Hydraulic Motor Angular acceleration limitation
Hydraulic Motor Angular acceleration limitation
(OP)
I have a hydraulic motor that has an angular acceleration limit of 87,000 rad/s². The motor is driving a drill rod which is of cylindrical section and when it operating at full torque can be wound up by as much as 4 turns (length is 1000m). When the rod breaks into a void the energy is released and accelerates the motor. Does any one know a calculation method to ascertain if the motor limitation is exceeded? If you need more info let me know.
Cheers Ian
Cheers Ian





RE: Hydraulic Motor Angular acceleration limitation
Your big problem will be working out a damping value, for the motor, and for the shaft.
Is the moment of inertia of the motor significant compared with that of the shaft?
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
RE: Hydraulic Motor Angular acceleration limitation
If the rod breaks into a void and the rod unwinds won't it
be opposing normal motor rotation in which case it would try to slow the motor down as opposed to accelerating it
or am I misunderstanding your problem?
Regards
desertfox
RE: Hydraulic Motor Angular acceleration limitation
What you need is a partial differntial equation with interesting boundary conditions to describe the motion, since the energy is distributed along the shaft.
But the solution is only as good as the assumption of where the shaft breaks.
RE: Hydraulic Motor Angular acceleration limitation
Thinking further about your problem what your sayimg is the motor is under load when the drill breaks through the void the torque load is released and therefore the motor wants to accelerate.
If the motor is designed with an acceleration limit and is run under the conditions required by the manufacturer I can't see why it would exceed that acceleration limit unless your over driving the rotor to start with.
regards
desertfox
RE: Hydraulic Motor Angular acceleration limitation
RE: Hydraulic Motor Angular acceleration limitation
RE: Hydraulic Motor Angular acceleration limitation
At what point of this dynamic are you worried about motor acceleration? Is it when the void is hit (and the load on the motor suddenly drops off) or is it the oscillating load on the motor as the unloaded bit is allowed to torsionally vibrate?
RE: Hydraulic Motor Angular acceleration limitation
Where will the stored energy go? Towards accelerating the now unconstrainted end of the drill, or into the motor.
Do you know the drag losses of the drill in the bore?
It seems more likely that the near-instataneous drop in torque at the bit is faster than the motor can respond, so the motor accelerates as it sees the reduction in load.
RE: Hydraulic Motor Angular acceleration limitation
The system is a flywheel on a continuous shaft. I suspect the inertia of the flywheel is irrelevant, so the mode shape becomes the first mode of a uniform shaft. Therefore the motor will oscillate with an initial semipeak amplitude of 8pi
Simple harmonic motion tells you the maximum acceleration is w^2*theta, where w is the first natural frequency of the system, w=1/L*sqrt(C*G/mu/Ip) from Blevins, table 8-19
C=pi*R^4/2
Ip=polar area moment of inertia in torsion
mu=mass density of shaft material
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
RE: Hydraulic Motor Angular acceleration limitation
RE: Hydraulic Motor Angular acceleration limitation
Greg: motor MOI would low compared to the shaft I believe (and I did give the star for the second post)
Desert fox: how did you get a 2 x star when I didn't give them to you?
Ed: I don't believe hydraulic restraints will work in this as the problem is mechanical caused downstream of the oily bit
Cheers Ian
RE: Hydraulic Motor Angular acceleration limitation
A hydraulic motor will act as a brake if the flow and pressure out of the motor are limited. I have seen motor shafts broken by limiting flow out with over running loads.
If you would like to bet the flow limitation won’t slow the motor down contact me through www.danzcoinc.com
RE: Hydraulic Motor Angular acceleration limitation
ud^2f/dt^2=GIpd^2f/dx^2
where:
u=moment of inertia per unit length of shaft
GIp=torsonal stiffness of shaft
This is the wave equation (I use "d" here as a partial derivitive)
with boundaries:
GIpdf/dx(0,x)=initial torsional condition in shaft
df/dt(0,x)=angular velocity of shaft at start
df/dx(t,L)=0 (stress at unconstrained end of shaft is zero
At motor end I would use
Jd^2f/dt^2=-udf/dx at (o,t)
The solution is probably in the form of the sum of
e^-kt(Asinkx+Bcoskx) for discrete values of k that satisfy the boundaries.
In the end you are looking for GIpdf/dx at x=0 which is the torque on the motor mass.
RE: Hydraulic Motor Angular acceleration limitation
The form of the solution is approximately
(Asin(k1t)+Bcos(k1t))*(Csin(kx)+Dcos(kx))
RE: Hydraulic Motor Angular acceleration limitation
I can only think of two reasons for the angular acceleration limit. The first is torque related. The second is to prevent a vacuum in the inlet due to flow restrictions, which would cause havoc with the slippers. An overrunning check valve would cover both of these in your application.
A mechanical solution would be an overrunning clutch on the pump output.
ISZ
RE: Hydraulic Motor Angular acceleration limitation
RE: Hydraulic Motor Angular acceleration limitation
I doubt there is anyone there that could help. That hasn't seen this thread. Go ahead. Give it a try.
Greg Locock has the answer. I would work the formula backwards and find the highest natural frequency permissible
sqrt(87,000/(8*PI))=58.8 rad/s or about 9.36 Hz. It doesn't seem likely that a pipe 1000m long could twist 8 turns in about .1 seconds, but I will leave that to the mechanical guys with the numbers to work out. What I do know is that .1 or even 0.05 seconds is an eternity to electronics. One can easily monitor the differential pressure across the motor and look for a sudden drop in differential pressure.
This would be the key for the controller to resist velocity changes by using a position differentiator and a derivative gain.
RE: Hydraulic Motor Angular acceleration limitation
The max acceleration forward would be
ti/Im
I don't think your motor moment of inertia, Im, is small enough to get the 87000 rad/sec^2
If, however, you attempt to restrain the motor with braking, the torque could get exceedingly high as the total system energy will come into play.