The formula to calculate Torque Required on Shaft B to Accelerate Itself (TB) is:
\[ T_B = G \cdot I_B \cdot \alpha_A \]
Where:
The torque required on shaft B to accelerate itself is the measure of the force that can cause an object to rotate about an axis. Force is what causes an object to accelerate in linear kinematics.
Gear Ratio is the ratio of output gear speed to the input gear speed or the ratio of the number of teeth on the gear to that on the pinion.
Mass Moment of Inertia of mass attached to shaft B is a quantity expressing a body's tendency to resist angular acceleration.
Angular Acceleration of Shaft A is also known as rotational acceleration. It is a quantitative expression of the change in angular velocity per unit time.
Let's assume the following values:
Using the formula:
\[ T_B = G \cdot I_B \cdot \alpha_A \]
Evaluating:
\[ T_B = 3 \cdot 36 \cdot 25 \]
The Torque Required on Shaft B to Accelerate Itself is 2700 N·m.
| Gear Ratio (G) | Mass Moment of Inertia (IB) | Angular Acceleration (αA) | Torque Required (TB) |
|---|---|---|---|
| 2 | 30 | 20 | 1,200.000000000000000 |
| 2 | 30 | 22 | 1,320.000000000000000 |
| 2 | 30 | 24 | 1,440.000000000000000 |
| 2 | 30 | 26 | 1,560.000000000000000 |
| 2 | 30 | 28 | 1,680.000000000000000 |
| 2 | 30 | 30 | 1,800.000000000000000 |
| 2 | 32 | 20 | 1,280.000000000000000 |
| 2 | 32 | 22 | 1,408.000000000000000 |
| 2 | 32 | 24 | 1,536.000000000000000 |
| 2 | 32 | 26 | 1,664.000000000000000 |
| 2 | 32 | 28 | 1,792.000000000000000 |
| 2 | 32 | 30 | 1,920.000000000000000 |
| 2 | 34 | 20 | 1,360.000000000000000 |
| 2 | 34 | 22 | 1,496.000000000000000 |
| 2 | 34 | 24 | 1,632.000000000000000 |
| 2 | 34 | 26 | 1,768.000000000000000 |
| 2 | 34 | 28 | 1,904.000000000000000 |
| 2 | 34 | 30 | 2,040.000000000000000 |
| 2 | 36 | 20 | 1,440.000000000000000 |
| 2 | 36 | 22 | 1,584.000000000000000 |
| 2 | 36 | 24 | 1,728.000000000000000 |
| 2 | 36 | 26 | 1,872.000000000000000 |
| 2 | 36 | 28 | 2,016.000000000000000 |
| 2 | 36 | 30 | 2,160.000000000000000 |
| 2 | 38 | 20 | 1,520.000000000000000 |
| 2 | 38 | 22 | 1,672.000000000000000 |
| 2 | 38 | 24 | 1,824.000000000000000 |
| 2 | 38 | 26 | 1,976.000000000000000 |
| 2 | 38 | 28 | 2,128.000000000000000 |
| 2 | 38 | 30 | 2,280.000000000000000 |
| 2 | 40 | 20 | 1,600.000000000000000 |
| 2 | 40 | 22 | 1,760.000000000000000 |
| 2 | 40 | 24 | 1,920.000000000000000 |
| 2 | 40 | 26 | 2,080.000000000000000 |
| 2 | 40 | 28 | 2,240.000000000000000 |
| 2 | 40 | 30 | 2,400.000000000000000 |
| 2.5 | 30 | 20 | 1,500.000000000000000 |
| 2.5 | 30 | 22 | 1,650.000000000000000 |
| 2.5 | 30 | 24 | 1,800.000000000000000 |
| 2.5 | 30 | 26 | 1,950.000000000000000 |
| 2.5 | 30 | 28 | 2,100.000000000000000 |
| 2.5 | 30 | 30 | 2,250.000000000000000 |
| 2.5 | 32 | 20 | 1,600.000000000000000 |
| 2.5 | 32 | 22 | 1,760.000000000000000 |
| 2.5 | 32 | 24 | 1,920.000000000000000 |
| 2.5 | 32 | 26 | 2,080.000000000000000 |
| 2.5 | 32 | 28 | 2,240.000000000000000 |
| 2.5 | 32 | 30 | 2,400.000000000000000 |
| 2.5 | 34 | 20 | 1,700.000000000000000 |
| 2.5 | 34 | 22 | 1,870.000000000000000 |
| 2.5 | 34 | 24 | 2,040.000000000000000 |
| 2.5 | 34 | 26 | 2,210.000000000000000 |
| 2.5 | 34 | 28 | 2,380.000000000000000 |
| 2.5 | 34 | 30 | 2,550.000000000000000 |
| 2.5 | 36 | 20 | 1,800.000000000000000 |
| 2.5 | 36 | 22 | 1,980.000000000000000 |
| 2.5 | 36 | 24 | 2,160.000000000000000 |
| 2.5 | 36 | 26 | 2,340.000000000000000 |
| 2.5 | 36 | 28 | 2,520.000000000000000 |
| 2.5 | 36 | 30 | 2,700.000000000000000 |
| 2.5 | 38 | 20 | 1,900.000000000000000 |
| 2.5 | 38 | 22 | 2,090.000000000000000 |
| 2.5 | 38 | 24 | 2,280.000000000000000 |
| 2.5 | 38 | 26 | 2,470.000000000000000 |
| 2.5 | 38 | 28 | 2,660.000000000000000 |
| 2.5 | 38 | 30 | 2,850.000000000000000 |
| 2.5 | 40 | 20 | 2,000.000000000000000 |
| 2.5 | 40 | 22 | 2,200.000000000000000 |
| 2.5 | 40 | 24 | 2,400.000000000000000 |
| 2.5 | 40 | 26 | 2,600.000000000000000 |
| 2.5 | 40 | 28 | 2,800.000000000000000 |
| 2.5 | 40 | 30 | 3,000.000000000000000 |
| 3 | 30 | 20 | 1,800.000000000000000 |
| 3 | 30 | 22 | 1,980.000000000000000 |
| 3 | 30 | 24 | 2,160.000000000000000 |
| 3 | 30 | 26 | 2,340.000000000000000 |
| 3 | 30 | 28 | 2,520.000000000000000 |
| 3 | 30 | 30 | 2,700.000000000000000 |
| 3 | 32 | 20 | 1,920.000000000000000 |
| 3 | 32 | 22 | 2,112.000000000000000 |
| 3 | 32 | 24 | 2,304.000000000000000 |
| 3 | 32 | 26 | 2,496.000000000000000 |
| 3 | 32 | 28 | 2,688.000000000000000 |
| 3 | 32 | 30 | 2,880.000000000000000 |
| 3 | 34 | 20 | 2,040.000000000000000 |
| 3 | 34 | 22 | 2,244.000000000000000 |
| 3 | 34 | 24 | 2,448.000000000000000 |
| 3 | 34 | 26 | 2,652.000000000000000 |
| 3 | 34 | 28 | 2,856.000000000000000 |
| 3 | 34 | 30 | 3,060.000000000000000 |
| 3 | 36 | 20 | 2,160.000000000000000 |
| 3 | 36 | 22 | 2,376.000000000000000 |
| 3 | 36 | 24 | 2,592.000000000000000 |
| 3 | 36 | 26 | 2,808.000000000000000 |
| 3 | 36 | 28 | 3,024.000000000000000 |
| 3 | 36 | 30 | 3,240.000000000000000 |
| 3 | 38 | 20 | 2,280.000000000000000 |
| 3 | 38 | 22 | 2,508.000000000000000 |
| 3 | 38 | 24 | 2,736.000000000000000 |
| 3 | 38 | 26 | 2,964.000000000000000 |
| 3 | 38 | 28 | 3,192.000000000000000 |
| 3 | 38 | 30 | 3,420.000000000000000 |
| 3 | 40 | 20 | 2,400.000000000000000 |
| 3 | 40 | 22 | 2,640.000000000000000 |
| 3 | 40 | 24 | 2,880.000000000000000 |
| 3 | 40 | 26 | 3,120.000000000000000 |
| 3 | 40 | 28 | 3,360.000000000000000 |
| 3 | 40 | 30 | 3,600.000000000000000 |
| 3.5 | 30 | 20 | 2,100.000000000000000 |
| 3.5 | 30 | 22 | 2,310.000000000000000 |
| 3.5 | 30 | 24 | 2,520.000000000000000 |
| 3.5 | 30 | 26 | 2,730.000000000000000 |
| 3.5 | 30 | 28 | 2,940.000000000000000 |
| 3.5 | 30 | 30 | 3,150.000000000000000 |
| 3.5 | 32 | 20 | 2,240.000000000000000 |
| 3.5 | 32 | 22 | 2,464.000000000000000 |
| 3.5 | 32 | 24 | 2,688.000000000000000 |
| 3.5 | 32 | 26 | 2,912.000000000000000 |
| 3.5 | 32 | 28 | 3,136.000000000000000 |
| 3.5 | 32 | 30 | 3,360.000000000000000 |
| 3.5 | 34 | 20 | 2,380.000000000000000 |
| 3.5 | 34 | 22 | 2,618.000000000000000 |
| 3.5 | 34 | 24 | 2,856.000000000000000 |
| 3.5 | 34 | 26 | 3,094.000000000000000 |
| 3.5 | 34 | 28 | 3,332.000000000000000 |
| 3.5 | 34 | 30 | 3,570.000000000000000 |
| 3.5 | 36 | 20 | 2,520.000000000000000 |
| 3.5 | 36 | 22 | 2,772.000000000000000 |
| 3.5 | 36 | 24 | 3,024.000000000000000 |
| 3.5 | 36 | 26 | 3,276.000000000000000 |
| 3.5 | 36 | 28 | 3,528.000000000000000 |
| 3.5 | 36 | 30 | 3,780.000000000000000 |
| 3.5 | 38 | 20 | 2,660.000000000000000 |
| 3.5 | 38 | 22 | 2,926.000000000000000 |
| 3.5 | 38 | 24 | 3,192.000000000000000 |
| 3.5 | 38 | 26 | 3,458.000000000000000 |
| 3.5 | 38 | 28 | 3,724.000000000000000 |
| 3.5 | 38 | 30 | 3,990.000000000000000 |
| 3.5 | 40 | 20 | 2,800.000000000000000 |
| 3.5 | 40 | 22 | 3,080.000000000000000 |
| 3.5 | 40 | 24 | 3,360.000000000000000 |
| 3.5 | 40 | 26 | 3,640.000000000000000 |
| 3.5 | 40 | 28 | 3,920.000000000000000 |
| 3.5 | 40 | 30 | 4,200.000000000000000 |
| 4 | 30 | 20 | 2,400.000000000000000 |
| 4 | 30 | 22 | 2,640.000000000000000 |
| 4 | 30 | 24 | 2,880.000000000000000 |
| 4 | 30 | 26 | 3,120.000000000000000 |
| 4 | 30 | 28 | 3,360.000000000000000 |
| 4 | 30 | 30 | 3,600.000000000000000 |
| 4 | 32 | 20 | 2,560.000000000000000 |
| 4 | 32 | 22 | 2,816.000000000000000 |
| 4 | 32 | 24 | 3,072.000000000000000 |
| 4 | 32 | 26 | 3,328.000000000000000 |
| 4 | 32 | 28 | 3,584.000000000000000 |
| 4 | 32 | 30 | 3,840.000000000000000 |
| 4 | 34 | 20 | 2,720.000000000000000 |
| 4 | 34 | 22 | 2,992.000000000000000 |
| 4 | 34 | 24 | 3,264.000000000000000 |
| 4 | 34 | 26 | 3,536.000000000000000 |
| 4 | 34 | 28 | 3,808.000000000000000 |
| 4 | 34 | 30 | 4,080.000000000000000 |
| 4 | 36 | 20 | 2,880.000000000000000 |
| 4 | 36 | 22 | 3,168.000000000000000 |
| 4 | 36 | 24 | 3,456.000000000000000 |
| 4 | 36 | 26 | 3,744.000000000000000 |
| 4 | 36 | 28 | 4,032.000000000000000 |
| 4 | 36 | 30 | 4,320.000000000000000 |
| 4 | 38 | 20 | 3,040.000000000000000 |
| 4 | 38 | 22 | 3,344.000000000000000 |
| 4 | 38 | 24 | 3,648.000000000000000 |
| 4 | 38 | 26 | 3,952.000000000000000 |
| 4 | 38 | 28 | 4,256.000000000000000 |
| 4 | 38 | 30 | 4,560.000000000000000 |
| 4 | 40 | 20 | 3,200.000000000000000 |
| 4 | 40 | 22 | 3,520.000000000000000 |
| 4 | 40 | 24 | 3,840.000000000000000 |
| 4 | 40 | 26 | 4,160.000000000000000 |
| 4 | 40 | 28 | 4,480.000000000000000 |
| 4 | 40 | 30 | 4,800.000000000000000 |