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What is slip of the belt? How slip of belt affect the velocity ratio?

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When the driver pulley rotates, it carries the belt, due to a firm grip between its surface and the belt. The firm between the pulley and the belt is obtained by friction. This firm grip is known as frictional grip. But sometimes the frictional grip is not sufficient. This may cause some forward motion of the driver pulley without carrying the belt with it. This means that there is a relative motion between the driver pulley and the belt. The difference between the linear speeds of the pulley rim and the belt is a measure of slip. Generally, the slip is expressed as a percentage. In some cases, the belt moves faster in the forward direction, without carrying the driver pulley with it. Hence in case of driven pulley, the forward motion of the belt is more than that of driver pulley. Slip of belt is generally expressed in percentage(%). 

Let v = Velocity of belt, passing over the driver pulley/min 

N1 = Speed in R.P.M. of driver 

N2 = Speed in R.P.M. of follower 

S1 = Slip between driver and belt in percentage 

S2 = Slip between follower and belt in percentage 

The peripheral velocity of the driver pulley

Now due to Slip between the driver pulley and the belt, the velocity of belt passing over the driver pulley will decrease

Velocity of belt,

Now with this velocity the belt pass over the driven pulley, 

Now Velocity of Driven = Velocity of Belt - Velocity of belt X (S2 /100)

Equate the equation (iii) and (iv)

= N1D1[1-(s1+s2)/100], Neglecting s1.s2/10,000, since very small

If s1 + s2= S = Total slip in %

N2/N1 = D1/D2[1–S/100]

This formula is used when total slip in % is given in the problem 

NOTE: If Slip and thickness both are given then, Velocity ratio is,

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