Finite element analysis and experimental study of strain for a vehicle rear suspension

In this paper, aspects of the study of the durability of rear suspension components of a vehicle are discussed. These aspects are addressed in two ways, namely the study by CAD modelling and finite element method simulation, and secondly by experimental analysis on a durability test bench. In order to develop these research problems, an experimental stand is virtually modelled and studied by simulation using ADAMS software. Results are obtained that characterize the operation of the test bench system kinematically and dynamically. The studies are then completed by finite element analysis of the dependent rear axle and helical springs in the suspension structure. These results are corroborated with those obtained experimentally, i.e. stresses and strains recorded on the stand. The usefulness of these studies is that they allow the validation of different components of the rear suspension in terms of fatigue strength and different types of rear axles from cars can be tested, as the stand has a modular construction and the test parameters can be adjusted.


Introduction
In the automotive industry, durability and fatigue resistance testing is imperative for a wide range of automotive components such as bearings, anti-roll bars, springs, shock absorbers, bushings, ball joints, as well as more complex elements such as rear axle or suspension arms.
Thus, within our team at the Faculty of Mechanics-University of Craiova, there has been a concern for the study of the durability of automotive components.Thus, in the works [1,2], the fatigue behavior of the stabilizer bar of the rear and front axle of a car is studied.The stiffness characteristic of a torsion bar spring is calculated experimentally, as well as the fatigue strength by the finite element method (FEM) using ANSYS software.The construction of a stand for testing the stabilizer bar at the front and rear axle of a passenger car are presented in the paper [2].The kinematics of the connecting rod-crankbalancer mechanism through which the alternating rotational motion of the stabilizer bar is achieved is presented in [3].Another concern was to study the frictional moment in radial ball bearings.Research addressing this topic is published at the CONAT 2017 conference [4].The 3D modeling of a stand allowing fatigue testing of the rear axle is presented in the paper [5], published at the AITS 2021-Chisinau conference.Here, the translational displacements of the stabilizer bar and the stresses and strains in the rear axle assembly are presented.Nationally and internationally, we find concerns in these directions.Thus, in the paper [6] the housing of a truck rear axle is optimized.The optimized structure was verified on a test stand and in operation on the truck by experimental measurement of deformations.Fatigue failure is a common occurrence in parts subjected to variable stresses.An example is that of a planetary shaft under torsional stress that failed [7].A very important role in the correct operation of a 1303 (2024) 012024 IOP Publishing doi:10.1088/1757-899X/1303/1/012024 2 mechanical system is played by vibrations, which must be eliminated from the operation of mechanical transmissions.An example of such a study, is presented in the paper [8], where the vibration behaviour of a hypoid bevel gear central transmission is simulated.One of the most commonly used tools for fatigue studies is finite element analysis in conjunction with experimental analysis, usually on test stands.Thus, in the paper [9], finite element simulation of the fatigue bending behaviour of a rigid truck rear axle is presented.The influence of motors installed in passenger car wheels on the torsion beam of the rear axle suspension is presented in paper [10].Also, in [11] the simulation and optimization of truck cab suspension system based on ADAMS is studied.In [12] the functional testing of both vehicle suspension components and characteristics, namely the actuators and the vehicle dynamics logic control, there are performed on an MTS 6DOF bench test.These tests are made prior to physical track testing on a prototype vehicle using Ferrari facility which exists in Maranello, Italy.An important component of the suspension structure is the stabiliser bar.This component must have high elasticity and resistance to fatigue, so from the design phase of such a component the aim is to optimise the design, reducing stress concentrators [13,14,15].Obviously for validation of the automotive component, tests performed on test stands are required [16,17].
The present paper is a continuation of the paper presented at the AITS 2021 conference [5].The paper is structured in 3 parts.After the "Introduction" the 3D modeling of the test stand is presented.In the third part a finite element analysis (FEM), of the tested rear axle is presented, corroborated with experimental analysis of deformations and stresses in the axle structure.

Design of a bench for fatigue test of the rear axle of a passenger car
Fatigue testing methodology is approached in two ways, modelling and simulation and testing on an experimental bench.The kinematic scheme of the rear axle fatigue test bench is shown in Fig. 1.The components of the stand are: 1-crank; 2-adjustable length rod; 3-rocker arm; 4-bushing; 5-assembled rear axle.According to the kinematic scheme, the virtual model is also made (Fig. 2), in order to simulate the kinematics and dynamics of the stand, as well as the finite element modeling of the rear axle.As results of the kinematic and dynamic modelling of the stand in ADAMS, we present the kinematic parameters of the stabilizing bar considered as a deformable solid, modelled as shown in Fig. 3.The model constructed by means the ADAMS program allows us the dynamic modal analysis for every kinematic element of the mobile mechanical system and also for the entire assembly when the kinematic elements are considered as deformable solids.In a first stage of the research, we have modelled the experimental fatigue test stand of the rear axle using the 3D modelling program Solid Works.The 3D model we have produced is useful for the optimization of the experimental stand but also for the simulation in ADAMS of the dynamic modal behaviour of the axle assembly.We performed the dynamic modal modelling in ADAMS of the test bench entire whole assembly, and presented the results obtained in simulation, namely displacements, velocities, and translational accelerations of the marker attached to the centre of mass of the axle stabilizer bar mounted on the test stand.

Dynamic finite element analysis of the rear axle
In this paragraph, we propose to determine the state of stresses and strains in the experimentally tested rear axle assembly mounted on the test bench.This is necessary for the following two reasons: we will determine where is the location of the critical areas with stress concentrators where the maximum equivalent stresses occur; the mechanical stresses and specific strains obtained by FEA simulation will be compared with the values obtained with the experimental method.
For the finite element analysis, we will use a licensed software, namely AnsysWorkbench.This FEA software has the possibility to perform several types of FEA analysis: static structural, transient structural or explicit dynamics.Since the rear axle assembly model is particularly complex, it has elements in its structure with non-linear behaviour (such as rubber flexiblocks, as shock absorbers) and the Ansys Explicit Dynamics module is suitable for use in this FEA simulation case.This module allows us to perform explicit dynamics analysis, it allows us to utilize from the database materials with nonlinear characteristics (steel with non-linear behaviour, rubber).
The results that are obtained for the mechanical stresses, we will compare with the results obtained experimentally.This comparison will be carried out considering the location of the specific strain and stress measurement points as shown in Figure 8.
For the central part of the axle beam, a stress-strain rosette consisting of three strain gages was used to measure the specific strains at -45, 0 and 45 degrees to the principal direction.This rosette was set with the middle grid at 90 from the axle longitudinal axis, as shown in Figure 8. Figure 9. Rear axle mounted on the test stand.The rear axle assembly model developed in Solid Works was transferred to the AnsysWorkbench software database.In order to check the correctness of the file import, it is opened and verified with the Ansys Design Modeler preprocessor.Here geometry corrections can be made, which prevent erroneous analysis results.For example, it is possible to make radii, to join several bodies in a kinematic link or structure component's, to divide the surfaces of parts into two or several surfaces.The last described utility is needed to define joints between bodies, to place loads.The constructed model of the rear axle contains 26 deformable bodies (parts).Some of the structure components bodies we have joined together by means of Boolean operations, to form a single element or part, namely: the U-shaped cross member, the arms made of the bent sheet metal.The end elements made of the bent sheet metal have been joined together to form the rear axle assembly element.As data to define the simulation model, we defined the kinematic torques corresponding to the rear axle mounting mode on the vehicle and on the test stand.We simulated the situation when a disturbing force acts on the right wheel axle.For this purpose, we 1, 2, 3 6, 7 4, 5 9 8 considered the maximum value of the force occurring on this axle, measured in the dynamic simulation studied in ADAMS.The value of the force is 15000 N and is acting on the rear wheel right axle.
With these considerations, the construction of the finite element analysis model is completed, and we can perform a run of the analysis.Since the model of the axle is particularly complex and large, because it contains a number of over 5 million elements, the simulation takes quite a long time, namely 1400 hours.We performed the simulation on a graphics workstation with 2 Intel OCTA Core Xeon E5-2650 v2 2.60 GHz processors, and 32GB DDR3 ECC memory, a 960GB SSD drive, and an nVidiaQuadro K2000 graphics card.After the analysis there are obtained results concerning strain and stress maps and we selected some important results that are shown in Figs.10-14.The X and Y axes are oriented as shown in Fig. 10 as follows: X-axis is the longitudinal axis of the deck and y-axis the transverse axis.These results, as graphical variations laws, are shown in Fig. 14.For the last three start cycles 3, 4 and 5, a stabilized area was selected for which the mean value, RMS (rms) value, maximum value and minimum value were calculated.For these values the mean value and standard deviation were calculated for the three records and are shown in Table 1.On the last line is calculated the peak-to-peak amplitude of the recorded parameters, force in the rod and mechanical stresses.
Table 1.Recorded values of connecting rod force and mechanical stresses.

F_Rod
Sigma-1 Sigma-2 Sigma-3 Sigma-4 Sigma-5 Sigma-6 Sigma-7 Sigma-8 Sigma-9 -The values for obtained experimentally stresses in the central portion, measured by strain gauge sensors in points 1, 2 and 3 reaches values of 50.65 MPa; These values are similar to those obtained by simulation in ANSYS; -Location of points 4, 5 and 6, 7 is symmetrically placed; The values obtained for the equivalent stresses in these points are different in the finite element analysis.This obtained result is correct, because the stress force is applied only on the right spindle, and points 4, 5 are placed nearby this spindle.Thus, in by FEA simulation in points 4, 5 are obtained stresses with 34 MPa value, and in location of points 6, 7 the equivalent stresses have values of 46 MPa.We also observe an area with values of 57 MPa for the stresses, shown in figure 13.So there is a correspondence between the results obtained by simulation and experimental analysis.

Conclusions
Fatigue testing methodology is approached in two ways.First, based on the virtual model a dynamic simulation model is built in ADAMS.Through this dynamic simulation we obtain results on the kinematic and dynamic parameters of the drive mechanism in the stand structure, but also data on the stresses of the rear axle elements (springs, rear axle and stabilizer bar).In order to study the distribution of mechanical stresses and specific deformations in the rear axle components we used finite element analysis in ANSYS.Finally, the simulations are validated by experimental analysis on the test stand.Strain gauge transducers have been mounted on the rear axle to measure the deformations.These are compared with those obtained by simulation.The results obtained by simulation and experiment are similar.The result of the research is that by experimental testing each component of the rear axle can be validated in terms of fatigue strength.Furthermore, through finite element analysis, areas with stress concentrators can be found which can be eliminated by design optimization.We performed dynamic finite element analysis for the tested rear axle assembly.This is important because we can compare the stresses obtained by finite element analysis with those determined experimentally.It should be noted that experimentally the stresses can be measured at a limited number of points, in our case nine points.

Figure 1 .
Figure 1.Kinematic scheme of the stand.Figure 2. CAD model of the stand in SW.

Figure 2 .
Figure 1.Kinematic scheme of the stand.Figure 2. CAD model of the stand in SW.

Figure 3 .
Figure 3. Rear axle and stabilizer bar modeled as deformable solids in ADAMS.

Figures 4
Figures 4 and 5 show the graphs obtained for the following parameters: displacements of the marker attached to the centre of mass of the stabiliser bar, the components along the X and Y axes (longitudinal and transversal axis).The plots shown are obtained with respect to the global reference system.

Figure 4 .
Figure 4. Obtained displacement of the marker from centre of mass of the stabiliser bar along the X-axis.

Figure 5 .
Figure 5. Obtained displacement of the marker from centre of mass of the stabiliser bar along the Y-axis.

Figures 6
Figures 6 and 7 show the plots as obtained in ADAMS for the deformations of the marker attached to the centre of mass of the stabilizer bar along the X and Y axes.The plots shown are computed in reference to the model assembly global reference system.

Figure 6 .Figure 7 .
Figure 6.Computed deformation of the centre of mass of the stabiliser bar along the X-axis Figure 7. Computed deformation of the centre of mass of the stabiliser bar along the Y-axis.The model constructed by means the ADAMS program allows us the dynamic modal analysis for every kinematic element of the mobile mechanical system and also for the entire assembly when the kinematic elements are considered as deformable solids.In a first stage of the research, we have modelled the experimental fatigue test stand of the rear axle using the 3D modelling program Solid Works.The 3D model we have produced is useful for the optimization of the experimental stand but also for the simulation in ADAMS of the dynamic modal behaviour of the axle assembly.We performed the dynamic modal modelling in ADAMS of the test bench entire whole assembly, and presented the results obtained in simulation, namely displacements, velocities, and translational accelerations of the marker attached to the centre of mass of the axle stabilizer bar mounted on the test stand.

Figure 8 .
Figure 8. Deformation recording points.Figure9.Rear axle mounted on the test stand.The rear axle assembly model developed in Solid Works was transferred to the AnsysWorkbench software database.In order to check the correctness of the file import, it is opened and verified with the Ansys Design Modeler preprocessor.Here geometry corrections can be made, which prevent erroneous analysis results.For example, it is possible to make radii, to join several bodies in a kinematic link or structure component's, to divide the surfaces of parts into two or several surfaces.The last described utility is needed to define joints between bodies, to place loads.The constructed model of the rear axle contains 26 deformable bodies (parts).Some of the structure components bodies we have joined together by means of Boolean operations, to form a single element or part, namely: the U-shaped cross member, the arms made of the bent sheet metal.The end elements made of the bent sheet metal have been joined together to form the rear axle assembly element.As data to define the simulation model, we defined the kinematic torques corresponding to the rear axle mounting mode on the vehicle and on the test stand.We simulated the situation when a disturbing force acts on the right wheel axle.For this purpose, we

Figure 10 .
Figure 10.Map with the distribution of von Mises equivalent stresses (Top view).

Figure 11 .
Figure 11.Map with the distribution of von Mises equivalent stresses (Side view).

Figure 12 .
Figure 12.Map with the distribution of von Mises equivalent stresses (Back view).

Figure 13 . 6 -
Figure 13.Map with the distribution of von Mises equivalent stresses (Front view).

Figure 14 .
Figure 14.Detail of middle cycle number 4, recording parameters: rod force and mechanical stresses.
The maximum stress in structure is 104 MPa, as shown in Figs.10-13;It occurs in the corner area of the joint of the bent side plate with the bent side arm.This area is the most stressed in this stress case; -Values of 46 MPa for the equivalent stresses occur on the central cross member middle, which decrease to values by 34 MPa in the area nearby to this central area;