperature readings : Units TOil M563.29 ◦C TOil M12 64.00 ◦C TW all 62.89 ◦C TAmb 32.13 ◦C Additional Information: Units TOil M5−TAmb 31.16 ◦C Efficiency 98.46 % TQLoss 35.7Nm S2: Reducer Gearbox Actual Working Conditions: Units n1149.8rpm TQ12321.7Nm TQ2588.6Nm Temperature readings: Units TOil M568.60 ◦C TOil M12 68.57 ◦C TW all 67.23 ◦C TAmb 34.80 ◦C Additional Information: Units TOil M5−TAmb 33.80 ◦C Efficiency 98.61 % TQLoss 32.7Nm 111
B. Test Reports Test Number:7 Date:13/03/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 200 rpm TQin 1600 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1200.7rpm TQ11549.2Nm TQ2379.3Nm Temperature readings : Units TOil M568.44 ◦C TOil M12 69.50 ◦C TW all 68.97 ◦C TAmb 31.27 ◦C Additional Information: Units TOil M5−TAmb 37.17 ◦C Efficiency 97.94 % TQLoss 32.0Nm S2: Reducer Gearbox Actual Working Conditions: Units n1200.0rpm TQ11547.2Nm TQ2393.0Nm Temperature readings: Units TOil M570.63 ◦C TOil M12 73.72 ◦C TW all 72.68 ◦C TAmb 33.55 ◦C Additional Information: Units TOil M5−TAmb 37.07 ◦C Efficiency 98.41 % TQLoss 25.0Nm 112
B.1. PAOR Oil: 16 Test Grid Test Number:8 Date:14/03/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 200 rpm TQin 2000 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1201.8rpm TQ11935.8Nm TQ2475.4Nm Temperature readings : Units TOil M572.85 ◦C TOil M12 73.06 ◦C TW all 72.63 ◦C TAmb 31.75 ◦C Additional Information: Units TOil M5−TAmb 41.10 ◦C Efficiency 98.24 % TQLoss 34.1Nm S2: Reducer Gearbox Actual Working Conditions: Units n1200.2rpm TQ11940.8Nm TQ2492.8Nm Temperature readings: Units TOil M574.48 ◦C TOil M12 77.34 ◦C TW all 76.32 ◦C TAmb 34.04 ◦C Additional Information: Units TOil M5−TAmb 40.44 ◦C Efficiency 98.46 % TQLoss 30.3Nm 113
B. Test Reports Test Number:9 Date:17/03/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 200 rpm TQin 2400 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1201.8rpm TQ12322.3Nm TQ2571.3Nm Temperature readings : Units TOil M574.82 ◦C TOil M12 74.63 ◦C TW all 74.15 ◦C TAmb 31.26 ◦C Additional Information: Units TOil M5−TAmb 43.55 ◦C Efficiency 98.40 % TQLoss 37.2Nm S2: Reducer Gearbox Actual Working Conditions: Units n1200.0rpm TQ12319.6Nm TQ2589.2Nm Temperature readings: Units TOil M578.11 ◦C TOil M12 80.82 ◦C TW all 79.77 ◦C TAmb 33.27 ◦C Additional Information: Units TOil M5−TAmb 44.84 ◦C Efficiency 98.42 % TQLoss 37.1Nm 114
B.1. PAOR Oil: 16 Test Grid Test Number:10 Date:18/03/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 250 rpm TQin 1600 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1250.4rpm TQ11549.0Nm TQ2377.5Nm Temperature readings : Units TOil M582.08 ◦C TOil M12 82.64 ◦C TW all 82.38 ◦C TAmb 32.82 ◦C Additional Information: Units TOil M5−TAmb 49.26 ◦C Efficiency 97.48 % TQLoss 39.1Nm S2: Reducer Gearbox Actual Working Conditions: Units n1250.5rpm TQ11550.1Nm TQ2395.0Nm Temperature readings: Units TOil M584.69 ◦C TOil M12 87.40 ◦C TW all 86.50 ◦C TAmb 35.00 ◦C Additional Information: Units TOil M5−TAmb 49.70 ◦C Efficiency 98.10 % TQLoss 30.0Nm 115
B. Test Reports Test Number:11 Date:19/03/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 250 rpm TQin 2000 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1250.5rpm TQ11935.7Nm TQ2475.5Nm Temperature readings : Units TOil M585.78 ◦C TOil M12 84.92 ◦C TW all 84.62 ◦C TAmb 34.07 ◦C Additional Information: Units TOil M5−TAmb 51.71 ◦C Efficiency 98.26 % TQLoss 33.7Nm S2: Reducer Gearbox Actual Working Conditions: Units n1250.5rpm TQ11935.9Nm TQ2492.3Nm Temperature readings: Units TOil M586.70 ◦C TOil M12 88.37 ◦C TW all 87.71 ◦C TAmb 36.87 ◦C Additional Information: Units TOil M5−TAmb 49.84 ◦C Efficiency 98.32 % TQLoss 33.1Nm 116
B.1. PAOR Oil: 16 Test Grid Test Number:12 Date:20/03/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 250 rpm TQin 2400 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1250.5rpm TQ12321.6Nm TQ2572.0Nm Temperature readings : Units TOil M588.02 ◦C TOil M12 86.55 ◦C TW all 86.47 ◦C TAmb 34.32 ◦C Additional Information: Units TOil M5−TAmb 53.70 ◦C Efficiency 98.55 % TQLoss 33.6Nm S2: Reducer Gearbox Actual Working Conditions: Units n1250.5rpm TQ12322.4Nm TQ2589.1Nm Temperature readings: Units TOil M589.71 ◦C TOil M12 90.15 ◦C TW all 90.14 ◦C TAmb 36.86 ◦C Additional Information: Units TOil M5−TAmb 52.85 ◦C Efficiency 98.56 % TQLoss 33.9Nm 117
B. Test Reports Test Number:17 Date:03/04/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 100 rpm TQin 2800 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n199.6rpm TQ12709.0Nm TQ2668.1Nm Temperature readings : Units TOil M551.48 ◦C TOil M12 51.57 ◦C TW all 50.07 ◦C TAmb 26.31 ◦C Additional Information: Units TOil M5−TAmb 25.17 ◦C Efficiency 98.65 % TQLoss 36.5Nm S2: Reducer Gearbox Actual Working Conditions: Units n199.6rpm TQ12709.0Nm TQ2685.8Nm Temperature readings: Units TOil M555.32 ◦C TOil M12 54.27 ◦C TW all 52.45 ◦C TAmb 28.72 ◦C Additional Information: Units TOil M5−TAmb 26.60 ◦C Efficiency 98.75 % TQLoss 34.4Nm 124
B.2. PAOR Oil: 5 Test Grid Test Number:18 Date:04/04/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 150 rpm TQin 2000 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1149.8rpm TQ11935.0Nm TQ2475.6Nm Temperature readings : Units TOil M557.29 ◦C TOil M12 59.35 ◦C TW all 57.71 ◦C TAmb 27.93 ◦C Additional Information: Units TOil M5−TAmb 29.36 ◦C Efficiency 98.32 % TQLoss 32.6Nm S2: Reducer Gearbox Actual Working Conditions: Units n1149.8rpm TQ11935.3Nm TQ2491.3Nm Temperature readings: Units TOil M562.86 ◦C TOil M12 62.23 ◦C TW all 60.58 ◦C TAmb 30.72 ◦C Additional Information: Units TOil M5−TAmb 32.14 ◦C Efficiency 98.47 % TQLoss 30.0Nm 125
B. Test Reports Test Number:19 Date:07/04/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 150 rpm TQin 2400 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1149.8rpm TQ12321.7Nm TQ2574.8Nm Temperature readings : Units TOil M558.97 ◦C TOil M12 60.47 ◦C TW all 58.98 ◦C TAmb 28.47 ◦C Additional Information: Units TOil M5−TAmb 30.50 ◦C Efficiency 99.03 % TQLoss 22.6Nm S2: Reducer Gearbox Actual Working Conditions: Units n1149.8rpm TQ12321.7Nm TQ2590.6Nm Temperature readings: Units TOil M565.08 ◦C TOil M12 64.10 ◦C TW all 62.41 ◦C TAmb 29.50 ◦C Additional Information: Units TOil M5−TAmb 35.59 ◦C Efficiency 98.28 % TQLoss 40.7Nm 126
B.2. PAOR Oil: 5 Test Grid Test Number:20 Date:08/04/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 150 rpm TQin 2800 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1149.8rpm TQ12709.4Nm TQ2671.2Nm Temperature readings : Units TOil M562.43 ◦C TOil M12 63.35 ◦C TW all 61.85 ◦C TAmb 30.17 ◦C Additional Information: Units TOil M5−TAmb 32.26 ◦C Efficiency 99.09 % TQLoss 24.8Nm S2: Reducer Gearbox Actual Working Conditions: Units n1149.8rpm TQ12709.1Nm TQ2687.7Nm Temperature readings: Units TOil M568.84 ◦C TOil M12 67.44 ◦C TW all 65.64 ◦C TAmb 31.47 ◦C Additional Information: Units TOil M5−TAmb 37.37 ◦C Efficiency 98.48 % TQLoss 41.9Nm 127
B. Test Reports Test Number:21 Date:09/04/2014 By: Raquel Camacho Oil: PAOR Imposed Working Conditions: Units nin 200 rpm TQin 2800 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1200.0rpm TQ12707.9Nm TQ2671.0Nm Temperature readings : Units TOil M574.06 ◦C TOil M12 74.36 ◦C TW all 72.52 ◦C TAmb 33.28 ◦C Additional Information: Units TOil M5−TAmb 40.78 ◦C Efficiency 99.11 % TQLoss 24.0Nm S2: Reducer Gearbox Actual Working Conditions: Units n1200.0rpm TQ12709.7Nm TQ2686.8Nm Temperature readings: Units TOil M578.03 ◦C TOil M12 76.87 ◦C TW all 75.46 ◦C TAmb 34.79 ◦C Additional Information: Units TOil M5−TAmb 43.24 ◦C Efficiency 98.64 % TQLoss 37.3Nm 128
B.3. PAOR: comparison between test grids B.3. PAOR: comparison between test grids Test & Direction Grid n1TQ1TQ2TOil M5TAmb ∆T 100rpm/2800Nm (S1) 16 99.7 2708.6 667.6 53.84 28.40 25.44 5 99.6 2709.0 668.1 51.48 26.31 25.17 100rpm/2800Nm (S2) 16 99.7 2708.7 685.6 56.24 29.92 26.32 5 99.6 2709.0 685.8 55.32 28.72 26.60 150rpm/2000Nm (S1) 16 149.9 1936.4 475.7 61.00 31.07 29.93 5 149.8 1935.0 475.6 57.29 27.93 29.36 150rpm/2000Nm (S2) 16 150.6 1935.8 490.7 64.04 34.49 29.55 5 149.8 1935.3 491.3 62.86 30.72 32.14 150rpm/2400Nm (S1) 16 149.9 2322.3 571.7 63.29 31.13 35.7 5 149.8 2321.7 574.8 58.97 28.47 30.50 150rpm/2400Nm (S2) 16 149.8 2321.7 588.6 68.60 34.80 33.80 5 149.8 2321.7 590.6 65.08 29.50 35.59 150rpm/2800Nm (S1) 16 149.8 2708.3 667.1 62.78 28.32 34.47 5 149.8 2709.4 671.2 62.43 30.17 32.26 150rpm/2800Nm (S2) 16 149.8 2708.4 685.3 68.46 30.99 37.47 5 149.8 2709.1 687.7 68.84 31.47 41.9 200rpm/2800Nm (S1) 16 200.1 2700.8 666.2 76.79 31.20 45.59 5 200.0 2707.9 671.0 74.06 33.28 40.78 200rpm/2800Nm (S2) 16 200.0 2708.4 685.7 79.99 32.79 47.20 5 200.0 2709.7 686.8 78.03 34.79 43.24 129
B.4. MINR Oil: 5 Test Grid B.4. MINR Oil: 5 Test Grid 131
B. Test Reports Test Number:22 Date:10/04/2014 By: Raquel Camacho Oil: MINR Imposed Working Conditions: Units nin 100 rpm TQin 2800 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n199.6rpm TQ12709.4Nm TQ2668.2Nm Temperature readings : Units TOil M557.64 ◦C TOil M12 56.70 ◦C TW all 54.83 ◦C TAmb 25.80 ◦C Additional Information: Units TOil M5−TAmb 31.83 ◦C Efficiency 98.65 % TQLoss 36.7Nm S2: Reducer Gearbox Actual Working Conditions: Units n199.6rpm TQ12708.9Nm TQ2688.0Nm Temperature readings: Units TOil M560.26 ◦C TOil M12 58.11 ◦C TW all 56.12 ◦C TAmb 26.78 ◦C Additional Information: Units TOil M5−TAmb 33.48 ◦C Efficiency 98.43 % TQLoss 43.3Nm 132
B.4. MINR Oil: 5 Test Grid Test Number:23 Date:14/04/2014 By: Raquel Camacho Oil: MINR Imposed Working Conditions: Units nin 150 rpm TQin 2000 Nm Test duration 240 + 90 min S1: Multiplier Gearbox Actual Working Conditions: Units n1150.0rpm TQ11933.0Nm TQ2478.3Nm Temperature readings : Units TOil M560.72 ◦C TOil M12 62.25 ◦C TW all 60.10 ◦C TAmb 30.03 ◦C Additional Information: Units TOil M5−TAmb 30.69 ◦C Efficiency 98.98 % TQLoss 19.8Nm S2: Reducer Gearbox Actual Working Conditions: Units n1150.0rpm TQ11937.3Nm TQ2494.1Nm Temperature readings: Units TOil M568.50 ◦C TOil M12 66.67 ◦C TW all 64.85 ◦C TAmb 32.24 ◦C Additional Information: Units TOil M5−TAmb 36.26 ◦C Efficiency 98.02 % TQLoss 39.0Nm 133