# Effect of Gear Mass on Motor Torque

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1. Mar 26, 2016

### gwynnbleid

I am new here to the forum, so I hope I am posting in the right section.

I am working on a school project, planning to design a robotic wing. I am first devising a way to use gears with a servo motor (Hitec MG995 - http://www.electronicoscaldas.com/datasheet/MG995_Tower-Pro.pdf) as the driver. As you can see, it has a stall torque of 8.5 to 10 kgf-cm (not much, hence why I am planning to use gears). What I am trying to find out is if adding a gear to the end of the shaft will add resistance to the motor's rotation, and therefore will I have to consider that resistance when calculating the overall output? I tried to look this up online, but nothing specifies whether or not that will be the case (in fact, a lot of explanations about how gears work don't seem to consider the mass of the gear adding any resistance to the rotational force of the driving force, i.e. the motor). Since I am hoping to incorporate metal gears into the design, this is an important question whose answer I cannot find.

Also, while I am posting this, I may as well ask: I am wondering if anyone can consider good material to work with that is both light yet sturdy and is able to hold a decent amount of weight. I've considered aluminum, but I do plan to make this a little bit bigger so as to be proportional to a human so I don't know if it may be too much weight.

Any help is greatly appreciated.

2. Mar 26, 2016

### Randy Beikmann

The effect of the gear's mass will be to resist being accelerated. When rotating at a constant velocity, the gear has no effect on power transferred at all. So it boils down to an inertial effect.

In this type of problem, it's useful to combine all the inertias (whether mass, or mass moment of inertia) that move proportionately to each other, as an effective inertia or effective mass. Remember to include the motor inertia, gear inertia, etc. Then consider the motor output to be unaffected by the gear, but the system's mass/inertia to be increased by it.

3. Mar 27, 2016

### CWatters

The output of that servo is only designed to rotate +/-60 degrees. If you add gears to increase the torque you will reduce the throw eg double the torque = half the throw. You might be able to achieve a similar effect using a lever. Model engineers typically make such levers from fibreglass plate (as used for PCBs) or Paxolin which is a paper/resin laminate.

I wouldn't recommend taking that servo apart. The torque is only as high as it is because there is a complex gear train inside. The gears inside have small teeth and are lubricated with grease. Get any dirt in there and they can jam.

4. Mar 27, 2016

### gwynnbleid

My studies lean more towards the electrical side of things, so I am not all too familiar with what you are explaining. When you say that "it boils down to an inertial effect," are you saying that inertia is the only resistance against the gear because there's no acceleration, and therefore no reacting torque? Because I thought torque was related to mass moment of inertia, much like how force is related to linear inertia. And would I not have to consider gravitational force acting on the frame, therefore forcing it to rotate downward around an axis that could either directly or indirectly act on the motor shaft?

I guess this relates to my concerns above, but I'm assuming that what you're saying is that, when I am calculating the overall (mass moment of) inertia of the system I should include the gear, but the torque of the motor is unchanged by the addition of the gear to the shaft?

Thank you for the help.

I assume you mean to use these levers in order to avoid having to use gears and to use the servos directly instead? If so, I will look into that, thank you for giving me the heads up. Do you know of any brick-and-mortar stores I can go to that would sell these kind of materials, like Home Depot or other such hardware stores?

Last edited: Mar 27, 2016
5. Mar 27, 2016

### CWatters

I'm not familiar with stores in the USA but many model aircraft or model car shops will have these materials. Could also use aluminium sheet but its harder to work and metal on metal contacts can sometimes cause radio noise.

6. Mar 27, 2016

### Baluncore

Light-weight sturdiness or rigidity is not so much a property of the material as of the structure.

A structural 3D truss will have great strength and rigidity with very low mass. Look at the construction of lattice towers. 100 years ago aircraft were built from wooded struts with wire bracing and covered in a painted or doped cloth. The only problem with wooden aircraft, was people with wooden heads.

A foam sandwich would also give good fixed surfaces and structures.
https://en.wikipedia.org/wiki/Sandwich-structured_composite

7. Mar 28, 2016

### gwynnbleid

I didn't think to look there, as a matter of fact. Thanks for the heads up.

By sturdy I meant that it wouldn't collapse under its own weight, as it would have to support itself without bending or snapping in two. I see how that word doesn't apply too well to what I was asking, although I don't know the proper term for what I am trying to describe.

8. Mar 28, 2016

### Baluncore

What is it ?

9. Mar 28, 2016

### CWatters

It would help if we knew a bit more about the application. I very much doubt that the mass of any gears or levers you plan to add would significantly slow the servo.

However if you plan to operate it near it's max torque that's much more likely to significantly slow the servo.

10. Apr 1, 2016

### Randy Beikmann

Sorry to take so long to chime back in.

Where I had said "Then consider the motor output to be unaffected by the gear, but the system's mass/inertia to be increased by it.", what I meant was that it's easy to confuse yourself when adding components into a system (I've learned this the hard way).

In this system, you can think of it in terms of its inertia, its energy source (the motor torque), and its energy dissipation (friction). When you add in a gear set, you do introduce some friction, but mainly what you do is 1) change the ratio of speeds between the different parts, and 2) introduce some additional inertia to the system.

But the motor itself will still run the same, capable of producing the same torque at the same motor speed. The difference is that the motor now acts on a system that has been altered by the gear set. That is what you need to adjust.

For the other point, remember that the inertia of the system has no effect on the required motor torque unless that inertia is being accelerated (torque = rotational inertia x angular acceleration alpha). In other words, the inertia of the system takes no torque (or power) to drive at a constant speed. Friction, of course, does take torque to drive, constant speed or not.

So the way to analyze it is to "lump" all the inertias and masses into the "effective inertia" seen by the motor (I found a few references to this with google). Then do the same for frictional torques, finding out what torque it takes at the motor to drive each friction source, considering the gear ratios (an effective friction torque). Then the required motor torque is Tmotor = Jeffective x alpha_motor + Tfriction. If the torque calculated from this is greater than the motors capability, it will simply not be able to achieve that performance, and you need a bigger motor.

11. Apr 2, 2016

### Baluncore

Are you building a flapping wing that will be powered by the servo motor, or is the servo motor being used to adjust a control surface ? What will the robotic wing be attached to ?

If you want a flapping wing then it might be better done with a crank that is driven continuously in one direction, rather than by reversing a servo motor.

12. Apr 2, 2016

### Randy Beikmann

Baluncore is right. Take a look at how a windshield wiper mechanism works.

13. Apr 2, 2016

### CWatters

The servo you mentioned earlier is unlikely to be fast enough for a flapping wing flying model.