# The influence of the transmission ratio and center distance of the worm gear combination on the rotation accuracy

The two-stage transmission mechanism combined with worm and gear is widely used because of its advantages of high transmission power, high efficiency, long service life, accurate transmission ratio, compact structure, large transmission ratio and reverse self-locking. With the development of science and technology, the requirement of transmission accuracy of two-stage combined mechanism is higher and higher.

At present, there are many researches on the transmission accuracy of worm and gear mechanisms, but there are few researches on the accuracy of two-stage combined mechanism. Zhygear senior engineer team has carried out research on the transmission accuracy of worm gear two-stage combined transmission mechanism.

The parameters that have nothing to do with the transmission ratio are set as constant, only the influence of the transmission ratio on the transmission accuracy is studied, and the rotary error can be obtained by the same method.

For single head worm, the number of teeth Z4 is the theoretical transmission ratio IW. Therefore, z4ic is the transmission ratio of the whole transmission mechanism. It can be seen that the transmission error caused by the second stage transmission has nothing to do with the distribution of the transmission ratio, only the total transmission ratio reduces the error. In order to reduce the error caused by worm gearing, it is necessary to reduce Δ C1. The expression of the transmission error δ φ C of the mechanism of formula (9) is expanded to obtain formula (11). In order to facilitate the calculation, the transmission equation is further simplified. By substituting R2 / R1 = I, R1 + R2 = L, φ = π / 2 – α = 70 ° into the formula, the expression of gear transmission error φ cc with I and l as variables is obtained. The expression is adapted into matlab code to calculate the three-dimensional figure shown in Figure 2.

The relationship between transmission ratio I and center distance L on transmission error can be obtained from the figure: when the transmission ratio I is greater than 6, its influence on transmission error decreases; when the center distance L is from 0.02 to 0.15 m, the transmission error decreases sharply; when the center distance is greater than 0.2 M, the transmission error decreases with the change of center distance. Generally speaking, the center distance plays a decisive role in the transmission error. When the center distance becomes larger, the radius of the worktable gear becomes larger and the moment of inertia becomes larger. It can be seen that the larger the center distance is, the smaller the transmission error is, but it is limited by the motor torque.

According to the influence of turntable transmission ratio and center distance on transmission error, the center distance of the research object is 0.2025 m, and the transmission ratio of gear pair 8 is reasonable.

(1) According to the meshing principle and geometric analysis method, the transmission accuracy model of the combined mechanism is established considering the factors of machining error, eccentricity error, phase angle, load and deformation.

(2) Through the calculation of an example, it is verified that the transmission accuracy calculated by this method is consistent with that measured by the actual turntable.

(3) For the transmission ratio distribution of the two-stage combined mechanism, it is found that the first stage transmission ratio is more than 6 and the center distance is more than 0.2 m under the manufacturing and assembly errors. 