# LEAD SCREW CALCULATOR for FORCE TORQUE CALCULATIONS

Lead screw calculator for force, torque, efficiency and self-locking calculations of ACME lead screws.

A Lead screw (or Power screw) is a device which converts rotational motion to a linear motion and transmits power. Square, Acme and Buttress thread forms are generally used as lead screws. Common applications are lead screw of lathes, screw presses, screw type of jacks and micrometer screw.

There is a large contact area between male and female threads in lead screws and this results large frictional loss during the operation. Due to these frictional losses, lead screws are not very efficient but generally self-locking. In self locking lead screws, the load can’t lower itself without an external effort. This feature is generally used to hold loads.

Ball screws are efficient alternatives to lead screws. In ball screws, ball bearings are recirculating between the screw rod and nut. This results a significantly less friction than the power screws. However,  brakes are needed to stop ball screws from overhauling.

### Lead Screw Calculator:

 INPUT PARAMETERS Parameter Value Acme Thread Type General Purpose Stub --- Nominal diameter (inches) - threads per inch 1/4-16 5/16-14 3/8-12 7/16-12 1/2-10 5/8-8 3/4-6 7/8-6 1-5 1 1/8-5 1 1/4-5 1 3/8-4 1 1/2-4 1 3/4-4 2-4 2 1/4-3 2 1/2-3 2 3/4-3 3-2 3 1/2-2 4-2 4 1/2-2 5-2 Number of Start [n] 1 1 2 3 4 Load [F] lbf Coefficient of Thread Friction [f]2 --- Coefficient of Collar Friction [fc]2 Mean Collar Diameter [dc] in

Note: 1 Single or multiple start Acme thread.

 RESULTS Parameter Value Nominal Diameter [D] --- in Threads per inch [n] --- --- Basic Pitch Diameter [D2] --- in TORQUE AND EFFICIENCY CALCULATIONS Torque to Raise the Load [TR] --- lbf*in lbf*ft Torque to Lower the Load [TL]0 --- Efficiency during Lifting [e] --- --- Self Locking ---

Note: 0 If TL is negative, the lead screw is not self-locking.

### Definitions:

Lead: The distance that screw (or nut) advances in one revolution.

Major Diameter: The maximum diameter of a thread which is diameter of the crest of a male thread or root of a female thread.

Minor Diameter: The minimum diameter of a thread which is diameter of the root of a male thread or crest of a female thread.

Multi Start Acme Thread: Provides fast relative traversing motion with lower mechanical advantage.

Stub Acme Thread: The thread height is less than general purpose and centralizing acme threads. The thread height is 0.3 pitches for Stub Acme thread. In general purpose form this is 0.5 pitches. Stub Acme thread form is provided for unusual applications where a coarse-pitch thread of shallow depth is required due to mechanical or metallurgical reasons.

Thread class: A classification system to classify the threads for interchangeability and manufacturability.

Threads per inch: Number of full thread per an inch length.

### Lead Screw Formulas:

 Parameter Equation Torque required to raise the load [TR] 1,2,3 $${ T }_{ R }=\frac { F\cdot { d }_{ m } }{ 2 } (\frac { l+\pi f{ d }_{ m }\sec { \alpha } }{ \pi { d }_{ m }-fl\sec { \alpha } } )+{ T }_{ c }$$ Torque required to lower the load [TL]1,2,3 $${ T }_{ R }=\frac { F\cdot { d }_{ m } }{ 2 } (\frac { -l+\pi f{ d }_{ m }\sec { \alpha } }{ \pi { d }_{ m }+fl\sec { \alpha } } )+{ T }_{ c }$$ Frictional torque of the thrust collar [Tc] $${ T }_{ c }=\frac { F{ f }_{ c }{ d }_{ c } }{ 2 }$$ Efficiency during lifting the load [e] 3 $$e=\frac { Fl }{ 2\pi { T }_{ R } }$$

Note 1: dm is mean diameter and basic pitch diameter (D2) is used as mean diameter in the calculations.

Note 2: 2α is thread angle and 29 deg for Acme thread.

Note 3: l is the lead distance.