Nonlinear Finite Element Analysis and Test of Lateral Loading for Two-post ROPS

Jixin Wang1,a, Xun Yang1,b and Xiangjun Yu1,2,a

1College of Mechanical Science and Engineering, Jilin University, Changchun, Jilin Province, China 2Department of Automatic Control and Mechanical Engineering, Kunming College, Kunming, China

ajxwang@jlu.edu.cn, byangxun08@mails.jlu.edu.cn

Keywords: Engineering vehicle, ROPS, Lateral deformation mode, Nonlinear finite element

Abstract. According to the structural characteristic and the test requirement of tow-post ROPS, a nonlinear finite element model of ROPS based on large-strain shell element was established, and the influence of elastic-plastic deformation of ROPS was taken into consideration. Then the computer simulation of ROPS was performed in lateral loading case, which obtained the deformation mode and the distribution law of equivalent plastic stress of ROPS followed by the discussion of deformation mechanism of ROPS. The simulation results accorded with test results. This paper can provide theoretical basis for the structural design of two-post ROPS.

Introduction While wheel loader is rolling over, adding roll-over protective structures (called ROPS for short) to wheel loader is the most effective method in protecting the diver [1, 2, 3]. Presently, there are two types of ROPS: safety-cab ROPS and independent two-post ROPS [4]. There are many differences between two-post ROPS and safety-cab ROPS, such as the structural characteristic, the connection mode and the position of lateral load, which result in the different elastic-plastic and failure mode during test [5, 6], as shown in Fig.1. As the post or the beam of ROPS are made by the butt-welding of thick steel plates but not section steel, material yield will occur along the welding seams where the maximum bending moment and the stress concentration are generated. And the poor resistant ability in plastic stage and the embrittlement fractures of welding seams will develop significantly with the increasing of lateral loads, so the weld cracking of these parts results in the decrease of bearing capacity in the lateral loading case. Therefore, two-post ROPS of ZL60G was taken as an example, and the computer simulation method of the deformation mode and failure mechanism of ROPS was discussed in this paper, which was verified by the test. This paper can provide theoretical basis for the structural design of two-post ROPS.

Cracked Weld

(a) Safety-cab ROPS (b) Two-post ROPS Fig.1 Cracked weld in safety-cab ROPS and two-post ROPS

Establishment of Finite Element Model The finite element model of two-post ROPS of ZL60G loader is shown in Fig.2, which contains 260 beam elements and 14269 shell elements. The material of ROPS and frame are Q235A and Q345C respectively. The top cantilever components (to be called falling object protective structure, called

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FOPS for short) are welded by thick steel plates and support beams with groove sections. As the local plastic strain and stress of the joints can not be obtained by beam elements, the plastic-large-strain shell elements are adopted to establish the FE model of joints between the beams and posts of ROPS [5,6]. In order to simulate the elastic-plastic deformation of brackets, frame and FOPS components accurately, they are simulated by plastic-large-strain shell element as well. The beam elements are adopted to simulate the bolt connection between ROPS and brackets.

Fig.2 Finite element model

Boundary Conditions and Calculation Method Fig.3 shows the finite element model with constraint conditions and lateral loads. The simulation includes two parts: lateral bearing capacity test and lateral energy absorption test. According to the relative position of seat index point (short for SIP) and DLV as well as the length of top components, the acting position of lateral loads which point to Z-axis are determined at the joint between left post and top beam. The minimum lateral bearing force of ROPS is 129615N, and the minimum lateral energy absorption is 27884J by ISO3471 [4].

Fig.3 Boundary conditions

large plastic deformation will appear in the ROPS components when the wheel loader rolling over, therefore the isotropic bilinear elastic-plastic material model is adopted, and its constructive relation can be obtained using Von Mises yield criterion and corresponding flow rule and hardening rule as [5]

{ } { }epσ ε= D , (1) where is elastic plastic constitution matrix. epD

Post of ROPS Bottom plate of cab

Top beam of ROPS FOPS

DLV

Bracket of ROPS Frame

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The geometric relation which is described as incremental form in large deformation case can be written as

euε = B , (2) where is strain-displacement transformation matrix with large deformation and is

displacement increments of nodes. B eu

According to the virtual work principle, Eq.1 and Eq.2, the elastic-plastic equilibrium equation of ROPS with lateral loading is

t t tT u Qτ += −K Q , (3)

where is tangent stiffness matrix as the function of displacement vector in ROPS, is the incremental displacements of ROPS nodes, is the load applied on the ROPS and t is the internal node force.

Tτ K u

t tQ+ Q

Newton-Raphson method is adopted to solve Eq.3, and the convergence tolerance can be chosen from 0.001 to 0.1.

Results Performance Analysis. The lateral loading test and simulation of this two-post ROPS of ZL60G loader is performed in accordance with ISO3471. The results indicate that the lateral bearing capacity satisfies the requirement firstly, and then the lateral energy absorption satisfies the requirement. When the lateral capacity satisfies the requirement at 129615N, the lateral deformation is 119.5mm. When the energy absorption satisfies the requirement at 27884J with increasing lateral force, the lateral force and the lateral deformation are 137275N and 202mm respectively.

Deformation Mode. Fig.4a and Fig.4b show the simulated deformation of ROPS and the tested deformation of ROPS respectively. The results show that the plastic deformation of ROPS mainly occurs at the joints between brackets and frame firstly as well as the joints between post and top beam. The posts and the beams don’t invade the DLV at the end of loading indicating that the ROPS meets the requirement of deformation in ISO3471.

(a) Simulated deformation (b) Tested deformation

Fig.4 Deformation Comparison between the simulation and the test

Deformation of Brackets. Fig.5 shows the deformation of the brackets. As the brackets are the foundation of ROPS which are used to transfer loads, the top of ROPS will produce a large deflection while the bottom bracket deformation is small. When the top plastic deformation of ROPS reaches 202mm, the deformation of brackets of ROPS is only 69mm, so the amplification coefficient is 2.93. This result shows that the stiffness of the brackets and frame has a significant influence on the lateral bearing capacity and the energy absorption capacity.

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Fig.5 Deformation of the brackets

The welds at joints between brackets and frame gradually begin to crack with increasing of lateral

loads (as shown in Fig.6a), which made ROPS absorb more energy. So how to control the cracking rate of weld in the ROPS design is very important. At the end of test, the plastic deformation at these joints develops into plastic hinges, and deformation mechanism is shown in Fig.6b.

(a) Cracked weld at the joints between brackets and frame (b) Deformation mechanism of two-post ROPS

Weld cracks

Lateral force

BoltsBracket

FOPS

Plastic hingeFrame

Fig.6 Deformation mode and plastic hinges of two-post ROPS

Stress Analysis. When the lateral energy absorption reaches 27884J, the loading is stopped, and the Von Mises stress of ROPS is shown in Fig.7. The major plastic stress occurs at the joints between brackets and frame, and the maximum stress reaches 393MPa. The second largest stress mainly concentrates at the joints of posts and beams.

Comparative Analysis of Loading-unloading Curves. The simulated loading-unloading curve compared with the tested one is shown in Fig.8, and two curves match well. The area below the curve represents the energy absorption of ROPS during lateral loading case. The lateral load of simulation is 137252N when the energy absorption meets the requirement, and the lateral bearing capacity is matching with the lateral energy absorption well. The lateral bearing capacity is affected by the cracked welds in the test, so the tested load is smoother than the simulation value (137252N). Although the lateral displacement is quite large, the posts and the beam don’t invade the DLV, which indicate that the ROPS meets the requirement of deformation. However, the anti-impact and the anti-deformation capacity should be reappraised since ROPS and frame has produced permanent plastic deformation. The constraints applied on the simulated model are ideal rigid, hence there are some differences between the tested curve and the simulated one as shown in Fig.8. In addition, the material model and geometric simplification used in simulation can also cause the errors.

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Fig.7 Von Mises stress of two-post ROPS Fig.8 Comparison between the tested and the simulated curve

Test

Lateral displacement (mm)

Late

ral l

oadi

ng (k

N)

Simulation

Conclusions The mechanical characteristics of two-post ROPS are different from that of safety-cab ROPS. The computer stimulation of ROPS operated with the shell element obtains the deformation mode and analyses the deformation mechanism. Compared with the results of test, this progress makes the conclusion that the simulation method of ROPS based on large-strain shell element can forecast the lateral loading capacity of ROPS accurately, and the plastic hinges occurred at the joints between brackets and frame as well as the joints between posts and beams. The stiffness of brackets and frame as well as the weld quality affect the performance of ROPS significantly in the capacity of lateral bearing and energy absorption, which should be considered cautiously in the process of designing.

Acknowledgement The work described in this paper is supported by the National Natural Science Foundation of China (50775095) and also supported by the National High Technology Research and Development Program (2007AA04Z126). The authors would like to thank correlative members of the projects.

References [1] M. McCann: Journal of Safety Research, Vol. 37 (2006) No.5, pp.511-517.

[2] K. Jacek, R. Eugemiusz and S. Tadeusz: Automation in Construction, Vol. 17 (2008) No.3, pp.232-244.

[3] B.J. Clark, P.D. Thambiratnam and N.J. Perera: The Structure Engineer, Vol. 84 (2006) No.1, pp.29-34.

[4] ISO3471: Earth-moving Machinery Roll-over Protective Structures-Laboratory Tests and Performance Requirements (China, 2005).

[5] J.X. Wang: Design Method and Experimental Study on the Roll-over Protective Structures for Engineering Vehicles (Ph.D., Jilin University, China 2006).

[6] D.P. Thambiratnam, B.J. Clark and N.J. Perera: Computer-Aided Civil and Infrastructure Engineering, Vol. 23 (2008) No.6, pp.448-464.

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e-Engineering & Digital Enterprise Technology VII 10.4028/www.scientific.net/AMM.16-19 Nonlinear Finite Element Analysis and Test of Lateral Loading for Two-Post ROPS 10.4028/www.scientific.net/AMM.16-19.866

DOI References

[6] D.P. Thambiratnam, B.J. Clark and N.J. Perera: Computer-Aided Civil and Infrastructure Engineering,

Vol. 23 (2008) No.6, pp.448-464.

doi:10.1111/j.1467-8667.2008.00551.x [1] M. McCann: Journal of Safety Research, Vol. 37 (2006) No.5, pp.511-517.

doi:10.1016/j.jsr.2006.08.005 [6] D.P. Thambiratnam, B.J. Clark and N.J. Perera: Computer-Aided Civil and Infrastructure ngineering, Vol.

23 (2008) No.6, pp.448-464.

doi:10.1111/j.1467-8667.2008.00551.x