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| Home> Dynamic braking> Calculating resistor sizes |
How do you calculate the stopping energy put into a DBR?
Stop energy (Remember friction, drag, etc all work in your favour)
Remember first of all to convert everything into the right units: metres, kilograms, seconds and (for rotational energy) radians.
Kinetic energy = m v2/2
e.g. man on bike (60kg man, 20kg bike, 15mph or 7m/s)
= 80 x 7 x 7 / 2
≈ 2000J
≈ 2kJ
Rotating energy = J.ω2/2
eg flywheel 600mm diameter x 300mm thick at 1500rpm
(J is the moment of inertia of the flywheel)
= (m.r2 /2) x ω2/2
= (ρπr2d x r2/2) x ω2/2
= (8000 x π x 0.34 x 0.3/2) x (2π x 1500/60)2/2
≈ 375,000J
≈ 375k
Potential energy = m.g.h
e.g. crane with a 10ton container lowered 20m on to a ship
= 10,000 x 10 x 20
= 1,000,000J
= 2MJ
How do you calculate the size of a DBR?
To specify the resistor we need to know three things: the energy per stop, the duty cycle and the ohmic value. The first two are usually combined into one variable, the power of the resistor.
Power
In an ideal world you calculate the mechanical energy involved in each stop, using one or more of the above formulae. This will be the sum of the kinetic, rotational and potential energies, less any friction losses if these are significant, less the electrical losses in the motor/inverter system.
Unfortunately the real world is different and it is much more likely that you will have little or no hard information about the application. As resistor manufacturers we like this – for safety you will probably order a bigger DBR than you really need – but you still need to make a decision. Our suggestion is as follows: if you know what the drive is being used for and can guess at the run-up time, then:
stop energy = start energy (approximately)
= start time x power during starting
= start time x max. power/2
= start time x drive power/2
Knowing the stop energy and the duty cycle you can calculate the average power into the resistor and for most duty cycles this will be the right power to specify.
When the stop time is short in relation to the total duty cycle we may also need to consider the thermal capacity of the resistor, to ensure that it does not overheat during a single stop. This is tabulated graphically below, showing the short-term power ratings for different sizes of our resistor range.
Ohms
The ohmic value sets the rate at which we put the energy into the resistor – the braking power. The lower the ohmic value, the higher the power.
The minimum ohms are set by the drive manufacturer, and will produce braking power at the peak rating of the drive (or its braking module).
Ohms = (DC bus volts)2/(Peak power)
Higher ohmic values can be used; they will reduce the braking power proportionally, and hence increase the stop times for any given load.
Specialist advice: Just call us on 0116 273 3633, or contact one of our distributors
Downloads: DBR installation instructions • ES series Data Sheet • HP Data Sheet
Cressall Resistors Ltd, Evington Valley Road, Leicester, LE5 5LZ U.K. Tel: (+44) (0)116 273 3633