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Wind Powered Water Pump by Andrés GalánEscalada Santiago Pastor Pérez PROJECT REPORT Mechanical design June 2011 - II - - III - Mechanical Design Dalgas Avenue, 2. 8000 Aarhus C (Denmark) Telephone: +45 4789 3000 Fax: +45 4189 3001 E-mail: [email protected] Title: Abstract: Wind powered water pump Project period: Spring 2011 Project group: MIAFP1/group 05 Members of the group: IY10227 Andrés Galán Escalada IY10226 Santiago Pastor Pérez Supervisor: Flemming Hammer Copies: 2 Pages: 111 The wind is a removable source of energy. Usually it is used to generate electricity, but it can be used for different goals. In Israel there are different social classes. Some of them are very poor. During the summer, some regions are very very dry. The access to water is not that easy, but there are some wells. Joining these two ideas the wind powered water pump was thought. With a low maintenance and cheap construction materials this is a good idea and solution. The wind turbine provides movement to raise the water with a rope water pump able to move bigger flow with less energy than a membrane pump. - IV - Wind Powered Water Pump - 1 - Contents 1 Introduction ............................................................................................................. - 7 - Background ............................................................................................................... - 7 - Project aims .............................................................................................................. - 8 - Location .................................................................................................................... - 9 - 2 Design ...................................................................................................................... - 12 - 2.1 Rotor ................................................................................................................. - 12 - 2.1.1 Blades ........................................................................................................ - 12 - 2.1.2 Join parts .................................................................................................... - 16 - 2.2 Nacelle .............................................................................................................. - 18 - 2.2.1 Box ............................................................................................................ - 18 - 2.2.2 Tail ............................................................................................................. - 19 - 2.2.3 Shaft ........................................................................................................... - 21 - 2.2.3.1 Bearings .............................................................................................. - 24 - 2.2.4 Bearing ...................................................................................................... - 27 - 2.3 Tower ................................................................................................................ - 28 - 2.4 Transmission ..................................................................................................... - 34 - 2.4.1 Vertical shaft.............................................................................................. - 35 - 2.4.1.1 Bearings .............................................................................................. - 37 - 2.4.2Pump shaft .................................................................................................. - 39 - 2.4.2.1 Bearings .............................................................................................. - 41 - 2.4.3 Gears .......................................................................................................... - 43 - 2.5 Rope pump ........................................................................................................ - 46 - 3 Manufacture ........................................................................................................... - 50 - 3.1 Blades ............................................................................................................... - 50 - 3.2 Nacelle .............................................................................................................. - 51 - Wind Powered Water Pump - 2 - 3.3 Transmission ..................................................................................................... - 51 - 3.4 Tower ................................................................................................................ - 51 - 3.5 Water pump ...................................................................................................... - 52 - 3.5.1 Pistons ........................................................................................................ - 52 - 3.5.2 Wheel ......................................................................................................... - 52 - 3.5.3Guide .......................................................................................................... - 53 - 4 Maintenance ........................................................................................................... - 55 - 5 Economic balance .................................................................................................. - 56 - 6 Technical considerations ....................................................................................... - 60 - 7 Conclusion .............................................................................................................. - 62 - 8 Bibliography ........................................................................................................... - 63 - Annex I: Join parts ................................................................................................... - 65 - Annex II: Rotor bolts calculations .......................................................................... - 67 - Annex III: Tail .......................................................................................................... - 72 - Annex IV: Shaft calculations ................................................................................... - 75 - Annex V: Vertical shaft ............................................................................................ - 84 - Annex VI: The pump shaft ...................................................................................... - 99 - Annex VII: The pump ............................................................................................ - 109 - Wind Powered Water Pump - 3 - Figures Figure 1.Location of places of wind speed measurements ........................................... - 9 - Figure 2Profilecoefficients of drag and lift ................................................................ - 13 - Figure 3 NACA 23012 coefficients ratio ................................................................... - 14 - Figure 4Power of the rotor dependingonthewindspeed .............................................. - 14 - Figure 5 Join part ........................................................................................................ - 16 - Figure 6Forcesonthejoinpart ....................................................................................... - 16 - Figure 7Nacelle box.................................................................................................... - 18 - Figure 8 Forces on the tail .......................................................................................... - 19 - Figure 9 Rotor shaft .................................................................................................... - 21 - Figure 10 Bending moments in Z-axis in the rotor shaft ........................................... - 22 - Figure 11 Bending moments in Y axis on the rotor shaft ........................................... - 22 - Figure 12 Torque on the rotor shaft ............................................................................ - 23 - Figure 13 Y bearingplummer block........................................................................... - 24 - Figure 14 Y bearing .................................................................................................... - 24 - Figure 15 Y bearinghousing ...................................................................................... - 24 - Figure 16 Y bearing information ................................................................................ - 25 - Figure 17 Second Y bearing information ................................................................... - 25 - Figure 19Thrust bearing information ......................................................................... - 26 - Figure 18 Axial bearing .............................................................................................. - 26 - Figure 20Forcesonthetower ........................................................................................ - 30 - Figure 21Detail of thetower ........................................................................................ - 30 - Figure 22 Displacements on the tower ....................................................................... - 31 - Figure 23 Stresses on the tower .................................................................................. - 32 - Figure 24 Tower fixingpiece ...................................................................................... - 32 - Figure 25Diagram of Y bendingmomentsonthe vertical shaft ................................... - 35 - Figure 26Diagram of Z bendingmomentsonthe vertical shaft .................................... - 36 - Figure 27 Y-bearing FY 30 TF .................................................................................. - 37 - Figure 29 Thrust bearing information ........................................................................ - 38 - Figure 28 Axial bearing .............................................................................................. - 38 - Figure 30: Pump shaft ................................................................................................ - 39 - Figure 31Bendingmoments in Z axis onthepumpshaft ............................................... - 40 - Wind Powered Water Pump - 4 - Figure 32 torque in thepumpshaft ............................................................................... - 40 - Figure 33 Y bearingplummer block ........................................................................... - 41 - Figure 34 Y bearinghousing ....................................................................................... - 41 - Figure 35 Y bearing .................................................................................................... - 41 - Figure 36 Y bearing information ................................................................................ - 42 - Figure 37 Second Y bearing information ................................................................... - 42 - Figure 39 Bevel gears dimensions .............................................................................. - 43 - Figure 38Bevelgears ................................................................................................... - 43 - Figure 41 Miter gear dimensions ................................................................................ - 45 - Figure 40Mitergears ................................................................................................... - 45 - Figure 42Ropepump ................................................................................................... - 46 - Figure 43 Part of the tyre needed................................................................................ - 47 - Figure 44Ropepumpwheel .......................................................................................... - 47 - Figure 45Tee-jointtooultlet ......................................................................................... - 48 - Figure 46 Pipes ........................................................................................................... - 48 - Figure 47Ropepump pipes dimensions ...................................................................... - 48 - Figure 48Pistonsmountingsystem ............................................................................... - 49 - Figure 49Join part before being twisted ..................................................................... - 50 - Figure 50Nacelle box.................................................................................................. - 51 - Figure 51Pistonsmoulds ............................................................................................. - 52 - Figure 52 Guide construction 1 .................................................................................. - 53 - Figure 53 Guide construction 2 .................................................................................. - 53 - Figure 54 Guide construction 3 .................................................................................. - 53 - Figure 55 Guide construction 4 .................................................................................. - 53 - Figure 56 Guide construction 5 .................................................................................. - 54 - Figure 57 Guide construction 6 .................................................................................. - 54 - Figure 58 Guide construction 7 .................................................................................. - 54 - Figure 59 Guide construction 8 .................................................................................. - 54 - Wind Powered Water Pump - 5 - Tables Table 1 Wind speeds measurements in Israel ............................................................. - 10 - Table 2 Main sections of the blade ............................................................................. - 12 - Table3Powercalculation in the rotor.......................................................................... - 14 - Table4Power in thesections of the rotor ..................................................................... - 15 - Table5Roughnessdependingonthelandscape .............................................................. - 29 - Table 6Bevel gears dimensions and characteristics ................................................... - 43 - Table7Bevelbearingsspecifications ............................................................................ - 44 - Table8Mitergearsdimensions ..................................................................................... - 45 - Table9Mitergearsspecifications .................................................................................. - 45 - Table10Advantages of ropepumps ............................................................................. - 46 - Table11Dimensions of theblade ................................................................................. - 50 - Table 12 Table of rope pump maintenance frequency ............................................... - 55 - Wind Powered Water Pump - 12 - 2 Design 2.1 Rotor The rotor is made by six main pieces: three blades and three pieces that join each blade with the shaft. The reason why three blades were chosen instead of a different number is that three is an odd number, what means that the rotor can be considered to be similar to a disc when calculating the dynamic properties of the machine, while the efficiency is only 2% smaller that if it would have four blades. 2.1.1 Blades The rotor is formed by three blades, which are attached to the hub with one piece that gives the correct angle and bolts. The diameter of the rotor is 3.4 m, which means it can sweep an area of 8.95m2. The blades are made of pine wood, which is very common and cheap in Israel. The blades have a NACA profile; it is a NACA 23012, which has to be handmade with the information attached in the drawings. Each blade has a length of 1.5 meters. The cross section of the blade is changing along its length, as the chord goes from 416 mm to 100 mm the twist is also changing from 0 to 30.4 degrees in the length of the blade. The next table represents the mean parts in which the blade is divided: Sect1 Sect2 Sect3 Sect4 Sect5 Sect6 Sect7 Chord c m 0.39 0.30 0.23 0.19 0.16 0.14 0.12 Pitch angle theta ° 21.7 13.0 8.2 5.2 3.1 1.6 0.5 Solid ratio sigma - 0.59 0.27 0.15 0.10 0.07 0.05 0.04 Speed of blade r*omega m/s 4.7 7.8 11 14.1 17.2 20.3 23.5 Table 2 Main sections of the blade Wind Powered Water Pump - 13 - The NACA five-digit series describes complex airfoil shapes: 1. The first digit, when multiplied by 0.15, gives the designed coefficient of lift (CL). 2. Second and third digits, when divided by 2, give p, the distance of maximum camber from the leading edge (as per cent of chord). 3. Fourth and fifth digits give the maximum thickness of the airfoil (as per cent of the chord). The NACA 23012 would give an airfoil with maximum thickness of 12% chord, maximum camber located at 15% chord, with a lift coefficient of 0.30. Figure 2Profilecoefficients of drag and lift The maximum value of coefficient of lift is 1.653 at 16º but the reason why is not the chosen one is because an angle of 7º degrees provides better glide ratio. The glide ratio is the result of the lift coefficient divided by the drag coefficient. The next graphic shows the glide ratio for different angles: 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 010 20 30 40 50 60 70 80 90 Cland Cd[-] Alfa [°] NACA 23012 C_L C_D Rotor specification sheet Blades material: Pine wood Length: 1.5 m Mass per blade: 2.38 kg Efficiency of the rotor: 55.5% Power on the rotor: 268 W Angular speed: 140 rpm Av. axial force: 96 N CL(=7º) = 0’877 CF (=7º) = 0’0077 Wind Powered Water Pump - 14 - Figure 3 NACA 23012 coefficients ratio The rotor has been designed to work with an average speed of 4.5 m/s. During the design of the blades the size of them, the tip speed ratio and the efficiency were considered. Power calculation Pitch control dteta 0 ° Wind speed V0 4,5 m/s Rotational speed n 140,625 rpm Rotational speed ω 14.73 rad/s Power P 268.1 W Efficiency eta 90,7 % Torque T 18.20 N·m Axial force Fa 96 N Tip speed ratio X 5,56 Mean angle of attack alpha 7.0 ° Table3Powercalculation in the rotor Figure 4Power of the rotor dependingonthewindspeed 0 20 40 60 80 100 120 0 5 10 15 20 25 30 35 C l/ Cd Alfa [º] 0 1000 2000 3000 4000 1 2 3 4 5 6 7 8 9 10 Power (W) Wind speed (m/s) Power the rotor gets Wind Powered Water Pump - 15 - Radius m 0,32 0,53 0,74 0,96 1,17 1,38 1,59 Ring nº - 1 2 3 4 5 6 7 Power W 12 23 32 41 50 57 53 Table4Power in thesections of the rotor The conclusion of this table is that the smaller rings get less power that the bigger rings, so if during the fabrication work there were less material than needed the part that should be modified is the wider end. Pine wood as material: Wood was chosen as material to make the blades because of his lightness and reduced price. Also, pine wood is a very common material in Israel. It is a strong wood and it holds its shape for long time. Wind Powered Water Pump - 16 - 2.1.2 Join parts In order to join the blades with the correct angle to the shaft one piece has been designed. These pieces have to support the bending moments, the axial loads because of the centripetal force and the shear loads because of the wind. Figure 5 Join part The calculations are detailed in the annex I but the values that have to support are: - 357 N in the wind direction - 1845 N in the radial direction - 368.363 N·mm Figure 6Forcesonthejoinpart Wind Powered Water Pump - 17 - The Von Mises stress is 117 MPa which means a safety coefficient of more than 2 using a carbon steel with a yield resistance of 282 MPa. The bolts needed to support all the loads have been also calculated. In the annex II there is a detailed study about them. The bolts that join the blade to the join part are M5 and the ones that are screwed to the rotor are M10. The safety coefficient is higher than other parts because bolts can be lost between every maintenance and if the blade will come lose it would be very dangerous. Wind Powered Water Pump - 18 - 2.2 Nacelle It is a device placed on the top of the tower. It connects the rotor with the truss and is able to orientate the rotor into the wind using the yaw mechanism. Its main function is to keep all the pieces necessary to transmit the mechanical energy from the rotor to the vertical shaft. It is designed to be mounted and maintain easily. 2.2.1 Box The nacelle box has the main and important function of covering the transmission. It is smaller than the internal diameter of the rotor to avoid the blades crashing, and it has two different parts: The bottom part is made of steel and has been designed to fix all the pieces in the right position. It has a hole where the vertical shaft passes through. Concentric to this hole, there is a recess to keep the bearing, and a cylindrical steel plate to avoid dirt damage the bearing. There are also three holes to fix the yaw mechanism tail. The top part is much lighter because its only function is covering the devices. It is made of aluminum and designed to mount and dismount easily. It can be fixed with the bottom part in the last moment to avoid the disturb to the operator when the assembly is done. To fix both parts, there are ten holes, five in each side of the nacelle. Figure 7Nacelle box Wind Powered Water Pump - 19 - 2.2.2 Tail The tail is a device to face the rotor into the wind. This case is different to small American turbines because this tail will be turned 45 degrees to compensate de torque transmitted to the vertical shaft. This torque is 18.21 N·m, so the torque that has to be generated is that one. Figure 8 Forces on the tail The calculations have been done with a wind speed of 4.5 m/s. The tail is 1300x800x1 mm. The thickness is not important because the drag and lift forces do not depend on it but on the surface against the wind. In order to know the drag and lift coefficient an experiment was done with the wind tunnel and a piece done to scale.Detailed calculations can be found in annex III.The drag and lift forces can be calculated as: Being: - ρ : air density - A : area of the tail - Cd : drag coefficient - Cl: lift coefficient - v : wind speed Wind Powered Water Pump - 20 - The distance from the center of the nacelle to the center of the tail is 1.7 m but it is turned 45º so to calculate the torque the distance is 1.7 x sin 45. So the moment created is: As it can be seen in the formulas to calculate the drag and lift forces, those force are directly proportional to the squared wind speed. The same situation happens with the torque generated by the rotor. The power of the rotor is proportional to the cubed wind speed, but the power is the torque times the speed so both torques are proportional to the squared wind speed. The next formulas will demonstrate this statement. Vtip: blade tip speed V: wind speed X: tip speed ratio r: rotor radius µ: rotor efficiency D: rotor diameter As it can be seen those momentums are proportional to the squared wind speed. Wind Powered Water Pump - 21 - 2.2.3 Shaft This shaft is one of the most important parts of the wind powered water pump. This shaft connects the rotor to the rest of the transmission elements, supporting at the same time the weight of the rotor. It has three bearings, one gear, and a rotor on it. All detailed calculations can be seen in annex IV. Figure 9 Rotor shaft The rotor weighs 163.8 N and applies a horizontal force to the shaft. This force is due to the wind, the wind when generates a torque on the shaft, also push the rotor against the shaft. Every force used to calculate the proper dimensions for the pieces in this project are calculated for a wind speed of 15 m/s. For this wind speed the force that the wind will apply on the shaft is 868 N. This has been calculated with the blade element momentum (BEM) theory. There are forces in every bearing as a response of the forces generated by the rotor and the gear that will be calculated below. But gear forces have to be calculated before. If the wind speed is 15 m/s the torque generated by it is 164000 N·mm. The pitch diameter of this gear is 100 mm so the force to transmit is 3277.4 N. The direction of this force is perpendicular to the drawing. The angle of pressure (α) of the gear is 20º what means that there is a separating force between the two gears. The value of this force can be calculated as F·tan(α), what is 1192 N. Knowing the forces acting on the shaft, the forces that the bearings have to support can be calculated. These values are 2603 N and 802 N. In the axial bearing the force to support is 263 N. Following this the load diagrams can be drawn. Wind Powered Water Pump - 28 - 2.3 Tower Instead of a pole a steel truss was used due to a greater rigidity that reduces vibrations and because it is easier to place the different parts needed for the design. But in order to make pieces smaller than 3 m long to be easier to transport and dismount, the tower is made by two trusses than can be joined with screws. The function of the tower is to get the turbine at a certain height. In the ground level there are some obstacles like houses, hills, trees…which slow the wind and change the wind direction. Due to this friction forces the wind speed increases with the height, the higher the faster the wind is. Knowing the wind velocity at a certain level, this variation can be known with the “Wind shear formula”:     0ref 0 ref /ln zzln vv zz /  where: v = wind speed [m/s] at height z above ground level vref = reference speed [m/s], i.e. a wind speed known at height z ref . z = height [m] above ground level for the desired velocity, v. z0 = roughness length [m] in the current wind direction, see below Note: ln(...) is the natural logarithm function. 0 2 4 6 8 10 12 0 1 2 3 4 5 6 z (m) v (m/s) vref = 5 m/s & Zref = 6 m Wind Powered Water Pump - 29 - Class Roughness Length: m Landscape features No. Name 1 sea 0.0002 open water, tidal flat, snow with fetch above 3 km 2 smooth 0.005 featureless land, ice 3 open 0.03 flat terrain with grass or very low vegetation, airport runway 4 roughly open 0.10 cultivated area, low crops, obstacles of height H separated by at least 20 H 5 rough 0.25 open landscape, scattered shelter belts, obstacles separated by 15 H or so 6 very rough 0.5 landscape with bushes, young dense forest etc separated by 10 H or so 7 closed 1.0 open spaces comparable with H, eg mature forest, lowrise built-up area 8 chaotic over 2.0 irregular distribution of large elements, eg city centre, large forest with clearings Table5Roughnessdependingonthelandscape The truss is a structure comprising triangular units constructed with straight pipes whose ends are connected at joints referred to as nodes. It is composed of triangles because that shape has a great structural stability. External forces and reactions to those forces are considered to act only at the nodes and result in forces in the members which are either tensile or compressive forces. Moments (torques) are explicitly excluded because, and only because, all the joints in a truss are treated as revolutes. A triangle is the simplest geometric figure that will not change shape when the lengths of the sides are fixed. Truss structures are easy to make. It is possible to use materials like stainless steel tubes, which are very cheap. Of course these tubes will have to be deformed and welded together. Calculations have been made supposing a maximum wind speed of 13.5 m/s because statistics say that wind speed in Israel doesn´t reach that magnitude very often. In addition, the tower can be dunk easily to avoid a collapse. Wind Powered Water Pump - 30 - Using the BEM method with the Excel sheet, forces acting in the blades can be known. Adding these forces to other forces acting on the rest of the rotor, an axial force is obtained. The tower must support also the weight of all the components. So the final forces distribution is: The horizontal force has a value of 868 N and the tower has to support around 500 N weight. Drag force on the tower will act as a distributed force and can be calculated: [N] with: CD=1,2 m² ρ = 1,225 kg/m³ v = 13.5 m/s The tubes used are: Tube A: ISO pipe 26,9 x 3,2 mm Tube B: ISO pipe 33,7 x 4,0 mm Height = 5 m Width x length = 0,5 x 0,5 m Figure 20Forcesonthetower Figure 21Detail of thetower Wind Powered Water Pump - 31 - Study The structure can be studied using SolidWorks and it is possible to determinate that the model is strong enough. Displacement Figure 22 Displacements on the tower From the simulations it is concluded that the tower will bend with a maximum displacement of 7,4 mm at the top. This is a worst case scenario at a wind speed of 13 [m/s] and is an acceptable value. Wind Powered Water Pump - 32 - Having a look at the stress in the construction: Stress Figure 23 Stresses on the tower The study shows that there will be a maximum stress of 61,5 [MPa] in the lower part of the tower. To assure this is an acceptable value the tubes will be made of stainless steel ferritic, which has a Yield Strength of 172 MPa, so it’s strong enough for the construction. It is resistant to corrosion and has a good weldability. To fix the truss to the ground the next piece of metal is used. The bolts used are calculated: The force on the top of the tower is 1000 N and the drag force of the truss is 100 N (and will be simplified as a force hitting the tower in the middle). Figure 24 Tower fixingpiece Wind Powered Water Pump - 33 - So the moment these forces will generate on the bottom of the tower will be: Using four connectors, one on each side of the truss, axial forces due to this moment can be calculated: Axial So if one connection has two screws, and a safety coefficient of 2 is used, the force in each screw will be: per screw. Radial The radial force on the screws will be the sum of the horizontal forces, which is equal to 1100 N. The bolts will be M8 with grade 8.8(Max. axial force: 24 kN) and they will be screwed in a concrete block, so an excavation in the ground filled with concrete has to be done. Wind Powered Water Pump - 34 - 2.4 Transmission The transmission had to be one of the improvements of the project. There was a problem with it, because the best way to transmit the movement seemed to be two pulleys with one belt. Each pulley would be in one of the horizontal shafts there are in this project. The problem with that kind of transmission is that the nacelle cannot twist 360 degrees so the orientation is not as good as it was wanted for this project. The solution was a vertical shaft inside the tower that would transmit the torque and the speed. So the transmission has five parts, three shafts and two couples of gears. The first designs about the nacelle were working with friction wheels instead of gears. The main reason was that the efficiency of friction wheels is higher than the gears. But one problem was found with that system, the force needed to transmit the torque from one wheel to the next one was too big. The solution to make them work would be more complicated and expensive, so the friction wheels were discarded. The rotor shaft has been explained in the design of the nacelle design part and calculations can be checked in annex V. Wind Powered Water Pump - 35 - 2.4.1 Vertical shaft The vertical is going to transmit the torque and the angular velocity from the rotor shaft to the pump shaft. In this case the forces can change their direction because the rotor is going to be faced to the wind so the analysis has to be more detailed and thorough. All calculations can be seen in the annex V. It has to support the separating forces of both gears, the forces of the bearings, the bending moments created by those forces and the torque. Detailed calculations can be found in annex V. The case were the loads are bigger on it is when the plane, where the rotor shaft and the vertical shaft are, is perpendicular to the plane where the vertical shaft and the pump shaft are. The next diagram shows the bending moments that the shaft has to support in Y axis: Figure 25Diagram of Y bendingmomentsonthe vertical shaft Wind Powered Water Pump - 36 - The next diagram shows the bending moments that the shaft supports in Z axis: Figure 26Diagram of Z bendingmomentsonthe vertical shaft In this case the biggest bending moment is where the lower bearing is, and its value is can be calculated as: The torque transmitted by the shaft is 196600N mm, so the minimum diameter for the shaft is Being 2 the safety coefficient (ns) and 710 MPa the yield strength of the material (σy). The bearings in that part of the shaft have to have a diameter of 30 mm so the diameter has also to be 30 mm. In the widest part is 35 mm diameter. The maximum stress in the shaft is: The safety coefficient is: After the calculations the shaft had to be modified because of the requirements of the bearings, that is why next to the top of it, its diameter is 46 mm. Wind Powered Water Pump - 37 - 2.4.1.1 Bearings After calculating the loads and forces on the shaft, the values of the force to support by the bearings are known. The radial forces to support by the bearings are 2295 and 3698 N respectively while the maximum value to support by the axial bearing is 205 N. They have been chosen from the SKF catalog. Radial bearing The chosen radial bearing is known as Y-bearing units with square flange. These units comprise: A “Y-bearing” (insert bearing) which is a single row deep groove ball bearing with convex sphered outside diameter. A “Y-bearing housing”, which has a correspondingly sphered but concave bore. . Information about the bearing unit, housing, and Y-bearing can be read in the next figure: Figure 27 Y-bearing FY 30 TF Wind Powered Water Pump - 44 - Specifications Precision grade JIS B 1704 grade 4 Core hardness HB165 194 Gear teeth Gleason Surface hardness HRC48 53 Pressure angle 20° Surface treatment Black oxide Helix angle 35° Surface finish Hobbed Material S45C (Carbon steel) Datum reference surface for gear curring Bore Heat treatment Induction hardened teeth Table7Bevelbearingsspecifications Wind Powered Water Pump - 45 - The next pair is used to transmit the torque from the vertical shaft to the pump shaft. This time the ratio needed is 1:1. These gears are called miter gears. They have to support a torque of 197 N m. The gears chosen are made by Quality Transmission Components. The website where can be found is: http://www.qtcgears.com/RFQ/default.asp?Page=../KHK/newgears/KHK180.html Figure 41 Miter gear dimensions Catalog No. Module Nº of teeth A (mm) C (mm) J (mm) Face angle L (°) Shape Allowable torque (N·m) MMS4-25R 4 25 25 120 25 47° 48’ B3 238 MMS4-25L Table8Mitergearsdimensions Table9Mitergearsspecifications Specifications Precision grade JIS B 1704 grade 4 Core hardness HB 250-300 Gear teeth Gleason Surface hardness HRC55-60 Pressure angle 20° Surface treatment Black oxide Helix angle 35° Surface finish Cut Material SCM415 (Alloy steel) Datum reference surface for gear curring Bore Heat treatment Teeth induction hardened after carburizing Figure 40Mitergears Wind Powered Water Pump - 46 - 2.5 Rope pump The pump designed in this project is a rope pump. When the different kinds of pumps were studied to choose the best of them, most of them were discarded because of their complexity to be manufactured and be installed in a well. After a shallow study this table was written: Type Advantages Disadvantages Membrane -Easier transportation -Easier to face the turbine into the wind -Longer lifetime -Less deep -Difficult starting -Low efficiency Rope -Very deep -Less power needed -Can be connected to a second energy source easily -Simple construction -Cheaper materials -More difficult transport -More complex orientation mechanism -Higher friction -Lower durability Table10Advantages of ropepumps A rope pump is a circuit between the water source and the desired level, using an endless rope with pistons. The rotation of a wheel moves the rope. This rope with pistons pushes the water column up at the top, and sucks another column of water below through a pipe made of PVC. Some of its advantages are high efficiency, high reliability, it is able to pump a big flow and from deep wells, and above all, low cost and very easy to construct, install and maintain. Figure 42Ropepump Wind Powered Water Pump - 47 - A rope pump is composed of the following components: Wheel (Pulley) It transmits the input power to all the pump mechanism. The diameter of the wheel is 16 inches so old parts from cars can be used. A 16” tire is used to make the parts in contact with the rope. The parts which section can be seen in the picture below are the lateral parts of the tire, the ones closest to the rim. They have to be cut and joined in “V”. For this, six clamps (metal plates) are used. It greatly improves the adhesion of the rope. Each metal plate is joined with two spokes to the central bushing by welding. Rope A 5 mm diameter polypropylene fibre rope is used. It will support the weight of the water. It must be at least 30 meters long. Polypropylene is water resistant, this rope can support a load of 1600 N, but it is recommended to work with a load of 10% of the maximum capacity.Another good property is that it is not very smooth, so it will not slide on the wheel. The rope, together with the pistons, functions as an endless band transporting water. The pistons are located the entire length of the rope, and are attached with two knots, one in front of the piston and one directly behind it. When installing, the ends are attached by braiding. Knots are not used for this because they are difficult to untie when tautening the rope or for repairs. Once all the knots are installed and the pipes are also ready the pretension of the rope has to be between 20 and 70 N, approximately between 2 and 7 kgf. Figure 44Ropepumpwheel Figure 43 Part of the tyre needed Wind Powered Water Pump - 48 - Pipes Pumping pipes are a fundamental part of the rope pump. They vary according to the depth of the well. The deeper the well is, the smaller the diameter of the pipe. The chosen pipes have a nominal diameter of 32 mm, and an external of 40 mm. They are made of PVC, 3 meters long and threaded in both ends, so it is easy to join them. Four 3 meters pipes are needed to reach 11,5 m. The lower end should be bellshaped to allow the movement of the rope and the pistons without damage them. This can be made heating the end of the pipe and pushing with a bottle. At the higher end a “Tee” connection has to be coupled to allow the diversion of water to the tank and avoid losses from the top. Figure 46 Pipes Figure 45Tee- jointtooultlet Figure 47Ropepump pipes dimensions Wind Powered Water Pump - 49 - Guide The guide is installed at the bottom of the well and is where the pumping process is initiated. Its function consists of guiding the rope with pistons so that it enters into the pumping pipe from below. It serves as well as a counterweight to tauten the rope in order to avoid sliding on the wheel. Therefore, the guide has various functions integrated into one piece. The guide is a concrete box with a base piece, an entry pipe, a pumping pipe, a PVC elbow 180 degree and a transversal cavity. These parts of the guide must be made in such a way that the rope never touches the concrete, which would cause wear to it as well as to the pistons. The entry and pumping pipes on the guide have a wide mouth to facilitate the entry of the rope and pistons. The water enters the guide through the transversal cavity. The guide is placed at 50 cm from the bottom of the well. This allows taking water up to 50 cm deep. Pistons The pistons are one of the most sensitive parts of the pump. Together with the rope they form an endless chain. When the rope rotates it leads the piston through the pumping pipe, pushing the water inside upwards. The piston is a cone shaped part to reduce friction, with a hole for the rope. They are made of polyethylene; which is very easy to get in the market. A perfect fit is required between the pistons and the pumping pipe. The space between piston and inner wall of the pipe is around 0.50 mm, which is large enough to avoid friction and small enough to avoid loss of water. So the diameter is 31 mm and the distance between two pistons is around two meters. Figure 48Pistonsmountingsystem Wind Powered Water Pump - 50 - 3 Manufacture 3.1 Blades The blades are handmade. There are nine sections defined. The profile is a NACA 23012. The nine sections define the angle and the chord of each section. It is also defined the distance where they are from the end of the blade. Table11Dimensions of theblade The join parts need a CNC work, starting with a 230x130x15 or bigger part. It has to be mechanized to get the next dimensions: Figure 49Join part before being twisted Then it has to be twisted 30° the middle area. Section number 1 2 3 4 5 6 7 8 9 Distance 0 0,12 0,33 0,54 0,76 0,97 1,18 1,39 1,5 Chord 0,23 0,39 0,30 0,23 0,19 0,16 0,14 0,12 0,117 Angle 30,4 21,66 12,973 8,19 5,18 3,12 1,3 0,5 0 Wind Powered Water Pump - 51 - 3.2 Nacelle The nacelle is made by two pieces: the base of the nacelle and the cover. The base of the nacelle is made by three steel parts welded. First of it is a 10 mm wide part. The front sheet is a 2 mm wide sheet that has to be cut and welded. To protect the bearings there is also a cylinder that has to be welded under the tower. Some holes have to be made by drilling process. The cover is made by a 2 mm wide aluminum sheet that has to be bended and welded. T has also some holes that have to be made with a drill. 3.3 Transmission The shafts of the transmission have to be made with CNC. The round shapes with lathe and the keyway with milling machine. In the rotor shaft, the round plate where the blades are screwing has to be welded to the shaft. This welding has only to support the torque because the force of the wind is pushing it against the shaft. 3.4 Tower For the tower, the ISO tubes have to be bought and bend and weld them together. The welding will take place in Israel itself because transporting an already welded tower from another country is more difficult, time demanding and thus more expensive. Also other parts have to be welded. The parts that support the pipes have to be welded at 0.5 m high and 1976 mm high from the floor. There is one part to support the radial bearing that fix the shaft to the center of the tower. After this work the second part consists in installing some screws that fix the two parts of the tower. Figure 50Nacelle box Wind Powered Water Pump - 52 - 3.5 Water pump 3.5.1 Pistons Piston production requires a small plastic injection machine, and moulds. Polyethylene is poured in the injection machine hopper. As the plastic passes through the heated hopper bottom, it becomes fluid and is injected into the mould. As it cools, the plastic adopts the mould's form. Figure 51Pistonsmoulds 3.5.2 Wheel The wheel is made from the two 16” tires usually used by cars, buses and trucks. The lateral parts of the tire (the ones closest to the rim) are cut and joined in “V”. For this, six clamps are used. These clamps squeeze and join the two rims together. There are two spokes on each clamp. They must be welded in one side to the clamps and in the other to the central bushing. Finally, this bushing can be fixed to the shaft with a key. Wind Powered Water Pump - 53 - 3.5.3Guide The production process includes the following steps: -Cut the final extreme of the elbow (The water will flow through this cut). - Join the entry pipe with one of the ends of the elbow and the pumping pipe with the other. Place a piece of polystyrene (or a similar material easy to break) covering the cut made before in the elbow. - Nail four sticks on the other side of the polystyrene like legs to support the guide. Figure 52 Guide construction 1 Figure 53 Guide construction 2 Figure 54 Guide construction 3 Figure 55 Guide construction 4 Wind Powered Water Pump - 60 - 6 Technical considerations This part of the report is about different problems that have happened during the process and how have they been solved. Here are shown the main problems: 1. The transmission was supposed to be two pulleys and one belt joining them; this kind of transmission did not allow the rotor change its orientation 360°. The idea was designing a vertical shaft that could transmit the torque and the power to the pump. This means that instead of one step (from the rotor shaft to the pump shaft) there are two steps between the rotor and the pump (from the rotor shaft to a vertical shaft and from the vertical shaft to the pump shaft). This decreases the efficiency of the transmission. 2. This kind of transmission has one problem. When a torque is transmitted to a shaft, that shaft transmits a torque in opposite direction with the same value to the shaft that transmitted first. This is the same effect that happens in the helicopters. In the helicopters there is another rotor that controls the direction of the helicopter but in this case something cheaper and simpler was needed. The solution of this problem was changing the orientation of the tail creating a moment with the same value but opposite direction. 3. In order not to decrease the efficiency that much friction wheels were thought as a way to do what gears do. The problem with friction wheels is that they need a big force not to slide. If they work with the force of the wind, they should be 400 mm diameter not to slide.This meant a very big nacelle that would slow down the wind. Finally gears were decided to be the best way to transmit the power and the torque, although the efficiency is not as good as the friction wheels neither the price. 4. The forth problem was the braking system. All the ideas about this were discarded. The one that looked better was a bicycle brake acting on the pulley of the pump but it could be also in the middle of the vertical shaft. Before starting the calculations the tail was supposed to break it, turning it from the wind at higher speeds but as it has been demonstrated it will not. This problem has not been solved because we did not have ideas or time enough. Wind Powered Water Pump - 61 - 5. The truss was made later than the nacelle and the rotor and when they were mounted there were problems because the blades were hitting the truss. To solve this problem, three actions were done. The shaft was made longer and all the calculations were made again, changing the diameter as well as the material. Also the distribution inside the nacelle was changed in order to have the bearing between the rotor and the gear as near the wall as possible. Last change was the dimensions of the tower, they used to be 500x500 instead of 400x400 in the base of it. 6. Once the upper pulley of the pump was designed, the shaft to connect it to the transmission was the following step. The problem was that the height was the water outlet pipe was 2.1 m, and the pulley is 402 mm diameter. That means that at least the height of the shaft should be 2302 mm from the floor. The center of the rotor was 4050 mm height and the blades are 1700 mm long from the center of the rotor. There are less than 50 mm were the shaft is, and that distance is too small to be sure that if something is not correctly mounted, it could break itself. 7. Once the tower was joined to the nacelle another problem cropped up. There was no space enough to fit the bar that supports the tail. This problem was solved designing a new join between the nacelle and the tower, the one that is working in the final design. 8. The last problem found is that the separating between the rotor shaft and the vertical shaft is bigger than the force of the weight of the whole nacelle with rotor and tail. This problem appears only when the wind speed is very faster than usual, the wind speed that has been used for the resistance calculations: 13.5 m/s. To solve this problem an additional weight is needed over the nacelle. Also if the bevel gears were installed were the miter gears are and vice versa that force would have been smaller, but we did not have time to change them are recalculate the shafts dimensions. 9. The gears used are very expensive. The reason why these gears are needed is that the torque is very high in comparison to the power. If the angular velocity had been faster, with the same power the torque would have been much smaller. One possible way to improve this characteristic could be designing a rotor with a higher tip speed ratio. Wind Powered Water Pump - 62 - 7 Conclusion Before starting making this project our meaning was creating something new and helpful. The idea was designing a new kind of water pump with a very low cost and a high efficiency. The flow that this wind powered water pump can raise is bigger than other pumps that were shown to us before, and also the distance that it raises is also longer. We started watching an example of a membrane pump able to raise about3% of the flow that this pump can raise, and only 3 meters high, needing a stronger wind at the same time. This demonstrates that the idea of connecting a rope pump to a wind turbine is good, but some developing ideas are needed in order to make this project real. After doing all the calculations and make them fix, a lot of expensive parts have been getting more and more needed; especially in the transmission. The problem with the transmission is that although the power is not very high, the rotor has a slow angular velocity which means that the torque is very high.But even with these expensive pieces this pump is 126 times more powerful than the one we had as example. We do not know the price of that pump but we think that this kind of turbine is much cheaper if you compare the final output of water. Wind Powered Water Pump - 63 - 8 Bibliography Brief information about rope pumps: http://www.cubasolar.cu/biblioteca/energia/energia19/html/articulo02.htm Roughness length classification: http://www-das.uwyo.edu/~geerts/cwx/notes/chap14/roughness.html Optimal rotor tip speed ratio: https://netfiles.uiuc.edu/mragheb/www/NPRE%20475%20Wind%20Power%20Systems /Optimal%20Rotor%20Tip%20Speed%20Ratio.pdf NACA 23012 coordinates: http://www.ae.illinois.edu/m-selig/ads/coord_database.html - N Manual threaders: http://www.terrajastafs.com/ http://www.ehow.com/how_5095599_thread-pvc-pipe.html Wind statistics: http://www.windfinder.com/windstats/windstatistic_map_israel_year.htm Bevel Gears cataloge: http://www.qtcgears.com/RFQ/BevelGears.htm Transmissions: http://iesvillalbahervastecnologia.files.wordpress.com/2009/04/02-arboles-ejes-ruedas- de-friccion.pdf http://www.societyofrobots.com/mechanics_gears.shtml - bevelgears Friction coefficient values: http://es.wikibooks.org/wiki/F%C3%ADsica/Est%C3%A1tica/Rozamiento PVC pipes dimensions and price: http://www.coplastic.es/catalogo/3-Caracteristicas_y_medidas.htm http://www.bueni.es/electronica-ferreteria/tubo-rigido-roscado-gris-40mm-3- mts_d15fdf9f8560f1de3ba5eddf48e7a980_933157 Bolt properties: http://misumiusa.com/CategoryImages/Metric_2009_pdf/p2849.pdf SKF Group. “Bearings”: http://www.skf.com/portal/skf/home Wind Powered Water Pump - 64 - Steel properties: http://www2.ing.puc.cl/~icm2312/apuntes/materiales/aceros/sabimet.html Gears: http://www.qtcgears.com Gears information about calculation: http://www.roymech.co.uk/Useful_Tables/Drive/Bevel_Gears.html Plastic ropes: http://www.plasticord.cl/tabladeresistencia.asp Key calculations: http://www.tribology-abc.com/calculators/key.htm http://www.emc.uji.es/d/mecapedia/calculo_resistente_de_chavetas.htm http://www.elesa-ganter.com/es/30/sp/8291/4/86/chavetas/din-6885/eg/ PVC properties: http://www.asperpro.com.ar/pvc.html Wood information: http://www.woodfibre.com/cgi-bin/exview.cgi?wscg=07-050560 Normalicedparts http://www.wuerth.com/web/en/wuerthcom/index.php?scLang=EN&x=5&y=3 Israel documentation: http://www.minimum-wage.org/international/en/Israel Shaftsteel: http://www.onlinemetals.com/merchant.cfm?id=255&step=2 Othermetals: http://www.metalprices.com/index.asp Wind Powered Water Pump - 65 - Annex I: Join parts To calculate the joins between the blades and the shaft some previous equations and calculations are needed. For a critical wind speed of 15 m/s there are the next values on the blades. Axial force = 1071.89 N Rotational speed (ω) = 49.125 rad/s Power (P)= 9931 W Those values have been calculated using the Blade Element Momentum (BEM) theory. We have three blades, so the torque generated by each one (Tb) is 67.44 N·m There are three forces acting in this piece: centripetal force of the blade, axial force and force created by the torque. Centripetal force (Fc): Blade mass = 2.4 kg Wind Powered Water Pump - 66 - Distance between the blade centre of gravity to the rotor centre (r)= 0.316 m Axial force in one blade (Fa): Force generated by torque ( ): Once these three forces are known stresses can be also calculated. Yield stress (σy) = 282 Mpa Cross-sectional area (A) = w · t = 1440 mm2 Inertia (I) = = 17280 mm4 Moment of resistance (Wy)= mm3 Shear force (V) = Axial force in this piece (N) = Fc = 1845 N Momentum (M) = = 357.3 · 0.93 = 332600 N · mm Shear stress (τ)= = 0.341 MPa Axial tension (σ) = = 117 MPa Von Mises stress (σVM) = = 117 MPa Safety coefficient (ns) = = 2.42 Wind Powered Water Pump - 67 - Annex II: Rotor bolts calculations In this annex the calculation of the bolts that appear in the rotor are going to be calculated. The pieces studied are those that join the blades to the shaft. There is one piece for each blade that joins it to a disc welded to the shaft. First of all the blots that join the blade to the join piece are going to be calculated. In this case there are four bolts in a row and they do not have to support any bending moment, only the centrifugal force and the weight of the blades. The mass of the blades are 2.38 kg each and the maximum angular velocity expected is 49.125 rad/s. The radio of the turn is 0.316 m. The bolts have a yield stress of 260 MPa. The centrifugal force can be calculated as: But the critical moment is when the blade is under the rotor because the centrifugal force has to be added to the gravity force that can be calculated as: So the force to consider in the following studies is the sum of both: Wind Powered Water Pump - 68 - There are four bolts with a diameter of 5 mm so the section of all of them can be calculated as: Being n the number of bolts. There are three studies that have to be done to calculate the bolts size. - Shear failure: Safety coefficient - Join piece failure Stress area: Stress: Safety coefficient: - Bolt flattening failure Stress area: Stress: Wind Powered Water Pump - 69 - Safety coefficient: - Blade failure Stress area: Stress: Safety coefficient: The safety coefficients are so high because the maintenance of the turbine is not going to be very frequent so some bolts may lose between the checking. The second part of this annex is the study of the belts that support the forces between the disc welded to the shaft and the join piece bolted to the blades. This case has four bolts distributed in two rows and the diameter of the bolts is 10 mm. Also the mass changes because the forces that the bolts have to support include the weight and the centrifugal force of the pieces where they are bolted. Each piece has a mass of 2.4 kg. Wind Powered Water Pump - 76 - Values to consider: - Mp≡ torque on the pinion shaft (N·mm) - Pp ≡ power at the Pinion shaft (W) = 7329 W - np ≡ rotational speed of the pinion shaft (rpm) = 44,18 - Ft ≡ tangential force on the pinion (N) - dp≡ pinion pitch circle diameter (mm) = 100 mm - α ≡ angle of pressure = 20° - Fs ≡ separating force - εp ≡ pinion pitch angle =63° 6’ - εg ≡ gear pitch angle = 26° 54’ - Fp ≡ pinion thrust - Fg≡ gear thrust The momentum created by the Fp is this value times the distance to the center of the shaft: Wind Powered Water Pump - 77 - The next diagram shows the forces acting on the shaft. The forces are calculated for a wind speed of 13.5m/s, which is an extreme situation. The forces represented below are the forces of the weight of the rotor, the torque and the forces generated by the gear in opposition to the other gear. The two ovals represent torque and the force with the value of 3277 N is a force perpendicular to the paper, while the rest of them are in the plane of the paper. To calculate the reactions forces and the efforts in the shaft the forces are going to be separated in different axis: X, Y and Z. The X axis is parallel to the shaft, the Y axis is vertical and the Z one is perpendicular to both of them. During the calculations the different points of the shaft are going to be named like in the next picture, being the units mm: Wind Powered Water Pump - 78 - X-axis: The only forces in the X-axis are the force of the wind in the rotor, the separating force of the gear and the reaction in the bearing. The negative value means that the force is to the left So the axial loads diagram, being the units Newton, is: In the X-axis there are also torques both with the same value, first one coming from the rotor and the second one to transmit this one to the next part of the transmission: So the torque diagram is, being the units N·mm: Wind Powered Water Pump - 79 - Y-axis The forces on the Y-axis are the weight of the rotor, vertical separating force of the gears and the two reaction forces, one in each bearing. The forces in the shaft create a bending moment on Z-axis, that is the reason why the moments in Z-axis are studied in this part. Next diagram shows the forces and bending moments in N and mm: To calculate the reaction forces in the bearings B and D, two equations are going to be used: The negative signal means that the force is downwards. The next picture is a diagram of the shear loads in the Y-axis, units are in N: Wind Powered Water Pump - 80 - The next picture shows the bending loads in Z-axis, units are in N·mm: What is most important in these diagrams is that there is a bending moment of 1.08·105N·mm where the gear is. To be calculated: Z-axis The forces on Z-axis are the force creating by transmitting the torque from the gear in this shaft to the next one and the reaction forces of the bearings. To calculate these reactions, the equations needed are the same as the last time but applying them to different forces. Wind Powered Water Pump - 81 - The next picture is a diagram of the shear loads in the Z-axis, units are in N: The next picture shows the bending loads in Y-axis, units are in N·mm: The most important datum in these diagrams is that there is a bending moment of 2.6·105 N·mm where the gear is. To be calculated: Analyzing the preview figures, the most affected part of the shaft is where the gear is. In that point the bending moment in the Y-axis is 1.9·105 and in the Z-axis is 7.76·104. To calculate the total bending moment next equation will be used: In that point the bending moment is 282500 N·mm and the torque is 164000 N·mm. For this torque and this bending moment the diameter can be calculated: Being: -ns= 2 -σy= 710 MPa Wind Powered Water Pump - 82 - The steel needed is one with a high strength, good for shafts, AISI 4340 steel normalized. The reason why the chosen diameter is 22 is because the gear has an hub diameter of 22 mm and is bigger than needed so it will not break. The shame way to calculate the total moment the reactions can be calculated: As this result the reaction forces are 2187 N in the left bearing, 1212 N in the middle bearing and 315 N in the right one. Key In order to transmit the torque from the shaft to the pinion a key is going to be designed. Because of the shaft diameter is 22 mm the main dimension are 6x6. The yield strength of the key is 60kg/mm2 = 588 N/mm2 The keyway depth shaft (t1) = 3.5 mm The keyway depth hub (t2) = 2.8 mm The force we want to transmit is: Wind Powered Water Pump - 83 - Nominal torsional stress Shearing stress: Bearing stress: Von Mises stress: If the design safety coefficient is 2, 12 is chosen because is the minimum length Wind Powered Water Pump - 84 - Annex V: Vertical shaft This annex explains the procedure to calculate the needed diameter for the shaft. It is not going to be as detailed as the rotor shaft calculations but everything needed will be explained. This shaft has some differences from the rotor one. In this case instead of one pinion there are two gears, one in every end of the shaft. The one that is in the upper end (in the diagrams on the left) is going to be called bevel gar and the one at the bottom (in the diagrams on the right) is called miter gear. This is because of the rotor, as the rotor can turn 360° the gear on it can also be in different positions. The calculations must be done with different cases depending on the position. The picture below shows the vertical shaft, but drawn in horizontal: First of all we have to calculate all the forces that are acting on the shaft. Values to consider: - Ps≡ power on the shaft (W) - n≡ rotational speed (rpm) - Ms≡ torque on the shaft (N·mm) - Fbg ≡ tangential force on the bevel gear (N) - Fmg≡ tangential force on the miter gear (N) - dbg≡ bevel gear pitch circle diameter (mm) - dmg ≡ miter gear pitch circle diameter (mm) - α ≡ angle of pressure = 20° - Fsb ≡ separating force on the bevel gear (N) Wind Powered Water Pump - 85 - - Fsm ≡ separating force on the miter gear (N) - εmg ≡ miter gear pitch angle = 45° - εbg ≡ bevel gear pitch angle = 26° 54’ - Fmgt≡ miter gear thrust (N) - Fpt ≡ pinion thrust (N) - Fbgt≡ bevel gear thrust (N) - Mbg ≡ bending moment created by the vertical separating force in the bevel gear - Mmg ≡ bending moment created by the vertical separating force in the miter gear Wind Powered Water Pump - 92 - Z axis The next diagram shows the forces in Z axis: The momentum in the point where the bearing B is: The momentum in the point where the bearing D is: The maximum momentum is where the bearing D is. The bearing B has to support: Wind Powered Water Pump - 93 - The bearing D has to support: Forth case In the fourth case the plane where the rotor shaft and the vertical shaft is 90° from the plane of the vertical shaft with the pump one. Y axis The diagram shows the forces in the Y axis and also the bending moments in the Z axis. The next diagram shows the bending moments in Z axis: Wind Powered Water Pump - 94 - Z axis The next diagram shows the forces in Z axis: The momentum in the point where the bearing B is: The momentum in the point where the bearing D is: The maximum momentum is where the bearing D is. Wind Powered Water Pump - 95 - The bearing B has to support: The bearing D has to support: In that point the bending moment is 329430 N·mm and the torque is 196629 N·mm. For this torque and this bending moment the diameter can be calculated: Being: -ns= 2 -σy= 710 MPa Because of the hub diameter of the gear, the diameter of the shaft has to be bigger so the safety coefficient will be more than 2. The biggest force than the bearing B has to support is 2295 N. The biggest force than the bearing B has to support is 3698 N. As the diameter is quite big, the bearings used will support easily that loads. Top key In order to transmit the torque from the shaft to the pinion a key is going to be designed. Wind Powered Water Pump - 96 - Because of the shaft diameter is 25 mm the main dimension are 8x7. The keyway depth shaft (t1) = 4 mm The keyway depth hub (t2) = 3.3 mm The force we want to transmit is: Nominal torsional stress Shearing stress: Bearing stress: Von Mises stress: Wind Powered Water Pump - 97 - If the design safety coefficient is 2, 12 is chosen because is the minimum length Bottom key In order to transmit the torque from the shaft to the pinion a key is going to be designed. Because of the shaft diameter is 25 mm the main dimension are 8x7. The keyway depth shaft (t1) = 4 mm The keyway depth hub (t2) = 3.3 mm The force we want to transmit is: Wind Powered Water Pump - 98 - Nominal torsional stress Shearing stress: Bearing stress: Von Mises stress: If the design safety coefficient is 2, 12 is chosen because is the minimum length Wind Powered Water Pump - 99 - Annex VI: The pump shaft The picture below shows the shaft with the main parts that is going to have: one welded piece (part of the rotor) in the front, three bearings and one gear. First of all, the forces acting on the shaft must be calculated. On the leftmost the rotor is pump is supported. There are four forces acting here: the weight and the tension on the pump, the force that transmits the torque and the separating forces. The weight of the pump is 68 N and the tension is 230 N. The forces of the gear can be also calculated with the following procedure: Wind Powered Water Pump - 100 - Values to consider: - Ms≡ torque on the pump shaft (N·mm) - Pp ≡ power at the pump shaft (W) = 4633 W - n ≡ rotational speed of the pinion shaft (rpm) = 281,25 rev/min - Ft ≡ tangential force on the pinion (N) - dg≡ pinion pitch circle diameter (mm) = 100 - α ≡ angle of pressure = 20° - Fs ≡ separating force - εg ≡ gear pitch angle = 45° - Fg≡ gear thrust The momentum created by the Fg is this value times the distance to the center of the shaft: Wind Powered Water Pump - 101 - The next diagram shows the forces acting on the shaft including only forces in Y axis and Z axis; bending moments in Z axis. The next diagram shows the forces in X axis and torques in the shaft: To calculate the reactions forces and the efforts in the shaft the forces are going to be separated in different axis: X, Y and Z. The X axis is parallel to the shaft, the Y axis is vertical and the Z one is perpendicular to both of them. During the calculations the different points of the shaft are going to be named like in the next picture: Wind Powered Water Pump - 108 - Bearing stress: Von Mises stress: If the design safety coefficient is 2, 12 is chosen because there are not 12 mm long keys Wind Powered Water Pump - 109 - Annex VII: The pump The rotor has a power of 286 Watts working with a wind speed of 4.6 m/s. Because of the transmission efficiencies, the power that gets to the pump is 229 W. The pump efficiency is not 100% but 80%. So the power for the calculations is 183 W. This power is going to be used to raise the water, and is directly proportional to the flow of water. The power is the product of force times the speed: As the speed is constant there is no acceleration so the system is balanced. Then, the force is only the weight of the water that is being raised. This force can be calculated as: Being: l : the length of the pipe r : the radius of the pipe ρ : the water density g : gravity acceleration The length is 11.5 meter, from the bottom of the well to the pipe that goes to the tank. The values of the density and the gravity are always the same so the only values that can be changed are the radius and the speed. The flow can be calculated as: Joining all the equations the power is: Wind Powered Water Pump - 110 - It has been demonstrated that the power is directly proportional to the flow and the length. Clearing the flow: What has to be designed is the radius of the pipe and the speed that depends on the radius. But the force also depends on the diameter and the rope has to support it. The final diameter is 32 mm so the speed is: The wheel that will support the rope has a diameter of 16 inches which is 406 mm. With the diameter and the speed of the rope the angular velocity can be also calculated: Having all this data, the force that the rope has to support because of the water is: This force is just the weight of the water but for the rope not to slide on the pulley bigger tension is needed. This drawing represents the pulley, the bigger tension (T2) is the one that supports the water. To measure the maximun difference the next equations have to be used: Where: µ is the friction coefficient Δθ is the angle that the rope is touching the wheel Wind Powered Water Pump - 111 - To solve the equation another one is needed in order to have system of equations. Being Wwaterthe weight of the water. The rope is made of polypropylene and the surface of the wheel that is in contact is made of rubber. The friction coefficient between those materials is 0.55 and the angle is 180°. The value of T1 is the minimum value needed for the rope not to slide over the pulley. This value is a pretension that has to be installed. The maximum tension the rope maker recommends is 160 N so the maximum values of the tension should be: The end of the pipe has to support a force between 130 and 230 N that can make it buckle. In order to avoid that a heavy piece of concrete will be installed, weighting the force needed. In order to minimize the buckling of the pipes there is a heavy part of concrete. The weight of the pipe is 6 kg, what is 59 N. So the weight of the guide of the pump has to be at least 70 N of weight and no more than 170 N. As the PVC works better with tension loads than compression loads the weight of the piece is approximately the tensions of the rope. Date: Student ID: Initial: Drawing no.: A.G. IY10227 23/5/2011 Group ID: Scale: 1:50 WIND TURBINE 1.0 Engineering College of Aarhus Ingeniørhøjskolen i Århus Department of Mechanical Engineering Description: Item no Item Material Qty 1 Upper Truss Stainless Steel 1 2 Lower Truss Stainless Steel 1 3 Bearing support 3 1023 Carbon Steel 1 4 Pipe support 1023 Carbon Steel 4 5 SKF SY25TF - 1 6 SKF SY20TF - 1 1:50 TRUSS 2.0 Engineering College of Aarhus Scale: Group ID: Date: 22/5/2011 IY10227 Student ID: Initial: Drawing no.: A.G. Ingeniørhøjskolen i Århus Department of Mechanical Engineering Description: 1 3 5 4 2 6 A 97 8 10 200 8 22/5/2011 A.G. IY10227 Description: 1:20 UPPER TRUSS 2.1 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 1Item no. Drawing no. Material / Model no. Stainless Steel (ferritic) Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering Upper truss DETAIL A SCALE (1 : 5) 31 103 50 13 50 110 82,50 82,50 400 60 7° 175 28 10 5 150 1902 2400 383 97 R4 R4 8 10 10 200 DETAIL C SCALE (1 : 5) 15 5 20 20 10 C 400 434 45° 533 40 Description: IY10227 IY10227 22/5/2011 1:20 LOWER TRUSS 2.2 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 1Item no. Drawing no. Material / Model no. Stainless Steel (ferritic) Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering Lower truss Description: A.G. IY10227 22/5/2011 1:1 BEARING SUPPORT 3 2.3 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 1Item no. Drawing no. Material / Model no. 1023 Carbon Steel Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering Support 3 127 32 97 10 R20 R2 2 144 5 10 30 40 10 Description: A.G. IY10227 22/5/2011 1:1 PIPES SUPPORT 2.4 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 4Item no. Drawing no. Material / Model no. 1023 Carbon Steel Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering Pipes support 73 22/5/2011 A.G. IY10227 Description: 1:2 BEARING SUPPORT 2 3.6 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 1Item no. Drawing no. Material / Model no. 1023 Carbon Steel Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering Support 12 130 36 102 22/5/2011 A.G. IY10227 Description: 2:1 ROTOR SHAFT PLATE 3.7 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 1Item no. Drawing no. Material / Model no. 1023 Carbon steel Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering Plate 535 7 22/5/2011 A.G. IY10227 Description: 1:20 TAIL 3.8 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 1Item no. Drawing no. Material / Model no. 1060 Alloy Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering Tail 550 5 800 400 2 1300 BSCALE 1:2 22/5/2011 A.G. IY10227 Description: 1:20 TAIL SUPPORT 3.9 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 1Item no. Drawing no. Material / Model no. 1023 Carbon Steel Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering Tail support 20 20 2 DETAIL A SCALE (1 : 10) 12525 5 DETAIL B SCALE (1 : 10) 550 5 550 100 A 2650 1 2 3 Date: Student ID: Initial: Drawing no.: A.G. IY10227 23/5/2011 Group ID: Scale: 1:50 ROTOR ASSEMBLY 4.0 Engineering College of Aarhus Ingeniørhøjskolen i Århus Department of Mechanical Engineering Description: Item no Item Material Qty 1 Blade Pine wood 3 2 Join part 1023 Carbon Steel 3 3 Rotor plate 1023 Carbon Steel 1 NACA 23012 117 1500 361 F F 22/5/2011 A.G. IY10227 Description: 1:20 BLADE 4.1 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 3Item no. Drawing no. Material / Model no. Pine Wood Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering NACA profile 23012 F-F G DETAIL G SCALE (1 : 5) 4x 50 5 120 35 70 50 30° Description: A.G. IY10227 22/5/2011 1:2 JOIN PART 4.2 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 3Item no. Drawing no. Material / Model no. 1023 Carbon Steel Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering Join Part 5035 120 30 BB 220 1525 B-B 24 5 12 24 R75 22/5/2011 A.G. IY10227 Description: 1:5 CONCRETE GUIDE 5.1 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 1Item no. Drawing no. Material / Model no. Concrete Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering Concrete guide 110 300 40 CC C-C 40 20 300 22/5/2011 A.G. IY10227 Description: 1:5 PUMP WHEEL 5.2 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 1Item no. Drawing no. Material / Model no. 1023 Carbon Steel Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering Wheel DETAIL A SCALE (1 : 2) 40 6 2,80 R10 A 25 25 70 70 399 3 22/5/2011 A.G. IY10227 Description: 1:1 PISTON 5.3 Drawing no.: Initial: Engineering College of Aarhus Qty. Item 15 Item no. Drawing no. Material / Model no. Polyethylene Scale: Group ID: Date: Student ID: Ingeniørhøjskolen i Århus Department of Mechanical Engineering Piston A-A 17 10 2 22 14,20 4 31 AA