Evaluation of the strength performance of the steering system of hybrid off-road vehicles

2.1. Steering system structure

A structural diagram of the automobile steering system is shown in Fig. 1. It is mainly composed of two parts: electric power steering system and mechanical steering system. The electric power steering system contains steering angle sensor, steering torque sensor, position sensor, power steering control module and power assist motor assembly. The mechanical steering actuator part includes steering wheel, steering column, universal joint, steering rack and pinion, and steering tie rod.

Fig. 1Steering Gear Structure Composition: 1 – steering outer link and ball pin assembly; 2 – steering column and universal joint; 3 –steering whee; 4 – steering input shaft; 5 –housing; 6 –steering inner link

2.2. Force analysis for steering tie rods

As shown in simplified model of vehicle steering structure in Fig. 2, the steering tie rod is subjected to tension and pressure in the vehicle steering system. Therefore, during the strength analysis of the steering cross tie bar, it can be converted into a two-force bar structure as shown in Fig. 3.

Fig. 2Simplified model of vehicle steering structure: 1 –left steering rod; 2 – right steering rod; 3 –steering trapezoidal arm; 4 – steering gear

Fig. 3Steering cross tie bar compression simplified mode

2.3. Steering tie rod failure analysis

Based on section 1.2, the steering cross-tie bar is only subject to two kinds of forces, tension and pressure. The failure of the bar under pressure will generally be in the form of strength damage and instability damage.

The former, strength damage, is mainly caused by insufficient material resistance, while the latter, instability damage, is the result of bar geometry deformation during force application.

According to the magnitude of the slenderness ratio, press bars can be categorized into three types: long thin, medium long, and short thick. The bar flexibility factor $\lambda$ is:

where $\mu$ is the length coefficient, $l$ the length of the rod, $i$ is the inertial radius of the cross-sectional area, $E$ is the material elastic modulus, ${\sigma }_p$ is the material proportionality limit, ${\sigma }_s$ is the material yield limit, a and b are coefficients related to the material properties.

The steering tie rod analyzed in this paper is made of 40Cr. The center distance between the two ends of the installation point is 360 mm, the elastic modulus E of the material is 206 GPa, and the proportionality limit ${\sigma }_p$ is between 450 MPa and 785 MPa. In this paper, two specifications of steering tie rods with diameters at the minimum of 13.8 mm and 14.0 mm were selected for the study, and the minimum scale limit ${\sigma }_p$ of 450 MPa was used for the calculations. Therefore, the minimum flexibility coefficient of the steering cross tie rods is:

According to the calculation, the steering cross tie rod classified as slender rod. The theoretical calculated critical instability pressure $F_{cr1}$ of 13.8 mm diameter tie rod is:

According to the calculation, the steering cross tie rod classified as slender rod. Based on the stability principle of Euler compression bars, the theoretical calculated critical instability pressure $F_{cr1}$ of 13.8 mm diameter tie rod is:

The theoretically calculated critical instability pressure $F_{cr2}$ for a 14 mm diameter tie rod is:

3.1. Proving ground bad road conditions

The bad road conditions of the test site were mainly collected from Belgium road, railroad intersection, short-wave road, vibration road, 26-inch pits and other bad road conditions that have a greater impact on the steering tie rod force. In order to accurately obtain the force extremes of the vehicle’s steering tie rods under bad road conditions, each condition was collected five times. As shown in Fig. 5, the time domain curve of the steering rod under a certain bad road condition was tested at the Yancheng Test Site in China.

Table 2 present the steering tie rod force test data for Belgian Road, respectively. Based on data in the table, it can be seen that the left and right steering tie rods in the five kinds of bad road conditions are basically the same size. 26-inch pit conditions vehicle steering tie rods are subjected to the greatest force, the maximum tension is 14816 N, and the maximum pressure is 12947 N. The minimum force is applied to the steering tie rod for the railroad junction condition, with a maximum tension of 5861 N and a maximum pressure of 6238 N. The results of the Belgian, shortwave, and vibratory road steering tie rod forces are between the railroad junction condition and the 26-inch pit condition.

The data also indicates that the maximum pressure value of the steering tie rod is greater than the value of the steering tie rod pull force for the three conditions of railroad intersection, short wave road and vibration road. The steering tie rods are subjected to greater pressure, and the maximum pressure on the steering tie rods of the short wave road is 37.86 % greater than the maximum tension. The maximum pressure of the vibration road steering tie rod is 42.43 % greater than the maximum tension.

Fig. 5Time domain curve of steering tie rod test for a bad road condition

Fig. 6Time domain curve of steering tie rod test for abuse condition 1

3.2. Abusive work conditions

The strength test conditions are mainly collected from five types of vehicle impact abuse conditions that significantly affect the steering tie rod force. Each condition was collected five times. As shown in Fig. 6, the time-domain curve of the steering tie rod test for abusive condition 1 is shown.

The steering tie rod force test data under working conditions are shown in Table 3. It can be seen from the test data that the pressure and tension loads on the steering tie rods are maximum at abused condition 5 under both bad road conditions and abused conditions. The maximum pressure load was 32043 N and the maximum tension load was 26482 N.

4.1. Simulation analysis for steering tie rod bending failure

This paper presents the bending strength simulation of the steering tie rod for two parameters with minimum diameters of 13.8 mm and 14 mm.

In the simulation, both ends of the steering tie rods are set up as hinged connections. Pressure is applied to the steering tie rods along the center line of the hinges. The bending deformation of the steering tie rods in the pressure state stage as shown in Fig. 7(a).

Fig. 7(b) shows the simulated bending force and displacement curves of the steering tie rods. The bending force of the steering tie rods with diameters of 13.8 mm and 14 mm are 32.9 kN and 35.8 kN respectively. The simulation results are basically consistent with the theoretical calculation results in section 1.3.

Fig. 7Steering tie rod bending force of: a) stress distribution and b) displacement curve

4.2. Steering tie rod bending failure test analysis

Five sets of compression bending failure tests were conducted on steering tie rods with diameters of 13.8 mm and 14 mm, respectively. The loading mode of the steering tie rods during the test is shown in Fig. 8(a). Fig. 8(b) shows the failure state of the steering tie rods after the test.

Table 4 shows steering tie rod bending test results. By statistically analyzing Table 4 data, 13.8 mm diameter and 14 mm diameter steering tie rod life probability distribution can be obtained. Table 5 show the life probability of the 13.8mm diameter steering tie rod. The data points out that the median pressure endured by the 13.8 mm diameter steering tie rod is 32.95 kN, which is relatively consistent with the theoretically calculated values and simulation results. However, the B10 life of the part at the lower 95 % confidence limit is 28.9 kN, which does not satisfy the strength requirement of a maximum load of 32.043 kN for abusive service pressures.

Fig. 8Steering tie rod buckling strength bench tests of: a) during the experiment and b) after the experiment

Table 6 shows the life probability of the 14 mm diameter steering tie rod. The data indicates that the median pressure on the 14 mm diameter steering tie rod is 37.65 kN, which is in agreement with the theoretically calculated values and the simulation results. The B10 life of the component at the lower 95 % confidence limit is 33.37 kN, which meets the strength requirement of the maximum load of 32.043 kN for abusive working condition pressure. The test results suggest that the B10 life of the parts is different from the results obtained from the simulation calculations. Therefore, it is necessary to consider the effect of production process differences on part quality during part design.