Worm Gear Calculator

Example data table

Formula used

These equations are simplified for quick estimation. For final design, include contact stress, bending stress, lubrication regime, and detailed thermal modeling.

How to use this calculator

1. Choose whether you know input power or input torque.
2. Enter the worm starts, wheel teeth, and input speed.
3. Provide module and diameter factor to estimate geometry.
4. Set μ manually or choose a friction preset.
5. Apply a service factor if your duty has shocks or starts.
6. Press Calculate to see results above the form.
7. Use CSV or PDF buttons to save your run for records.

Sizing ratio and speed

Gear ratio i equals z2 divided by z1, so a 2‑start worm with 40 teeth gives i=20. Output speed n2 is n1/i; at 1450 rpm, n2 is 72.5 rpm. Higher ratios increase reduction but also raise sliding and heat. Use z1 from 1 to 6 for compact drives, and adjust z2 to hit target speed.

Torque and service factor

Input torque T1 can be derived from power using T1 = 9550·P/n1. The calculator estimates output torque T2 = T1·i·η, then applies the service factor for design torque. For steady fans, Ks near 1.1 is common; for conveyors and frequent starts, 1.5–2.0 is typical. Use the design torque when selecting shafts, keys, and couplings.

Efficiency and heat loss

Efficiency varies strongly with lead angle γ and friction μ. The estimate uses η ≈ tan(γ)/tan(γ+φ), where φ = arctan(μ). Lower μ and larger γ improve η, but may reduce holding behavior. Heat loss is Pin−Pout, shown in kW. If loss is high, plan for better lubrication, smoother finishes, and a housing that can dissipate heat continuously.

Geometry and packaging checks

Basic geometry is summarized from module m and diameter factor q. Worm pitch diameter is d1 ≈ q·m, wheel pitch diameter is d2 ≈ m·z2, and center distance is a = (d1+d2)/2. Increasing m grows diameters and strength, but increases size and cost. Adjust q to balance worm stiffness against packaging limits and center distance targets.

Typical module choices for industrial units range from 2 to 8 mm, while q often sits between 8 and 16. Keep wheel pitch line velocity moderate to reduce noise and scuffing, and review duty temperature limits for your lubricant. As a quick check, aim for efficiency above 0.7 when continuous power is high, or provide extra cooling for demanding industrial duty cycles.

Forces and component selection

The design tangential force at the wheel is Ft ≈ 2000·T2,design/d2(mm). This load drives tooth contact stress and bearing reactions. Higher Ft may require wider faces, stronger wheel material, and larger bearings. Sliding velocity is also reported to support lubricant selection. Combine Ft, speed, and duty cycle to estimate wear risk and to set maintenance intervals.

FAQs

1) What does q represent in a worm drive?

q is the diameter factor that links worm pitch diameter to module: d1 ≈ q·m. Larger q increases worm diameter and stiffness, but usually increases center distance and packaging size.

2) How accurate is the efficiency value?

It is a practical estimate based on lead angle and friction. Real efficiency depends on lubrication regime, surface finish, materials, temperature, and manufacturing quality, so validate with vendor data for critical designs.

3) When is a worm drive likely self-locking?

Self-locking is more likely when the lead angle is smaller than the friction angle. The calculator flags this condition, but backdriving can still occur with vibration, wear, or low loads.

4) Why apply a service factor?

Service factor covers shocks, starts, stops, and duty severity. It increases the design torque and tangential force so shafts, teeth, and bearings are sized with a safety margin for real operating conditions.

5) Which output torque should I use for sizing?

Use the design output torque shown after service factor is applied. The “available” torque is a baseline estimate; the design value is intended for component selection and durability checks.

6) How should I interpret heat loss?

Heat loss is the power not delivered to the load. If it is substantial, consider improving lubrication, reducing ratio per stage, increasing lead angle, or adding cooling capacity to prevent excessive temperature rise.