0 4th International Conference on Comuter Modeling and Simulation (ICCMS 0) IPCSIT vol. (0) (0) IACSIT Press, Singaore Deformation Effect Simulation and Otimization for Double Front Axle Steering Mechanism Jungang Wu, Siqin Zhang,Qinglong Yang China Automotive Engineering Research Institute Co.,Ltd Anhui Hualing automobile Co.,Ltd Abstract. This aer research on tire wear roblem of heavy vehicles with Double Front Axle Steering Mechanism from the flexible effect of Steering Mechanism, and rooses a structural otimization method which use both traditional static structural theory and dynamic structure theory Equivalent Static Load (ESL) method to otimize key arts. The good simulated and test results show this method has high engineering ractice and reference value for tire wear roblem of Double Front Axle Steering Mechanism design. Keywords; Double front axle steering mechanism, Deformation effect, Simulation, ESL. Introduction According to the limit of domestic road conditions and traffic regulations, the double front axle steering system is used in heavy vehicles to increase carrying caacity and imrove handling stability. But this steering system often gives rise to vehicle tire wear roblem [] [] []. Furthermore, the load of double front axle steering mechanism has more than ten thousands ewton under normal working conditions, and the heavy truck is usually drive with large deadweight and oor road conditions. For this reason, a large flexible deformation aears in double front axle steering mechanism in the rocess of steering which is an imortant factor for tires wear roblem. But few literatures analyzed flexible deformation on influence of wheels steering angle error comletely, let alone comlete structure otimization method. For the above roblems, this aer takes double front axle steering mechanism of Hualing truck as research object to carry out flexible deformation analysis and otimization. A new structure dynamic otimization algorithm Equivalent Static Load (ESL) method is alied to otimize steering systems structure. It made a beneficial exloration for ESL dynamic otimization algorithm using in double front axle steering system otimization design.. Flexible effect Simulation An 8 x 4 heavy truck with double front axle steering mechanism multi-body dynamics model is show as Fig.. In order to study the effect of steering mechanism deformation for wheels steering angle error, we established rigid multi-body dynamics model and flexible multi-body dynamics model for the double front axle steering mechanism, and comared the simulation results [4]. In flexible multi-body model, the key arts of steering mechanism are treated as flexible body (As shown in Tab.), so flexible deformation must be considered. However the flexible deformation in rigid body multi-body model is ignored. 7
.Steering wheel.first axle swing arm. First axle steer rod 4.Steer tire 5.First axle steering knuckle 6. First axle steering traezium 7.Steer drag rod 8. Middle swing arm bearing 9. Middle swing arm 0.Power steering cylinder. Second axle steer rod.second axle steering traezium Fig. Double front axle steering mechanism Steering mechanism would bear much more resistance than other conditions when vehicle is steering. The main resistance for steering mechanism is friction resistance between road and wheels whose maximum is observed at the condition of zero-radius turning (ZRT) with fully loaded. This resistance is difficult to calculate accurately, so engineers usually use semi-emirical equation () to calculate aroximately [5]. μ F M r = () Where μ is road friction factor, F is axle load, P is the tire ressure. Steer angle error (Degree) 6 5 4 0 First axle left tire First axle right tire Second axle left tire 4 Second axle right tire 7 5 6 0 0 0 0 40 50 60 First axle swing arm rotating angle (Degree) Fig. Steer angle error vs. swing arm rotation angle Simulation results of tire steer angle error for rigid multi-body model and flexible multi-body model in condition of zero-radius turning (ZRT) with fully loaded is showed in Fig.. The result shows that the flexible deformation of double front axle mechanism makes a tire steer angle error maximum at 5.4 degrees between the first axle and the second axle, which is 5% higher than target value 4.0 degrees. This error will aggravate tire wear and lower vehicle steering erformance and traffic safety. Considering conditions of overload and the worse road, the influence of error will be larger. The steering roblem of Hualing heavy truck those had been sold also confirms this conclusion. In order to further research contribution degree of various comonents flexible deformation on the overall flexible deformation, Tab. lists the maximum deformation of various arts of vehicle steering mechanism and deformation rate. It is obvious that Parts ID, 7, make the main contribution to flexible deformation. Therefore, these arts need to be otimized in order to reduce the effect of flexible deformation and make them lightweight. Tab. Flexbody deformation results of double front axle steer systems Parts ID Parts name Max Deformation(mm) Percentage First axle swing arm 0.9.7% First axle steer rod 6.9 8.% 6 First axle Steering traezium. 4.9% 7 Steer drag rod 8..5% 8 Middle swing arm bearing 0. 0.5% 8 9 0 8
9 Middle swing arm 0.9.7% Second axle steer rod 4.9 0.0% Second axle steering traezium. 5.4%. Results of structural otimization The structure otimization algorithms are mainly toology otimization, shae otimization, size otimization and shae otimization. There are lenty of references about these otimization algorithms, and the first three otimization methods are alied to the structure otimization of double front axle steering mechanism. All the forces in the real world act dynamically on structures. Since dynamic loads are extremely difficult to handle in analysis and design, static loads are usually utilized with dynamic factors. Generally, the dynamic factors are determined from design codes or exerience. Therefore, static loads may not give accurate solutions in analysis and design and structural engineers often come u with unreliable solutions. An analytical method based on modal analysis is roosed for the transformation of dynamic loads into Equivalent Static Loads (ESLs). The ESLs are calculated to generate an identical dislacement field with that from dynamic loads at a certain time [6] [7]... ESL otimization method Using the vibration theory with the finite element method (FEM), the dynamic behavior of a structure is exressed by the following differential equations:.. M ( b) + K( b) = f ( = { 0 0 f } T i f i + l 0 0 () Where M is the mass matrix, K is the stiffness matrix, f is the vector of external dynamic loads, d is the vector of dynamic dislacements, and l is the number of nonzero comonents of the dynamic load vector. The static analysis with FEM formulation is exressed as: K ( b) x = s () Where x is the static dislacement vector and s is the external static loads vector. An ESL set, which generates the same dislacement field as that of the dynamic loads at an arbitrary time t a is defined as: s = K t a ) (4) Therefore, according to equation () () (4), the relation between dynamic load and static load at an arbitrary time is exressed as:.. s = f ( M ( b) (5) Equation (5) shows that the object in the function of an equivalent static load can roduce the same dislacement field as in the function of a dynamic load. According to the finite element theory, stress is getting through the node dislacement calculation, so the same dislacement field will lead to the same stress field. If x = d ( ta )( =,,, ), then the two fields from the dynamic and the static load sets are identical. Therefore, the following equations are obtained: d (t ) = x = u u s (P,, ) a = k jk j k w (6) = k Where w k is the k order natural frequency, Equation (6) is a system of linear simultaneous equations which have variables of s, and needs a modal analysis and a lot of calculations. Since equations (4) and (6) can be extremely large, the external static force vector s is aroximated for engineering alications as follows: [ 0 0 ] T s = 0 (7) 0 s i s i + l The non-zero comonents s can be made arbitrarily. In engineering sense, the nonzero comonents can be imosed on the imortant laces where the dynamic loads act. Equation (6) is transformed into equations as follows: 9
d ( t a i + l ) = x = u k w = k i k u jk s j ( P =,, l ) i + l d (ta ) x = u ku j (P = l +,, ) k w (9) k = Equation (8) is a system of linear simultaneous equations with l` variables for s j. Therefore, vector s is determined from Equation (8). As l` becomes larger, the number of aroximated dislacements is reduced. If a static load set is calculated by solving equation (8) directly to make the same dislacement field as that from the dynamic load set, it can be awkward in the engineering sense. That is, the magnitude of the loads can be extremely large in order to satisfy all the conditions at many nodes. Therefore, the equations are modified to inequality equations as follows: n i + l d = ( ta ) x u ku ( P =,, h) when d j is ositive (0) k= wk n i + l d = ( ta ) x u ku j ( P =,, h) when d is negative () k= wk The rocess of transformation of dynamic load to Equivalent Static Load is shows in Fig.. Dynamic load (8) Interval time t 0 t t Dislacement d 0 d d Transient analysis t n d n Time s = n Kd ( t a ) ESL s s 0 s s s n Fig. Transformation of dynamic load to ESL The mathematical model of ESL otimization rocess is exressed by the following exression: Minimize F(b)= sum((f(a)- F(a`)) ) () Subject to K(b)x=s i (b) (i=,,m) () φ(b,x) j 0 (j=,,n) (4) Where F(b) is target function, F(a)and F(a`) are steer angle simulation and target value function resectively, b is design variable vector, K is stiffness matrix, m is interval time, n is constraints number, s i (b) is the number of i equivalent static load vector, φ(b,x) j is constraint function... Results of structural otimization Items Max Deformation (mm) Max Stress (MPa) Weight (kg) Tab. The comarison results of before and after otimization Part ame Middle First Second Steer Steer swing arm axle axle steer drag rod drag rod bearing steer rod rod -ESL Before 0. 6.9 4.9 8. 8. After 0..4... Change 8.% 5% 57% 7% 6% Before 40 568 54 764 764 After 56 40 0 64 8 Change 5% 8% 40% 5% 50% Before 8.8 5. 6.5 7.6 7.6 After 7.47 7.76 8.5.9 9. Change % 5% 5% 56% 9% The comarison result of before otimization and after otimization of various steer comonents is shown in Tab.. Since the original design of double front axle steer mechanism aears large flexible 0
deformation, even occurs lastic deformation roblem. Therefore, some comonents would be imroved the stiffness erformance and increased weight at the same time, such as First axle steer rod. Some comonents had achieved better stress erformance and lighter weight, such as Middle swing arm bearing. If the otimization method is alied to early roduct develoment stage, the results will be more obvious. The ESL method is alied to otimize Steer drag rod, and discrete ste is 00 which meets the accuracy requirements of ESL... Test verification Tab. is the mean and variance value of steer angle test results of before and after otimization comarison with the theoretical values. The results show: )The otimization design can reduce front and rear tire steer angle error. ) The ESL method gives more accurate solutions than static structural otimization. That means the ESL otimization design meets the design target and achieves the more light weight. 4. Conclusion Tab. Test results of before and after otimization Test results First axle right tire steer angle Second axle right tire steer angle Items Before After Target Before After Target Mean value ( O ).48.06.0..4. Variance value ( O ).6.87 -.8.6 - In allusion to the tire wear roblem caused by large deformation of double front axle steering mechanism of hualing heavy truck, this aer creates the flexible multi-body dynamics simulation model of steering mechanism, analyse the flexible deformation influence on wheels steer angle error comletely and systematically, uts forward a otimization method which contains static and dynamic otimization theory, and obtains a good result.this otimization design method for double front axle steering mechanism rovides an overall structural solution, and has good value of engineering alication for tire wear roblem of double front axle steering mechanism. 5. References [] Gerald Miller; Robert Reed; Fred Wheeler. Otimum Ackerman for Imroved Steering Axle Tire Wear on Trucks. SAE aer 969, 99: 57-578 [] He Yusheng, Xiong Tingchao. Design and Analysis of Multi-axle Steering System of Heavy Duty Vehicle. SAE aer 999,99: 60-66 [] Yufeng Gu; Zongde Fang; Yunbo Shen. Otimization Design of Double Front Axle Steering Swing Arm Mechanism in Heavy-duty Trucks. China Mechanical Engineering, 009(8). [4] Mohamed Kamel Sallaani. Hearvy tractor-trailer vehicle dynamics modeling for the ational Advanced Driving Simulator. SAE 00() [5] Wangyu Wang. Vehicle Design. Beijing: China Machine Press, 004. (In Chinese) [6] W.S.Choi; G.J.Park. Transformation of dynamic loads into equivalent static loads based on stress aroach. KSME(A),999, : 64~78 [7] W.S.Choi; G.J.Park. Transformation of dynamic loads into equivalent static loads based on modal analysis. International Journal for umerical Methods in Engineering, 999, 46: 9~4.