How Low Is “Low” Backlash? DIN 3967 and Gear Grinding

Core answer: backlash is the angle through which one gear of a pair can turn freely while the other is held fixed; it originates in tooth thinning and center distance deviation. Under DIN 3967 the tooth thickness tolerance is marked as “number + letter”: numbers 21–30 set the tolerance zone width, letters a–h set the backlash magnitude, and the h zone has zero upper deviation — the smallest backlash, close to zero. Angular backlash can be estimated as θ′ ≈ 6875.5 × jt / d (jt = circumferential backlash in mm, d = pitch circle diameter in mm). On the manufacturing side, holding tooth thickness tolerance steady depends on grinding — grinding accuracy reaches DIN 4-5, with batch production stable at GB 4~5 — and combined with selective pairing or anti-backlash structures, the backlash of a precision indexing mechanism can be pushed down to the arcminute level.

1. First, What Backlash Actually Is#

Backlash is the lost motion that appears in a gear pair when the drive direction reverses, expressed as an angle or as flank clearance. A meshing pair cannot run with zero clearance: for the gears to turn at all, the flanks must leave room for the lubricant film, thermal expansion and manufacturing error. That clearance is backlash.

Three quantities are used in engineering practice:

Backlash is not “the smaller the better”. Positioning and indexing mechanisms need low backlash, while power drives need normal backlash — the flanks need an oil film, temperature rise changes the center distance, and too little clearance causes seizure. The first step in design is to separate the two applications.

2. How Backlash Is Calculated: One Formula, a Set of Numbers#

The relation between angular backlash and circumferential backlash is simple: θ′ (arcmin) ≈ 6875.5 × jt / d. A few examples:

Two rules follow: for the same clearance, the larger the pitch circle, the smaller the angular backlash; for the same diameter, halving the clearance halves the angular backlash. Small-diameter precision gears are more sensitive to clearance and therefore demand tighter tooth thickness tolerances.

3. How It Is Marked on the Drawing: the DIN 3967 “Number + Letter”#

DIN 3967 is the German standard for the gear fit (backlash) system and specifies tooth thickness tolerances. The marking is “number + letter”, number first, letter second, for example 25c:

• Numbers 21–30: grades of tooth thickness tolerance zone width — the higher the number, the wider the zone and the larger the tooth thickness variation;
• Letters a–h: position of the tooth thickness tolerance zone (backlash magnitude) — the a zone gives the largest backlash, the h zone has zero upper deviation and the smallest backlash, close to zero.

The zone is chosen by application: general power drives use the c/d zones for normal backlash; precision indexing and servo drives can move toward the h zone, but temperature rise and lubrication must be evaluated at the same time — a zero-backlash design that ignores thermal expansion can seize after a short run.

4. Manufacturing: What Controls Backlash#

Tooth thickness is the direct source of backlash, so controlling backlash starts with controlling tooth thickness tolerance. The process route determines how far that control can go:

Heat treatment is the other variable. Gears distort after carburizing and quenching, and the amount depends on material, module and geometry; standard practice is to leave grinding stock, correct the distortion by grinding, then measure tooth thickness and base tangent length on a gear measuring center and group the mating gears by measured value. Before shipment the backlash is measured again on a meshing tester, and the inspection report ships with the goods.

5. Structure: Four Anti-Backlash Methods#

Manufacturing accuracy cannot solve everything, so precision mechanisms often add a structural measure:

6. Selection Points: Six Steps#

1. Define the working conditions: reversing frequency, temperature range, load character — first decide whether this is a positioning drive or a power drive;
2. Mark the tooth thickness tolerance to DIN 3967: choose the tolerance zone width (number) and the backlash group (letter);
3. Assess zero-backlash risk: for the h zone, calculate thermal expansion and the oil film, do not look at the static case alone;
4. Set the manufacturing route: grinding where backlash requirements are tight, hobbing plus shaving and selective assembly for general drives;
5. Agree the inspection items: measured tooth thickness/base tangent length, backlash testing on a meshing tester, report shipped with the goods;
6. Reinforce structurally: add an anti-backlash mechanism where needed, working alongside manufacturing accuracy.

7. What Geyontech Can Do#

Geyontech manufactures spur and helical cylindrical gears (module M0.5–M12, outside diameter up to Φ600 mm); grinding accuracy reaches DIN 4-5, with batch production stable at GB 4~5. Bevel gears are made to GB/T 11365 grades 5~6 (M1–M12, ≤Φ500 mm); worm gear sets use Z1~Z6 tooth forms, bronze worm wheels running with steel worms. Materials include 20CrMnTi carburized and quenched (HRC 58~62), 42CrMo quenched and tempered, and 38CrMoAl nitrided. Inspection is equipped with a gear measuring center, CMM, hardness tester and meshing tester — tooth thickness, base tangent length and actual backlash are all measured and reported.

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

Send your drawings and working conditions — power, speed, reversing frequency, operating temperature — and the engineering team will verify them in KISSsoft and come back with tooth thickness tolerances, backlash group and process route. Contact Geyontech or visit the Geyontech website to submit your requirement.