TASARIMDAN İMALATA
Gear Speed and Torque Calculation
Calculate output speed and torque from gear ratio, input power and efficiency, with a two-stage gearbox example.
Basic relationships
z is tooth count and n is speed in rpm. Gear 1 is the input and gear 2 the output. For a fixed-axis gear pair, the ratio magnitude is i = z₂/z₁ = n₁/n₂. Externally meshing gears turn in opposite directions. Gears fixed to the same shaft have the same speed.
Power, torque and efficiency
P is in kilowatts, T in newton metres and n in rpm. The coefficient 9550 is rounded. η is total mechanical efficiency; use 1 for an ideal lossless calculation. Losses reduce the actual output torque.
P = T × 2πn / 60000
T ≈ 9550 × P / n
i = n₁ / n₂ = z₂ / z₁; n₂ = n₁ / i; T₂ = η × i × T₁
Two-stage worked example
Input power is 10 kW at 3000 rpm. The first pair has 10/40 teeth and the second 16/50 teeth. The 40-tooth and 16-tooth gears are fixed to the intermediate shaft. The following results assume no losses and retain unrounded intermediate values.
i₁ = 40 / 10 = 4; i₂ = 50 / 16 = 3.125
i = 4 × 3.125 = 12.5
n₂ = 3000 / 4 = 750 rpm; n₄ = 750 / 3.125 = 240 rpm
T₁ ≈ 9550 × 10 / 3000 = 31.833333… N·m
T₂ = T₁ × 4 ≈ 127.333333… N·m
T₄ = T₁ × 12.5 ≈ 397.916667 N·m
| Input | Intermediate shaft | Output | |
|---|---|---|---|
| n (rpm) | 3000 | 750 | 240 |
| T (N·m) | 31.83 | 127.33 | 397.92 |
Including efficiency
If each stage is assumed to be 98% efficient, overall efficiency is 0.9604. Output speed remains 240 rpm, output power is 9.604 kW and output torque is approximately 382.16 N·m. The 98% value is illustrative; use manufacturer data for the actual transmission.
η = 0.98 × 0.98 = 0.9604; T ≈ 397.916667 × 0.9604 ≈ 382.16 N·m
Design considerations
A ratio calculation does not establish tooth strength or service life. Check module, pressure angle, root strength, contact fatigue, lubrication, bearings and shaft loads separately. Multiply stage ratios to obtain the overall ratio. Equal torque at gears on the intermediate shaft assumes negligible losses and no other loads.