Worm Gear Geometry, Sliding, and Efficiency Calculator

Content

Estimate standard cylindrical worm-drive geometry, pitch-line sliding, friction-dependent mesh efficiency, output torque, heat loss, and nominal mesh-force components.

Operating inputs

Whole number, 1–12

Rheologylab

Whole number, 5–500

Use a justified mesh value

Ready.

Estimated mesh efficiency
—%
Reduction ratio—
Lead angle (°)—
Sliding speed (m/s)—
Output torque (N·m)—
Mesh heat loss (kW)—
Wheel speed (rpm)—
Pitch diameters d1 / d2 (mm)—
Center distance (mm)—
Forces Ft2 / Fr / Fa2 (N)—
Static self-locking screen—

How to use

  1. Enter the worm starts and wheel teeth; their ratio sets the ideal speed reduction.
  2. Enter axial module in millimetres and diameter quotient for the nominal pitch geometry.
  3. Enter worm speed in rpm and steady input torque in N·m.
  4. Enter the normal pressure angle and a justified effective mesh friction coefficient for the actual materials, finish, lubricant, temperature, and sliding regime.
  5. Select Calculate to update the result panel, or Reset to restore the worked example.
  6. Read efficiency, output torque, heat loss, sliding speed, geometry, and nominal force components together. Correct any red input warning before using a result.
  7. Do not use this screening model for tooth rating, contact stress, thermal equilibrium, start-up, shock load, wear life, or safety-critical self-locking decisions.

Equations used

The worm is the driver. All angles in the equations are radians; displayed angles are degrees. Pitch dimensions use the axial module convention.

i = z2 / z1d1 = qm; d2 = z2ma = (d1 + d2) / 2γ = atan(z1 / q)ρ = atan(μ / cos αn)η = tan γ / tan(γ + ρ)n2 = n1 / ivs = π(d1/1000)n1/(60 cos γ)P1 = 2πn1T1/60 W = 2πn1T1/(60×1000) kWP2 = ηP1; Ploss = P1 − P2T2 = ηiT1Ft2 = 2T2/(d2/1000) = 2000T2/d2Fr = Ft2 tan αn / cos γFa2 = Ft2 tan γStatic self-locking screen = (γ ≤ ρ)

Symbols and units. z1 is worm starts; z2 is wheel teeth; m is axial module (mm); q is dimensionless diameter quotient; d1, d2, and a are pitch dimensions (mm); γ is lead angle; αn is normal pressure angle; μ and η are dimensionless; ρ is effective friction angle; n is rpm; T is N·m; vs is m/s; power is calculated in watts and divided by 1000 for the displayed kilowatt outputs; forces are N. The factors d1/1000 and d2/1000 explicitly convert pitch diameters from millimetres to metres in the sliding-speed and tangential-force equations. Positive speed and torque follow the driving direction. Heat loss is reported as a positive dissipation estimate.

Assumptions and limits. The model assumes steady worm-driving operation, standard cylindrical pitch geometry, constant user-supplied friction, and rigid alignment. It excludes bearings, seals, churning, windage, housing heat rejection, material/geometry tooth ratings, deformation, manufacturing deviations, and transient friction. The static screen reports possible self-locking when γ ≤ ρ, but must not be treated as a back-driving guarantee.

References. Geometry terminology and dimension relationships: KHK Gear Technical Reference. Public engineering context and comparison: Engineers Edge Worm Gear Sizing Calculator. Confirm final design against the applicable gear standard and manufacturer data.