Gear Ratio Selection — Finding the Optimal Ratio for AGV Wheel Drives

What is a gear ratio?

The gear ratio (reduction ratio) is the ratio of input-shaft speed to output-shaft speed:

ratio = input RPM (motor) / output RPM (wheel)

e.g. motor 3,000 RPM, wheel 150 RPM
→ ratio = 3,000 / 150 = 20:1

Torque multiplication: a gearbox reduces speed but multiplies torque. With efficiency η:

T_output = T_motor × ratio × η

e.g. 0.5 N·m motor, 20:1 ratio, η = 0.90
→ T_output = 0.5 × 20 × 0.90 = 9.0 N·m

This is why AGVs use gearboxes. A small, high-speed BLDC motor (3,000 RPM) drives a heavy wheel at low speed (50–200 RPM) through the gearbox, multiplying the motor's torque into substantial wheel drive force.

AGV wheel-drive requirements

① Required speed (m/s → wheel RPM)

Define the AGV's target travel speed. Typical AGV speeds:

Calculating the required wheel RPM:

n_wheel = v × 60 / (π × D)

v = target speed (m/s)
D = wheel diameter (m)
n_wheel = required wheel RPM

② Required torque

The total required wheel torque is the sum of three components:

T_total = T_friction + T_slope + T_accel

T_friction = m × g × μ × r_wheel
T_slope    = m × g × sin(θ) × r_wheel
T_accel    = m × a × r_wheel

m       = total AGV mass (kg)
g       = 9.81 m/s²
μ       = rolling friction coefficient (rubber on concrete: 0.01–0.05)
θ       = maximum slope angle
a       = acceleration (m/s²)
r_wheel = wheel radius (m)

③ Wheel diameter

The calculation, step by step

Step 1: Required wheel RPM

n_wheel = v × 60 / (π × D)

where:
  v = speed (m/s)
  D = wheel diameter (m)
  π = 3.14159

Step 2: Required wheel torque

T_friction = m × g × μ × r
  μ = 0.02 (rubber wheel on smooth concrete)
  r = D/2 (wheel radius)

T_slope = m × g × sin(θ) × r
  θ = slope angle (degrees)
  sin(5°) = 0.0872

T_accel = m × a × r
  a = typically 0.3–0.5 m/s² for AGVs

T_total = T_friction + T_slope + T_accel

Step 3: Gear ratio

ratio = motor rated RPM / n_wheel

Choose a motor whose rated RPM fits well.
Typical BLDC motors: rated 2,000–4,500 RPM

Step 4: Required motor torque

T_motor = T_wheel_total / (ratio × η_gearbox)

η_gearbox = 0.90 (planetary, 1-stage)
          = 0.85 (planetary, 2-stage)
          = 0.40–0.70 (worm gear)

Apply a 1.5× safety factor to the T_motor result

Worked example — a 500 kg AGV

Specification:

• Total mass: 500 kg (200 kg vehicle + 300 kg maximum payload)
• Wheel diameter: ø200 mm (r = 0.1 m)
• Target speed: 1.0 m/s
• Maximum slope: 5°
• Acceleration: 0.3 m/s²
• Drive system: 2 drive wheels (50/50 load share)
• Motor rated RPM: 3,000 RPM

Mass per wheel: 500 kg / 2 = 250 kg

Step 1 — wheel RPM:
  n_wheel = 1.0 × 60 / (π × 0.2) = 60 / 0.6283 = 95.5 RPM

Step 2 — wheel torque:
  T_friction = 250 × 9.81 × 0.02 × 0.1 = 4.90 N·m
  T_slope    = 250 × 9.81 × sin(5°) × 0.1
             = 250 × 9.81 × 0.0872 × 0.1 = 21.37 N·m
  T_accel    = 250 × 0.3 × 0.1 = 7.50 N·m
  T_total    = 4.90 + 21.37 + 7.50 = 33.77 N·m

Step 3 — gear ratio:
  ratio = 3,000 / 95.5 = 31.4 → select 30:1 or 32:1

Step 4 — required motor torque:
  T_motor = 33.77 / (30 × 0.90) = 33.77 / 27 = 1.25 N·m
  with a 1.5× safety factor: 1.25 × 1.5 = 1.87 N·m

Result: BLDC motor ≥ 2.0 N·m rated torque @ 3,000 RPM
  + a 30:1 or 32:1 planetary gearbox

In this example, a compact 400 W BLDC motor (2.0 N·m @ 3,000 RPM) combined with a 30:1 planetary gearbox drives a 500 kg AGV at 1 m/s up a 5° slope. Direct drive without a gearbox would require a motor delivering 33+ N·m — large, heavy and expensive equipment.

Gearbox types compared

The optimal AGV combination — BLDC + planetary

The industry-standard AGV combination is a BLDC motor + integrated planetary gearbox unit (hub-motor style, or an in-line motor + gearbox). Here is why:

• High efficiency: planetary gearboxes run at 90–97% efficiency, minimizing battery drain — critical in an autonomous transport vehicle.
• Compact coaxial construction: input and output shafts are on the same axis, integrating compactly into a wheel hub.
• Low backlash: precision planetary units (≤5 arcmin) support accurate positioning even during low-speed starts.
• High torque density: more torque per kg at the same ratio than worm or spur gearing.
• Maintenance-free: sealed planetary units need no lubrication management under normal service conditions.

What to avoid:

• Worm gears for the main AGV drive: self-locking is convenient, but at 40–70% efficiency a large share of motor power is wasted as heat.
• Very high ratios (single-stage >50:1): AGVs need responsive speed control. Too high a ratio reduces controllability and increases inertia mismatch.

The 8-point selection checklist

• Target speed (m/s) defined and converted to required wheel RPM.
• All torque components calculated: friction + slope (maximum grade) + acceleration.
• 1.5× safety factor applied to the total torque.
• Ratio selected so the motor operates at 60–90% of its rated RPM.
• Planetary efficiency (η) applied in the motor-torque calculation.
• Backlash specification checked: ≤5 arcmin for positioning applications, standard specification for point-to-point.
• Gearbox radial and axial load ratings compared against wheel side loads.
• Overall dimensions and weight of the motor + gearbox package confirmed within the AGV design constraints.

Common mistakes

1. Ignoring gearbox efficiency. Calculating with η = 1.0 underestimates the required motor torque. For a 2-stage planetary (η = 0.85) the motor torque is 18% higher than the ideal value — easily enough to end up under-sized.
2. Neglecting the inertia ratio. A high ratio reduces the load inertia reflected to the motor by the square of the ratio. Too low a ratio (e.g. 5:1) combined with heavy wheels causes inertia mismatch and vibration during acceleration.
3. Ignoring backlash in positioning applications. Standard planetary units have 5–15 arcmin of backlash. For AGVs that must dock precisely at stations, specify a low-backlash unit (≤3 arcmin).
4. Over-selecting the ratio "to be safe". Using 50:1 where 25:1 is needed leaves the motor running at 50% of rated RPM — lower efficiency, more heat, worse responsiveness. Select the ratio the actual requirement calls for.