Help in Newton's Laws of Rotation in Electric Motor and Electric Motor Dynamics

In summary, the conversation discusses the motor and load models, as well as the meaning and derivation of the equations used in the model. The equations involve Newton's Laws of Rotation and Kirchoff's Laws, and can be put into state space form. The conversation also touches on the back EMF and electrical power in the DC motor model. The equations and their meaning are explained, and it is mentioned that the DC motor constant can be represented as V/w.
  • #1
tehipwn
16
0
Here is a copy of my notes on the motor. Basically it's just some of Newton's Law of Rotation combined with Kirchoff's Laws. Then we put the model into state space form.

Could someone just please explain to me the meaning of the equations? It's been a while since I've had physics. Thanks a lot for any help!

I would just love to be able to derive these equations instead of just copying them down, but they're not explained in my book.
 
Last edited:
Physics news on Phys.org
  • #2
Sorry there must have been a problem with the image linking. I am putting it in an attachment instead.

A quick explanation of the motor and load models would be helpful.

In particular, I'm having problems understanding the derivations of the differential equations of the model. I'm an electrical engineer in school and have had little exposure to mechanical modeling. A thorough explanation of the differential equations would be appreciated. I understand how to put the equations in state-space form.

Thanks to all for looking.
 

Attachments

  • motor_dynamics.jpg
    motor_dynamics.jpg
    21.9 KB · Views: 860
Last edited:
  • #3
The equation [tex]T = J \stackrel{..}{\theta}[/tex] is basically just the equivalent of "F=ma" for rotational systems. Mass is replaced with "moment of inertia" (J) and acceleration is replaced by angular acceleration ([tex]\stackrel{..}{\theta}[/tex]).

The torque available for angular acceleration is equal to the electrical torque [itex]k_m \omega[/itex] minus the mechanical loss term [itex]B \omega[/itex]. That's pretty much all there is to the mechanical part of the model.
 
  • #4
Re the electrical part of the system. Notice in the DC motor model there is a back EMF that is proportional to angular speed. This is actually where all the energy conversion takes place. The electrical power being absorbed by this back EMF is actually the raw mechanical output power. So just put together P=VI and T=P/w and you'll get the expression, [itex]T = k_m I[/itex], for the torque produced by the motor.
 
  • #5
Thank you very much. That actually made it easy! It's just been so long since I've seen rotational motion that I forgot where the basis for the equations came from. But now I see [tex]T = J \stackrel{..}{\theta}[/tex] should be the starting point for rotational systems...High school physics, I know.

Using your equations, I put P=VI and P=Tw. Setting them equal yields VI=Tw meaning T=(VI)/w. Does that mean that Km=V/w? If so, what's the meaning of this?

Thanks.
 
  • #6
I did a quick search of DC motor constant and found that the units can be V/rad/sec, so yes Km=V/w. This is for Advanced Control Systems by the way. I really like control systems but my mechanical modeling ability must be greatly improved.
 

1. What are Newton's Laws of Rotation?

Newton's Laws of Rotation are three physical laws that describe the behavior of objects in rotational motion. They are:

  • First Law: An object will remain at rest or in uniform rotational motion unless acted upon by an external torque.
  • Second Law: The angular acceleration of an object is directly proportional to the net torque applied to it and inversely proportional to its moment of inertia.
  • Third Law: For every torque exerted on an object, there is an equal and opposite torque exerted by the object.

2. How do Newton's Laws of Rotation apply to electric motors?

In an electric motor, Newton's Laws of Rotation explain how the motor converts electrical energy into rotational motion. The first law states that the motor will remain at rest until an external torque (from the electric current) is applied. The second law describes how the amount of torque and speed of rotation are related, and the third law explains the equal and opposite forces between the stator and rotor of the motor.

3. What is the role of inertia in electric motor dynamics?

Inertia is the resistance an object has to changes in its motion. In electric motor dynamics, the moment of inertia (a measure of an object's rotational inertia) affects the motor's response to changes in torque and speed. A higher moment of inertia means the motor will be more resistant to changes in rotational motion, while a lower moment of inertia allows for quicker changes in speed and direction.

4. How does the design of an electric motor impact its performance?

The design of an electric motor can impact its performance in several ways. The size and shape of the rotor and stator, the type of materials used, and the arrangement of the coils and magnets can all affect the motor's efficiency, torque, and speed. Additionally, the design of the motor can impact its durability and ability to handle different loads and operating conditions.

5. Can Newton's Laws of Rotation be applied to all types of electric motors?

Yes, Newton's Laws of Rotation can be applied to all types of electric motors, including AC motors, DC motors, and brushless motors. These laws are fundamental principles of physics and apply to all types of rotational motion, including the motion of electric motors.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
7
Views
906
  • Engineering and Comp Sci Homework Help
3
Replies
102
Views
4K
Replies
9
Views
2K
  • Mechanical Engineering
Replies
2
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
4
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Replies
3
Views
2K
  • Classical Physics
Replies
0
Views
493
  • Electrical Engineering
Replies
5
Views
1K
  • Classical Physics
Replies
11
Views
1K
Back
Top