VALICALC / MECHANICAL ENGINEERING SUITE / DS14

Worm Drive Geometry & Thermal Balance Design Sheet

Define matching worm/wheel geometry and the driving member. Mesh efficiency is calculated from explicitly entered friction, rather than copied from a generic table. A separate bounded heat-balance solve can couple a supplied friction-versus-temperature model to an entered housing conductance.

Verified mathematical models with explicit assumptions. Component capacity and applicability are shown as separate checks.

Labeled example inputs • SI calculations • Project revision 0 • No account or cloud upload

01 / ENGINEERING INPUTS

Define the operating point

Driving memberFriction assumptionThermal evaluation

Actual worm starts

Actual wheel teeth

Axial module

Worm reference diameter quotient q

Normal pressure angle

deg

Driving member RPM magnitude

rpm

Driving member mechanical power

Effective running friction at reference temperature

Friction reference temperature

°C

Entered temperature for fixed-friction evaluation

°C

Ambient temperature

°C

Documented lumped housing conductance UA (0 = unknown)

W/K

Entered qualified housing temperature limit

°C

02 / CALCULATE → SELECT → RECALCULATE

Calculation & checks

Actual ratio wheel teeth / starts

Worm reference pitch diameter

40 mm

Wheel reference pitch diameter

160 mm

Unshifted center distance

100 mm

Worm lead

25.13274 mm

Reference lead angle

11.30993 deg

Effective entered running friction

0.05

Equivalent running friction angle

3.04577 deg

Forward mesh efficiency

0.78146

Reverse sliding efficiency (0 = inapplicable)

0.72623

Worm RPM

1,500 rpm

Wheel RPM

75 rpm

Output mechanical power

1.17218 kW

Input member torque

9.5493 N·m

Output member torque

149.24713 N·m

Mesh heat generation

0.32782 kW

Evaluated housing / model temperature

40 °C

Pitch-line sliding speed

3.20381 m/s

Original schematic; not a manufacturing drawing. Worm drives wheel · Entered running friction · Lumped housing heat balance. Actual dimensions and model checks are listed in the calculation record.

Intermediate values and comparisons - SI units
Quantity	Worm	Wheel
Teeth / starts	2	40
Reference pitch d (m)	0.04	0.16
RPM	1,500	75
Driver / driven	Driver	Driven

Criterion-specific verification

PASSED · Defined unshifted axial-module geometry
Actual integer starts/teeth and q define the reference diameters, ratio, lead and center; no shifted/generated tooth approval.
UNKNOWN · Entered lumped heat-balance criterion
Uses the entered operating temperature; no housing heat balance is solved.
PASSED · Entered model-temperature limit
Entered temperature/model output compared with supplied housing limit only.
UNKNOWN · Running friction / housing-data applicability
Constant or local linear friction is an entered assumption. Startup/static friction, viscosity, churning/bearing/seal heat and cooling conditions require qualified data.
BLOCKED · Self-locking / load holding
A reverse-slip screen is not a brake, safety device or static/dynamic self-locking approval.
BLOCKED · Material strength, wear and certified thermal rating
Current applicable product/standard load factors, materials, lubricant and housing evidence are unavailable.

Method and calculation trace

d1 = q mx; d2 = z2 mx; tanγ = starts/q; unshifted 90° cylindrical worm geometry.

ρ = atan(μ/cosαn); forward η = tanγ/tan(γ+ρ); reverse sliding η = tan(γ−ρ)/tanγ only for γ>ρ. Bearing/churning losses are excluded.

Steady lumped balance: UA(T−Tamb) = Pin[1−η(μ(T))]. The bounded scan rejects missing/multiple roots; the selected bracket is bisected and residual-checked.

A PASSED thermal equation is only a comparison under supplied assumptions. Friction, UA and temperature applicability remain UNKNOWN; material/rating/holding checks stay BLOCKED.

Assumptions & scope

Unshifted cylindrical worm with axial module and 90° shaft angle: d1 = q m, d2 = z2 m. Shifted/enveloping worm generated geometry and strength remain blocked.

Friction is an entered effective running assumption for the actual lubricant/material/finish and sliding regime. Forward/reverse mesh efficiency excludes bearing, seal and churning losses; no self-locking safety claim is made.

The heat solver uses an entered lumped UA and a constant/local linear μ(T), no empirical housing table. A converged housing temperature is not a verified oil temperature or thermal rating. Multiple/no roots or invalid friction below the entered limit are blocked.

Full contact/root/overload, wear, support deflection, lubricant life, startup friction and product selection require independent qualified data.

Worked example

A two-start worm, 40-tooth wheel, axial module 4 mm and q = 10 gives 20:1, diameters 40/160 mm, 100 mm center and 11.310° lead angle. With 1500 RPM worm input, output is 75 RPM. Running friction and supplied UA control the calculated mesh loss and illustrative housing heat balance separately.

Calculation methods and sources

i=z2/starts; d1=q mx; d2=z2 mx; lead=pi mx starts; tan(gamma)=starts/q

Unshifted axial-module cylindrical worm, right-angle shafts. No shifted/enveloping manufacturing geometry.

KHK Gear Technical Reference worm dimension section; Tập 1 Chapter 7 geometry context pp150-153.

rho=atan(mu/cos(alpha_n)); etaForward=tan(gamma)/tan(gamma+rho); etaReverse=tan(gamma-rho)/tan(gamma)

Entered effective running friction; reverse sliding only for gamma>rho. Excludes bearing/churning/seal losses and static self-locking approval.

KHK/KG worm mesh friction force equilibrium; independently derived inclined-contact balance. No empirical friction table is copied.

UA(T-Tambient)=Pin[1-eta(mu(T))]

User supplied lumped conductance and constant/local-linear running friction, bounded root scan plus bisection. A converged model temperature is not a certified oil/housing thermal rating.

Independent energy balance; Tập 1 7.29-7.32 printed pp156-157 / PDF155-156 identify thermal context. Historical transfer coefficients are not used.

n out = n in/i; P out = ηP in; η total = Πη; T out = ηiT in

Serial passive motoring power flow; 0 < η ≤ 1. Rotation signs do not imply a reversible loss model.

Tập 1, 2.15–2.18 and 3.23–3.25; independent conservation-of-energy derivation.

Textbook references identify the method context. Historical numerical catalog, material and service-factor tables have not been copied or treated as current product ratings.

Related calculators and references

Existing component-selection Jobs → · All mechanical worksheets →

Common questions

Does this approve a real component?

No. The worksheet separates mathematical results from criterion-specific checks. Actual motor, belt, gear, shaft, bearing and joint capacity need applicable current source data and engineering review.

What changes after choosing a physical size?

The worksheet recalculates the outputs and geometry from the entered actual dimensions or discrete tooth/link count. Dependent checks are reevaluated; previously saved results are not restored as approvals.