Optimal Design of Frame Structure of Center Axle Trailer Under Heavy Load Conditions

Abstract

In recent years, the mid axle train has gradually entered the transportation market because of its large loading capacity and flexible steering. The static simulation of full load bending, full load torsion and full load braking were carried out for the upper and lower platforms of the trailer frame, and the stress and deformation were obtained. Through the topology optimization design, the pseudo density cloud image with material removal as the optimization objective was obtained. The response surface optimization method was used to adjust the main optimization parameters of the frame platform, and the sensitivity value of its influence on the strength, stiffness and mass of the lightweight frame was analyzed. Finally, the actual value of the optimization parameters was determined. The results showed that the strength, stiffness, and stability of the lightweight frame met the requirements, and the total weight loss of the lightweight frame is 437.07 kg, and the weight loss ratio reached 14.51%. Finally, the static strength test of the lightweight frame was carried out, and the results showed that the lightweight frame met the use requirements.

1 Introduction

With the rapid development of China's automobile industry, the problem of commodity vehicle transportation has gradually become prominent [1, 2]. The mid-axle car carrier is connected by the tractor and trailer through couplers, which reduces the turning radius while improving the steering flexibility of the vehicle, and can give full play to the advantages of large loading capacity and high transportation efficiency [3, 4]. As the key part of the mid-axle car carrier, the working state of the car frame directly affects the safety of transportation, so the optimization of the frame is particularly important. Zhang Kaicheng et al. [5] conducted modal analysis and typical working condition static analysis on a commercial frame, and optimized both the size and material of the frame. The results showed that while ensuring the strength and modal characteristics, the weight of the new frame was reduced by 5.6%. Hu Zhaohui et al. [6] proposed a lightweight design method for truck frame based on interval separation. Based on this method, a truck frame was optimized, and the results showed that the optimized frame weight decreased by more than 10%. Xin Yong et al. [7] used orthogonal experimental method and compromise programming method to improve the stiffness, stability and lightweight of an SUV frame, resulting in a weight reduction of 6.7 kg. Wang Xinyan et al. [8] used stress test method and finite element analysis method to determine the dangerous parts of a certain type of frame, and used MATLAB to obtain the reliability index, and realized the weight reduction of the frame. Jiang Jinxing et al. [9] adopted SIMP variable density method to carry out multi-objective optimization of 300t mining dump truck, and the results showed that the performance of the new vehicle frame was greatly improved. Wang Shuting et al. [10] established a comprehensive weight sensitivity analysis model for frame stiffness, modal frequency, and structural response to analyze the life of the frame, forming an analysis system for frame lightweight. Fan Wenjie et al. [11] adopted the compromise programming method and the average frequency method to obtain a vehicle frame multi-objective topology optimization method suitable for continuum structure. Ding Xiaolin et al. [12] obtained the random stress spectrum of vehicle frame through finite element numerical simulation and the fourth strength theory, and accurately predicted the fatigue life of the mid-axle sedan trailer. Chen Wuwei et al. [13] used kriging surrogate model and multi-objective genetic algorithm to optimize the dynamic characteristics of a pickup truck frame, and the results showed that the frame not only avoided low-order modal resonance, but also realized lightweight and stiffness optimization of the frame. Based on genetic algorithm, Wei Zhong et al. [14] proposed a multi-objective optimization method for vehicle frame through static and modal analysis, and the results showed that the frame weight was reduced by 3.43%. Guo Z Q et al. [15] carried out static and modal analysis of vehicle frame through computer-aided design and finite element platform, and obtained the optimization method of the static and dynamic characteristics of the frame.

In this paper, a mid-axle trailer frame is taken as the research object, the finite element software is used to nalyse the stress state of the frame under three typical working conditions, and the topological optimization is carried out under the goal of “removing materials”, the lightweight design of the frame is carried out, and a new frame with good performance is obtained, which provides certain engineering practical significance for the lightweight design of the mid-axle train.

2 Frame Performance Analysis

A mid-axle trailer frame designed and produced by Jiangsu Tianming Company is taken as the research object, as shown in Fig. 1a. Figure 1b is the specific crossbeam position of the upper platform frame, and the specific measurement position of the lower platform frame is also arranged and named from left to right, so we will not go into details here.

Fig. 1

Center axle car trailer

The main material of the frame is Q235 steel, and the main failure form is plastic deformation. The fourth strength theory is used as the evaluation theory of the strength of the frame, and the frame is analyzed under three working conditions: full load bending, torsion, and braking.

2.1 Full Load Bending Condition Analysis

Full load bending condition means that when the train is full load, the torsion bending deformation is small, and the frame is mainly vertical bending deformation. Through static analysis, the large stress on the upper platform is mainly concentrated at the junction of the front end of the vehicle frame connecting the base and the column oil cylinder, and the maximum value is as high as 50.58 MPa, as shown in Fig. 2a; the lower platform stress is mainly concentrated at the connection between the rear part of the frame and the support part of the axle, with a maximum value of 83.48 MPa, as shown in Fig. 2b. These parts of the stress are more concentrated, easy to cause damage.

Fig. 2

Stress distribution of frame under full load bending condition

The analysis suggests that the upper platform vehicle frame is finally borne by the four points at the junction of the front end of the frame connecting the base and the column oil cylinder, which causes the stress concentration here. The back half of the lower platform is in a cantilever beam state without support, so the connection between the back part of the vehicle frame and the support part of the axle has the greatest stress. The rest of the vehicle frame is well stressed and has a large redundancy.

2.2 Full Load Torsional Condition Analysis

In this analysis, the full load torsional working condition of the upper platform simulated the simultaneous failure of the right front pillar oil cylinder and safety pin, and the loss of support in the right front part of the upper platform caused torsional deformation of the frame. The full load torsional working condition of the lower platform simulated the right-side collapse deformation caused by the suspension of the right wheel. Through static analysis, the stress in the side beam area connected to the left front connecting base and the right rear connecting base of the upper platform is relatively concentrated, and the maximum value is 155.31 MPa, as shown in Fig. 3a. The maximum stress at the connection between the left longitudinal beam of the lower platform and the plate spring of the central axle wheel group reached 157.3 MPa, as shown in Fig. 3b.

Fig. 3

Stress distribution diagram of frame under full load torsion condition

The analysis suggests that the right connecting base of the upper platform loses support and sinks, and the load-bearing task of the left front connecting base and the right rear connecting base increases, resulting in the stress concentration in this part. Similarly, the connection between the middle and back section of the left longitudinal beam responsible for support at the lower platform and the side beam bears a large load, resulting in increased stress there.

2.3 Full Load Braking Condition Analysis

The full load braking condition simulates the strength and stiffness of the mid-axle car under the emergency braking condition, and this braking acceleration is calculated according to a =  −0.7 g. Through static analysis, the maximum stress on the upper platform is located at the junction between the front end of the frame connecting base and the column oil cylinder, and the maximum stress is 50.98 MPa, as shown in Fig. 4a. The maximum stress of the lower platform is in the connecting part of the rear longitudinal beam of the axle and the plate spring of the wheel group, and the maximum value is 78.88 MPa, as shown in Fig. 4b.

Fig. 4

Frame stress distribution diagram under full load braking condition

The analysis shows that the stress under full load braking conditions of the upper and lower platforms is like that under full load bending conditions, which is far lower than the yield limit of 235MPa, and the performance of the frame is far beyond the use requirements.

2.4 Frame Structural Strength Evaluation

The safety factor n specified in material mechanics is.

$$ n = \frac{{\sigma_{s} }}{{\sigma_{\max } }} $$

(1)

In the above formula, $\sigma_{s}$ is the material yield limit of 235MPa and $\sigma_{\max }$ is the maximum composite stress of the frame.

The calculated safety factor of the frame is shown in Table 1.

Table 1 Frame safety factor table

The maximum allowable safety factor of special vehicle materials should be above 1.5, leaving a certain redundancy, that is, when n <1.5, fatigue damage may occur to the frame. The analysis shows that there are hidden dangers in the maximum stress structure of the platform under full load torsion condition. But at the same time, the safety factor of other structural parts of the frame under the three working conditions is above 5.0, which has a large redundancy and a large lightweight design space.

3 Frame Optimization Design

3.1 Frame Topology Optimization

Based on the SIMP topology optimization model, “removal of 40, 50, 60% of frame materials” was adopted as the optimization objective under normal working conditions (full-load bending conditions), and the results were shown in Figs. 5 and 6.

Fig. 5

Pseudo-density cloud map of the upper platform frame for the optimization target

Fig. 6

Pseudo-density cloud map of the lower platform frame for the optimization target

Under the fully loaded bending condition on the upper platform, the fourth, eighth and ninth crossbeams of the frame have the most significant changes on the platform, and their redundancy is relatively large. Therefore, it is considered to remove or merge with other structures. During the process of increasing the material removal from 40 to 60%, the red area in the middle of the edge beam gradually increases, and it is considered to open a weight reduction hole in this area. In addition, the changes in the third, fourth, fifth, and eighth groups of longitudinal bars have also begun to be significant. Considering that this part mainly plays a connecting role in the actual work process and does not directly bear the load, it is considered to reduce the cross-sectional area during the optimization process to reduce weight.

Similarly, consider reducing the weight of the eleventh crossbeam in the lower platform. Consider cutting the seventh crossbeam and adjusting the eighth crossbeam to the center to consider the weight reduction effect and mechanical properties. For the four column parts, it can be considered to increase the weight reduction holes or reduce the cross-sectional area. Appropriately remove one of the first and second connecting beams, and reduce the cross-section area of the third connecting beam.

3.2 Frame Structure Improvement Design

Based on the topological optimization results, the outer section size of the vertical bar of the upper platform was adjusted from 80 × 60 mm to 60 × 48 mm, a weight reduction hole was drilled in the middle of the side beam, and the fourth, seventh and tenth crossbeams were removed, and the positions of the fifth, eighth and ninth beams were adjusted to make the eighth and ninth crossbeams serve as the bearing beams. The optimized upper platform was shown in Fig. 7.

Fig. 7

The overall structure of the upper platform frame after optimization

Remove the seventh and eleventh crossbeams of the lower platform and adjust the eighth crossbeam to the middle position. Based on the analysis results and practical needs, the low-density entities such as the first connecting beam at the front end of the longitudinal beam and the third connecting beam at the middle front are removed. At the same time, adjust the cross-sectional area of the column and drill weight reduction holes every 600 mm. After adjustment, the cross-sectional area of the column is shown in Fig. 8.

Fig. 8

The optimized lower platform frame column cross-sectional structure

The above optimization greatly adjusted the structure of the upper platform. In order to obtain accurate topological optimization structure parameters, the response surface optimization method was selected to adjust the 7 main optimization parameters of the upper platform to obtain the best combination of strength, stiffness, and mass. Beam spacing, thickness and the hole diameter of the side beam were selected as optimization variables, and the optimization variables of beam spacing were shown in Fig. 9.

Fig. 9

Beam spacing optimization variables

In addition, the thickness of the entire section of the beam is selected as x₆, and the diameter of the weight reduction hole of the side beam is selected as x₇. The optimization objective is the best combination of strength, stiffness and mass, and the optimization variable is expressed as: X = x₁, x₂, x₃, x₄, x₅, x₆, x₇.

The constraint conditions are: $x_{i}^{0} \le x_{i} \le x_{i}^{1}$ .

The objective function is: $\left\{ {\begin{array}{*{20}c} {\max K = f(X)} \\ {\max S = f(X)} \\ {\min M = f(X)} \\ \end{array} } \right.$

In the above formula: x_i—Optimize the parameters of the variable; $x_{i}^{0} x_{i}^{1}x_{i}^{0} x_{i}^{1}$—Value range of $x_{i}$ $x_{i}$, K—Stiffness; S—Intensity; M—Quality.

The Custom method was used to screen 80 sample points for normalization processing, and the response surface model of the neural network was established. The fitting degree between the predicted value and the actual value was shown in Fig. 10 below.

Fig. 10

Fit degree between predicted value and actual value of response surface model

After the response surface is generated, the correlation sensitivity between input and output parameters is constructed. The closer the sensitivity value is to 1, the stronger the positive correlation between input parameters and corresponding output parameters, and the closer the sensitivity is to −1, the greater the negative correlation between the two, and the closer the sensitivity is to 0, the weaker the correlation between the two. The sensitivity histogram is shown in Fig. 11. It can be seen from the analysis in Fig. 11 that x₂ has the most significant influence on the strength. x₃ and x₅ have the most significant influence on stiffness. The x₆ has the most significant impact on quality.

Fig. 11

Parameter sensitivity histogram

The multi-objective genetic algorithm was selected, and the initial population number was set to 100, the sample number of each genetic iteration was set to 100, the maximum genetic algebra was set to 20, the maximum Pareto percentage was 70%, and the maximum number of iterations was set to 20. The initial optimization values and results on the platform were shown in Table 2.

Table 2 Parameter optimization initial values and results

After optimization, the unloading frame is shown in Fig. 12.

Fig. 12

Lower frame after optimization

Set the same boundary conditions as the original frame, and analyze full-load bending conditions, full-load torsion conditions and full-load braking conditions. The results are shown in Tables 3 and 4 below.

Table 3 Comparison of the corresponding data of the upper platform frame before and after optimization

Table 4 Comparison of the corresponding data of the lower platform frame before and after optimization

As can be seen from Tables 3 and 4, the overall weight loss of the upper platform frame after optimization is 197.87 kg, which is about 16.6% of the original frame. After the optimization of the lower platform frame, the weight is reduced by 239.20 kg, about 13.1% of the original frame. At the same time, in addition to the maximum braking stress of the lower frame, the optimized stress is far below the yield limit, and the error of the maximum stress calculated by the simulation of the new frame under the remaining three working conditions is less than 3%, and the strength and stiffness performance of the optimized frame are not decreased, while the weight is greatly reduced.

4 Frame Static Test Verification

Due to the large size of the frame, it is impossible to test all positions, so the stress concentration point and the load point are selected as the test points. The test points are shown in Figs. 13 and 14 below.

Fig. 13

Schematic diagram of the strain measurement position of the upper platform frame

Fig. 14

Schematic diagram of the strain measurement part of the lower platform frame

The strain gauge is arranged in a right-angle strain flower scheme, as shown in Fig. 15.

Fig. 15

Right angle rosettes

The stress calculation results of strain gauge with three angles of strain flower are $\sigma_{0}$, $\sigma_{45}$ and $\sigma_{90}$, respectively. The maximum, minimum and direction Angle of the principal stress are calculated according to the following formula:

$$ \sigma_{{{\text{max}}}} = \frac{1}{2}\left[ {\frac{{_{{\sigma_{0} + \sigma_{90} }} }}{1 - \mu } + \frac{\sqrt 2 }{{1 + \mu }}\sqrt {\left( {\sigma_{0} - \sigma_{45} } \right)^{2} + \left( {\sigma_{45} - \sigma_{90} } \right)^{2} } } \right]$$

(2)

$$ \sigma_{\min } = \frac{1}{2}\left[ {\frac{{_{{\sigma_{0} + \sigma_{90} }} }}{1 - \mu } - \frac{\sqrt 2 }{{1 + \mu }}\sqrt {\left( {\sigma_{0} - \sigma_{45} } \right)^{2} + \left( {\sigma_{45} - \sigma_{90} } \right)^{2} } } \right]$$

(3)

$$ \alpha = \frac{1}{2}tg^{ - 1} \frac{{2_{{\sigma_{45} }} - \left( {\sigma_{0} + \sigma {}_{90}} \right)}}{{\sigma_{0} - \sigma_{90} }}$$

(4)

In the above formula.

$\mathop \sigma \nolimits_{\max }$——Maximum principal stress, MPa;

$\mathop \sigma \nolimits_{\min }$——Minimum principal stress, MPa;

$\mu$——Poisson's ratio, 0.3;

$\alpha$——Principal stress direction Angle (relative to 0 °).

Strain flowers are evaluated by equivalent stress, as shown in formula 5.

$$_{{\sigma_{e} = \sqrt {\left( {\frac{{\sigma_{0} + \sigma_{90} }}{{2\left( {1 - \mu } \right)}}} \right)^{2} + 3\left( {\frac{1}{{2\left( {1 + \mu } \right)}}} \right)^{2} \left[ {\left( {\sigma_{0} - \sigma_{90} } \right)^{2} + \left( {2\sigma_{45} - \left( {\sigma_{0} + \sigma_{90} } \right)} \right)^{2} } \right]} }} $$

(5)

In the above formula:

$\mathop \sigma \nolimits_{e}$——Equivalent stress, MPa;

After the arrangement of strain gauges is completed, part of the position is shown in Fig. 16.

Fig. 16

Strain gauge after fixation

After the preparation of the test, the static strength test under bending and torsion conditions was carried out. The test was tested three times under each working condition, and the average value was calculated as the result. The test stress values obtained at the 12 test points tested by the upper platform frame under the two working conditions were shown in Tables 5 and 6. The test stress values obtained at 20 test points tested by the lower platform frame under two working conditions are shown in Tables 7 and 8.

Table 5 Stress values of upper platform under full load bending condition (unit: MPa)

Table 6 Stress values of upper platform under full load torsion condition (unit: MPa)

Table 7 Stress value of lower platform under full load bending condition (unit: MPa)

Table 8 Stress value of lower platform under full load torque condition (unit: MPa)

The elastic modulus of Q235A steel is ${\text{E}} = 2.06 \times 10^{5}$ MPa, Poisson's ratio is 0.3, and the yield strength is 235 MPa. When the safety factor n is 1.5, $\left[\delta \right]$ can be obtained by calculation as 157 MPa.Therefore, the stress of the above measuring points is less than the maximum allowable safety stress, so the structure of the frame meets the requirements. However, the test result value is smaller than that of the simulation, because the stress peak under the simulation condition is inside the solid structure, while the test is on the surface of the component, so certain errors will be generated.

5 Conclusion

The results show that the stress value of the frame under torsion condition is much higher than the other two conditions, but the value is much lower than the material properties, and it has a large space for lightweight design. Through topology optimization, the redundant structure and unreasonable layout of the frame were evaluated and optimized. Simulation and test results showed that the lightweight trailer frame lost 437 kg, accounting for 15.7% of the original weight, while maintaining the original strength and stiffness performance. The weight reduction effect was remarkable, and the lightweight goal was achieved.