The universal energy-saving cross shaft enables the two shafts that are not on the same axis or the axis to be bent at a large angle to rotate continuously at equal angular speed, and reliably transmit torque and movement. Its biggest feature is compact structure, high transmission efficiency, large transmission torque, and maintenance. convenient. In ship engineering, cross-shaft universal joints are commonly used in series with several intermediate shafts to form a propulsion shaft system. In the propulsion shaft system, its main purpose is to transmit power and torque, offset radial, axial and angular errors, and compensate for oscillations caused by rotational momentum. , Adjust the propulsion power when starting and reversing, and provide anti-overload protection [1]. The cross shaft universal joint drive will generate additional load, vibration and noise. The additional load will also cause the bending vibration of the components connected with the cross shaft universal joint. It may also cause periodicity at the universal joint input shaft, output shaft and support. Change the radial load to excite vibration at the support. The literature [2] ~ [7] analyzed the transmission characteristics of a single cross-shaft universal joint and a double cross-shaft universal joint. However, in practical applications, several universal joints in series are often used. The study of how various rotation angles affect the transmission characteristics of the shaft system when the universal joints are connected in series. Therefore, it is necessary to carry out modeling and simulation research on any universal joints and systems with any type of rotation angles in series, and analyze various types of universal joints. How does the steering angle affect the speed, angular acceleration, torque, etc. of each shaft in the shafting system. This paper analyzes the shafting system of any universal joint and multiple rotation angles in series. The universal joint is not only the cause of the unsteady movement of the shafting and the increase of the vibration of the shafting, but also the reasonable arrangement of the universal joints during the shafting design. Position and rotation angle, use the interaction between multiple universal joints to offset this negative effect, as far as possible to ensure the constant speed rotation and transmission of the same torque of the coupling shaft, so as to suppress the friction and vibration generated in the transmission, to achieve the extension of the shaft The service life of components and the purpose of reducing vibration and noise [8]. The movement analysis of the cross shaft The mechanism principle and movement diagram of the single cross shaft universal joint is shown in Figure 1. Figure 1 'Schematic diagram of cross shaft universal joint structure Fig. 1' Schematicdiagram of the driving shaft angle of the driving shaft? 1. The driven shaft angle? 2. The following relationship exists between the angle between the main shaft and the driven shaft [3] tanφ2 u003d the initial axis of the cross axis when the cross axis is connected to the first axis cos 1 φ 1 When the position is in the horizontal plane, the transmission relationship can be regarded as the situation of adding 90° to the initial angles of φ1 and φ2 in the previous case, so that the two-axis rotation angle relationship of 2, 3 can be obtained. Substitute equation (1) into equation ( 2) Obtain tanφ3 u003d cosα2 cosα1 tnφ1 (3) The driving relationship of the double cross-shaft universal coupling is obtained. When the conditions are met: ① All shafts are in the same plane; ② The forks of the forks of the two ends of the intermediate shaft (or the forks of the flanges on the same shaft) are located in the same plane, and formula (3) is extended to obtain any number The transmission relationship of the series shaft system of the cross shaft universal coupling tanφnu003dcosα2·cosα4·cosα6cosαn-1 cosα1·cosα3·cosα5cosαn-2tanφ1　(n is an odd number) (4) ton4·cosαcon4·cosαcon4·cosαcosαcosαn cosα5cosαn-1tanφ1” (n is an even number) (5) Let in1 u003d cosα2·cosα4·cosα6cosαn-1 cosα1·cosα3·cosα5cosα2·cosα5cosα4·cosα5cosα2·cosα5cosα2·cosα5cosα2·cosα5cosα2·cosα5 ), Equation (5) Derivative time on both sides of the equation can be obtained after finishing the main and driven shaft speed relationship ωn u003d in11 + (i2n1-1) sin2φ1 · ω1 (6) When the driving shaft rotates at a constant speed, dwdt u003d 0, and the equation (5) Derivation of the time on both sides obtains the relationship between the angular acceleration speed of the driven shaft and the rotation angle of the master shaft αn u003d-in1(i2n1 -1) sin2φ1[1+(i2n1 -1) sin2φ1]2·ω.