Inertia and equlibrium of machines

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SUMMARY

The discussion centers on the concept of equilibrium in machines, specifically addressing the confusion surrounding inertia forces and torque calculations. The key equations presented include Newton's second law (F=ma) and the torque equation (Tm = Te + fw + Ja), where Tm represents mechanical torque, Te is electromagnetic torque, fw is the friction coefficient, J is moment of inertia, and a is acceleration. The user seeks clarification on when a machine part is not in equilibrium and the implications of inertia forces on equilibrium states. The consensus emphasizes that equilibrium occurs when the net forces and torques acting on a machine part are balanced, leading to no acceleration.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with torque and its calculation in mechanical systems
  • Knowledge of inertia and its role in dynamics
  • Basic concepts of electrical machines and their components
NEXT STEPS
  • Study the principles of mechanical torque in electrical machines
  • Learn about the role of friction in machine equilibrium
  • Explore the concept of moment of inertia and its calculations
  • Investigate the conditions under which machines fail to achieve equilibrium
USEFUL FOR

Mechanical engineers, electrical engineers, students studying dynamics and machine theory, and anyone involved in the design and analysis of mechanical systems.

ahmedbadr
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well, i would like to ask abt sth we studied in theory of machines ' we studied chapter named(equilibrium of machines) but i am really so confused abt concept of this equilibrium
because in this chapter we have studied that any part of machines under equlibrium
u can apply these equations to it
(1)f=ma
where f is inertia force
(2)inertia torque=mass x angular acceleration
and i think for any object under any forces u can apply Newton's second law on it
total forces= ma where (ma is the inertia force) so i understand from this equation that this part of machine comes to equilibrium due to its inertia force
well,my question here is that every object is under inertia force when some forces acts on it so any part of machine will be in equilibrium even without calculations i know this maybe wrong but i can't find interpretation

this maybe because i have misunderstanding abt concept of equilibrium like sometimes iam asking when part of machine not in equilibrium ?what happens to it if it's not in?sth like that
or maybe i ve problem abt concept of inertia force or inertia torque

but really i am so confused abt the equations above every object or every part of machine will be in equlibrium ?even without calculations?
 
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I had a bit of a hard time understanding your post. If you could re-write it without so many short handed works and better structure I could probably better understand what your asking. Anyways, I'm going to assume that you are confused about how the torque on a electrical machine is calculated. A simple model use for the armature for most machines is:

Tm = Te + fw + Ja

Where:
Tm = mechanical torque
Te = electromagnetic torque
f = friction coefficient (not always linear)
J = moment of inertia
a = acceleration

If an equilibirum state is obtained that usually means that there is no acceleration of the armature (a = 0). Because of this the only forces acting on the armature are the loading torque (Tm), the electromagnetic torque (Te) and the force of friction (fw). In other words, in equilibrium

Tm = Te + fw
 

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