Torque losses through gears due to inertia

In summary, the conversation discussed the calculation of torque loss in a two gear system due to acceleration. The formula used to calculate effective inertia on the G1 side was G1's inertia + (1/(GearRatio)2) * G2's inertia, while on the other side it was equal to 4 + (1/(0.125)2) * 2. The overall loss of torque in both gears was also discussed, with a desire to find a formula for calculating effective torque using the gear ratio and inertia. However, it was concluded that there are only two options for calculating torque loss: balancing torques and solving for angular acceleration, or using effective moment of inertia.
  • #1
ZachGriffin
20
0
I'm trying to work out a formula to calculate the amount of torque lost in a two gear system due to the acceleration the second gear. I'm assuming there is nothing lost to friction etc

For example, If I have two gears, G1 and G2, with respective inertia's of 2 and 4. G1 has 10 teeth and G2 has 80 teeth for a ratio of 8.0 or 0.125 depending on which way you are going. When looking on the G1 side, the effective inertia of the geared system can be found as:

G1's inertia + (1/(GearRatio)2) * G2's inertia

which equates to 2 + (1/(8)2) * 4 = 2 + 0.015625 * 4

So the effective inertia is 2.0625, as the high gear ratio of 8 reduces the influence of G2's inertia.

Applying 100Nm of torque to the first gear, the acceleration now becomes 100/2.0625 = 48.48

On the other side the effective inertia is equal to 4 + (1/(0.125)2) * 2
= 4 + 64 * 2
= 132

As the torque is now multiplied by the gear ratio, we have 800Nm of torque so the acceleration now becomes 800/132 = 6.06, exactly 8 times less than G1's acceleration, so the formula is correct.

What I'd like to know is how to calculate the effective torque, so for example G1 has an inertia of 2, and accelerates at 48.48 which means the effective torque was 96.96Nm. The overall loss from accelerating G2's inertia was 100 - 96.96 = 3.04Nm. On the other side, G2 has an inertia of 4 and accelerates at 6.06 which means the effective torque was 24.24Nm. The overall loss from accelerating G1's inertia was 800 - 24.24 = 775.76Nm.

I've been trying to work out a way to calculate the effective torque using the gear ratio and inertia in a formula, rather than using the effective moment of inertia calcs as above. I'm hoping somebody here knows, fingers crossed. Any help is much appreciated
 
Physics news on Phys.org
  • #2
You either have to balance torques and solve for angular acceleration, or use effective moment of inertia. There isn't really a third option.
 

1. What is torque loss through gears due to inertia?

Torque loss through gears due to inertia is the decrease in torque that occurs when power is transferred through a series of gears. This is due to the rotational inertia of the gears, meaning that the energy required to accelerate or decelerate the gears reduces the amount of torque available at the output shaft.

2. How does gear ratio affect torque loss through gears due to inertia?

The gear ratio is a major factor in determining the amount of torque loss through gears due to inertia. In general, the higher the gear ratio, the greater the torque loss. This is because a higher gear ratio means that more gears are involved in the power transfer, resulting in more rotational inertia and thus more torque loss.

3. Can torque loss through gears due to inertia be prevented or reduced?

Torque loss through gears due to inertia is an inherent aspect of gear systems and cannot be completely eliminated. However, it can be reduced by using high-quality gears with lower rotational inertia, minimizing the number of gears in the system, and properly lubricating and maintaining the gears.

4. What factors contribute to torque loss through gears due to inertia?

In addition to gear ratio and gear quality, other factors that can contribute to torque loss through gears due to inertia include the speed of the gears, the angle of the gear teeth, and the level of friction between the gears.

5. How does torque loss through gears due to inertia affect the efficiency of a system?

Torque loss through gears due to inertia reduces the efficiency of a system by decreasing the amount of torque available at the output shaft. This means that more power is required to achieve the desired output, resulting in a lower overall efficiency. It is important to consider torque loss when designing and optimizing gear systems for maximum efficiency.

Similar threads

Torque and Moment of Inertia of a Lever Arm
    • Mechanics
Replies
2
Views
2K
How can I design a gear train to meet specific torque and RPM requirements?
    • Mechanical Engineering
Replies
2
Views
1K
Find the gear ratio for maximum angular acceleration
    • Introductory Physics Homework Help
Replies
28
Views
6K
Why do the works of two objects in rotation differ when friction is present?
    • Mechanics
Replies
5
Views
2K
Energy by Impluse Momentum Through a Gear Reducer
    • Mechanics
Replies
19
Views
4K
How Does Torque Affect Gear Movement on a Rack?
    • Mechanics
Replies
1
Views
2K
Compound planetary gear problem
    • Mechanical Engineering
Replies
1
Views
1K
Unreasonable values for engine torque in vehicle simulation
    • Electrical Engineering
Replies
4
Views
713
Understanding Gear Ratios and Torque in Torsional Problems
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Torque calculations: Rotating vertical shaft
    • Mechanical Engineering
Replies
5
Views
3K

Hot Threads

Recent Insights

Back
Top