Efficiency Calculation of a Screw Jack
What is the efficiency to lift the load?
Given the load of 5 kN, pitch of 8 mm, diameter of 40 mm, coefficient of friction of 0.15, and lever radius of 400 mm, how do we calculate the efficiency to lift the load?
Efficiency Calculation:
To calculate the efficiency to lift the load, we need to follow these steps:
First, let's convert the given values to consistent units:
Load = 5000 N
Pitch = 0.008 m
Diameter = 0.04 m
Coefficient of friction = 0.15
Lever radius = 0.4 m
i) Efficiency to lift the load (η_lift):
- Calculate the Mechanical Advantage (MA_lift):
MA_lift = (π * Lever Radius) / Pitch
- Calculate the Frictional Force (F_friction):
F_friction = Coefficient of friction * Load
- Calculate the Actual Mechanical Advantage (AMA_lift):
AMA_lift = MA_lift - (F_friction / Load)
- Calculate the Efficiency to lift the load (η_lift):
η_lift = (AMA_lift / MA_lift) * 100%
ii) Effort to lift the load (E_lift):
E_lift = Load / MA_lift
iii) Efficiency to lower the load (η_lower):
- Calculate the Mechanical Advantage (MA_lower):
MA_lower = (π * Lever Radius) / Pitch
- Calculate the Actual Mechanical Advantage (AMA_lower):
AMA_lower = MA_lower + (F_friction / Load)
- Calculate the Efficiency to lower the load (η_lower):
η_lower = (AMA_lower / MA_lower) * 100%
iv) Effort to lower the load (E_lower):
E_lower = Load / MA_lower
By following these calculations, we can determine the efficiency to lift the load and the corresponding effort required.