Harmonic Drive Gearbox Calculator

Input Parameters

Circular Spline

Material:

Module (mm):

Teeth Count:

Flex Spline

Material:

Cup Width/Thickness, t (mm):

Cup Height Ratio, λ = L/R_m: (typical: 0.4-0.8, default: 0.5)

Cup Height, L (mm): (calculated from λ)

Module (mm):

Teeth Count:

Wave Generator (Cam) - Elliptical Geometry

Major Axis, a (mm): (calculated)

Minor Axis, b (mm): (calculated)

Eccentricity, e: (calculated)

Preload/Interference, ε (mm):

Advanced Parameters

Tooth Count Difference, Δz:

Pressure Angle, φ (°):

Face Width, b (mm):

Radial Allowance, δ_allow (mm):

Transmitted Torque at output, T (N·m):

Results

Kinematics

Reduction Ratio (magnitude):

i = z_FS / Δz

Reduced Speed Ratio:

i = -Δz / z_FS

Gear Geometry - Flex Spline Diameters

Pitch Diameter, d (mm):

d = mz

Tip/Outside Diameter, d_a (mm):

d_a = m(z + 2)

Root Diameter, d_f (mm):

d_f = m(z - 2.5)

Gear Geometry - Circular Spline Diameters

Pitch Diameter, d (mm):

d = mz

Tip Diameter, d_a (mm):

d_f = m(z - 2)

Root Diameter, d_f (mm):

d_a = m(z + 2.5)

Cup Geometry Parameters

Mean Cup Radius, R_m (mm):

R_m ≈ r_in0 + t/2

Cup Height, L (mm):

L = λ × R_m

Cup Height Ratio, λ:

λ = L / R_m (typical: 0.4-0.8)

Additional Geometry

Pitch Radius Mismatch, Δr_p (mm):

Δr_p = r_CS - r_FS = mΔz/2

Required Radial Expansion, δ (mm):

δ = Δr_p + δ_allow

Flex Spline Inner Radius (mm):

r_in0 ≈ r_f,FS - t

Circular Pitch (mm):

p = πm

Base Circle Radius - FS (mm):

r_b = r·cos(φ)

Ellipse Parameters

Pitch Ellipse - Major Axis, a (mm):

a = r_FS + δ

Pitch Ellipse - Minor Axis, b (mm):

b = r_FS - δ

Wave Generator - Major Axis, a_WG (mm):

a_WG = (r_in0 + δ) + ε

Wave Generator - Minor Axis, b_WG (mm):

b_WG = (r_in0 - δ) + ε

Pitch Ellipse Eccentricity:

e = √(1 - (b/a)²)

Fatigue Analysis (Primary Design Criterion)

Alternating Stress, σ_a (MPa):

σ_a = K_b·E·(3/2)·(t·δ₀)/R_m²

Mean Torsional Stress, τ_m (MPa):

τ_m = K_t·(1000T)/(2πR_m²t)

Mean Equiv. Normal Stress, σ_m' (MPa):

σ_m' = √3·τ_m

Von Mises Stress, σ_vm (MPa):

σ_vm = √(σ_a² + 3τ_m²)

Modified Endurance Limit (Marin Factors)

Modified Endurance Limit, S_e (MPa):

S_e = k_a·k_b·k_c·k_d·k_e·k_f·(0.5·S_ut)

Surface Finish Factor, k_a:

k_a ≈ 0.85-0.95 (ground/honed)

Size Factor, k_b:

k_b ≈ 0.9-1.0 (thin wall)

Load Factor, k_c:

k_c = 1.0 (bending)

Temperature Factor, k_d:

k_d ≈ 1.0 (T ≤ 80°C)

Reliability Factor, k_e:

k_e = 0.814 (99% reliability)

Miscellaneous Factor, k_f:

k_f ≈ 0.9-1.0 (misc. effects)

Fatigue Safety Analysis (Goodman Criterion)

Goodman Ratio:

(σ_a/S_e) + (σ_m'/S_ut) ≤ 1/n

Fatigue Safety Factor, n:

n = 1 / Goodman_Ratio (target: 1.5-2.5)

σ_a / S_e Ratio:

σ_a / S_e (target: ≤ 0.5 for excellent)

Yield Safety Factor:

n_y = σ_y / σ_vm (secondary check)