GearLab

User guide for designing involute gears to ISO 53, DIN 867 and DIN 3960

1. What does the program do?

GearLab designs cylindrical gears with involute teeth, spur or helical. It computes the true tooth shape as generated by a rack-type cutter (the basic rack to ISO 53 / DIN 867), including the root fillet. You can:

• find a gear pair that fits a given centre distance and ratio;
• make a single gear with any dimensions;
• design a pinion with rack;
• design an internal gear pair (pinion inside a ring gear), with an interference check;
• run a strength calculation (flank pressure, tooth root, shaft and key);
• add a hub and keyway;
• export the result as DXF (2D), STEP (solid model) and STL (for 3D printing).

2. Terms in brief

Module m (mn)

The measure of tooth size: pitch divided by π. A gear with module 2 and 20 teeth has a pitch diameter of 40 mm. Preferably use the DIN 780 standard series (series 1). For helical gears this is the normal module mn, measured perpendicular to the tooth.

Number of teeth z

Small numbers of teeth (below about 17 at 20°) cause undercut without profile shift: the cutter removes part of the tooth root.

Pitch circle d, tip circle da, root circle df, base circle db

d = m · z (spur). The tip circle is the outside of the teeth, the root circle the bottom of the spaces. The involute "unwinds" from the base circle db = d · cos α.

Pressure angle α

The flank angle of the basic rack, normally 20°. A larger pressure angle gives stronger teeth but higher bearing loads.

Profile shift x

The cutter is placed x · m outwards (x > 0) or inwards (x < 0) during manufacture. A positive x makes the tooth thicker at the root and thinner at the tip, prevents undercut and increases the centre distance. This is how a pair is made to fit an exact centre distance.

Σx and Δx

For an external pair the sum Σx = x1 + x2 sets the centre distance; for an internal pair the difference Δx = x2 − x1.

Tip shortening k · m

After profile shift the tip circle is sometimes reduced slightly to keep enough tip clearance (DIN 3960). The program does this automatically.

Helix angle β and hand

On helical gears the teeth are inclined at an angle β to the axis. Right or left hand is the direction of the helix. In an external pair the gears have opposite hands; in an internal pair and with a rack they have the same hand.

Transverse contact ratio εα, overlap ratio εβ, total contact ratio εγ

The average number of tooth pairs in mesh. εα must be greater than 1 (preferably 1.2 or more). Helical teeth add εβ and therefore run more smoothly.

Backlash jn

The clearance between the flanks, needed for lubrication, thermal expansion and tolerances. A guide value is 0.04 to 0.1 · m. The program makes the teeth slightly thinner for this (the thickness allowance As).

Pointed tooth

With a large positive profile shift the tooth becomes too narrow at the tip. The program reports this and reduces the tip circle. Keep the tip thickness preferably above 0.25 · m (hardened: 0.4 · m).

3. The screen and controls

The inputs and results are on the left, the drawing on the right.

• At the top: the buttons Open, Save, Save as and Help.
• Four tabs: Pair, Single, Rack and Internal. The active tab determines what is drawn, calculated and exported.
• Rotate, with the slider for the speed, animates the gears. Line of action shows the meshing diagram.
• Strength... and Hub/key... open a window of their own.
• Below these are the export choice, the export buttons and the STL tolerance.
• The information panel at the bottom shows all dimensions, checks and warnings. Lines starting with ! are warnings.

If the left column does not fit on your screen, a scroll bar appears. Numbers may be typed with a point or a comma.

4. Pair tab

Finds a gear pair that fits a given centre distance exactly.

Procedure

1. Enter the centre distance a and the ratio i = z2 / z1. The tolerance sets how much the actual ratio may deviate.
2. Choose the pressure angle (usually 20°) and, if required, a helix angle β with the hand.
3. Set the limits for Σx (default −0.5 to 1.0) and the smallest number of teeth, z min.
4. Click Calculate modules. The list shows all combinations of module and numbers of teeth that fit the centre distance exactly, with a profile shift within the limits.
5. Pick a row. The pair is drawn and the information panel is filled.
6. If required, split the profile shift with x1; x2 follows from Σx. The program proposes a split that avoids undercut on the pinion.
7. Enter the face width, the backlash and the bores.

β search

With β search the program chooses, for each combination, the helix angle at which the centre distance fits without profile shift (Σx = 0). The β field then acts as the maximum. This is a common way to achieve a given centre distance.

5. Single tab

A single gear with freely chosen module, number of teeth, profile shift, pressure angle, helix angle, face width, thickness allowance and bore. Every change is drawn immediately. The thickness allowance As makes the tooth thinner for backlash: two gears each with As give a normal backlash of about jn = 2 · As · cos α.

6. Rack tab

A pinion meshing with a rack. Enter the module, the number of pinion teeth, the profile shift, the helix angle, the face width, the backlash, the number of rack teeth and the rack height Hp (from the back to the pitch line).

• The rack tooth is the ISO 53 basic rack.
• A helical rack has its teeth at the same angle as the pinion.
• The information panel shows, among other things, the distance from the pinion axis to the pitch line and to the rack back, and the travel per revolution.
• In the animation the rack moves along and now and then jumps back by a few pitches.

7. Internal tab

A pinion running inside a ring gear. Both rotate in the same direction. The procedure is the same as for the pair, but the module list shows Δx = x2 − x1.

Points to watch

• Tooth difference z2 − z1: with too small a difference (roughly below 10 at 20°) the tips touch when the teeth enter and leave the mesh. The field min. tooth diff. limits the module list.
• Shorten ring tip: on by default. The tip circle of the ring is then made just large enough for the ring tip to clear the pinion root fillet. This is almost always needed for internal gears.
• Interference check: the program rotates the pair through one full pitch and checks all teeth. It reports "no interference" or the size of the overlap.
• Rim thickness: the ring material outside the root circle. It fixes the outside diameter.

Profile shift of the ring: x2 > 0 makes the spaces wider and the circles larger.

8. The drawing

• Mouse wheel: zoom around the cursor. Drag: pan. Double-click: fit everything in view.
• Lines: dashed blue is the pitch circle, dotted green the base circle, red the centre lines and dashed grey the hub.
• Line of action:
  • T1 and T2 are the tangent points on the base circles; the teeth are in contact between A and E (magenta).
  • Between B and D only one tooth pair carries the load (red); this part is the most heavily loaded. C is the pitch point.
  • The green dots are the current contact points. Purple are the operating pitch circles (or the pitch line for the rack).
• Critical section: with the strength window open, a red line in the tooth root shows where the tooth would break under overload (spur gears).

The drawing and the DXF show the section perpendicular to the axis.

9. The information panel and inspection dimensions

The information panel shows the main dimensions of each gear and the data of the pair, such as the centre distance, the operating pressure angle, Σx, the tip shortening, the backlash and the contact ratios. For measuring the finished gear:

The dimensions apply to the finished gear, so they include profile shift and backlash.

10. Strength calculation

The Strength... window checks whether the active pair (Pair, Rack or Internal) can carry the load. It follows the geometry: if you pick another row or change a dimension, the result is updated immediately.

Input

• Load: power and speed, or torque and speed (of gear 1 or the pinion).
• Application factor KA: for shocks from motor and machine; 1.0 for a uniform drive and load, 1.25 to 2.0 with shocks.
• Service life in hours, the accuracy grade ISO 1328 (5 is fine, 10 is coarse), the flank finish and the lubrication.
• Material per gear, with the endurance limits σH,lim (flank) and σF,lim (root). If you change a value, it becomes a "custom material".
• Shaft: the shaft material with the permissible torsional stress, the number of keys and the key length.

Results

• Flank pressure (pitting): the contact stress σH and the safety factor S_H; minimum 1.0 to 1.3.
• Root stress (tooth breakage): σF and the safety factor S_F; minimum 1.4 to 2.0. The form factors YF and YS are taken from the actual tooth shape.
• Transmissible: the maximum torque and power at the minimum safety factors.
• Shaft and key connection:
  • the minimum shaft diameter in torsion, with the DIN 748 standard size;
  • a check of the bore;
  • with a keyway: the surface pressure on the key (DIN 6892 method C), the safety factor S_p and the required key length, with advice.

The status bar at the top turns green (sufficient), orange (tight) or red (insufficient). Copy report puts all inputs and results on the clipboard.

11. Hub and keyway

The Hub/key... window has settings for gear 1 (also the pinion with rack and internal gears) and gear 2 (gear pair only).

• Keyway: none, DIN 6885-1 (the size follows from the bore) or custom size (width b and depth t2 in the hub). The keyway lies under a tooth and runs the full length.
• Hub: left, right or both sides, with diameter D and length L per side. If you leave D empty, the program chooses a suitable diameter.

The information panel warns if there is too little material between the keyway and the tooth root, or if the hub is larger than the root circle. Ring gears and racks get no hub or keyway.

12. Export (DXF, STEP, STL)

The list above the buttons selects:

• both together, as shown and in the current rotation (useful for checking the mesh in CAD);
• gear 1 / pinion only, at the origin;
• gear 2 / rack / ring only. A rack on its own runs from x = 0 to its length, with the pitch line at y = 0.

13. Saving and opening projects

A project (.tdw) stores:

• all inputs of the four tabs and the active tab;
• the selected rows in the module lists, with your own x1;
• the settings for hub, keyway, strength, display and export.

Projects can be exchanged between the Dutch and the English version. With unsaved changes the title bar shows a *, and the program asks whether to save when you close it.

14. Standards, assumptions and limits

• Basic rack ISO 53 / DIN 867 (profile A): addendum 1.0 · m, dedendum 1.25 · m, cutter tip radius 0.38 · m. The ring gets a root fillet of 0.25 · m.
• Geometry to DIN 3960: profile shift, operating pressure angle, tip shortening and inspection dimensions.
• Modules to DIN 780, keyways to DIN 6885-1, shaft diameters to DIN 748.
• Strength simplified to ISO 6336 / DIN 3990. K_V, K_Hβ and K_Hα follow from approximations per accuracy grade; the factors for lubricant film, roughness and contact pattern have default values.
• Internal gears: the interference check is numerical over one full pitch. For heavily undercut pinions it is an approximation.
• Not included: bevel gears, worm gears, plastic gears (VDI 2736), profile modifications (tip relief, crowning) and a full shaft calculation.

15. Keyboard shortcuts

16. Problems and questions

"No combinations found"

Increase the ratio tolerance, widen the limits of Σx or Δx, lower z min, switch on series 2 or use β search.

Undercut warning

Use a positive profile shift (at least the x min shown), more teeth or a larger pressure angle.

Pointed tooth or tip thickness too small

Reduce the profile shift or split Σx differently between the two gears.

Contact ratio too small

Choose a smaller module with more teeth, less profile shift, or helical teeth.

Interference on an internal pair

Switch on "Shorten ring tip", increase the tooth difference or adjust Δx.

Strength is insufficient

See which value is red. Flank pressure improves with a larger module or wider face, a harder material or a larger centre distance. Root stress improves with a larger module, a wider face or a positive profile shift.

The STEP does not open properly in my CAD program

Try another program to see whether the file is the cause. For Boolean checks, export with a small backlash, because exactly touching faces are difficult for CAD kernels.