DIN 3967 Backlash Groups and How Gear Grinding Fits In

Short answer: in a gear pair, backlash is the angle one member can rotate while its partner stays locked; it comes from tooth thinning plus centre distance deviation. DIN 3967 expresses tooth thickness tolerance as a number followed by a letter — numbers 21–30 fix the width of the tolerance zone, letters a–h fix how much backlash is present, and the h zone carries zero upper deviation, i.e. the least backlash, near zero. For angular backlash, θ′ ≈ 6875.5 × jt / d, where jt is circumferential backlash in mm and d is pitch circle diameter in mm. On the shop floor, keeping tooth thickness tolerance repeatable is a grinding task: the achievable accuracy class is the one stated on the drawing, and with selective pairing or an anti-backlash arrangement a precision indexing mechanism can be brought down to the arcminute range.

Defining Backlash and Its Three Measures

A gear pair loses motion the moment the drive direction flips. Whether that lost motion is quoted as an angle or as flank clearance, it is backlash. Zero clearance is not an option for a running mesh: lubricant film, thermal growth and production error all demand space between the flanks, and without it the gears simply will not rotate.

Three quantities appear in engineering practice:

• Circumferential backlash jt — flank clearance measured along the pitch circle, in mm.
• Normal backlash jn — clearance measured along the normal to the flank, in mm.
• Angular backlash θ — the angle through which one gear turns freely while the other is fixed, in arcmin.

Smaller is not automatically better here. Indexing and positioning mechanisms want backlash kept low, while power drives need a normal amount: an oil film must form on the flanks, temperature rise shifts the centre distance, and too little clearance ends in seizure. Telling these two duties apart is the opening design decision.

Reading the DIN 3967 Marking

The gear fit (backlash) system and its tooth thickness tolerances are laid down in the German standard DIN 3967. A number comes first in the marking and a letter second, for instance 25c.

• Element Number: Width of the tooth thickness tolerance zone
  • Range: 21–30; a higher number means a wider zone and greater tooth thickness variation
• Element Letter: Position of the tooth thickness tolerance zone, i.e. backlash magnitude
  • Range: a–h; the a zone gives the largest backlash, the h zone has zero upper deviation and the smallest backlash, close to zero

Choosing the zone is a design call. General power drives sit in the c/d zones for normal backlash. Precision indexing and servo drives can move toward the h zone, but temperature rise and lubrication have to be evaluated at the same time — a zero-backlash design that ignores thermal expansion may seize after a short run.

Converting Between Angular and Circumferential Backlash

One formula covers the conversion: θ′ (arcmin) ≈ 6875.5 × jt / d.

Two consequences follow. At equal clearance, a larger pitch circle yields a smaller angular backlash. At equal diameter, halving the clearance halves the angular backlash. Small-diameter precision gears are therefore more sensitive to clearance and need tighter tooth thickness tolerances.

Process Routes and Their Effect on Tooth Thickness

Tooth thickness is where backlash originates, so backlash control starts with holding tooth thickness tolerance in check. The process route decides how far that control can be pushed.

• Process Hobbing/shaving: DIN 7~8
  • Effect on tooth thickness consistency: Relatively large tooth thickness variation; suits drives insensitive to backlash
• Process Grinding (batch): GB 4~5
  • Effect on tooth thickness consistency: Tooth thickness tolerance held narrow, good batch consistency
• Process Grinding (single part): Tolerance class as stated on the drawing
  • Effect on tooth thickness consistency: Profile and helix corrected together; suits precision pairing

Heat treatment is the second variable. Carburizing and quenching leave gears distorted, and how much depends on material, module and geometry. The usual sequence is to leave stock for grinding, grind the distortion away, then record tooth thickness and base tangent length on a gear measuring center and sort mating gears into groups by measured value. A final backlash check on a meshing tester precedes dispatch, and the inspection report travels with the shipment.

Structural Anti-Backlash Options

Where manufacturing accuracy on its own falls short, precision mechanisms frequently gain a structural addition.

• Anti-backlash method Two-piece gear (spring preload): Two gear discs offset and preloaded to remove backlash in one direction
  • Where it fits: Light-load instruments, servo drives
  • Watch out for: Removes one direction only; the preload element wears under heavy load
• Anti-backlash method Variable tooth thickness (tapered) gear: Tooth thickness tapers along the axis, axial adjustment removes backlash
  • Where it fits: Indexing mechanisms, machine tools
  • Watch out for: Needs axial adjustment space
• Anti-backlash method Eccentric bushing for center distance: Reducing the center distance directly reduces clearance
  • Where it fits: Housings with adjustable center distance
  • Watch out for: Limited by the minimum center distance
• Anti-backlash method Dual-lead worm: The two flanks of the worm have different pitches; axial shift adjusts clearance
  • Where it fits: Worm indexing tables, rotary tables
  • Watch out for: Easy adjustment, but the worm must be axially movable

What PinyiGear Supplies

Spur and helical cylindrical gears leave PinyiGear with module range and outside diameter per the values stated on the drawing. Grinding accuracy and batch production follow the tolerance class stated on the drawing. Bevel gears follow the GB/T 11365 grade stated on the drawing. Worm gear sets are available in the tooth forms specified on the drawing, with bronze worm wheels running against steel worms. Among the material choices are 20CrMnTi carburized and quenched, 42CrMo quenched and tempered, and 38CrMoAl nitrided, with hardness per the drawing. A gear measuring center, CMM, hardness tester and meshing tester stand in the inspection area, so tooth thickness, base tangent length and actual backlash are measured and documented.

• Custom Spur Gears
• Custom Helical Gears
• Bevel Gears
• Worm Gear Sets
• Gear Manufacturing Capabilities

Send drawings along with the operating conditions — power, speed, reversing frequency, operating temperature — and the engineering team will run them through KISSsoft, then come back with tooth thickness tolerances, the backlash group and a process route. Contact PinyiGear or go to the PinyiGear website to submit your requirement.

Selection Sequence

1. Establish the duty first: how often the drive reverses, the temperature band it sees, the nature of the load — the answer decides whether a positioning drive or a power drive is being specified;
2. Translate that into a DIN 3967 tooth thickness tolerance: pick the number for zone width and the letter for backlash group;
3. Check the zero-backlash exposure: in the h zone, work out thermal expansion and oil film thickness rather than trusting a static calculation;
4. Fix the production path: grinding when backlash must be tight, hobbing plus shaving with selective assembly for ordinary drives;
5. Settle what will be inspected: tooth thickness and base tangent length as measured, backlash verified on a meshing tester, documentation accompanying the delivery;
6. Add structure where accuracy alone is not enough: an anti-backlash mechanism chosen to complement the manufacturing tolerances.