Question

. A belt drive is desired to couple the motor with a mixer for processing corn syrup. The 25-hp electric motor is rated at 950 rpm and the mixer must operate as close to 250 rpm as possible. Select an appropriate belt size, commercially available sheaves, and a belt for this application. Also calculate the actual belt speed and the center distance.

Answer 1

Hello the table which is part of the question is missing and below are the table values

For a 5V belt the available diameters are : 5.5, 5.8, 5.9, 6.2, 6.3, 6.6, 12.5, 13.9, 15.5, 16.1, 18.5, 20.1

Answers:

belt size = 140 in with diameter of 20.1n

actual speed of belt = 288.49 in/s

actual center distance = 49.345 in

Step-by-step explanation:

Given data :

Electric motor (driver sheave) speed (w1) = 950 rpm

Driven sheave speed (w2) = 250 rpm

pick D1 ( diameter of driver sheave) = 5.8 in ( from table )

To select an appropriate belt size we apply the equation for the velocity ratio to get the diameter first

VR =
`(w1)/(w2)` = 950 / 250

also since the speed of belt would be constant then ;

Vb = w1r1 = w2r2 ------- equation 1

r = d/2

substituting the value of r into equation 1

equation 2 becomes :
`(w1)/(w2) = (d2)/(d1)` = VR

Appropriate belt size ( d2) can be calculated as

d2 =
`(w1d1)/(w2)` =
`(950 * 5.8)/(250)` = 22.04

From the given table the appropriate belt size would be : 20.1 because it is the closest to the calculated value

next we have to determine the belt length /size

`L = 2C + (\pi )/(2) ( d1+d2) + ((d2-d1)^2)/(4C)`

inputting all the values into the above equation including the value of C as calculated below

L ≈ 140 in

Calculating the center distance

we use this equation to get the ideal center distance

`d2< C_(ideal) < 3( d1 +d2)`

22.04 < c < 3 ( 5.8 + 20.1 )

22.04 < c < 77.7

the center distance is between 22.04 and 77.7 but taking an average value

ideal center distance would be ≈ 48 in

To calculate the actual center distance we use

`C = (B+√(B^2 - 32(d2-d1)^2) )/(16)` -------- equation 3

B =
`4L -2\pi (d2 + d1 )`

inputting all the values into (B)

B = 140(4) - 2
`\pi`( 20.01 + 5.8 )

B ≈ 399.15 in

inputting all the values gotten Back to equation 3 to get the actual center distance

C = 49.345 in ( actual center distance )

Calculating the actual belt speed

w1 = 950 rpm = 99.48 rad/s

belt speed ( Vb) = w1r1 = w1 *
`(d1)/(2)`

= 99.48 * 5.8 / 2 = 288.49 in/s