Analysis of the unevenness of motion in chain drives

Chain entrySprocketsAfter the formation of folded lines, so the movement of the chain drive and the belt drive around the polygonal wheel is very similar, see Figure 9. side length corresponds to the chain pitch p, the number of sides corresponds to the number of teeth of the sprocket z. sprocket wheel every turn a week, the chain moves a distance of zp, set z1, z2 for the two sprocket teeth, p is the pitch (mm), n1, n2 for the two sprocket rotational speed (r/min), then the chain's average speed v (m), the chain's average velocity is v (m/s), the chain's average velocity is v (m), the chain's average velocity is v (m), the chain's average velocity is v (m). / s) is

v=z1pn1/60*1000=z2pn2/60*1000 (4)

From the above equation, the average ratio of chain drive i=n1/n2=z2/z1 (5)

In fact, the instantaneous chain speed and the instantaneous transmission ratio of the chain drive are variable. The analysis is as follows: let the tight side of the chain be in a horizontal position during transmission, see Fig. 6.9. Let the main wheel rotate with equal angular velocity ω1 , then its indexed circumferential velocity is R1ω1 . When the chain link enters the main wheel, its pin always keeps changing its position with the rotation of the sprocket. When located at the instant of β angle, the instantaneous velocity of the horizontal motion of the chain is equal to the horizontal component of the pin circumferential velocity. That is, the chain speed v

v=cosβR1ω1 (6)


The angle varies between ±φ1/2, φ1=360./z1. When β=0, the chain speed is large, vmax=R1ω1; when β=±φ1/2, the chain speed is small, vmin=R1ω1cos(φ1/2). Therefore, even when the active sprocket rotates at a uniform speed, the chain speed v varies. It changes periodically every time a chain pitch is turned, see Fig. 10. Similarly, the instantaneous speed v`=R1ω1sinβ of the vertical movement of the chain also changes periodically, thus making the chain shake up and down.


slave (wheel, pulley)SprocketsSince the chain speed v ≠ constant and the angle γ is constantly changing (Fig. 9), thus its angular velocity ω2 = v/R2cosγ is also changing.

The instantaneous transmission ratio i of the chain transmission ratio is i=ω1/ω2=R2cosγ/R1cosβ (7)

Obviously, the instantaneous transmission ratio cannot be obtained as a constant value. Therefore the chain drive does not work stably.