Worm gears

A compatible two-start worm and 40-tooth wheel give 20:1 and 60 r/min output at 1,200 r/min input. With assumed 500 W input and 70% whole-drive efficiency, output is 350 W and 55.7 N·m, with 150 W lost. Ratio alone leaves efficiency, heat rejection and backdrivability unresolved. Verify the selected pair, lubrication and duty.

Geometry and component identity

A worm and wheel mesh on nonparallel, nonintersecting shafts. A two-start worm advances a compatible wheel by two teeth per worm revolution. KHK, Calculation of Gear Dimensions, §4.6.

Ratio is wheel teeth divided by worm starts. Axial pitch is thread spacing, while lead is advance per revolution. For axial module mₓ and z₁ starts, L = πmₓz₁ and tan γ = L/(πd₁) at reference diameter d₁. Keep axial and normal module conventions separate. KHK, §4.6, tables 4.22–4.24.

Mating parts are a system

The same nominal module does not by itself prove compatibility. KHK provides a mating-selection matrix by product series, thread count, and helix direction, and requires the mating wheel to have the same module as its worm. Use the specified combination rather than substituting a visually similar wheel. KHK, Worm Gears — Technical Information, mating selection.

A concrete catalog distinction is KHK's KWG1-R1 versus KWG1-R2: both have axial module 1 and a 16 mm pitch diameter, but the former has one start and nominal lead angle 3°35′, while the latter has two starts and 7°08′. Their AG wheel listings identify the required number of mating-worm starts. The KWG specification also identifies SCM440 steel, induction-hardened teeth, and 50–60 HRC tooth hardness; those are series-specific properties, not properties of all worms. KHK, Ground Worm Shafts, KWG/AG product tables.

Forces, sliding, and efficiency

Tooth forces have tangential, radial, and axial components. Bearings and the housing must support the resulting thrust and separating loads as well as transmit torque. KHK's force analysis for a 90° worm pair explicitly includes tooth-surface friction because sliding affects both mesh forces and transmission efficiency. A torque-only shaft calculation leaves these reactions unresolved. Force direction must follow the actual helix hand, rotation, and driving member in the assembly drawing. KHK, Gear Forces, §12.3.

Efficiency needs a defined boundary. Gear-mesh efficiency excludes losses elsewhere in the drive. Nidec identifies additional losses in bearings, seals, and lubricant, and explains that worm-gearbox efficiency varies with speed, ratio, load, ambient temperature, duty cycle, lubricant viscosity, and break-in. Consequently, a single efficiency percentage cannot describe every operating point of a nominal ratio. Nidec Drive Technology, Worm Gearing: The Underrated Performer in Motion Control, efficiency considerations.

Startup also deserves a separate check. SEW-EURODRIVE states that starting efficiency is lower than efficiency at operating speed, particularly for its helical-worm and SPIROPLAN right-angle units. Its thermal guidance identifies mounting positions that immerse the first stage in lubricant and high mean input speeds as causes of churning losses. Thermal suitability therefore requires the actual operating and mounting conditions, not just a tooth-strength rating. These observations concern SEW's gear units; they supply no numerical rating for an unboxed KHK pair. SEW, General information, DRN Gearmotors, churning losses and thermal rating.

Backdriving and self-locking

Backdriving means the wheel drives the worm. Self-locking describes resistance to that reverse transmission under particular conditions. It is not an automatic consequence of being a worm drive or having a large reduction ratio. Nidec relates it to helix angle and friction, distinguishes static from dynamic behavior, and notes that lubrication, surface condition, speed, and vibration affect the result. It recommends a brake rather than relying on theoretical self-locking to hold a load. Nidec, self-locking discussion.

Tsubaki likewise warns that shock or vibration can reduce the effect and calls for a separate brake where reliable reverse-rotation prevention is required. Its ratio-specific expectations apply to its Croise Motor products; they are not transferable acceptance criteria for another gearbox. For engineering records, state the actual holding device and required behavior after power loss instead of treating “self-locking worm” as a safety function. Tsubaki, About Self-Locking.

Materials, lubricant, and assembly

A bronze wheel makes lubricant chemistry particularly important. Boston Gear warns that additives such as sulfur or chlorine can degrade worm-gear components and emphasizes manufacturer-approved lubricants. An EP label alone does not establish suitability for a particular bronze alloy. Correct lubricant quantity matters too: insufficient lubrication can cause premature failure, and mounting orientation affects oil delivery in conventional gearboxes. Follow the actual unit's fill and lubricant instructions rather than borrowing a viscosity or oil quantity from a similar-size reducer. Boston Gear, Getting the Most Out of Your Gearboxes.

KHK recommends H7 centre-distance tolerance for its ground stock worm gears and H8 for cut gears, with backlash values in the product tables. It also requires alignment of the worm shaft with the wheel tooth-width centre, checking tooth contact, and avoiding zero backlash at startup. These are KHK stock-product instructions, not universal housing tolerances or permission to adjust any worm pair by moving its shafts. KHK, assembly and starting precautions.

Bounded ratio and power example

Assume a compatible two-start worm, a 40-tooth wheel, and worm input at 1,200 r/min. The kinematic result is i = 40/2 = 20 and wheel speed 60 r/min. Replacing only the worm with a single-start part is not an approved way to obtain 40:1; the mating geometry must also be appropriate.

For assumed whole-drive efficiency η = 0.70 and mechanical input power 500 W:

Output power = η × input power = 350 W
Loss power = input − output = 150 W
Output angular speed = 2π × 60 / 60 = 2π rad/s
Output torque = 350 / (2π) = 55.7 N·m

The 70% figure is an assumption, not a measured or catalog efficiency. The 150 W loss illustrates the heat burden during steady operation; it does not calculate housing temperature, permissible duty, starting torque, or tooth capacity. Ratio follows the KHK geometry above; power and torque results are derived arithmetic.

Selection and failure boundaries

KHK bases catalog strength values on stated application assumptions and asks users to calculate with actual conditions. Its selection procedure considers load torque and sliding speed. Its startup precautions call for stopping on abnormal noise or vibration and checking contact, eccentricity, and looseness. A torque table alone is not a service-life guarantee. KHK, selection and starting precautions.

As an engineering synthesis, a useful selection record connects both mating identifiers to ratio, input speed, load spectrum, starting and reversing duty, thrust support, contact/backlash checks, lubricant, mounting orientation, and thermal conditions. Wear, overheating, or noise should trigger examination of those conditions before substitution of a larger motor or a tighter mesh. This article does not provide a universal efficiency, self-locking angle, lubricant grade, allowable temperature, or torque rating.

Related reference

Production planning references explains how the identities of a worm, wheel, and complete reducer belong in an assembly definition.