Static and Dynamic Strength Analysis on Rear Axle of Small Payload Off-highway Dump Trucks

Transcription

1 Static and Dynamic Strength Analysis on Rear Axle of Small Payload Off-highway Dump Trucks Ji-xin Wang, Guo-qiang Wang, Shi-kui Luo, Dec-heng Zhou College of Mechanical Science and Engineering, Jilin University, Nanling Campus, No. 142 Renmin Street, Changchun , PR China Qiang Zhang, Jian-min Xue Inner Mongolia North Hauler Joint Stock Co. Lit. Abstract Aiming at early breakage of rear axle in small payload off-highway dump trucks, a 3D solid finite element model including nonlinear hydropneumatic suspension has been created by means of ANSYS software. Then static strength and dynamic characteristics of rear axle are analyzed in five typical load cases. According to the analytical results, the weak locations of rear axle are obtained and the modified design has been determined. Using ANSYS software can avoid expensive and time-consuming development loops, so the design period is shortened. Introduction Some off-highway dump truck is a kind of newly exploited economical small payload product to meet the extensive market demand of the digging in the various middle and small type mines and the transportation of raw material. Since the rear axle transfers kinds of loads from the ground and the truck body, it is the key part of the truck. But the semi-spindle sleeve of it often presents breakage phenomena, so the strength of the original rear axle has to be analyzed by the liner and nonlinear functions of ANSYS. According to the analytical results, a modified design, which is thickening the wall of the semi-spindle sleeve and enlarging fillet radius, is brought up, and the strength analysis is performed too. The analytical results attain the requirement of the design. Finite element model of rear axle Introduction of the structure An A-frame, a lateral link and 2 hydropneumatic springs connect the rear axle to the frame of truck. The main speed reducer receives input torque from an engine. Planetary reducers on the wheel drive the wheels. When braking, brake apparatuses connect wheels to the rear axle. Figure 1 shows the components of rear axle. The stiffness or rotation angle of the A-frame, lateral link, hydropneumatic spring and main reducer housing can affect on strength of rear axle. Therefore, all the above-mentioned components shall be taken into account. The rear axle itself is composed of two semi-spindle sleeves and one rear axle housing. They are joined up by welded connection and interference fit, as shown in Figure 2. The axle housing and semispindle sleeves are complex casting structures, which are formed by kinds of complicated surface.

2 Figure 1. Components of rear axle Figure 2. Structure of rear axle Simplification of rear axle structure By surface modeling technique of PRO/E, the complex casting curved surface and a 3D solid model of rear axle housing are established. The geometrical model is very complex. In order to reduce calculating scale, simplification measures of non-critical structures are as follows: neglecting some casting fillet radii, small holes, some bulges and some groove etc. in uninterested region, and meanwhile treating the strength of welded connection and bolt connection as the material strength of rear axle. An equivalent model is established to simulate the interference fit between semi-spindle sleeve and the axle housing with the contact nonlinear function of ANSYS. The average fitting pressure is 20Mpa, and the average stress is 80Mpa, so the connection strength is enough. Furthermore, this kind of prestress is only near the fitting interface. Therefore, two components joined each other by interference fit can be regarded as a continuous body too. A simplified geometry model of rear axle is imported into ANSYS, and then the ideal analytical model could be established by the powerful finite element modeling technique of ANSYS software.

3 Element choosing Axle housing and semi-spindle sleeve are so thick that they can t be simplified as shell element. Therefore, the 20-node SOLID95 and 10-node SOLID92 are chosen. Pins and hydropneumatic springs are simulated by BEAM4 and LINK8, respectively. The mesh in the critical positions shall be refined. Methods of controlling mesh size are as follows: Firstly, number of elements on lines and length of elements in areas are controlled. Secondly, areas and volumes are meshed by SHELL93 and SOLID95, respectively. Thirdly, the auxiliary element SHELL93 in areas is deleted. Lastly, when all of the volumes are meshed, the tetrahedral SOLID95 is converted into SOLID92. Figure 3 shows the finite element model of rear axle, which is made up of solid elements, 8 beam elements and 2 link elements. Figure 3. Finite element model of rear axle Boundary conditions and loads In the Supports of rear axle, suppose that the A-frame is rigid body and the Young s modulus of its material is times of rear axle s, it only transfers forces and torques. Ball-and-socket joint of A-frame is simulated by 3 displacement DOFs shown in Figure 4. At the same time the 3 displacement DOFs of hinges between the hydropneumatic suspension and the frame are constrained, as shown in Figure 4. Figure 4. Constraints

4 Loads applied to the rear axle in each load case are as follows: 1) The vertical reaction forces from the ground, distributing on the semicircle of bearings by the cosine regulation, in Figure 5a. 2) The forward or backward horizontal forces from the ground, distributing on the semicircle of bearings by the cosine regulation, in Figure 5b. 3) The tangential forces equalizing the torque of the wheels, distributing on the end of semi-spindle sleeve, in Figure 5c. 4) The nodal force equalizing the torsion around the axis of rear axle, acting on the head face of the main speed reducer housing, in Figure 5d. 5) The brake pressure from the brake apparatus, distributing on the holes of the brackets of break apparatus, in Figure 5e. 6) The lateral force from steering load case, acting evenly on the alignment face of bearings, in Figure 5f. Figure 5. Loads. (a) Vertical loads, (b) Horizontal loads, (c) Torques of wheels, (d) End face load, (e) Brake loads, (f) Lateral loads. When vertical forces and horizontal forces are in the same position, the resultant force can be automatically calculated by ANSYS.

5 Static strength Analysis of rear axle Load case analysis The breakage position of the original rear axle occurs at the bracket of brake apparatus. Because of complicated construction and the nonlinear characteristic of hydropneumatic suspensions in the model, computation is so time-consuming that the optimization technique cannot be adopted. Aiming at the abovementioned phenomena, two kinds of modified designs are put forward in Figure 6 and Figure 7. The first: enlarge the fillet radius in the breakage position from the original 1.0in to 1.5in, and thicken the wall by in at the same time. The second: enlarge the fillet radius from the original 1.0in to 3.0in, but keep original wall thickness all the same. Figure 6. Modified design 1 of rear axle Figure 7. Modified design 2 of rear axle

6 The important load cases of finite element analysis of rear axle are as follows: fully loaded static, dynamic, start-up, brake and sideslip. The constraints and loads direction in each load case are shown in Figure 8. The load values in each load case can be confirmed through the force analysis in different load case [1-2]. Figure 8. Constraints and loads directions. (a) Static and dynamic load case, (b) Start-up load case, (c) Brake load case, (d) Sideslip load case The material of rear axle is high strength alloy steel whose Young s modulus is 30E106 psi and density is lb/in3. Results Through synthetically analyzing the static strength in different load cases, it can be concluded that the maximum stress region mainly occurs at the sections near inboard bearing of the semi-spindle sleeve, the bracket of the brake apparatus, the interference fit between the semi-spindle sleeve and the rear axle housing. Table 1 presents the results of safety factor of static strength. Figure 9 shows the corresponding position of the maximum stress. Table 1. Safety factor of static strength Structure Original structure Modified design 1 Modified design 2 Fully loaded static Safety Factor Dynamic Start-up Brake Sideslip Figure 9(b) 2.99 Figure 9(b) 3.08 Figure 9(b) 1.28 Figure 9(c) 1.28 Figure 9(c) 1.28 Figure 9(c)

7 Figure 9. Corresponding positions of the maximum stress In the dynamic load case, the critical sections occur at the inboard fillet of the bracket of the brake apparatus, and in the brake load case occur at the outboard fillet of the bracket of the brake apparatus, hence enlarging the inboard fillet radium has no effect on the peak value of stress in the brake load case. The structure at the inboard bearing of three semi-spindle sleeves is uniform, so the critical regions are the same and values of stress are basically equal in the sideslip and side-cross load case. The safety factor of static strength in this location is 1.28 in the sideslip load case. The stress convergence degree in the inboard fillet of the bracket of the brake apparatus gradually decreases with the fillet radium increasing from 1.5in. The second design is chosen through measuring the factors such as strength, producing techniques and cost etc. The stress value of the critical sections of the modified design structure at most descends as 1.54 times as the originals, the safety factor meets the requirement of the strength. Modal analysis The eligibility of the static strength of rear axle cannot prove that it will never break. In reality, the rear axle is loaded with kinds of stimulations, which result in breakages such as resonance, fatigue etc. It is very significant to analyze dynamic characteristic for the chosen modified design of rear axle. Modal analysis of rear axle is performed by Block Lanczos method. Because of the small difference of mass and stiffness between the original and the modified structure, there is small deference of the natural frequency. The first 5 natural frequencies of the modified design 2 are showed in table 2. The first modal shape is the bending vibration in the horizontal plane and the second modal shape is the bending vibration in the vertical plane. Figure 10 and Figure 11 are the corresponding modal shapes. The dynamic characteristics are much better because the natural frequencies are all bigger than the excitation frequency range of 0.33 ~ 28.3Hz from the ground [2].

8 Table 2. Natural frequencies of modified design 2 Mode Frequency(Hz) Figure 10. Mode shape 1 of the modified design Figure 11. Mode shape 2 of the modified design Conclusions The static strength and dynamic characteristics are analyzed by ANSYS software. Analytical results can confirm the modified design and help to avoid expensive and time-consuming development loops and also allow the number of high-cost test carriers to be substantially reduced, so design periods is shortened. In the mean time it can be used to determine testing positions of the load spectrum and examine testing results. On the premise of the load spectrum, fatigue strength analysis and optimization design can be carried out to lighten the weight of rear axle finally. References 1) Chang-ji Yu, Xue-bing Yu, Modern Design Techniques of Heavy Vehicles Structure, Dalian University of Technology Press, (In China). 2) Wei-xin Liu, Vehicle Design Tsinghua University Press, (In China). 3) Guo-qiang Wang, Practical Numerical Simulation Technology of Engineering and Practice in ANSYS, Northwest University of Technology Press, (In China).