Document [original]

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158 Technical Gazette 30, 1(2023), 158-168

ISSN 1330-3651 (Print), ISSN 1848-6339 (Online) https://doi.org/10.17559/TV-20220425205603

Original scientific paper

Influential Factors in the Loading of the Axial Bearing of the Slewing Platform Drive in

Hydraulic Excavators

Vesna JOVANOVIĆ, Dragan MARINKOVIĆ*, Dragoslav JANOŠEVIĆ, Nikola PETROVIĆ

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Abstract: The paper contains the results of the analysis of factors that influence the loading of the axial bearing of the slewing platform drive mechanism in hydraulic

excavators. The following influential factors are considered: the operations of the excavator manipulation tasks, the number of drives in the slewing platform mechanism,

and the configuration of the excavator kinematic chain. The importance of the influence of these factors is assessed on the basis of the comparison between certain equivalent

loads of the platform drive bearing with the diagrams of allowed load capacities of available bearings. The equivalent loads of the platform drive mechanism bearing are

determined using the approach of static and dynamic excavator simulation in the programs developed on the basis of the defined mathematical models of the excavator.

The equivalent loads are given with regard to the duration of the manipulation task and in the form of a spectrum of equivalent loads determined in the entire operating area

of the excavator. The analysis is performed for three different configurations of the kinematic chain of a tracked hydraulic excavator with the mass of around 100000 kg.

Keywords: axial bearing; hydraulic excavators; slewing platform drive

1 INTRODUCTION

Hydraulic excavators belong to the group of mobile

machines whose primary function is the cyclic transport of

various materials in a specific working space. Hydraulic

excavators perform different functions using the general

configuration of the kinematic chain that comprises: the

support and movement mechanism L1, Fig. 1a, the slewing

platform L2 and the manipulator with the boom L3, stick L4

and bucket L5. The spatial manipulation of the excavator is

enabled by the kinematic pair consisting of the support and

movement mechanism and the slewing platform,

connected using a slewing joint in the form of an axial

bearing that allows the unlimited rotation of the platform,

in both directions, around the vertical axis of the joint. The

general model of the platform drive comprises: the

hydrostatic part - a hydraulic pump 2.1, Fig. 1b and a

hydraulic motor 2.3, connected in an open or closed

hydraulic circuit, and the mechanical part - a reducer 2.4

with a gear on the output [1] shaft coupled with a toothed

rim of the axial bearing 2.5. Depending on the excavator

size, the concept of the slewing platform mechanism can

have one or multiple identical drives, Fig. 1c.

The research related to the rotation drive mechanism

of the excavator platform mainly deals with: a) loading of

large-diameter axial bearings and fatigue analysis of

bearing [2-6], b) loading of the track for rolling elements

of axial bearings [7-10], c) examination of influential

factors for determining bearing load capacity diagrams,

which are used, in comparison with equivalent loads, to

carry out the selection of axial bearings [11-15], d) loading

of the screw joint of axial bearings [16-20], e) hybrid drive

mechanisms of the excavator slewing platform [21-25],

and f) recovery of the energy generated when the platform

stops turning [26-30]. Hydraulic excavators are

characterized by a large number of different size models.

Furthermore, every excavator model can have various

configurations of the kinematic chain with different

variants of the movement mechanism Fig. 1a, different

types and configurations of the manipulator, as well as a

number of tools for performing all sorts of functions in the

working space. At that, for all the possible different

configurations of the excavator model, the drive

mechanism of the slewing platform remains the same. The

stated differences imply the complexity of the slewing

platform synthesis procedure in designing hydraulic

excavators. According to the developed methodology, for

the synthesis of the slewing platform drive mechanism it is

necessary to first determine the parameters of the kinematic

chain members and the parameters of the excavator

manipulator drive mechanisms [31, 32].

Figure 1 The general concept of the slewing platform drive mechanism in hydraulic excavators: a) kinematic chains of the excavator; b) functional schematic; c) physical

models of the drive mechanism

Vesna JOVANOVIĆ et al.: Influential Factors in the Loading of the Axial Bearing of the Slewing Platform Drive in Hydraulic Excavators

Tehnički vjesnik 30, 1(2023), 158-168 159

In the initial phase of the synthesis procedure for the

slewing platform mechanism, the axial bearing of the drive

is the first to be determined. For the proper selection of the

size, manner of installation and maintenance of the axial

bearing, specialized manufacturers of available bearing

models set out certain limitations, criteria and conditions

[33-35]. The basic limitation in choosing the axial bearing

relates to the allowed load capacity of the bearing given in

the form of a bearing load capacity diagram that represents

the dependence between the allowed force and the allowed

moment of the bearing load. The bearing size is chosen by

comparing the bearing load capacity diagrams with

equivalent bearing loads determined in line with the criteria

defined by bearing manufacturers on the basis of forces and

moments to which the bearing is subjected during the

operation of the excavator. In what follows, the paper will

provide the results of the research into the influence on the

loading of the axial bearing of the slewing platform

mechanism in hydraulic excavators exerted by the

following factors: operations of manipulation tasks, the

number of drives in the excavator slewing platform

mechanism, and the configuration of the excavator

kinematic chain.

2 MATHEMATICAL MODEL OF THE EXCAVATOR

A general mathematical model of the excavator is

developed using Newton-Euler dynamic equations [31, 36]

for the analysis of the factors that influence the loading of

the axial bearing of the slewing platform mechanism. The

mathematical model of the excavator encompasses the

configuration of the excavator kinematic chain with a

loading (Fig. 2a) and a digging (Fig. 2b) manipulator

comprising: the tracked support and movement member L1

(Fig. 2) the slewing member - slewing platform L2 and the

planar manipulator with the boom L3, stick L4 and bucket

L5. The members of the excavator kinematic chain form

kinematic pairs of the fifth class - slewing joints with one

degree of freedom. The center of joint O2 of the kinematic

pair that consists of the support and movement member and

the slewing member is the point of intersection of the joint

vertical axis and the horizontal plane defined by the centers

of the rolling bodies of the axial bearing that connect the

support and movement member to the slewing member of

the chain. The manipulator drive mechanisms are planar

lever configurations with actuators - hydraulic two-way

cylinders ci connected, directly or indirectly, to the

members of the kinematic pair Li‒1 - Li of the manipulator.

The assumptions of the general mathematical model of the

excavator are:

- the support surface and the members of the excavator

kinematic chain are modeled using rigid bodies;

- during the manipulation task the excavator is subjected

to external (technological) load - the digging resistance

force W, internal load - forces of gravity (weight), and

inertia forces and moments of the kinematic chain

members, drive mechanisms and material scooped by

the excavator bucket;

- hydraulic cylinders of the drive mechanisms are

modeled as rods with equally distributed mass along

the current length;

- friction is neglected in the joints of the kinematic chain

and excavator drive mechanisms, as well as the

influence of wind on the members of the excavator

kinematic chain;

- the vector of the digging resistance force W acts on the

cutting edge of the bucket in point Ow eccentrically

displaced in relation to the bucket plane for coordinate z5w.

The eccentric action of the digging resistance force

occurs when capturing inhomogeneous material, widening

canals, plucking various vegetation and lifting loads.

The space of the excavator model is determined with

an absolute coordinate system OXYZ (Fig. 2) with unit

vectors i, j, k in the direction and sense of coordinate axes

OX, OY and OZ. Each member of the excavator kinematic

chain Li is determined in its own local coordinate system

Oixiyizi with a set of quantities (marked with a circumflex

above the symbol), (Fig. 2) [32, 37]:



, , , , 1,...,5

iiiiii

LmJi



est (1)

where: i



e - the unit vector (ort) of the axis of the Oi joint

that links member Li to the previous member Li-1; i



s- the

vector of the position of the Oi+1 joint center that links

member Li to the following member Li+1, where the vector

intensity represents the kinematic length of member Li;



t - the vector of the position of the mass mi center of member

Li; - the moments of member Li inertia.

The manipulator drive mechanism Ci in the mathematical

model of the excavator is determined in its own local coordinate

system Ocbixciycizci using a set of quantities (Fig. 2):



, , , , , , 3,...,5

iciiiciciii

CDdmn i



eab

(2)

where: ci



e- the unit vector of the axis of joint Ocbi in which

the hydraulic cylinder is connected to the manipulator

kinematic chain member, Di/di - the diameter of the

piston/piston rod in the hydraulic cylinder; mci - the mass

of the hydraulic cylinder; nci - the number of the hydraulic

cylinders in the drive mechanism, ,



- the vectors, i.e.

coordinates, of the position of the centers of the joints in

which the hydraulic cylinders and transmission levers are

connected to the members of the drive mechanism

kinematic pair.

Generalized coordinates - angles



I determine the

relative position of member Li in relation to the previous

member Li‒1 [38]. The position of member Li in the

manipulator kinematic chain is determined in relation to

the horizontal absolute plane XOZ using angles φi (external

coordinates):

3,...,5









(3)

The vectors of the positions of joints ri centers, the

centers of masses rti of the members of the excavator

kinematic chain, and the vector of the position of the

attacking point of the digging resistance force on the

cutting edge of the bucket rw in relation to the absolute

coordinate system are determined using the equations:



Vesna JOVANOVIĆ et al.: Influential Factors in the Loading of the Axial Bearing of the Slewing Platform Drive in Hydraulic Excavators

160 Technical Gazette 30, 1(2023), 158-168

111

0, , ,

2,...,5

jo j jo j i io i

rAsrAsrAt





  









iwti

(4)

where: Ajo, Aio - the transformation matrices of the

excavator model used to translate the vector quantities

from the local coordinate system of the chain member Li to

the absolute coordinate system of the excavator model,

while matrices Aoi =T

are used vice versa from the

absolute to the local coordinate system.

3 EQUIVALENT LOADS OF THE AXIAL BEARING

By fictively breaking the excavator kinematic chain in

the center of joint O2, and observing the balance of the

discarded part of the chain (platform and manipulator), one

can determine the resulting force FO2 and moment MO2 in

the center of joint O2 using the equations Fig. 2a, b:

O2 23

ui cui

ii

 



FFFW

(5)

55 5 5

223 2 3

i ci Fui Fcui w

Oii i i  

   

  

MMMMMM

(6)



Figure 2 The mathematical model of the excavator with а a) loading and b) digging manipulator

where: Fui, Fcui - the internal force (inertia and gravity) in

the center of mass of the kinematic chain member and

actuators (hydraulic cylinders) of drive mechanisms, Mi,

Mci - the inertia moment in the center of mass of the

kinematic chain member and mass of the drive mechanism

actuators, MFui, MFcui - the moment of the internal force of

the kinematic chain member and drive mechanism

actuators for the center of joint O2, W, Mw - the digging

resistance force and the digging resistance force moment

for the center of joint O

2. Depending on the number of

platform drives and their distribution in relation to the

toothed rim of the axial bearing, additional loads of the

axial bearing may appear due to the reaction of the platform

drive subjected to the action of the loads occurring during

the manipulation task of the excavator.

Considering this additional load appearing due to the

reaction of the slewing platform drive, resultant F2 and

components F2x, F2y, F2z of the force in joint O2 of the

slewing platform that act on the axial bearing of the

slewing drive are determined using the equations

(Fig. 3a, c):

Vesna JOVANOVIĆ et al.: Influential Factors in the Loading of the Axial Bearing of the Slewing Platform Drive in Hydraulic Excavators

Tehnički vjesnik 30, 1(2023), 158-168 161

22c2

55 5 5

223 2 3

iciFuiFcuiw

Oii i i  



   

  

FF F

MMMMMM

(7)

where: Fc2 - the vector of the reaction of the slewing

platform drive determined by the equation:



c2 2 2 2 2

25 24

sin cos

 







Fik

(8)

where: Mp2 - the moment of the slewing platform drive, α2

- the angle of the platform drive position, D25 - the pitch

diameter of the toothed rim of the platform axial bearing,

d24 - the pitch diameter of the gear on the output shaft of

the drive reducer. The resulting force F2 loads the axial bearing

with the radial force F2r that is formed, in the horizontal plane

of the bearing, by components F2x and F2z, and the axial

force F2a that acts along the bearing axis O2y and is equal

to component F2y. In larger excavators with two identical

drives positioned under the angle of α2 = 180°, (Fig. 3d),

reactive forces of platform drives cancel each other and do

not load the bearing.

Resultant M2 and components M2x, M2y and M2z of

moments in joint O2 of the slewing platform that load the

axial bearing of the slewing drive are determined using the

equations (Fig. 3b, d):

2222

222222222

, ,

xyz



  

MM j

MMiMM

MMk

(9)

The resulting moment M2 loads the axial bearing with

moment M2r consisting of components M2x and M2z, whose

vector lies in the horizontal plane of the bearing.

Component M2y = 0 does not load the bearing, since the

loading moment component MO2y and the drive moment

Mp2 have the same intensity and the opposite direction of

action.

As suggested by manufacturers, the size of the axial

bearing of the slewing platform mechanism in mobile

machines is selected based on the equivalent bearing loads.

The diagram of the allowed bearing load capacity that

shows the dependence of the allowed equivalent force Fe

and the allowed equivalent moment Me of the bearing

defined by the equations [39] is used for this purpose:

 for the equivalent force:

()

ears

aF bF f  

(10)

 for the equivalent moment:

2ers

cM f  (11)

Figure 3 Components of the loading of the axial bearing of the excavator slewing platform drive: а) forces; b) moments; c) bearing loading forces with one drive; d) bearing

loading forces with two drives

where: F2a, F2r - the axial and radial bearing load force,

M2r - the bearing load moment, a, b, c - the coefficients

dependent on the type of bearing, type and size of the

machine and its working conditions, fs - the factor of static

safety. When choosing a bearing, the condition is that the

values of the calculated equivalent bearing loads in the

entire operating area of the machine do not exceed the

boundary curves in the bearing load capacity diagram.

4 INFLUENTIAL FACTORS IN THE LOADING OF THE

AXIAL BEARING

The factors that influence the loading of the axial

bearing of the slewing platform drive were analyzed for

three possible variants A, B and C of the same hydraulic

excavator model (Tab. 1) with the mass of around

100000 kg. The variants have different members of the

Vesna JOVANOVIĆ et al.: Influential Factors in the Loading of the Axial Bearing of the Slewing Platform Drive in Hydraulic Excavators

162 Technical Gazette 30, 1(2023), 158-168

kinematic chain with the same slewing platform

mechanism with two drives positioned relatively at the

angles: α2 = 0° and α2 = 180° (Fig. 3c, d) along the

circumference of the toothed rim of the axial bearing. The

excavator variants A and B possess different support and

movement mechanisms and loading manipulators with

different bucket volumes. Excavator variant A has the

bucket volume of V = 4.4 m3 for digging the material with

the density of ρ = 2200 kg/m3, while variant B has the

bucket volume of V = 6.5 m3 for digging the material with

the density of ρ = 1650 kg/m3. Variant C has a digging

manipulator with the bucket volume of V = 4.8 m3 for

digging the material with the density of ρ = 2200 kg/m3.

The importance of the influence of specific factors on

the loading of the slewing platform drive bearing is

assessed by comparing the calculated equivalent loads of

excavator variants A, B and C bearings with the allowed

loads - the diagram of load capacity of different available

single-line roller bearings AL0-AL6 (Tab. 2) [37].

4.1 Analysis of the Influence of Manipulation Task

Operations

Based on the defined mathematical model of the

excavator and the developed program, static and dynamic

numerical simulation of the excavator operation were

performed to analyze the influence of the manipulation task

operations for the loading of the axial bearing of the

excavator slewing platform drive. The manipulation task

parameters were set for the following operations: digging,

transferring, unloading and returning to the new digging

plane. The simulation was used to determine the change in

equivalent forces and equivalent moments of the loading of

the axial bearing in the slewing platform drive mechanism

of the excavator variants A and B with the loading

manipulator depending on the duration of the manipulation

task. Dynamic parameters of the excavator kinematic chain

members Li and drive mechanisms Ci, used in simulating

the excavator variants A, B and C were determined using

the developed 3D excavator models that correspond to the

physical model of the Liebherr R974C Litronic hydraulic

excavator. SolidWorks software [40] was used for the

purpose.

Simulated components of the digging resistance force

W (Fig. 4), that load the kinematic chain of excavator

variants A and B were defined using analytical

mathematical models depending on the bucket geometry,

changes in the cutting thickness and characteristics of the

material scooped during the digging operation [31].

Digging resistance force components perpendicular

(Wxy) and colinear (Wz) in relation to the cutting edge of the

excavator variant A and B buckets have similar intensities

and an insignificantly varying character of changes during

the digging operation. Conditions for simulating the stable

operation of the excavator (θ11 = 0°) are met because the

intensity of the perpendicular component of the digging

resistance Wxy is smaller than the intensity of the boundary

digging resistance forces Wsm, Wpm determined from the

stability conditions: absence of rolling over (Wsm) and

sliding (Wpm) of the excavator in the support plane.

Figure 4 Components of the digging resistance force perpendicular (Wx, Wy, Wxy) and colinear (Wz) in relation to the bucket cutting egde and forces (Wsm, Wpm) allowed by

the stability of the excavator model: а) A; b) B

Table 1 Possible variants of the excavator kinematic chain members [31]

Model

Tracked support and movement mechanism Manipulator material

density

ρ / kg/m3

excavatormass

m / kg

footprint

length

L1 / mm

track

span

B1 / mm

tread

width

b1 / mm

kinematic

chain

bucket

volume

V / m3

bucket width

b5 / mm

A 4770 3600 500 loading 4.4 2350 2200 92000

B 5035 3600 600 loading 6.5 3150 1650 100000

C 4770 3600 500 digging 4.8 2150 2200 89000

Table 2 Single-line roller axial bearings [37]

Bearing mark AL0 AL1 AL2 AL3 AL4 AL5 AL6

Rolling bodies track diameter / mm 2125 2237 2365 2363 2507 2651 2657

Bearing load coefficients a = 1, b = 2.05, c = 1 ,fs = 1.45

Vesna JOVANOVIĆ et al.: Influential Factors in the Loading of the Axial Bearing of the Slewing Platform Drive in Hydraulic Excavators

Tehnički vjesnik 30, 1(2023), 158-168 163

In the simulation the vector of the digging resistance

force acts upon the cutting edge of the bucket eccentrically

in relation to the center of the cutting edge at the distance

of w5z = l5/4, one fourth of the bucket width l5 away

(Fig. 2b). For excavator variants A and B, for the purpose

of a comparative analysis, the same working environment

parameters and the same working technology model was

simulated. Hence, the same manipulation task was

performed with the given external cycloid trapezoid model

of the character of changes in angular velocities i



of the

relative movement of the excavator kinematic chain

members (Fig. 5) [31]. As simulation results, the diagrams

of changes in equivalent static Fes and dynamic Fed forces

(Fig. 6a) and equivalent static Mes and dynamic Med

moments (Fig. 6b) of the axial bearing loading in the

slewing platform of excavator variants A and B are

presented.



Figure 5 Changes in the angular velocity of relative movement of the kinematic chain members for excavator variants A and B during the manipulation task

Figure 6 Equivalent loads of the axial bearing of the slewing platform drive in excavator models А and B: а) equivalent static (Fes) and dynamic (Fed) forces; b) equivalent

static (Mes) and dynamic (Med) moments; c) equivalent bearing loads in relation to the allowed load capacities of available bearings AL0-AL5

Vesna JOVANOVIĆ et al.: Influential Factors in the Loading of the Axial Bearing of the Slewing Platform Drive in Hydraulic Excavators

164 Technical Gazette 30, 1(2023), 158-168

The results show that the greatest equivalent bearing

loads appear during the digging operation. Comparing

static and dynamic equivalent loads according to Eq. (5)

and Eq. (6), the static bearing loading is subjected to the

influence of the digging resistance force and gravity of the

kinematic chain members and drive mechanisms, while the

inertia loading due to the acceleration of the excavator

kinematic chain members during the manipulation task is

neglected.

The difference between the dynamic bearing loads and

the equivalent static loads during the digging operation is

very small, due to the relatively slow movement of the

kinematic chain members.

The appearance of greater dynamic loads, which act

upon the platform axial bearing, occurs at the beginning

and the end of the material transfer operation and the

operation of returning to the new digging plane, caused by

less and more intense movement of the platform and

the manipulator kinematic chain members.

For the sake of comparison, Fig. 6c depicts the

allowed load capacities of available bearings AL0-AL5,

while the red line shows the dependence of the equivalent

forces and moments of the bearing loads, Fe and Me, in the

excavator variants A and B during the simulated

manipulation task in the digging operation. The blue line is

used for other operations.

The diagram shows that the equivalent loads of the

axial bearing determined during the digging operation are

pertinent for the selection of the bearing size. This is

because the flow of changes in the equivalent forces and

moments during the digging operation (Fig. 6c, red line) is

much closer to the boundary lines of the allowed load

capacities of available bearings in relation to the changes

in the equivalent bearing loads during other operations of

the excavator manipulation task (blue lines).

4.2 Analysis of the Influence of the Number of Platform

Drives

To assess the influence of the number of slewing platform

drives and their relative installation position on the equivalent

loads of the drive axial bearing, the analysis was performed in

which the equivalent bearing loads for excavator model B

variants with one (Fig. 3a, c and two identical drives

(Fig. 3b, d) were considered. In excavator variant B with one

slewing platform drive, the drive was taken to be positioned in

the local coordinate system of the platform, with the angles

α2 = 0o, α2 = 180° in relation to the O2x2 axis (Fig. 3a, c). This

corresponds to the most common type of installation in practice,

bearing in mind the available space and the proximity of the

hydraulic motor and the hydraulic pumps of the excavator drive

group. In the excavator model variant with two slewing

platform drives, the drives were positioned relatively under the

angles θ2 = 0o, α21 = 0º, α22 = 180º (Fig. 3b, d) in the local

coordinate system of the platform.

The analysis results obtained by simulation are presented

in Fig. 7. The allowed load capacities of available bearings

AL0-AL5 show that, during the digging operation (red line), the

dependences between the static and dynamic equivalent bearing

loads of excavator variant B with one slewing platform drive

(FesI, MesI and FedI, MedI) differ from the excavator variant B with

two slewing platform drives (FesII, MesII and FedII, MedII). It is

noticeable that the excavator variant B with one slewing

platform drive has greater equivalent forces (FsI, FdI) of bearing

loads compared to the equivalent forces (FsII, FedII) of the

excavator variant B with two drives.

The dependences of the equivalent bearing loads during

other operations of the manipulation task (transfer, unloading

and returning to the new digging plane - blue line in Fig. 6c)

done by the excavator variant B with one drive show that the

equivalent forces (FsI, FdI) of bearing loads are significantly

greater than the same of the excavator variant B with two drives

(blue line) (Fig. 6c) [31].

The reason behind the increased equivalent forces lies in

the fact that in the excavator variant with one drive a reactive

turning force appears, causing a further radial loading of the

axial bearing. The increased reactive forces in the slewing

mechanism with one drive appear during the manipulation task

in the digging operation in the case of the eccentric action of the

digging resistance force in relation to the longitudinal

symmetrical plane of the bucket, i.e. the manipulator, and in the

phases of increased and decreased movement of the excavator

slewing platform.

In the excavator variant with two drives, the reactive forces

of the drive positioned relatively, along the toothed rim of the

bearing, at the angle of α2 = 180º have the same intensities but

opposite directions of action so that they do not subject the axial

bearing to further loads. The equivalent moments of bearing

loads for both slewing drive variants of excavator variant B are

identical since the drive reactive forces have no influence on

them.

4.3 Analysis of the Influence of the Excavator Kinematic Chain

Configuration

Bearing in mind that during their operation hydraulic

excavators have a number of manipulation tasks with the

digging operation - scooping the material in the entire working

space, a spectrum of equivalent bearing loads is used for the

analysis of the influence of the excavator kinematic chain

configuration on the loading of the axial bearing.

The spectrum of equivalent loads of the axial bearing of the

excavator slewing platform drive (Fig. 8) represents a

constellation of points defined by the equivalent forces Fe and

equivalent moments Me of bearing loads as coordinates. Those

points are determined for each position of the excavator

kinematic chain and the direction in which the digging

resistance acts.

For a reliable selection of the appropriate size of the axial

bearing of the slewing platform drive mechanism in the same

excavator model, it is necessary to determine the spectra of

bearing loads for all possible configurations of the excavator

kinematic chain when performing functions in the entire

working space under different working conditions.

The spectrum of equivalent loads of the axial bearing of the

slewing platform drive is determined in line with the defined

mathematical model of the excavator and based on the set of

known parameters [30]:



max2345

,, , , , , , , ,

i i wp wk w

ULC pKnnnn



 (12)

where: Li - the set of parameters of the excavator kinematic

chain members, C

i - the set of parameters of the excavator

manipulator drive mechanisms, θwp/θwk - the initial/final angle

of action of the digging resistance force, pmax - the maximum

Vesna JOVANOVIĆ et al.: Influential Factors in the Loading of the Axial Bearing of the Slewing Platform Drive in Hydraulic Excavators

Tehnički vjesnik 30, 1(2023), 158-168 165

pressure of the excavator hydrostatic system, K2 - the set of

coefficients for determining the equivalent loads of the axial

bearing, n3 - the desired number of the manipulator boom

positions in its movement range, n4 - the desired number of the

stick positions in its movement range for the specific position of

the manipulator boom, n5 - the desired number of the bucket

positions in its movement range for the specific position of the

manipulator stick, nw - the desired number of changes in the

direction of the digging resistance force action in the range of

changes from θwp to θwk for each bucket position.

Figure 7 Comparison of equivalent bearing loads of excavator B with one (FesI, FedI, МesI, МedI) аnd two (FesII, FedII, МesII, МedII) platform drives in relation to the allowed load

capacities of bearings AL0-AL5

When determining the spectrum of equivalent loads

one takes into account that the loading of the axial bearing

is affected by the gravitational forces of the kinematic

chain members, the excavator drive mechanisms and the

bucket, and the possible digging resistance force Wxym

defined by the equation (Fig. 2b):



345

min , , , ,

xym sm pm m m m

WWWWWW (13)

where: Wpm - the force of the boundary digging resistance

determined from the non-sliding conditions of the

excavator in the support surface plane and Wsm - the force

of the boundary digging resistance determined from the set

excavator stability conditions for potential rollover lines,

W3m, W4m, W5m - the boundary digging resistance forces

limited by the maximal possibilities of the action of the

drive mechanisms in the manipulator boom, stick and

bucket.

Figure 8 Comparison of the spectra of the axial bearing loads in excavator model А with the loading manipulator with the bucket volume V = 6.5 m3 (the dark blue color)

and excavator mode C with the digging manipulator (bright blue) with the bucket volume V = 4.8 m3 [30]

An originally developed program based on the

presented mathematical model of the excavator was used

for the analysis of the influence of changes in the excavator

kinematic chain configuration. Fig. 8 shows the obtained

spectra of the loading of the slewing platform bearing of

excavator variant A with the loading manipulator (the dark

blue color of the spectrum) and excavator variant C with

the digging manipulator (the bright blue color of the

spectrum). The loading spectra are presented in the

diagrams of the allowed load capacity of the selected

Vesna JOVANOVIĆ et al.: Influential Factors in the Loading of the Axial Bearing of the Slewing Platform Drive in Hydraulic Excavators

166 Technical Gazette 30, 1(2023), 158-168

available bearings: AL3-AL6. They are determined according

to the following given conditions and parameters: the

manipulator is perpendicular to the transversal plane of the

support and movement mechanism, positions of the kinematic

chain n3 = 30, n4 = 20, n5 = 10; the number of changes in the

directions of the digging resistance force action is nw = 10; and

the initial/final angle of the direction of the digging resistance

force action is θwp/θwk = 200°/300° for variant A and θwp/θwk =

30°/50° for variant C.

Diagram in Fig. 8 shows that the spectra are very

different and that the selection of the axial bearing size

relies on the spectrum of the equivalent bearing loads of

excavator variant A with the loading manipulator

configuration. This is due to much greater equivalent

bearing loads than in the case of the equivalent bearing

loads of excavator variant C with the digging manipulator.

The difference occurs due to the different digging

technologies, i.e. different action of the digging resistance

force. In the digging manipulator, while digging, which

takes place mainly below the excavator support level, the

bucket movement kinematics is such that, in the majority

of the digging operation, the vertical component of the

digging resistance force has an opposite direction to the

direction of the gravitational forces of the excavator

kinematic chain members. This results in the smaller axial

loading force exerted on the bearing of the excavator

slewing platform drive. Conversely, in the loading

manipulator, the bucket movement kinematics is such that,

in the majority of the digging operations, the vertical

components of the digging resistance force and the

gravitational forces of the kinematic chain members have

the same direction of action.

This results in the greater axial bearing force acting

onto the axial bearing of the slewing platform drive. The

results of the analysis using the loading spectra show (Fig.

8) that for the same excavator model, changes in the

configuration, i.e. the kinematic chain members,

significantly alter the equivalent loads of the axial bearing

of the excavator slewing platform drive mechanism.

5 CONCLUSION

In the synthesis of the drive mechanism of the slewing

platform in hydraulic excavators, the axial bearing of the

mechanism is determined based on equivalent bearing

loads and the allowed bearing load capacity. Equivalent

loads - equivalent force and equivalent moment are

determined according to the criteria of bearing

manufacturers depending on the bearing loads that appear

during the excavator operation. It is characteristic of

hydraulic excavators that a number of factors influence the

loading of the platform drive axial bearing. The paper

singled out and analyzed the influential factors that are

related to: the operations of the excavator manipulation

tasks, the number of the slewing platform drive

mechanisms and the configuration of the excavator

kinematic chain.

The analysis results, obtained through static and

dynamic numerical simulation of the excavator operation -

by setting the manipulation task with the following

operations: digging, transferring, unloading and returning

to the new digging plane, show that the bearing loads in the

digging operation are pertinent for the selection of the

bearing size. The number of drives in the excavator slewing

platform mechanism affects the loading of the axial bearing

due to the action of the reactive drive force. In the

mechanism with two drives positioned relatively along the

circumference of the toothed rim of the axial bearing under

the angle of 180°, the reactive drive forces are in balance

and do not load the bearing. The obtained results also show

that a significant influence on the loading of the slewing

platform axial bearing is exerted by the kinematic chain

configuration and the excavator working technology. This

is emphasized by the example that the bearing loads

pertinent for its selection are much greater when the

excavator is equipped with the loading instead of the

digging manipulator.

The general conclusion from the conducted research is

that the choice of an axial bearing for the slewing platform

mechanism must account for the analyzed influential

factors that affect the loading of the axial bearing. This is

because the same excavator model can have different

configurations of its kinematic chain used to perform a

number of different functions.

Based on the axial bearing load spectrum for the entire

working area of the excavator, future research can

determine the cumulative loads for the analysis of the

reliability and service life of the axial bearing.

Acknowledgements

This research was financially supported by the

Ministry of Education, Science and Technological

Development of the Republic of Serbia (Contract No. 451-

03-9/2021-14/200109).

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Contact information:

Vesna JOVANOVIĆ, Assistant Professor

University of Niš,

Mechanical Engineering Faculty

Aleksandra Medvedeva 14, 18000 Niš, Serbia

E-mail: vesna.jovanovic@masfak.ni.ac.rs

Dragan MARINKOVIĆ, Full Professor

(Corresponding author)

1) University of Niš, Mechanical Engineering Faculty,

Aleksandra Medvedeva 14, 18000 Niš, Serbia

2) Technical University Berlin, Institute of Mechanics,

17. Juni 135, 10623 Berlin, Germany

E-mail: Dragan.Marink[email protected]

Vesna JOVANOVIĆ et al.: Influential Factors in the Loading of the Axial Bearing of the Slewing Platform Drive in Hydraulic Excavators

168 Technical Gazette 30, 1(2023), 158-168

Dragoslav JANOŠEVIĆ, Full Professor, retired

University of Niš,

Mechanical Engineering Faculty,

Aleksandra Medvedeva 14, 18000 Niš, Serbia

E-mail: [email protected].rs

Nikola PETROVIĆ, Assistant Professor

University of Niš,

Mechanical Engineering Faculty,

Aleksandra Medvedeva 14, 18000 Niš, Serbia

E-mail: nikola.petrovic@masfak.ni.ac.rs