Parker Hannifin 88-021610-01G - Manual (Page 177)

Parker Hannifin
Appendix B External Power-Dump Resistor Selection 177
Calculating Resistance—Rotary Motors
Because there are different types of motion profiles and application specific
conditions, you may need to modify the results to suit your particular
application. To keep it simple, the formulas assume a trapezoidal move
profile, in which the deceleration event is a single constant deceleration to
zero (0) velocity. For other motion profiles, you can modify the basic
concepts presented below.
Calculating the amount of energy to dissipate requires the motion profile
parameters, and the motor, drive, and load information. While significantly
more information is required, the calculations help tailor the size of power-
dump resistor to your application.
This is a multi-step process:
1. Calculate the motor’s kinetic energy.
2. Calculate the motor’s potential energy—vertical applications only.
3. Calculate the energy that can be absorbed by the drive capacitors
4. Calculate energy dissipated in the motor winding resistance
5. Calculate energy dissipated in load
6. Using the results from the previous four calculations, calculate the
amount of energy to dissipate through an external power-dump resistor.
With that result, you can then calculate the resistor necessary to dissipate
the excess energy.
Total Kinetic Energy
A body in motion produces energy. To stop motion, that energy must be
absorbed or dissipated elsewhere.
That energy can be defined in terms of inertia and velocity.
( )
2
2
1
ω
L M K
J J E
+ =
Where
E
K
= rotational kinetic energy (Joules)
J
M
= rotor inertia in kilogram meter squared (kg ⋅m 2 )
J
L
= load inertia in kilogram meter squared (kg ⋅m 2 )
ω = rotational speed in radians per sec (1 revolution/sec =
2
⋅π⋅radians/sec)
Total Potential Energy
A body at rest stores energy relative to the position of the body. When the
body moves, the potential energy is released and translated into kinetic
energy.
For purely horizontal applications, potential energy is negligible and therefore
not necessary for inclusion in your calculations. However, for vertical
applications, potential energy can greatly affect the selection of power dump
resistor. Regardless whether the incline is gentle or steep, it is important to
calculate the potential energy that must be absorbed or dissipated
elsewhere.