The method for solving the phase angle of the steering drive shaft based on the hard point of the steering system has a limited installation space in the cockpit, and is restricted by the layout of parts such as the brake pedal. Moreover, the height of the steering wheel can generally be adjusted, so that the transmission angle 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 the fluctuation of the rotational speed. According to the previous analysis, the optimal phase angle is equal to the angle between the transmission surfaces. Due to the influence of frame processing error and load deformation, the most direct and convenient method to obtain the angle of the transmission surface is to obtain the hard point of the steering system by measuring, to calculate the angle of the transmission surface, so as to obtain the optimal phase angle. Set the connection center of the steering wheel 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 face of the yoke connected to the rack and pinion steering gear as point D . As shown in Figure 7. It is known that the coordinates of four non-coplanar points 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 included angle of the plane BCD is: Let the equation of the plane ABC be A1x + B1y + C1 z + D1 u003d 0 (20) According to the three-point equation (determinant expression) of the plane, 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) Fig. 7 The spatial key point diagram of the steering transmission shaft is the same as Theoretically, let the equation of plane BCD be 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 plane and the BCD plane be γ , the calculation formula of the phase angle obtained by ψ u003d γ is ψ u003d arccos A1A2 + B1B2 + C1C2 + A1A1 + B1B1 + C1C1 + A2A2 + B2B2 + C2C2 ( 22 ). Programming and example verification Since the calculation formula (15) of the transmission shaft angular velocity ratio ω3 /ω1 and the formula (22) of the hard point coordinate calculation of the phase angle are relatively complicated, in order to easily and quickly apply the above theoretical analysis results in engineering applications, In this study, the phase angle analysis program of the double-cross shaft universal joint steering transmission shaft was compiled based on VB software (as shown in Figure 8). Fig. 8 Phase angle analysis program interface of double-cross shaft universal joint steering transmission shaft In the program, the calculation and analysis of phase angle has two modes: angle mode and hard point mode. In the angle mode, you can directly input the transmission angle and β, the included angle of the transmission surface γ, and the phase angle ψ, or you can change the angle values u200bu200bby clicking the scroll bar button. Any change in the angle value will make the right ω3 /ω1. The curve changes, which is convenient for engineers to dynamically check the speed change trend. 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 check the accuracy and practicability of the program, for the steering column intermediate drive shaft in literature [11] 19-22, the coordinates of the hard point (the coordinates in Figure 8) are input into the program, and the optimal phase angle is calculated. for 72． 4. At the same time, in the angle mode of this program, input the transmission angle and β, and the included angle of the transmission surface γ, and the optimal phase angle can also be calculated as 72． 4, and the ω3/ω1 curve is also drawn at the same time. The calculation results are consistent with the calculation results of literature [11] 19-22 and the structural parameters of the real vehicle, indicating that the calculation results of the program are accurate. 5 CONCLUSIONS In this paper, we have established a space coordinate system, using the method of spatial geometric projection, established the speed ratio and rotation angle equations of the double-cross shaft universal joint steering transmission shaft, and verified their correctness with constant velocity conditions. Using representative structural parameters, the influence of the phase angle on the speed ratio was quantitatively analyzed when the transmission angle and the included angle of the transmission surface took different values. The research results show that: when the two transmission angles are equal, and the phase angle is equal to the angle between the transmission surfaces, the constant speed transmission between the output shaft and the input shaft can be achieved; when the two transmission angles are not equal, the double cross shaft universal joint transmission shaft Constant speed transmission cannot be achieved, however, when the phase angle is equal to the angle between the transmission surfaces, the speed difference between the output shaft and the input shaft is the smallest. Therefore, when the phase angle of the transmission shaft is equal to the angle between the transmission surface and the direction is opposite, it is the optimal phase angle. On the basis of theoretical derivation and analysis, we deduced the optimal phase angle solution formula of the steering drive shaft based on the hard point of the steering system, and compiled the phase angle analysis program of the double-cross shaft universal joint steering drive shaft. The accuracy of the program's calculation results. The analysis conclusion and the program compiled in this paper have theoretical and practical significance for the design of automobile steering system and the transmission research of other types of universal joints.