Si-zhuang XIE, Fu-qiang HE, Qi-ming GUAN, Fu-gui ZHANG,2

(1College of Mechanical Engineering, Guizhou University, Guiyang 550025, China) (2Guizhou Mountain Intelligent Agricultural Technology Co., Ltd.， Guiyang 550025, China)

Abstract: There is redundancy in the design of suspension mechanism of electric farm vehicle. In order to optimize the suspension arm mechanism, a rigid-flexible coupling model of suspension mechanism is established. Through multi-body dynamics simulation, the maximum force of each hinge point of the suspension arm mechanism in the coordinate axis direction is determined. Through the single variable static simulation test, the single variable numerical fitting model between the maximum equivalent stress and the four structural parameters of the upper arm mechanism has been established. Through the orthogonal simulation test, the multivariable numerical fitting model between the maximum equivalent stress and the four structural parameters is established, and the simulation value and the calculated value of the numerical model are compared to verify the reliability of the model. Using the same method, a multi-variable numerical fitting model between the mass of the suspension arm and the four structural parameters is conducted. Finally, the optimal design parameters are obtained by genetic algorithm with the objective of minimizing the maximum equivalent stress and mass. The optimization results show that the optimized upper arm mechanism has relatively lower mass and greater strength, and its structure is more reasonable. This method could provide reference for other design.

Key words: Electric farm vehicle, Structural optimization, Dynamic simulation, Static simulation,Numerical fitting, Genetic algorithm

Electric farm vehicle is a modern environmental protection vehicle for cargo transportation. It has the advantages of small size, strong power, simple operation and convenient maintenance. It is a kind of transportation vehicle suitable for various occasions. As shown in Fig.1, an electric farm truck has a loading capacity of 0.5 tons, a hopper width of 1.2 meters, a hopper length of 1.4 meters and a total length of 2.7 meters. It is mainly used for the transportation of fruit seedlings, fertilizers, feedstuffs, fruits and flowers in orchards, aquaculture farms and flower greenhouses. When spraying equipment is installed, spraying operation can also be realized. In order to improve the maneuverability and ride comfort of the vehicle, independent suspension is used in the front wheel. It is found that there is redundancy in suspension design and material waste in large-scale production. The upper arm mechanism is particularly obvious, so it is necessary to optimize the upper arm mechanism of the front wheel suspension of the electric farm vehicle. At present, designers at home and abroad have a variety of structural optimization methods.

Fig.1 Electric farm vehicle sketch

Zhao Dianming [1] established a three-dimensional model of rotary tillage device of cultivated land machine. Stress and displacement of rotary tillage blade were analyzed by ANSYS. By optimizing blade structure, the flat effect of cultivated land machine was improved by 4%；Liu Yinding[2] established a multi-body dynamic model of sugarcane stalk-root-soil-cutter system, simulated and analyzed the effect of the cutter, and verified the reliability of the simulation by experiments；Wang Hongzhen[3] used ANSYS to carry out modal analysis and static analysis of the lifting mechanism of agricultural milling machine. By optimizing the parameters of the mechanism, it has better dynamic and static performance；Liu Dong[4] optimized the frequency of the motor of the cutting table by analyzing the vibration mode of the cutting table part of the chicken and cabbage harvester, and reduced the loss of the harvesting caused by the resonance of the cutting table；Yang Wang[5] used CREO and HyperMesh to establish a large eddy simulation turbulence model, and simulated and analyzed the two-way fluid-solid interaction between wind and sugarcane. This dynamic method provides an important reference for similar research；On the premise of guaranteeing the structural strength of dump truck container, Ma Zhiguo[6] optimized the structure of truck by changing the number and size of reinforcing bars. After optimization, the quality of truck decreased, but the strength and life increased；Through finite element simulation analysis, Jiang Qile[7] optimized the rear axle support mechanism of light bus, so that its structural stiffness and strength were improved at the same time；Wei Yanming[8] established the coupling vibration model of gearbox and base, and optimized the structure according to the results of finite element analysis, which improved the coupling vibration of gearbox；Zhu Mingjuan[9] used Solidworks and ANSYS to integrate and optimize the static model of excavator working device；Yin Liming[10] used topological optimization and orthogonal experiment to obtain the ideal structure of material distribution and realized the material saving design；W. Gutkowski [11] reduces the stress of excavator arm section through static analysis and topological optimization；Ming Long Wang[12] used the method of dynamic simulation to reduce the vibration and impact of the arm structure；Huangtian[13] used the dynamic software ADAMS to analyze the kinematics and dynamics of the single-wheel suspension system of the robot under the condition of D-level random simulation road surface, and then optimized the parameters to improve the reliability of the vibration absorption system.

Referring to the above research methods, taking the maximum equivalent stress and mass of the suspended upper arm mechanism as the breakthrough point, the force state of the upper arm mechanism is analyzed by dynamic simulation and static simulation methods, and a multi-objective optimization mathematical model is proposed by numerical fitting. Then, the genetic algorithm is used to optimize the parameters of the upper arm mechanism, so as to solve the redundancy problem in the design of the upper arm mechanism.

1 Multi-body dynamics analysis of upper arm mechanism

The rigid-flexible coupling model of suspension mechanism is modeled and simulated by using dynamic simulation software Recurdyn. The upper arm mechanism of electric farm vehicle suspension is treated as a flexible body and the rest as a rigid body. In order to reduce the complexity of the model, a three-dimensional model of single suspension is established, and a virtual shaking table is established to simulate the reality of medium-sized electricity. The displacement changes caused by the suspension during the moving of the motor vehicle are shown in Fig.2.

Fig.2 Rigid-flexible coupling model of suspension

mechanism

In the simulation, the change range of the actual road surface is set as the displacement of the vibration table. The wheel model is established by using the special tire module of Recurdyn software. The stiffness and damping of the virtual tire are set according to the stiffness and damping of the actual rubber tire. Using the special spring module of Recurdyn software, the suspension damping spring model is established, and the model parameters are set according to the actual spring parameters. Secondly, the suspension arm mechanism is treated as a flexible body, the rest as a rigid body, and then multi-body dynamics simulation is carried out. As shown in Fig.3, the comprehensive force curve of the three hinge points of the suspension arm is presented.

Fig.3 Force curve of hinge point of upper arm mechanism

According to the force information obtained from dynamic simulation, the maximum force of the three hinge points inX,YandZcoordinate axes is selected as the test parameters for stress analysis of upper arm mechanism in the next step.

2 Variable analysis and numerical fitting

2.1 Simulation test

ANSYS workbench is selected as the static analysis platform, and the attitude of the suspension arm at the maximum displacement during suspension vibration is taken as the test attitude, i.e., the suspension attitude of the wheel at the highest position (set as attitude 1). As shown in Fig.4 and Fig.5, the height m of the spherical hole of the upper arm is set as the first variable, the height n of the cylindrical hole of the upper arm is set as the second variable, the outer diameter a of the cylindrical hole of the upper arm is set as the third variable, and the gap repair distance b is set as the fourth variable. The maximum force obtained by one-step dynamic simulation is applied in theX,YandZcoordinate directions of each hinge point. Four suspended upper arms are found by setting a single variable test. The independent relationship between the parameters and the maximum equivalent stress is shown in Table 1. Based on the univariate relationship, the multivariate relationship between the four variables and the stress of the suspension arm is predicted. The correlation coefficients of the multivariate relationship are determined by setting orthogonal experiments, such as Tables 2 and 3.

Fig.4 The upper arm front view

Fig.5 Upper arm side view

Table1 Single variable test parameter table

Table 2 Level factor of orthogonal test

Table 3 Orthogonal test parameters

2.2 Numerical fitting

As shown in Fig.6 to Fig.9, the simulation results and numerical fitting curves between the maximum equivalent stress of the upper arm and the height of the spherical hole of the upper arm m, the height of the cylindrical hole of the upper arm n, the outer diameter of the cylindrical hole of the upper arm a and the repair distance b of the notch are obtained, respectively. The fitting formulas and determination coefficients are as follows:

Pm=0.039 5m2-2.797m+75.799

(1)

Pn=-0.000 9n3+0.1301n2-6.4222n+128.67

(2)

Pa=-0.001 6a3+0.2729a2-15.55a+325.85

(3)

Pb=0.000 3b3-0.0623b2+4.9955b-104.61

(4)

(5)

Fig.6 P-m curve

Fig.7 P-n curve

Fig.8 P-a curve

Fig.9 P-b curve

According to the results of univariate numerical fitting, the multivariate numerical relationship between the maximum equivalent stress of the upper arm and the four parameters of the upper arm could be predicted as follows:

P(m,n,a,b)=P1+P2+P3+P4

(6)

(7)

(8)

(9)

P4=d

(10)

X1=m,X2=n,X3=n,X4=b,Ai、Bi、Ci、Di、Apq、Bpq、Cpq、d…Al of them are constants.

The fitness criterion is set as follows:

(11)

P(m,n,a,b)=-0.214 5×10-3m3-

0.152 2×10-3n3-0.512 4×10-4b3+

1.354×10-2m2+1.85×10-3n2-

17.606×10-2a2+0.218 5b-

0.093 1×10-4m2n+2.163 4×10-2ab

(12)

The parameters of the orthogonal test table are substituted into the formula, and the maximum equivalent stressPof the upper arm is calculated. The error of the multivariable numerical model could be verified by the difference between the orthogonal test value and the calculated value. The error results are shown in Table 4.

Table 4 Stress error table

It can be seen from this table that there is a very small average error ratio between the calculated value of the multivariate numerical model of the maximum equivalent stress of the upper arm and the simulation test value. The error is about -9.3947e-03%, which can be almost neglected. Therefore, the multivariate numerical model of the maximum equivalent stress of the upper arm has very good reliability.

Similarly, using the same method, a multivariate numerical model between the upper arm mass and the four variable parameters can be obtained.

M=0.399 3×10-3b2+0.022 7m-

0.005 9n+0.051 1a-0.032 5b-

0.37×10-6mn2+0.132 4×10-4nm2-

0.311 3×10-5ab2+1.766 7×10-3an

(13)

The error ratio is shown in Table 5.

Table 5 Quality error table

From the above table, it can be seen that there is also a small average error ratio between the calculated value of the multi-variable numerical model of upper arm mass and the measured value of the model. The average error is about 0.0309%. Therefore, the multi-variable numerical model of upper arm mass has very high reliability and accuracy.

3 Upper arm structure optimizationbased on genetic algorithms

3.1 Objective function

W1=min[P(m,n,a,b)]

(14)

W2=min[M(m,n,a,b)]

(15)

(16)

In order to increase the strength of the structure and ensure that the structure can withstand the large external forces, the maximum equivalent stress of the upper arm is set as the first objective function. The smaller the value, the higher the strength of the structure. At the same time, the upper arm with the same strength may have different structures, and there are many design methods. Most of these design methods have redundancy, i.e., waste of materials. In order to select the most reasonable design method, the quality of upper arm is regarded as the second objective function, and the best design method is obtained by restricting the two objective functions at the same time, i.e., the design method with smaller mass and higher strength is a relatively more reasonable design method.

In order to facilitate the presentation of results and the optimization of functions, the bi-objective optimization model is normalized and transformed into a single-objective optimization model as follows:

minW(m,n,a,b)=W1+W2

(17)

The optimization software MATLAB is used to program the genetic algorithm to optimize the four parameters of upper arm. The related parameters are set as follows: initial population sizeM=100, maximum evolution algebraT=100, number of variablesv=4, mutation probabilityPm=0.1, crossover probabilityPc=0.9, and the fitness function is the smallest change of single objective function.

3.2 Optimized results

According to the constraints set, genetic algorithm is used to optimize the upper arm parameters. The optimal values of the upper arm parameters arem=24.197 5,n=24.254 3,a=42.200 3,b=70.704 7. The variation of fitness function with evolutionary algebra is shown in Fig.10.

Fig.10 Fitness function change curve

The orthogonal test results of similar structures, the calculation results of existing designs and the optimization results of genetic algorithm are compared. As shown in Table 6, one group is the orthogonal test results of similar structures, two groups are the calculation results of existing designs, and three groups are the optimization results of genetic algorithm.

From the data in the above table, it can be seen that the optimized results reduce the height of spherical hole about 7.8 mm, the height of cylindrical hole about 3.9 mm, the outer diameter of cylindrical hole about 9.8 mm, the gap repair distance about 9.3 mm, and the parameters in the orthogonal experiment more greatly than those in the existing design, but the optimized results reduce about 1.9 mm in the maximum equivalent stress compared with the existing design. 6.823 8%, which is about 19.126 7% less than the similar structure of orthogonal test. Therefore, the optimized structure consumes less material but achieves better structural performance.

Table 6 Optimization results

4 Conclusion

(1) In the highest posture position of the upper arm (posture 1), the maximum force of each hinge point in the direction ofX,YandZcoordinates obtained by dynamic simulation is applied to each hinge point of the upper arm. Univariate test and orthogonal test are carried out by static simulation. The results reflect the maximum equivalent stress of the upper arm under the maximum force, and also reflect the maximum equivalent effect of the change of different parameters. The influence degree of force change is different.

(2) Based on the single-variable test results, the single-variable numerical fitting model of the maximum equivalent stress for each variable is fitted. According to the single-variable numerical fitting model, the multi-variable numerical model is predicted. Combining with the orthogonal test results, the variable coefficients and constants in the multi-variable numerical model are determined, and a complete multi-variable numerical model is obtained. At the same time, the same method could be used to simulate the multi-variable numerical model. A multi-variable numerical model between upper arm mass and four variables was developed.

(3) Combining the multi-variable numerical model of the maximum equivalent stress of the upper arm with the multi-variable numerical model of the upper arm mass, the maximum equivalent stress of the upper arm and the minimum mass of the upper arm are set as objective functions, and the structural parameters of the upper arm are optimized by genetic algorithm. The optimization results show that compared with the orthogonal design and the existing design,W1is reduced by 19.162 7% and 16.823 8%,W2is also relatively reduced, the quality is smaller, but the strength is improved, i.e., the structure design is more reasonable. This optimization method could provide reference for other designs.