Helical Gear Calculator

Design quieter drives with accurate helical calculations fast. Validate ratios, diameters, and forces in minutes. Export results, compare scenarios, and share with teammates easily.

Inputs

Standard series: 1, 1.25, 1.5, 2, 2.5, 3, 4, …
Common range: 10°–25° for smoothness.
Typical choice: 20°.
Avoid undercut with very low tooth counts.
Ratio is z2/z1.
Often 8–14× module, depending on duty.
Used for torque and velocity.
Set 0 if torque is handled externally.
Example: 0.97 for a healthy mesh.
Accounts for shock, duty cycle, and risk.
Reset

Example data table

Scenario mn (mm) β (°) z1 z2 b (mm) n1 (rpm) Power (kW) Key output
Conveyor drive 3.0 15 20 60 35 900 7.5 Center distance ~124 mm
Packaging line 2.0 20 18 36 25 1500 4.0 Ft typically near 600–900 N
High-speed stage 1.5 25 24 48 20 3000 3.0 Velocity ~5–7 m/s, check ε

Formula used

  • Transverse module: mt = mn / cos(β)
  • Pitch diameters: d1 = mt·z1, d2 = mt·z2, center distance a = (d1+d2)/2
  • Transverse pressure angle: tan(φt) = tan(αn) / cos(β)
  • Torque from power: T = 9550·P / n1 (N·m), then design torque ≈ T·Ks / η
  • Pitch line velocity: v = π·d1·n1 / 60 (with d1 in meters)
  • Forces: Ft = 2·Tdesign / d1, Fr = Ft·tan(φt), Fa = Ft·tan(β)
  • Contact ratios (approx): ε = εα + εβ, with εβ ≈ b·tan(β)/(π·mt)

How to use this calculator

  1. Enter normal module, helix angle, and normal pressure angle.
  2. Set tooth counts for pinion and gear to match your ratio.
  3. Provide face width and pinion speed for realistic loads.
  4. Add power, efficiency, and service factor for design sizing.
  5. Press Calculate to see results above this form.
  6. Download CSV/PDF to share, archive, or compare options.

Helix Angle and Load Paths

Helix angle increases overlap and perceived smoothness, yet it introduces axial thrust that bearings must support. In the 15°–25° range, overlap ratio rises with face width, while the transverse module grows because mt = mn/cosβ. That raises pitch diameters and center distance for a fixed tooth count. Use smaller β when packaging is tight, and higher β when noise and load sharing are priorities.

Module, Tooth Count, and Geometry

Normal module sets tooth size, bending stiffness, and manufacturing scale. Because pitch diameter is d = mt·z, diameters change linearly with teeth, while ratio is governed mainly by z2/z1. Center distance equals (d1+d2)/2, so even a two‑tooth change can move shafts several millimeters. Confirm root diameter remains positive after dedendum, and keep face width typically 8–14× mn for balanced load distribution.

Power, Torque, and Pitch Line Velocity

Torque follows T = 9550·P/n for power P in kW and speed n in rpm. The calculator applies a sizing adjustment using Ks/η to reflect duty severity and efficiency losses, producing a conservative design torque. Pitch line velocity v = π·d1·n/60 indicates dynamic behavior; as velocity rises, surface finish, lubrication, and runout become more important. High speeds often justify tighter quality grades and better balancing.

Forces in the Mesh

Tangential force Ft transfers power and is computed from Ft = 2·Tdesign/d1. Radial force Fr = Ft·tanφt pushes shafts apart, increasing bearing radial loads and housing deflection risk. Axial force Fa = Ft·tanβ is characteristic of helical gearing and may dominate bearing selection at higher β. The normal force estimate helps compare contact loading across scenarios, especially when β and pressure angle change together.

Contact Ratios and Practical Checks

Total contact ratio ε = εα + εβ estimates how many tooth pairs share load at any instant. Higher ε generally reduces vibration, improves load sharing, and tolerates minor errors better. If ε is low, increase face width, adjust helix angle, or revisit tooth counts while maintaining center distance constraints. Treat outputs as geometry and force baselines, then confirm rating factors, material limits, and life with ISO or AGMA strength calculations. Document assumptions and compare multiple runs to guide design decisions.

FAQs

What does the calculator assume about tooth proportions?

It uses common full‑depth proportions: addendum ≈ mn and dedendum ≈ 1.25·mn in the normal system. Outside and root diameters are therefore approximate and may differ with profile shift, tooling, or standards.

Why is transverse module larger than normal module?

Helical teeth are angled, so spacing in the transverse plane stretches. The relationship mt = mn/cosβ increases mt as β increases, raising pitch diameters and center distance for the same tooth count.

How are forces Ft, Fr, and Fa interpreted?

Ft drives power transfer at the pitch circle. Fr pushes gears apart and loads bearings radially. Fa is axial thrust from the helix angle and can require dedicated thrust bearings or paired bearings.

What is a good total contact ratio?

Higher is usually smoother. Many designs target ε above about 1.4, but requirements vary with noise limits, quality grade, and load. Use ε as a comparative metric while confirming strength and durability separately.

Why does the tool adjust torque using Ks and efficiency?

Ks inflates load to reflect shocks and duty severity, while η accounts for losses. The combined adjustment provides a simple, conservative design torque for estimating mesh forces and comparing candidate geometries.

Can I use these results for final gearbox rating?

Use them as a baseline for geometry and load estimates. Final rating should include material properties, stress factors, reliability targets, and standard methods such as ISO or AGMA for bending and pitting resistance.

Notes for advanced users
  • Diameters assume standard full-depth teeth in a normal system.
  • Contact ratio is approximate and depends on profile shifts.
  • For bending/pitting capacity, apply ISO/AGMA methods separately.
  • Axial load can be significant; size bearings accordingly.
Quick check
If total contact ratio is low, try increasing face width, reducing module carefully, or adjusting helix angle within limits.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.