Analysis of the influence of phase angle of double cross shaft universal joint steering drive shaft (3)
The method for solving the phase angle of the steering transmission shaft based on the hard points of the steering system. The installation space of the steering transmission shaft in the cockpit is limited. Due to the layout of the brake pedal and other parts, the axes of the intermediate shaft and the main and driven shafts are not in the same plane. Moreover, the height of the steering wheel can generally be adjusted so that the transmission angle α between the input shaft and the intermediate shaft can be changed. Therefore, it is difficult for the double cross shaft universal joint drive shaft to meet the constant speed transmission conditions. At this time, adjusting the phase angle ψ of the intermediate shaft becomes an effective method to suppress or eliminate speed fluctuations. According to the previous analysis, the optimal phase angle is equal to the included angle of the transmission surface. Due to the influence of frame processing error and load deformation and other factors, the most direct and convenient way to obtain the included angle of the transmission surface is to obtain the hard point of the steering system through measurement to calculate the included angle of the transmission surface to obtain the best phase angle. Set the steering wheel connection center as point A, the cross axis of the upper steering shaft as point B, the cross axis of the lower drive shaft as point C, and the center of the spline hole on the lower end of the pitch fork connected to the rack and pinion steering gear as point D . As shown in Figure 7. Given that the coordinates of the four points that are not coplanar in space are A (Xa, Ya, Za), B (Xb, Yb, Zb), C (Xc, Yc, Zc), D (Xd, Yd, Zd), find the surface ABC and The method of the angle between the surface BCD is: Suppose the equation of plane ABC is A1x + B1y + C1 z + D1 u003d 0 (20) According to the plane three-point equation (determinant expression), it is x-Xa y-Ya z-Za Xb-Xa Yb － Ya Zb － Za Xc － Xa Yc － Ya Zc － Za u003d 0 (21) So A1 u003d (Yb － Ya) (Zc － Za) － (Yc － Ya) (Zb － Za) B1 u003d (Xc － Xa) (Zb － Za) － (Xb － Xa) (Zc － Za) C1 u003d (Xb － Xa) (Yc － Ya) － (Xc － Xa) (Yb － Ya) Principle, suppose the equation of plane BCD is A2x + B2y + C2 z + D2 u003d 0, then A2 u003d (Yb － Yd) (Zc － Zd) － (Yc － Yd) (Zb － Zd) B2 u003d (Xc － Xd) (Zb － Zd) － (Xb － Xd) (Zc － Zd) C2 u003d (Xb － Xd) (Yc － Yd) － (Xc － Xd) (Yb － Yd) Let the angle between the ABC surface and the BCD surface be γ , The formula for calculating the phase angle from ψ u003d γ is ψ u003d arccos A1A2 + B1B2 + C1C2 A1A1 + B1B1 + C1C1 A2A2 + B2B2 + C2C2 (22). Programming and verification of examples. Since the calculation formula (15) of the angular velocity ratio of the transmission shaft ω3 /ω1 and the formula (22) of the phase angle calculation by the hard point coordinates are more complicated, in order to be able to apply the above theoretical analysis results conveniently and quickly in engineering applications, In this study, the phase angle analysis program of the double cross-axis universal joint steering drive shaft was compiled based on VB software (as shown in Figure 8). Fig. 8 Phase angle analysis program interface of double cross-axis universal joint steering drive shaft. In the program, there are two types of phase angle calculation and analysis: angle mode and hard point mode. In the angle mode, you can directly input the transmission angle α and β, the transmission surface angle γ, and the phase angle ψ. You can also change the angle value by clicking the scroll bar button. Any change in the angle value will cause ω3 / on the right side. The ω1 curve changes, which is convenient for engineers to dynamically view the trend of speed changes. In hard point mode, you only need to input the three-dimensional coordinates of points A, B, C, and D to calculate the optimal phase angle of the intermediate axis. In order to test the accuracy and practicability of the program, for the intermediate transmission shaft of the steering column in literature  19-22, input its hard point coordinates (coordinate values u200bu200bin Figure 8) into the program, and calculate the optimal phase angle For 72. 4°. At the same time, in the angle mode of this program, input the transmission angles α and β, and the transmission surface angle γ, and the optimal phase angle of 72 can also be calculated. 4°, and the ω3/ω1 curve is also drawn at the same time. The calculation results are consistent with the calculation results of literature  19-22 and the actual vehicle structure parameters, indicating that the calculation results of the program are accurate. 5 Conclusions In this paper, we established a spatial coordinate system, using the method of spatial geometric projection, established the speed ratio and rotation angle equations of the double cross-axis universal joint steering drive shaft, and verified its correctness with constant velocity conditions. Using representative structural parameters, the influence of the phase angle on the speed ratio is quantitatively analyzed when the transmission angle and the included angle of the transmission surface take different values. The research results show that when the two transmission angles are equal and the phase angle is equal to the included angle of the transmission surface, the output shaft and the input shaft can achieve constant speed transmission; when the two transmission angles are not equal, the double cross shaft universal joint drive shaft Constant speed transmission cannot be realized, but when the phase angle is equal to the included angle of the transmission surface, the speed difference between the output shaft and the input shaft is the smallest. Therefore, when the phase angle of the transmission shaft and the transmission surface are equal and opposite in direction, it is the best phase angle. On the basis of theoretical derivation and analysis, we deduced the formula for solving the optimal phase angle of the steering drive shaft based on the hard points of the steering system, and compiled the phase angle analysis program of the double cross shaft universal joint steering drive shaft, which was verified by examples The accuracy of the calculation results of the program. The analysis conclusions and the programmed procedures in this article have theoretical and practical significance for the design of automobile steering systems and the transmission research of other types of universal joints.