Engineering Failure Analysis 23 (2012) 18–26

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Engineering Failure Analysis

journal homepage: www.elsevier .com/locate /engfai lanal

Frame fatigue life assessment of a mining dump truck based on finiteelement method and multibody dynamic analysis

Chengji Mi a,⇑, Zhengqi Gu a, Qingquan Yang a, Duzhong Nie b

a State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Chinab School of Mechatronic Engineering, Xi’an Technological University, China

a r t i c l e i n f o

Article history:Received 29 September 2011Accepted 31 January 2012Available online 10 February 2012

Keywords:Fatigue lifeFrameMining dump truckMultibody dynamic analysisFinite element method

1350-6307/$ - see front matter Crown Copyright �doi:10.1016/j.engfailanal.2012.01.014

⇑ Corresponding author.E-mail address: mcj20112011@hnu.edu.cn (C. M

a b s t r a c t

Aiming at precisely predicting fatigue life for frame of the 220t mining dump truck, a fati-gue life analysis method is presented, integrating multibody dynamic analysis and finiteelement method. The force of main joints at frame are measured from the multibodydynamic model, whose road is restructured based on ISO/TC108/SC2N67. According toGB/T27025-2008, the dynamic stress test of the whole truck is implemented to obtainthe peak stress of the mainly forced area, which is compared with the simulated stress.It is found out that the error is allowable so that the accuracy of the finite element modelis definitely ensured. The quasi-static stress analysis method is employed to acquire stressinfluence coefficient under unit load, which is associated with load histories of the frame toget the dangerous stress area. The fatigue life of the frame is calculated on the basis ofPalmgren–Miner damage theory. It is turned out that the minimum life area of the frameis located at the frame joints of suspension, which matches the practice.

Crown Copyright � 2012 Published by Elsevier Ltd. All rights reserved.

1. Introduction

The mining dump truck runs all the year round in the terrible mine road, which is prone to need higher performancesthan the general highway vehicle, such as stiffness, strength, and fatigue life. As the main part of the mining dump truck,the fatigue life for frame is focused on, especially when it is fully loaded. Actually, dynamic forces caused by the road surfaceroughness are the foremost factor to lead to fatigue failure of the frame during the mining dump truck services. However, ingeneral, the stress level of the frame does not exceed the fatigue strength of the material except the local stressconcentrations.

Research on structure fatigue life of mining dump truck is extremely rare by tests because of its hugeness in size andweight. Its special characteristics may lead to obtain fatigue life of the frame based on bench tests impossibly. However,it is difficult to predict exactly the fatigue life of the frame by means of pure computer simulation owing to the differencesbetween real situations and simplified conditions. To increase the accuracy of the predicted fatigue life of the frame, a fatiguelife analysis method is presented, which is based on dynamic stress measurement from the practical road surface and com-bined with multibody dynamic analysis and finite element analysis.

Some papers analyzing and predicting fatigue life of vehicles’ components based on simulations and tests have been pub-lished. Shao et al. proposed a new analysis method based on dynamic strain measurement from practical mine road surfaceconditions combined with finite element analysis, which is applied to drive axle housing failure analysis of a mining dumptruck [1]. Topac et al. presented some design enhancement solutions to improve fatigue life of a drive axle housing using

2012 Published by Elsevier Ltd. All rights reserved.

i).

C. Mi et al. / Engineering Failure Analysis 23 (2012) 18–26 19

finite element and bench tests [2].Combining with multibody dynamic analysis and finite element analysis, Lee et al. suc-cessfully estimated the fatigue life of the wheels by comparison of the results from test [3]. It is not hard to see that the fa-tigue life analysis combined with finite element method, multibody dynamic analysis and tests has become a tendency.

First of all, this paper establishes the multibody dynamic model of the mining dump truck, whose road is restructuredbased on ISO/TC108/SC2N67. Then, the finite element model of the frame is built to analyze the static stress in terms ofthe simulated force. The comparison between the simulated maximum stress and the tested peak stress implies that the er-ror is acceptable and the finite element model is reliable. Finally, the fatigue life of the frame is calculated on the basis of thequasi-static stress analysis method and Palmgren–Miner damage theory.

2. Multibody dynamic analysis of 220t mining dump truck

2.1. Reconstruction road surface

On the basis of ISO/TC108/SC2N67 document, road roughness is considered as vehicle vibration input utilizes power spec-trum density of road surface to describe its statistic characteristics, which can be expressed as follows:

GqðnÞ ¼ Gqðn0Þnn0

� ��W

ð1Þ

where n is spatial frequency, n0 = 0.1/m, W is frequency index.The rational function is used to express the PSD of the road surface, and the expression of the PSD on the road with ra-

tional function is as follows:

UðXÞ ¼ 2aqpða2 þ n2Þ ð2Þ

where a and q are constants.The time-domain mathematical model of road roughness can be deduced a expression from Eq. (2) [4]:

_qðtÞ ¼ �0:111 v � qðtÞ þ 40ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiGqðn0Þv

q�w0ðtÞ

h ið3Þ

where v is vehicle speed, w0(t) is unit white noise.In order to simulate the real road surface, standard D-class road is regarded as the road spectrum for dynamic analysis of

mining dump truck. According to the Eq. (3), the time-domain mathematical model is built in Matlab/Simulink.After solution, the simulated two-dimensional road roughness is shown in Fig. 1. In addition, the restructured road spec-

trum PSD is compared with the standard road spectrum as shown in Fig. 2, which indicates that two curves are similar. Thedata of two-dimensional road roughness can be exported as the road document format in Msc.ADAMS. Then the data can bestretched to be the 3D road model needed in the dynamic analysis.

Fig. 1. 2D Road roughness of D-class.

Fig. 2. Comparison of PSD between standard road spectrum and restructured road spectrum.

20 C. Mi et al. / Engineering Failure Analysis 23 (2012) 18–26

2.2. Nonlinear stiffness and damping characteristics of hydro-pneumatic suspension

In order to effectively weaken the impact of road roughness, the hydro-pneumatic suspension system with non-linearstiffness and damping characteristics is used to reduce vibration. The least square method is utilized to fit the curve ofnon-linear stiffness and damping characteristics, which can be expressed as follows:

Fk ¼ ki0 þ ki1Dzþ ki2Dz2 þ ki3Dz3 ð4ÞFc ¼ c1D _zþ c2D _z2 þ c3D _z3 ð5Þ

where Dz;D _z is displacement and speed of suspension, Fk is stiffness force and Fc is damping force. The curves of stiffnessforce and damping force can be obtained from Matlab as shown in Figs. 3 and 4 and be imported into the dynamic analysismodel.

2.3. Multibody dynamic analysis

The components of mining dump truck can be defined as parts in Adams and connected with motion pairs. If the cou-ple of parts do not have a motion pair, the relationship between them can be replaced with contact. In addition, the goods

Fig. 3. Rear suspension stiffness force.

Fig. 4. Suspension damping force.

C. Mi et al. / Engineering Failure Analysis 23 (2012) 18–26 21

heap of mining dump truck can be defined according to the SAE standard heap [5]. After finishing the dynamic analysismodel as shown in Fig. 5, the initial parameters can be set up like this: the speed of mining dump truck is 30 km/h and thesimulated time is 30 s. Then, the forced curve of rear suspension is shown in Fig. 6, which will be the load spectrum offatigue analysis.

3. Validation of the finite element analysis model of frame

3.1. Static stress analysis

The frame consists of different thick sheets which are welded to form the framework. This geometry model is built withSolidWorks and is imported into Hypermesh to build the finite element model with shell elements. In addition, the springelements are used to simulate the suspension property and the lower node is restricted. At the same time, the weight of theassemblies can be replaced with mass elements. The peak force from the dynamic analysis is considered as the load of thestatic stress analysis. Finally, the finite analysis model is shown in Fig. 7 with nodes and elements. The frame material ishigh-strength low-alloy quenched and tempered steel named SUMITEN 610F, whose parameters are shown in Table 1. Aftersolution, the von Mises stress contour is shown in Fig. 8.

According to the results, the high stress areas are located at the frame positions of P1 and P2 marked in Fig. 8, which bothis around 200 MPa. The high stress of the frame area of P1 mainly is caused by the impact of road roughness, while the abun-dant goods are dedicated to the high stress of P2.

Fig. 5. Multibody dynamic analysis model.

Fig. 6. Force curves of rear suspension.

Fig. 7. Finite element model of frame.

Table 1Physical properties of SUMITEN 610F.

Material Density Elastic modulus Poisson’s ratio Yield strength Ultimate strength

SUMITEN 610F 7800 kg/m3 209 GPa 0.276 480 MPa 600 MPa

22 C. Mi et al. / Engineering Failure Analysis 23 (2012) 18–26

3.2. Dynamic stress test

The 46 measuring points with 138 response channels consist of sensors and temperature compensators, which access toMOPS strength testing system. The whole sensors are set up in no-load state. The strain sensitivity coefficient in this test is2.12. The strain signals are amplified, filtered, transferred to digitals, and then imported to computer analysis system, whichis a German signal acquisition and analysis software. Before testing, the whole system is checked according to GB/T27025-2008 [6]. The 450 strain sensors are glued on the frame surface. The stress can be calculated with the following formula:

ri ¼E

1ð1� lÞ ðea þ ecÞ �Effiffiffi

2pð1þ lÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðea � ebÞ2 þ ðeb � ecÞ2

q

smax ¼ffiffiffi2p

E2ð1þ lÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðea � ebÞ2 þ ðeb � ecÞ2

q ð6Þ

where, Young modulus E is 2.07 � 105 MPa, Poisson ratio l is 0.27. The schematic diagram of strain sensors placement isshown in Fig. 9. The practical road surface is shown in Fig. 10 and the data acquisition system is shown in Fig. 11.

Fig. 8. Stress contour of static strength analysis.

Fig. 9. Schematic diagram of measuring points.

C. Mi et al. / Engineering Failure Analysis 23 (2012) 18–26 23

3.3. Comparison

In order to ensure the validity of the finite element analysis of a frame, the simulated von Mises stress is compared withthe tested peak stress, which is shown in Table 2. According to the comparison, the extremely close maximum stress be-tween them indicates that the finite element model of a frame is reliable, while most of the errors all are under 10%.

4. Frame fatigue life analysis

4.1. Fatigue life analysis method

Using transient analysis to obtain stress and strain time history about every node is a waste of time, because the framefinite element model has a number of elements. In addition, the first-order natural frequency of the frame is extremely larger

Fig. 10. Practical mine road surface route.

Fig. 11. Data acquisition system.

Table 2Comparison between simulated stress and tested peak stress (MPa).

J1–1 J1–2 J2–1 J2–2 J3–1 J3–2 J4–1 J4–2 J6–1 J6–2

Simulated stress 87.2 90.3 30.7 31.1 53.2 66.7 105.2 109.9 33.1 36.7Tested stress 83.9 87.9 27.4 28.2 49.7 64.5 101.7 106.2 31.8 34.4Error 3.9% 2.7% 12% 10% 7% 10% 3.4% 3.5% 4.1% 6.7%

J7 J8–1 J8–2 J9–1 J9–2 J81 J91 J10 W3 W4

Simulated stress 15.2 73.7 60.3 55.7 52.3 63.4 60.3 68.3 199.3 198.2Tested stress 13.9 66.1 54.8 52.3 48.2 59.9 54.9 61.4 195.3 189.7Error 9.4% 11.5% 10% 6.5% 8.5% 5.8% 9.8% 11.2% 2.1% 4.5%

24 C. Mi et al. / Engineering Failure Analysis 23 (2012) 18–26

than excitation frequency [7]. Consequently, the quasi-static stress analysis method used for analyzing frame fatigue life caneffectively simplify the simulation.

The dynamic load time history of mainly forced locations can be got from multibody dynamic analysis. Firstly, unit loadtakes the place of the practical force, which is applied to the corresponding node with the same orientation and placement.After solving the static condition, structure stress influence factor corresponded to component load of endangered nodes canbe got from the simulation. The dynamic stress time history can be obtained from the superposition of the dynamic load timehistory and structure stress influence factor. The dynamic stress time history of endangered placement can be estimated byEq. (7):

rxyðtÞ ¼Xm

i¼1

PiðtÞ �rixyst

Pistð7Þ

Fig. 12. Fatigue life contour of frame.

Table 3Simulated lives of four positions.

Position Life (number of cycles)

P1 1.03e6P2 1.78e6P3 3.23e6P4 3.58e6

C. Mi et al. / Engineering Failure Analysis 23 (2012) 18–26 25

where rxy(t) is stress time history about every node, Pi(t) is a dynamic load time history of i, Pist is the peak load of i, rixyst isstress of the single i load, m is whole load numbers.

When the dynamic stress of frame have obtained from simulation, it is possible to predict frame fatigue life combinedwith nominal stress method and Palmgren Miner rule. If there are k stress levels, suffering each mi cycles, the whole damageD can be defined as follows:

D ¼Xk

1

Di ¼Xk

1

mi=Ni ð8Þ

According the foregoing discussion and S–N curve theory, the fatigue life can be calculated as follow:

S ¼ 10CNb ð9Þ

where the exponents, C and b, is material parameters.

4.2. Fatigue life analysis of frame under load spectrum

According to the theory mentioned above, the stress influence coefficient can be got from stress analysis under unit load.What’s more, the load spectrum can depend on the force obtained from multibody dynamic analysis and the material char-acteristics of the frame are based on the parameters in Table 1. Finally, the stress influence coefficient is associated with loadhistories of the frame to get the dangerous stress area. Then, the fatigue life of the frame can be calculated, which is shown inFig. 12. It can be clearly seen in the figure that the lower fatigue life areas mainly are situated at positions of frame, P1, P2, P3and P4, which are marked in Fig. 12. The lowest fatigue life of the frame at the node 229856 is 1.03e6 cycles, which is locatedat frame’s suspension joint of left-rear suspension (P1). From the results, the four positions of fatigue life are low so thatsome enhancements should be presented to improve the fatigue life of the frame, while they still meet the demand of engi-neering. The minimum life of four positions at frame is shown in Table 3.

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5. Conclusions

It is not hard to see that combining multibody dynamic analysis, finite element analysis and tests can effectively solve thefatigue life analysis of frame. Actually, it is necessary to get some data based on practical mine road surface so that there issome evidence to ensure the accuracy of results. From the fatigue life analysis process of frame, the following conclusionscan be drawn:

(1) The multibody dynamic analysis provides effective load conditions for static stress analysis and fatigue life analysis offrame.

(2) According to the comparison of simulated stress and tested stress, the validity of finite element model is completelyensured.

(3) Based on the quasi-static stress analysis method and Palmgren–Miner damage accumulation theory, the fatigue life ofthe whole frame is obtained and the positions of P1, P2, P3 and P4 are mainly low fatigue life areas.

(4) The lowest fatigue life of frame at the node 229856 is 1.03e6 cycles, which is located at the frame’s suspension joint ofleft-rear suspension and can match the practice.

References

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[2] Topac MM, Günal H, Kuralay NS. Fatigue failure prediction of a rear axle housing prototype by using finite element analysis. Eng Fail Anal2009;16(2009):1474–82.

[3] Lee Soo-Ho, Park Tae-Won, Park Joong-Kyung, et al. A fatigue life analysis of wheels on guide-way vehicle using multibody dynamic. Int J Prec EngManuf 2009;10(5):79–84.

[4] Zhicheng Wu, Sizhong Cheng, Lin Yang, Bin Zhang. Model of road roughness in time domain based on rational function. Trans Beijing Inst Technol2009;29(9):795–8.

[5] SAE Standard. Adapting the off-highway truck body volumetric process to real world conditions. SAE 2000-01-1652.[6] Chinese Standard. Adjustment and testing laboratory capacity general requirements. GB/T27025 2008:1–27.[7] Chunxi Tang, tuo Nie, Meilong Li. The model analysis of motorized wheel dump truck based on ANSYS. Mod Manuf Eng 2009;1(2009):121–4.