How to size a planetary gearbox? Torque, speed, inertia, and service factor step by step

How to Size a Planetary Gearbox: Torque, Speed, Inertia, and Service Factor Step-by-Step

Planetary gearbox sizing is a systematic process that begins with the load requirements and works backward through the drivetrain to identify the gearbox specifications — gear ratio, rated output torque, radial load capacity, and input speed limit — that ensure reliable long-term operation. Under-sizing a gearbox causes premature failure (bearing fatigue, tooth fracture, or housing cracks within the first 500–1,000 hours); over-sizing wastes money and adds unnecessary mass and inertia to the driven axis, reducing system bandwidth and acceleration capability. This guide walks through the complete sizing procedure with formulas and worked examples applicable to servo, stepper, and induction motor drives.

Step 1: Define Load Torque at the Output Shaft

Start by calculating the torque required at the gearbox output shaft under the worst operating conditions. For a linear axis driven by a ball screw:

For a rotary load (conveyor drum, turntable, roller): T_load = J_load × α + T_friction, where α is angular acceleration (rad/s²) and T_friction includes all friction losses at the output (bearing drag, seal drag, gear mesh losses if any).

For gravity-loaded vertical axes, include the static holding torque required to prevent the axis from back-driving when the motor is powered off: T_static = (m × g × p) / (2π × η_screw). This value must be less than the gearbox output shaft static torque rating, and the motor brake (if used) must be sized to hold this torque.

Step 2: Apply the Service Factor

The required output torque calculated from load analysis should be multiplied by a service factor (SF) to account for shock loads, startup transients, vibration, ambient temperature, and safety margin. Service factors for planetary gearboxes typically range:

• Smooth load, uniform operation (conveyors, fans, pumps, winding reels): SF = 1.0–1.25
• Moderate shock (light presses, compressors, mixers, indexing tables): SF = 1.25–1.75
• Heavy shock (crushers, mills, heavy presses, punch presses, shredders): SF = 1.75–2.5

For applications with frequent direction reversals (more than 10 reversals per minute) or significant vibration, add an additional 0.25–0.5 to the service factor. The gearbox rated output torque must equal or exceed: T_required = T_load × Service Factor. Never select a gearbox with a rated torque lower than this calculated value — doing so will void the warranty and guarantee premature failure.

Step 3: Select the Gear Ratio

The gear ratio determines both output speed and the torque multiplication from motor to load. Calculate the required ratio as:

For servo systems, also calculate the inertia-matching ratio: i_optimal = √(J_load / J_motor). Selecting a ratio close to the inertia-matching value minimizes settling time and improves servo bandwidth (typically achieving 3–5× higher position loop gains). Round to the nearest standard ratio available in the gearbox catalog — common standard ratios are 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 16, 20, 25, 28, 30, 32, 35, 40, 48, 50, 64, 70, 80, 100.

Step 4: Verify Input Speed Against Gearbox Maximum

Every planetary gearbox has a maximum rated input speed (n_max_input), typically 3,000–6,000 RPM for precision servo gearboxes. Verify that the motor’s rated speed at the operating point does not exceed this limit. For motor speeds above the gearbox input limit, a different gearbox must be selected, or the motor speed profile must be adjusted. Operating above the rated input speed causes:

• Excessive lubricant churning losses and overheating
• Cage instability in planet bearings
• Noise levels exceeding the gearbox design limits (typically +3–5 dB(A) per 10% over-speed)

Our EP-306 Inline Planetary Gearbox supports input speeds up to 6,000 RPM on precision grades, compatible with most standard servo motor speed ranges (3,000–6,000 RPM).

Step 5: Check Radial and Axial Load on the Output Shaft

Gear, belt, or chain drives connected to the gearbox output shaft impose radial forces on the output shaft bearing. Similarly, helical gears and bevel gears impose axial loads. Compare the actual radial and axial loads against the gearbox output shaft load capacity published in the manufacturer’s catalog:

• For a belt or chain drive: F_radial ≈ 2 × T_output / (pitch circle diameter of sprocket/pulley)
• For a direct coupling: F_radial = 0 (assuming perfect alignment)
• Axial load from a helical output gear: F_axial = F_tangential × tan(helix angle)

If the calculated loads exceed the gearbox output shaft bearing capacity (typically specified as F_radial_max and F_axial_max at a given overhung load distance), select a larger gearbox housing size or add an external support bearing on the driven shaft. For belt drives, increasing the pulley diameter reduces radial force proportionally — doubling the pulley diameter halves the radial force.

Step 6: Verify Thermal Capacity for Continuous Duty

For applications running at continuous duty (100% on-time, 24/7 operation), verify that the gearbox thermal torque rating (T_thermal) is not exceeded. Thermal torque ratings are specified at standard ambient temperature (typically 20°C–25°C) with natural convection cooling. Derating applies for:

• Elevated ambient temperature (above 25°C): T_thermal_derated = T_thermal × derating factor from manufacturer table — typically 1% per 1°C above 25°C up to a maximum ambient of 50°C.
• Enclosed mounting (no free air movement): additional derating of 10–20% typically applies because heat cannot dissipate by natural convection.
• High altitude (above 1,000 m): derating of 1% per 100 m above 1,000 m due to reduced air density and cooling capacity.

For applications that exceed the thermal torque rating, consider forced ventilation (external fan blowing across the gearbox housing) or synthetic lubricant with higher thermal conductivity and viscosity stability.

Step 7: Check Inertia Ratio for Servo Applications

For servo-driven systems, the reflected load inertia at the motor shaft must be within the motor manufacturer’s recommended inertia ratio. Calculate reflected inertia:

The inertia ratio is then J_reflected / J_motor. Recommended maximum inertia ratios:

• High-performance positioning (CNC, robotics): ratio ≤ 3:1
• General automation (pick-and-place, indexing): ratio ≤ 5:1
• Velocity control (conveyors, fans): ratio ≤ 10:1

If the inertia ratio exceeds the recommended value, increase the gear ratio (i) to reduce J_reflected proportionally to 1/i², or select a larger motor with higher rotor inertia.

Worked Example: Sizing a Planetary Gearbox for a CNC Feed Axis

For this application, a single-stage 3:1 planetary gearbox rated for ≥ 5 Nm output torque would be selected, with input speed capacity ≥ 3,000 RPM. Review our inline planetary gearboxes for compatible sizing options in this torque class (30 mm to 180 mm frame sizes).