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# Important Formulae

## Calculation of the Contact Surface Pressure "p"

The contact surface pressure "p" of a Trapezoidal Lead Screw can be calculated by using the following formula:

F = Axial Force [N]
At = Total contact area between teeth of screw and teeth of nut in the plane perpendicular to the axis. [mm2]

dm = mean thread diameter [mm]
H1 = support radial size between teeth of
the nut and teeth of screw [mm]
Z = number of teeth gripping

For standard sized nuts, each At value can be found in the specification tables.

## Calculation of the Sliding Speed "Vst"

The sliding speed of a Lead Screw mechanism is calculated by using one of the following formulae:
- if rotational speed of screw has already been found:
n = round rotational speed/minute

- if the speed at which the nut must move has been established:

Vst = sliding speed on mean diameter of screw. [m/min]
Vtr = movement linear speed [m/min]

Note that the screw round rotational speed and motion linear speed relate as follows:

n = round rotational speed/minute
Vtr = movement linear speed [m/min]

## Torque

Calculating the torque necessary to move a Lead Screw mechanism is calculated by the following equation:
C = input torque [N●m]
F = axial force on the nut [N]
η = efficiency (assume efficiency with first breakaway friction factor f= 0.2)

The torque value does not take into account the efficiency of mechanical parts operating within the screw system, such as belts, bearings, or other transmission components. If a project is in the planning phase, a precautionary increase of between the 20 and 30% of the theoretical torque value is recommended. If using electric motors with low static torque values, assume another increase of around 50% to find adequate torque levels.

## Power

The power required to operate a trapezoidal Lead Screw and Nut system can be calculated by the use of the following equation:

P = power [kW]
C = torque [N●m]
n = rpm