Helical Gear Sizing Calculator evaluates normal and transverse gear geometry per AGMA 2001 and ISO 6336. Pitch diameter is governed by d = (m_n × z) / cos(β), where $m_n$ is the normal module, $z$ is the number of teeth, and $\beta$ is the helix angle.
Helical Gear Sizing Calculator
Calculate helical gear geometry, tooth bending strength, and contact stress per AGMA 2001 and ISO 6336 standards. Accurate geometry, mesh forces, and center distances for high-torque parallel and crossed gear trains.
Helical Gear Sizing Principles & Formulas
Normal vs Transverse Module
Cutters standardise the normal module ($m_n$). The apparent pitch in the plane of rotation is the transverse module:
m_t = m_n / cos(β)
Transverse Pressure Angle
Standard normal pressure angle ($\alpha_n = 20^\circ$) transforms into a larger transverse angle ($\alpha_t$):
tan(α_t) = tan(α_n) / cos(β)
Center Distance
Operating center distance for parallel-axis external helical pairs with pinion $z_1$ and gear $z_2$:
a = m_n · (z_1 + z_2) / (2 · cos(β))
Tangential Force (F_t)
Transmits torque ($T$) at pitch radius:
F_t = 2000 · T / d (in N)
Axial Thrust Force (F_a)
Thrust generated along the shaft axis by the helix angle:
F_a = F_t · tan(β)
Radial Separating Force (F_r)
Separation force pushing gear shafts apart:
F_r = F_t · tan(α_t) = F_t · tan(α_n) / cos(β)
Standards Verification
Formulas adhere strictly to AGMA 2001-D04 (Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth) and ISO 6336-1:2019. Valid for standard involute tooth profiles with normal modules 0.5 to 20 mm and helix angles 0° to 45°.
Worked Sizing Example
Pinion Geometry: m_n = 2.5 mm, z = 24 teeth, β = 20°.
Pitch Diameter: d = (2.5 × 24) / cos(20°) = 60 / 0.93969 = 63.85 mm.
Base Diameter: α_t = arctan(tan(20°)/cos(20°)) = 21.17°; d_b = 63.85 × cos(21.17°) = 59.54 mm.
Related Gear Design Standards & Drivetrain Calculators
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Frequently Asked Questions
Why do helical gears produce axial thrust forces?
Because the tooth flank is angled at helix angle $\beta$, normal contact force resolves into both a circumferential tangential component ($F_t$) and an axial thrust component ($F_a = F_t \cdot \tan\beta$). Bearings must be sized to carry this axial load or double-helical (herringbone) teeth can be used to balance thrust.
What is the advantage of helical over spur gears?
Helical gears engage gradually along the face width, resulting in higher contact ratios (often > 2.0), smoother load transfer, reduced noise, and greater load-carrying capacity compared to equivalent spur gears.
What helix angle is recommended for parallel gearboxes?
Typical single helical gears use helix angles between $12^\circ$ and $25^\circ$. Higher helix angles increase the face contact ratio but generate higher bearing thrust forces.
What standards govern tooth strength calculations?
AGMA 2001-D04 and ISO 6336 define the standard rating procedures for tooth root bending fatigue and flank contact pitting resistance.