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 P = thread pitch [mm] α = thread helical angle
- 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] α = thread helical angle
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] P = thread pitch [mm]
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] P = screw lead [mm] 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.
The power required to operate a trapezoidal Lead Screw and Nut system can be calculated by the use of the following equation: