How Convoloid® Gearing Works

The Problem

200 Years of Diminishing Returns

The involute gear tooth form has dominated engineering for over two centuries. It's been studied, refined, and optimized to near perfection, and the remaining gains come mostly from materials and finishing, not from the tooth form.

New materials, coatings, and surface finishing help at the margins. But the fundamental geometry hasn't changed. Convex meets convex, with maximum Hertz contact stress built in.

Convoloid changes the equation. A computer-optimized tooth form where convex meets concave, lowering contact stress while remaining compatible with the gear-cutting and inspection machines on your floor.

Involute

Convex–Convex Contact

High Contact Stress

VS

Convoloid^®

Convex–Concave Contact

Lower Contact Stress

Convoloid's S-curved flank creates a conformal mesh, naturally distributing load over more surface area.

Three Pillars

One Geometry. Three Breakthrough Outcomes.

The same physics that defines Convoloid's tooth form shows up in published rating analysis and in physical test. Every figure below is compared against an equivalent involute: same center distance, ratio, materials and heat treatment, face width, load and lubrication.

01

Higher Torque Capability

20–35 % Higher torque than equivalent involute designs

Rated per AGMA/ISO against an equivalent involute baseline, Convoloid shows 20–35% higher torque capability, published in AGMA 11FTM19 (Berlinger & Colbourne, 2011). The advantage is greatest in balanced designs with design freedom: face-width to center-distance ratios of about 0.2 and up, helix angles of 20–30° and higher ratios.

Published rating analysis, AGMA 11FTM19
Analysis shows power uprates approaching 20% in the same envelope, or the equivalent taken as longer life
Analysis shows higher single-stage ratios: smaller pinions with no undercut

02

Smaller & Lighter

Up to 20 % Smaller and lighter at equal power (analysis)

When a design is constrained to match an involute's power and stress levels, analysis shows the Convoloid gearbox can be up to about 20% smaller in enclosed volume and lighter. An analytical redesign of the Micon 108 wind gearbox came out 20.6% smaller in volume. (The unit DOE/NREL tested was a same-size retrofit, not this redesign.)

Up to ~20% smaller enclosed volume (AGMA 11FTM19)
Same materials, same power, same stress levels
Torque, size and ratio gains are alternative uses of the same stress margin; they don't add together

03

Durability

Tested Against Involute Two Test Programs

Convex-meets-concave contact lowers surface (Hertz) stress and root bending stress. In DOE/NREL gearbox testing at 200–240% of rated load, early micropitting on the Convoloid gears self-arrested and contact improved, while the involute's micropitting progressed to the end of the test.

Lower contact stress through the mesh (rating analysis)
Lower bending stress at the root (rating analysis)
DOE/NREL: Convoloid run-in stabilized; involute micropitting grew (see testing)
Penn State Gear Research Institute four-square testing confirmed Convoloid's surface-durability advantage and rating protocol

Hear It From the Inventor

Barney Berlinger Explains Convoloid®

Convoloid's inventor walks through what makes the tooth form different from the involute, and why that matters for power density, weight and life. It's the quickest way to understand the technology.

Convoloid® Gearing Technology Overview · Gear Innovations

The Technology

A Fundamentally Different Tooth

18T pinion × 33T wheel. Amber: path of contact · Glow: live contact · Orange: convex addendum · Steel: concave dedendum

01

The S-Curve Flank

Each Convoloid tooth has a characteristic S-curved profile. The dedendum (below pitch line) is concave; the addendum (above pitch line) is convex. This creates the conformal, lower-stress contact.

02

No Base Circle Limitation

Unlike involute gears, Convoloid has no base circle, eliminating undercut constraints on small pinions. More design freedom, optimized for each application via computer point-by-point calculation.

03

Conjugate Through the Full Flank

Convoloid is conjugate through most of the addendum and dedendum, with contact that accurately follows the Euler-Savary equation. Nearly constant relative radii of curvature maintain consistent Hertz stresses across the entire flank. No stress spikes.

04

Drop-In Manufacturing Compatibility

Convoloid is made on existing gear-cutting, grinding and inspection equipment at standard cycle times, and manufacturing sequences mirror involute processes. The transition is a design change, not a capital investment.

Gear Types Spur · Helical · Double Helical · Planetary · Epicyclic

Contact Ratio 1.1 – 1.3 (application optimized)

Helix Angle 20° – 30° optimal range

Rating Standards AGMA & ISO compatible methodology

Convoloid in Motion

Every Tooth, Generated True

These aren't illustrations. Every gear below is generated from the Convoloid® basic rack (convex addendum, concave dedendum, S-shaped transition through the pitch line) using the same rolling motion a hob uses on the shop floor. The amber dashed curve is the true path of contact; glowing points are live tooth contact.

Tooth Anatomy

From Involute to Convoloid®

Watch a standard 20° involute tooth become a Convoloid tooth. The flank turns into an S: a convex addendum above the pitch line, a concave dedendum below it, joined by a smooth transition where every junction is tangent.

The amber comb plots curvature along the flank. It flips sign at the pitch line, so a convex flank always meets a concave flank.

Spur

Small Pinion, No Undercut

A 13-tooth pinion driving 27 teeth. With no base circle there's no undercut limit, and the contact ratio stays above 1.0, so spur Convoloid gears run smoothly.

Helical · 3D

Helical Pair

The same transverse Convoloid profile swept along a 22° helix, in opposite hands. Contact lines stay unbroken across the full face width.

Double Helical · 3D

Herringbone

A 30° double helix cancels axial thrust. It's built for the heavy-duty drives (wind, mining, marine) where power density matters most.

Planetary

Epicyclic Set

A 21-tooth sun, three 15-tooth planets and a 51-tooth internal ring. The ring is generated to match the planet, so internal meshes get the same convex-to-concave contact.

Rack & Pinion

The Basic Rack

This is the rack that defines the whole Convoloid system. Every gear above is generated from it, which is why Convoloid can be cut on existing CNC hobbing and grinding machines.

Contact Close-Up

Convex Meets Concave

At the mesh, a convex addendum rolls against a concave dedendum. The two curves nest instead of touching at a single sharp point, so the load spreads over a wider band and contact stress drops.

Manufacturing & Inspection

Your Machines. Your Standards. A Better Tooth.

The differences between a Convoloid tooth and its involute equivalent are subtle, but they produce powerful results. Manufacturing sequences, tolerances and material allowances closely follow involute practice.

Convoloid tooth definition drawing: convex addendum, transition zone at the pitch diameter, concave dedendum, full-radius root, tip relief area, described in X-Y coordinates — The Convoloid tooth, defined point by point in X–Y coordinates

Same Processes

Hobbing, shaping, skiving, form grinding and threaded-wheel grinding all apply, at standard cycle times, and hob costs are comparable to special involute cutters. Shaving is not recommended. Pinion and gear need separate cutters. Because the tooth is described digitally, it is compatible with the CNC gear manufacturing and inspection equipment in use worldwide.

Same Inspection

Inspected on standard CNC gear checkers to AGMA, ISO, DIN and JIS quality grades. Accuracy classes use the same parameters, limits and identification. Lead modification, crowning, tip relief and root relief can all be designed in and measured. Center-distance tolerance practice is ±0.005 × transverse module.

Same Standards

Rating modifiers and tolerances from world-recognized standards apply directly:

Analysis	AGMA	ISO
Contact & bending	2001/2101, 6011, 6013, 6015	6336, 13593
Tolerances	2015-2	1328-1
Inspection	915	10064
Scuffing	925	13989, 14635-1

Sample Convoloid profile inspection chart (36T, DIN 3962)