The tool MC-01 computes the lead angle of power screws with Acme thread profile or square thread. It also determines the torque required to lift or lower a load and the efficiency of the screw.

In addition, a tutorial on how to use the tool in computation is provided and a subject review on fundamental theories and useful formulas is presented.

## Tutorial

Example: Power Screw

The input in the tool is

After clicking "Run", the results will be shown as follows in another page.

Pitch Diameter (dp) = 0.79 m

Lead Angle (α) = 4.60721214 (Degree)

Torque required to lift the load (Tlift) = 188.40738662 N*m

Torque required to lower the load (Tlower) = 122.99576671 N*m

Screw Efficiency (e) = 0.16894767

Self-locking condition is satisfied

## Subject Review

### Power Screws

Power screws are used to change angular motion into linear motion. Power screws have different thread profiles, such as Acme thread, square thread, etc. Fig. 1 and 2 shows the details of Acme and square thread profile, respectively.

Fig. 1 Details of standard Acme thread profile

Fig. 2 Details of square thread profile

The lead angle (α) is defined by

where

L: Lead (The distance traveled in the axial direction per revolution) and L=mp (m=1 for single threaded; m=2 for double threaded)

dp: Pitch diameter (Mean diameter)

### Case I: Lifting the Load

The equations of motion are

By solving the equation,

where

μ: friction coefficient

with β being the thread angle.

The screw torque required to lift the load is

If the collar friction is included, the total torque to lift the load is

where

Tc=Wμcrc: torque required to overcome the collar friction

μc: collar friction coefficient

### Case II: Lowering the Load

Similar to case lifting the load, the total torque required to lower the load is

For the case of square thread, θn=β=0. Then cosθn=cos(β/2)=1

If the friction cannot positively support the load, the load will fall due to the gravity effect. The condition to keep the load from lowering in an uncontrollable situation is that the torque required to lower the load is positive, which is called self-locking. If the collar friction is neglected, the condition for self-locking is

For the case of square thread, θn=β=0. Then cosθn=cos(β/2)=1

For a power screw with square thread, the condition becomes

Note that the above equation only assures self-locking in static condition.

### Efficiency

The efficiency of a screw is defined by

which is

If the collar friction is neglected, the efficiency becomes

For square thread, the efficiency is

### References

1. R.G. Budynas and J.K. Nisbett, Mechanical Engineering Design, 2011, McGraw-Hill.

2. S.R. Schmid, B.J. Hamrock and B.O. Jacobson, Fundamentals of Machine Elements, 2014, CRC Press Taylor & Francis Group.

3. A.C. Ugural, Mechanical Design: An Integrated Approach, 2004, McGraw-Hill.