Belt Drive power tramsmission and torque

[ben774]

Homework Statement

iv been given this problem having attmepted it I am stuck when it comes to calculating maximum torque and can't seem to find any equations to help me out.

in a belt drive system the speed of the belt over the pulleys is 170/min. The initial tension of the belt is 400N and the tension on the tight side is 700N. if the Driver pulley is 300mm diameter and the ddriven pulley is 180mm diameter. calculate:

a) The power tramsmitted by the belt drive
b) The maximum torque output

any help would be much appriciated!

Homework Equations

power transmitted P=(T2-T1)V
where T1 = tight side and T2 = slack side
v= wr rads/s

The Attempt at a Solution

iv attempted part a) which i got

(700-400)v

170/0.3 = 180.4
180 x 2$$\check{}\Pi$$/60 = 18.89

v = 18.89 x 0.3 = 5.67

P= (700-400)5.67=1.7 kw

 

[KataKoniK]

Hello, thank you for reaching out for help with your problem. Calculating maximum torque can be a bit tricky, but I can provide you with some equations and guidance to help you solve it.

First, let's define some variables:
- T1 = initial tension of the belt (400N)
- T2 = tension on the tight side of the belt (700N)
- N = speed of the belt over the pulleys (170/min)
- D1 = diameter of the driver pulley (300mm)
- D2 = diameter of the driven pulley (180mm)
- P = power transmitted by the belt drive
- Tmax = maximum torque output

To calculate the power transmitted by the belt drive (P), we can use the equation you provided:
P = (T2 - T1) * V

Where V is the velocity of the belt, which can be calculated using the following equation:
V = (N * D1 * \check{}\Pi) / (60 * 1000)

Plugging in the given values, we get:
V = (170 * 0.3 * \check{}\Pi) / (60 * 1000) = 0.00898 m/s

Now, we can plug this value for V into the equation for power:
P = (700 - 400) * 0.00898 = 2.69 watts

To calculate the maximum torque output (Tmax), we can use the following equation:
Tmax = (T2 - T1) * (D1 / 2)

Plugging in the given values, we get:
Tmax = (700 - 400) * (0.3 / 2) = 105 Nm

I hope this helps you solve the problem. Remember to always double check your units and make sure they are consistent throughout the calculations. Good luck!