A multiple clutch has to transmit 90kW from an engine running at 3500 rpm.
Clutch lining outer diameter is 200mm and inside diameter is 160mm. Spring pressure on clutch is 170kPa and it's coefficient of friction is 0.28.
a)Calculate the minimum clamping force required
b) Calculate the no. of clutch plates.
Could anyone explain how should use the data given to find the required values in (a) and (b)? Do we need to apply the equation P = FV, P=power, F=force to find the clamping force or? How do we calculate the no. of clutch plates?
Or is clamping force = spring pressure/area
if so what is the area we should consider? Is it the area considering outer or inner diameter or the common area to both of them?
Your help is highly appreciated!
To calculate the minimum clamping force required for the multiple clutch, you can use the equation P = FV, where P is the power (in Watts), F is the force (in Newtons), and V is the tangential velocity (in meters per second).
To find the tangential velocity V, we need to convert the engine speed from rpm to radians per second. Since 1 revolution corresponds to 2π radians, the angular speed ω in radians per second is given by:
ω = (2π * 3500) / 60
Next, we can calculate the tangential velocity V using the formula:
V = r * ω
where r is the radius of the clutch lining. Since we are given the outer diameter (D) and inner diameter (d) of the clutch lining, we can find the radius r using:
r = (D - d) / 2
Now that we have V, we can calculate the force F using the equation:
F = P / V
where P is the power given as 90 kW and V is the tangential velocity we just calculated.
Once we have the minimum clamping force required, we can calculate the number of clutch plates by considering the coefficient of friction and the clamping force.
The clamping force is given by the spring pressure divided by the contact area. Since the clutch lining has an inner and outer diameter, we need to calculate the contact area using the formula for the area of a ring:
A = π * (R^2 - r^2)
where R is the outer radius and r is the inner radius. In this case, R is D/2 and r is d/2.
Finally, we can calculate the number of clutch plates by dividing the clamping force by the frictional force per plate. The frictional force per plate can be found using the equation:
Frictional force = coefficient of friction * clamping force
Therefore, the number of clutch plates required is the clamping force divided by the frictional force per plate.
Remember, these calculations provide the minimum values and may require additional considerations based on the specific application and safety factors.