Gear Output Torque Speed Horsepower

Overview

Engineering reference data for Gear Output Torque Speed Horsepower in mechanics.

Key Formulas

Newton's Second Law

$F = ma$

Force = mass × acceleration.

Work

$W = Fd\cos\theta$

Work = force × displacement × cos(angle).

Kinetic Energy

$E_k = \frac{1}{2}mv^2$

Energy of motion.

Potential Energy

$E_p = mgh$

Gravitational potential energy.

Variables

Symbol	Description	Unit
$F$	Force	N
$m$	Mass	kg
$a$	Acceleration	m/s²
$v$	Velocity	m/s

Worked Examples

Example 1: Gear Output Torque

Calculate the output torque from a transmission with:

• Input torque: 500 Nm
• Gear transmission ratio: *3.8
• Gear efficiency: *0.9

$M_o = M_i \times r \times \mu = 500 \text{ Nm} \times 3.8 \times 0.9 = 1710 \text{ Nm}$

Example 2: Gear Output Speed

Calculate the output speed of a transmission with:

• Input speed: 2000 rpm
• Transmission ratio: *3.8

$S_o = \frac{S_i}{r} = \frac{2000 \text{ rpm}}{3.8} = 526 \text{ rpm}$

Example 3: Gear Output Power

Calculate the output power from a transmission with:

• Input power: 300 kW
• Efficiency: *0.9

$P_o = P_i \times \mu = 300 \text{ kW} \times 0.9 = 270 \text{ kW}$

Practical Notes

• Efficiency losses: Gear transmissions always produce less output power than input due to friction losses. Typical spur gear efficiency ranges from 94–98% per gear stage.
• Speed-torque tradeoff: When the transmission ratio ($r > 1$), output torque increases while output speed decreases proportionally.
• Power conservation: In an ideal system (100% efficiency), output power equals input power. The relationship $P = M \times \omega$ (power = torque × angular velocity) connects all three formulas.

References

• Original Source