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.