a vertical shaft 150mm in diameter rotating 100r.p.m resrs on a flat end foot step bearing.the shaft carries a vertical load of 20kN assuming uniform pressure distribution and coefficient equal to 0.05, estimate power lost in friction
To estimate the power lost in friction, we need to calculate the frictional force and then multiply it by the rotational speed of the shaft. Here's how you can do it:
Step 1: Calculate the area of the bearing surface.
The diameter of the shaft is given as 150mm, so we can find the radius by dividing it by 2:
Radius = 150mm / 2 = 75mm = 0.075m
The area of the bearing surface can be calculated using the formula for the area of a circle:
Area = π * Radius^2
Area = π * (0.075m)^2
Step 2: Calculate the pressure distribution acting on the bearing surface.
The load on the vertical shaft is given as 20kN. Since the pressure is assumed to be uniformly distributed, we can calculate the pressure by dividing the load by the bearing surface area:
Pressure = Load / Area
Step 3: Calculate the frictional force.
The frictional force can be calculated by multiplying the pressure distribution by the coefficient of friction:
Frictional force = Pressure * Coefficient of friction
Step 4: Calculate the power lost in friction.
The power lost in friction can be calculated by multiplying the frictional force by the rotational speed of the shaft:
Power lost = Frictional force * Rotational speed
Now, you can substitute the values given in the problem to calculate the power lost in friction.