Helical gears

KHK's KHG1-20R has transverse module 1 mm, 20 teeth, 20 mm reference pitch diameter and 21.5° helix angle. At an assumed 1.00 N·m, ideal tooth loads are 100 N tangential, 36.4 N radial and 39.4 N axial, using the 20° transverse pressure angle for radial force. Match the mating geometry and provide a thrust load path. These forces describe the assumed torque case. KHK, pp. 196–197.

Tooth geometry and reference planes

The helix angle describes the tooth trace relative to the axis. Helix lead is its axial advance per turn, πd/tan β, at reference diameter d. KHK, Calculation of gear dimensions, §4.3 and Fig. 4.7.

Normal measurements are perpendicular to the tooth trace; the transverse section is perpendicular to the gear axis. With normal module mn, transverse module mt, normal pressure angle αn and transverse pressure angle αt:

These are reference-geometry relationships, not tolerances or measurements of a particular delivered part. A label such as “module 1, pressure angle 20°” is incomplete without the plane convention. Working pitch diameter and working pressure angle can differ from reference values with profile shift or changed operating center distance. KHK, §4.3, Tables 4.9–4.11 and Eq. 4.16.

Compatible meshing and load paths

For external parallel-axis gears, mating helix angles have equal magnitudes and opposite hands, with compatible tooth geometry. Tooth count sets the ideal speed ratio. Matching module alone does not establish interchangeability. Profile shift, center distance and mounting interfaces also matter. Crossed-axis screw gearing is a different arrangement. KHK, Calculation of gear dimensions, §4.3.

The tooth contact transmits tangential force that produces torque, radial force that loads the shaft support, and axial thrust associated with the helix. For an ideal static mesh at reference geometry, neglecting friction and dynamic load amplification:

• Ft = 2000T/d, for torque T in N·m, d in mm, and force in N.
• Fa = Ft tan β, the magnitude of axial thrust.
• Fr = Ft tan αt = Ft tan αn/cos β, the radial force magnitude.

The factor 2000 combines radius d/2 with the millimeter-to-meter conversion. Thrust direction depends on helix hand, rotation and the driving/driven role; these magnitude equations do not determine its sign. KHK, Gear forces, Table 12.1 and Fig. 12.2.

As engineering synthesis, mesh forces reach the bearings and housing through the gear and shaft. Bearing reactions depend on gear position, support spacing, shaft bending and bearing arrangement; they need not equal individual mesh-force components. KHK, Gear forces, force directions and shaft/bearing context.

Backlash, clearance and lubrication

Backlash is clearance between mating tooth flanks, not the radial gap between a tooth tip and root. Normal, transverse and angular backlash values describe different quantities. KHK explains that tooth thinning or a change in center distance can alter backlash. Consequently, a table value needs its direction and assembly conditions; it is not automatically the lost motion of a complete gearbox. Zero nominal backlash can also impair smooth rotation rather than establish precision. KHK, Gear backlash, §§6.1–6.5.

Lubrication supports an oil film at tooth contacts, reducing direct metal contact and friction. Grease, splash lubrication and forced circulation have different operating scopes. Excess oil agitation can add heat; insufficient supply can impair both lubrication and cooling. Temperature changes viscosity and can reduce backlash through component expansion. Lubricant choice therefore depends on speed, load, temperature, supply method and the materials present; no universal viscosity or relubrication interval follows from “helical gear.” KHK, Lubrication of gears, §§13.1–13.2.

Named catalog example: KHK KHG1-20R

KHK's ground-gear specification and row identify the following catalog reference. Dimensions are nominal tabulated geometry; hardness is a specified range, not a lot measurement. KHK, pp. 196–197.

Derived nominal geometry and forces

Using β = 21.5° and the stated transverse convention gives:

These calculated quantities are not additional manufacturer tolerances. For an illustrative standard, unshifted pair of otherwise compatible 20-tooth gears with opposite hands, the nominal reference center distance is (20 + 20)/2 = 20 mm. That center-distance calculation is not evidence of a qualified installation or a compatible arbitrary mating part. KHK, geometry relationships in §4.3.

At an assumed steady T = 1.00 N·m and d = 20 mm, the ideal force equations give Ft = 100 N, Fr ≈ 36.4 N, and Fa ≈ 39.4 N. The chosen torque is an arithmetic input, not an allowable operating load. Fr uses the transverse 20° angle; using 20° as a normal angle would change the result. Friction, shock, misalignment and tooth load distribution are excluded. KHK, force equations, Table 12.1.

KHK labels strength-table torques as calculated reference values under assumed conditions. This article does not adopt them as an assembly rating or life guarantee. KHK, p. 192.

Source conflicts, dates and applicability

The catalog has an internal conflict: p. 204 prose reverses the KHG/SH plane labels relative to pp. 192 and 196. The example follows p. 196's explicit KHG transverse specification and d = zmt dimensions. No revision history is inferred. KHK, pp. 192, 196 and 204.

Sources were retrieved 2026-10-31 PDT. The chapter prints pp. 190–205 but no standalone edition/date; 2025 is its URL directory. Its PDF metadata records June 9, 2025 creation/modification, distinct from a printed revision. The technical web pages have no displayed article revision date; their copyright footer is not an edition declaration.

Geometry and force coverage includes the manufacturer's original diagrams as well as its technical text.

Full JIS/JGMA/ISO gear standards were not read. No gear pair, purchased lot or customer assembly was tested. This reference establishes no universal allowable torque, efficiency, contact ratio, backlash, service life, interchangeability or installation rule. Tooth-root bending, surface durability, alignment, lubricant supply, bearing capacity and the actual load spectrum remain application-specific.

Production planning references.