What Module Do You Need for 15 kW at 1450 rpm? — An ISO 6336 Strength Calculation Walkthrough with Material Data
Core answer: Module size is decided by strength calculation, not gut feel. For a steel gear at 15 kW, 1450 rpm and a ratio of 3.5: the pinion torque is 99 N·m. A 20CrMnTi carburized gear (HRC 58–62) at m 2.5, z 21 and face width 42 mm sees about 750 MPa contact stress, a safety factor of roughly 2.0 — enough, with margin to spare. The same size in quenched-and-tempered 40Cr gives 0.93, which fails; you need m 3 to barely pass. Three steps: calculate torque, check contact and bending stress, round up to a standard module.
1. What Is Module, and Why Guessing Is a Bad Idea
Module (m) is the ratio of pitch diameter to tooth count: m = d / z, in mm. Meshing gears must share the same module; it is the base dimension for everything else. Tooth depth is about 2.25m, and center distance and tooth thickness follow from it. The common GB/T 1357 series runs 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20; round up to a series value. Helical gears are rated by normal module mn; the transverse module is mt = mn / cosβ.
Too small a module leaves a thin tooth root that can break under load. Too large, and the gear grows heavier and costlier, and fewer teeth mean rougher meshing. The aim is not the biggest size you can fit; it is adequate size with a sensible margin.
2. Two-Step Check: Torque First, Then Stress
2.1 Torque Comes from Power and Speed
Torque is the rotating moment the gear carries, set by power and speed. Formula:
T = 9550 × P / n (P in kW, n in rpm, T in N·m)
Here P = 15 kW and n1 = 1450 rpm: T1 = 9550 × 15 / 1450 ≈ 99 N·m. Output speed is about 414 rpm and output torque about 346 N·m (efficiency ignored) — that is speed reduction buying torque.
2.2 Contact and Bending Strength: Check Both
Contact fatigue strength is the gear’s resistance to pitting on the tooth flank; root bending fatigue strength is its resistance to tooth breakage at the root. Together they cover the two typical failure modes. Simplified check formulas (GB/T 3480 / ISO 6336):
σH = ZE · ZH · Zε · √[ 2T1·K / (b·d1²) × (u+1)/u ]
σF = 2·T1·K·YF·YS·Yε / (b·d1·m)
Coefficients: ZE elasticity factor, 189.8 √MPa for steel on steel; ZH zone factor ≈ 2.5; Zε contact ratio factor ≈ 0.87; K combined load factor, usually 1.3–2.0, taken as 1.5 here; YF form factor ≈ 2.8 at z = 21; YS stress correction factor ≈ 1.55; Yε ≈ 0.7.
2.3 Worked Example: Three Options Compared
Input: P = 15 kW, n1 = 1450 rpm, ratio i ≈ 3.5 (z2 = 74, actual i = 3.52), face width factor ψd = 0.8.
Option A — 20CrMnTi, carburized (HRC 58–62): m 2.5, z1 = 21, d1 = 52.5 mm, b = 42 mm. σH ≈ 750 MPa against σHlim ≈ 1500 MPa (reference value from tables), safety factor SH ≈ 2.0; σF ≈ 164 MPa against σFlim ≈ 850 MPa, SF ≈ 5. Verdict: passes, with real margin on contact.
Option B — same size, quenched-and-tempered 40Cr (HB 241–286): σH is still 750 MPa, but σHlim ≈ 700 MPa, so SH ≈ 0.93, below the 1.05 floor. Verdict: fails; flank life will be short.
Option C — 40Cr, upsized: m 3, z1 = 20, d1 = 60 mm, b = 48 mm. σH ≈ 614 MPa, SH ≈ 1.14. Verdict: passes, but the margin is thin next to Option A.
| Option | Material | Module | d1 | Face width | σH | SH | Verdict |
|---|---|---|---|---|---|---|---|
| A | 20CrMnTi carburized | 2.5 | 52.5 mm | 42 mm | ≈750 MPa | ≈2.0 | Pass, good margin |
| B | 40Cr Q&T | 2.5 | 52.5 mm | 42 mm | ≈750 MPa | ≈0.93 | Fail |
| C | 40Cr Q&T | 3 | 60 mm | 48 mm | ≈614 MPa | ≈1.14 | Pass, tight |
Two takeaways. Material sets the allowable stress; module and face width set the actual stress. And carburized gears usually hit the contact limit first, with bending far from critical. Target safety factors: 1.0–1.3 for general machinery, 1.3–1.6 for critical drives (GB/T 3480 tables and common practice).
3. Choosing a Material: Five Options in One Table
Reference values per GB/T 3480 and machine design handbooks (pulsating loading); confirm with handbooks and sample tests before production:
| Material & treatment | Surface hardness | σHlim (MPa) | σFlim (MPa) | Distortion | Relative cost | Typical use |
|---|---|---|---|---|---|---|
| 45 steel, Q&T | HB 217–255 | 550–620 | 400–450 | low | 1.0 | light-duty general machinery |
| 40Cr, Q&T | HB 241–286 | 650–720 | 460–520 | low | 1.2 | medium-duty machine tools, general equipment |
| 42CrMo, Q&T | HB 280–320 | 700–780 | 500–560 | low | 1.4 | medium-heavy duty, large gears |
| 38CrMoAl, nitrided | HV 850–1000 | 850–950 | 480–550 | very low (0.02–0.05 mm class) | 1.6 | distortion-sensitive, high-precision gears |
| 20CrMnTi, carburized | HRC 58–62 | 1400–1500 | 800–900 | medium (needs grinding) | 1.8 | heavy-duty, high-load drives |
Three selection rules. Heavy load in a compact package → carburize. A big part that must not distort → nitride. Light load and a tight budget → quench and temper. In the 15 kW example, Option A fits in m 2.5 while Option C needs m 3 — the material upgrade buys a smaller gear.
4. Quick Module Table at 1450 rpm
Estimated for steel gears, ratio 3–5, face width factor 0.8. Take the upper end for slow, heavy or shock-loaded drives and the lower end for fast, light ones:
| Power at 1450 rpm | Torque | Suggested module range |
|---|---|---|
| 0.1–1 kW | 0.7–7 N·m | m 1–1.5 |
| 1–5 kW | 7–33 N·m | m 1.5–2.5 |
| 5–15 kW | 33–99 N·m | m 2.5–3 |
| 15–40 kW | 99–264 N·m | m 3–5 |
| 40–100 kW | 264–659 N·m | m 5–8 |
5. Five-Step Selection Checklist
- Torque: 9550 × power ÷ speed.
- Teeth: 17–25 on the pinion; scale up the gear by the ratio.
- Application factor: KA 1.0–1.25 for uniform load, 1.25–1.5 for moderate shock, 1.5–2.0 for heavy shock.
- Pick the material and treatment, look up the allowable stress.
- Calculate the module, round up to the GB/T 1357 series.
Every step has numbers behind it. When the safety factor comes up short, enlarge the module or face width first — a material upgrade usually costs more than a size change.
6. What Gyan Drive Can Do
Gyan Drive machines spur and helical gears from drawings in modules M0.5–M12, up to Φ600 mm OD, with tooth accuracy to DIN 5. Common materials — 20CrMnTi, 40Cr, 42CrMo, 38CrMoAl — are all in house, backed by carburizing, gas nitriding and full inspection (profile/helix/pitch testers, hardness testers, metallography).
Send the power, speed, ratio and shock level of your drive; the engineering team usually replies within 24 hours with a free strength check and quotation. Whether the module is enough — one calculation answers it.
👉 Visit the Gyan Drive website or the contact page with your duty data for a free strength calculation and process proposal.