Shaft torque from air gap torque
Shaft torque from air gap torque
(OP)
Hopefully a very simple question!
How do you calculate shaft torque from air-gap torque under transient conditions?
If my load inertia is J1 and my motor inertia is J2, is it as simple as Shaft Torque = J1/(J1+J2)*air-gap torque?
Thanks
How do you calculate shaft torque from air-gap torque under transient conditions?
If my load inertia is J1 and my motor inertia is J2, is it as simple as Shaft Torque = J1/(J1+J2)*air-gap torque?
Thanks





RE: Shaft torque from air gap torque
Imagine that you have a shaft with opposite-direction torques applied on two ends. If the same torque is applied on both ends, no acceleration/decel occurs and the torque felt on the shaft is the same as that applied on either end. Not too interesting.
Now apply two different opposing torques Ta and Tb on each end with Ta>Tb. What is the torque seen by the shaft.
If all of the inertia is located at the B end of the shaft, then the shaft will see the greater Torque Ta Throughout it's lenght.
If all of the inertia is located at the A end of the shaft, then the shaft will see the lower Torque Tb Throughout it's lenght.
If the inertia is split with inertia Ja located at the A end and Jb located at the B end, then the shaft will see an intermediate torque which might be viewed as a weighted average of Ta and Tb.
Tshaft = Ta*Jb/(Jb+Ja) + Jb*Ja/(Jb+Ja).
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: Shaft torque from air gap torque
Your equation for shaft torque is correct IF you can ignore the springiness of the shaft. If this is not true, the shaft torque is
Ts = TL + (Tag-TL)*(JL/(Jm + JL)*[1-cos (wn*t)]
where
TL = load torque
Tag = motor electrical torque
JL, Jm = load, motor moment of interia respectively
wn = mechanical first natural frequency
=sqrt(K*(Jm+JL)/(Jm*JL))
K = shaft spring constant
Reference "Bus Transfer of AC Induction Motors, A Perspective", paper PCIC-89-07 from the IEEE.
RE: Shaft torque from air gap torque
Tg = Tl + (Jm) d^2Q/dt + (Jl) d^2Q/dt---1
Tg = Tl + (Jm +Jl) d^2Q/dt
and then;
d^2Q/dt=(Tg-Tl)/(Jm+Jl)---2
Were:
Tg = Motor Torque at the air gap or rotor bars.
Tl = Load Torque
Q = Shaft angular position.
d^2Q/dt = second derivate of angular position ( angular acceleration)
Jm = Motor rotor inertia.
Jl = Load Inertia
Ts = Tl + (Jl)d^2Q/dt---3
Ts = Torque at the motor shaft extension.
by inserting (2) in (3)
Ts= Tl + Jl/(Jm+Jl)*(Tg-Tl)
Note that at steady speed d^2Q/dt =0
RE: Shaft torque from air gap torque
The reason I ask was this topic is not clearly covered in many electro or mechanical text books.
RE: Shaft torque from air gap torque
If the inertia is split with inertia Ja located at the A end and Jb located at the B end, then the shaft will see an intermediate torque which might be viewed as a weighted average of Ta and Tb.
Tshaft = Ta*Jb/(Jb+Ja) + Jb*Ja/(Jb+Ja).
///Please, would you clarify the equation in terms of Tb?\\\
RE: Shaft torque from air gap torque
http://regpro.mechatronik.uni-linz.ac.at/eu-projekt/theoryold/master.html
for:
Modeling of Electromechanical Systems
RE: Shaft torque from air gap torque
Tshaft = Ta*Jb/(Jb+Ja) + Tb*Ja/(Jb+Ja).
If you re-arrange aolalde's equation it is exactly the same result.
Thanks to aolalde for posting the proof.
It gives instantaneous shaft torque as function of instantaneous motor and load torque during the transient.
I would be interested to hear the assumptions and proof behind Gord's equation. It is the same as aolalde's execpt the multiplier [1-cos (wn*t)] after the 2nd term. I think maybe it applies for a step change in torque.
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: Shaft torque from air gap torque
1. Reference:
Daugherty, Roger H., "Bus Transfer of AC Induction Motors: A Perspective," IEEE Transactions on Industry and Applications, Vol. 26, No. 5, pp 935-942, Sept/Oct 1990.
Comment: Reference 1 does not include the detail derivations; however, it refers to previously published literature.
2. Another related reference:
Gill G. Richards, M.A. Laughton, "Limiting Induction Motor Transient Torques Following Source Discontinuities," IEEE Transactions on Energy Conversion, Vol 13, No 3, pp 250-256, September 1998
RE: Shaft torque from air gap torque
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: Shaft torque from air gap torque
If anyone can provide the assumptions and derivation here (not reference to a hardcopy textbook) I would be interested.
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: Shaft torque from air gap torque
Ts=JL/(JM+JL)xTe....(3)
d(dTs)/dt^2 + K x [(JM+JL)/(JM x JL)] x Ts = K x Te/JM - K x Tl/JL .... (4)
wn=2 x pi x Fn = Sqrt[(K x JM x JL / (JM x JL)] ....(5)
(wn is the first natural torsional frequency)
Assuming that the load torque Tl in (4) remains constant at A while the motor electrical torque Te abruptly changes from A to B, as would happen to the average value of the electromagnetic torque when switching operation takes place, the resulting shaft torque transient response is:
Ts=A+(B-A)x[JL/(JM+JL)]x[1-cos(wnxt)] ....(6)
Ts is a solution of the second order differential equation (4).
RE: Shaft torque from air gap torque
RE: Shaft torque from air gap torque
RE: Shaft torque from air gap torque
RE: Shaft torque from air gap torque
Constant A in my equation is equal to TL in your equation?
Constant B in my equation is equal to Tag in your equation?
RE: Shaft torque from air gap torque
RE: Shaft torque from air gap torque
wn=2 x pi x Fn = Sqrt[K x( JM + JL) / (JM x JL)] ....(5)
is the correct form.
RE: Shaft torque from air gap torque
Ts(t)=(K/wn^2)x[(Te/JM)-(Tl/JL)]x[1-cos(wnxt)]=
=[(JLxTe-JMxTl)/(JM+JL)]x[1-cos(wnxt)]....(7)
which is essentially what electricpete derived except the [1-cos(wnxt)] term and the sign that is - in (7) and + in electricpete equation.
The ordinary second order differential equation (4) may be solved quickly by Laplace or Fourier Transform.