Estimating Power Supply Required For The Flywheel Motor

Selecting a motor with the right amount of torque to spin up your flywheel to the desired speed is a good first step. However, you still need to figure out how much power (voltage and current values) you will need to get up to the desired operating speed.  There are several factors to consider in such a situation. The motor's speed/torque characteristics and its nominal values of voltage and speed play an important role in all this. Note that we are assuming it is a DC motor that we are using. The required voltage can be estimated as follows:

M_L = Operating Torque [mN-m]
N_L = Operating Speed [rpm]
V₀ = Nominal Voltage of the Motor Selected [V]
N₀ = No Load Speed of Motor @ Nominal Voltage [rpm]
Dn/DM = Speed/torque gradient of the Motor [rpm/mN-m]
V_L = Operating Voltage [V]


V_L = (V₀/N₀)*(N_L + (DN/DM)*M_L) [V]

For instance: For the example flywheel we used in sizing the motor,

M_L = 2400 mN-m
N_L = 16000 rpm

Suppose a motor we are considering has the following additional characteristics

V₀ = 24 V
N₀ = 8000 rpm
Dn/DM = 8.69 rpm/mN-m

Then we can calculate

V_L = 110.6 V

You will need to make sure that your motor is designed to accept this much voltage. If not, you will likely damage it and/or injuring yourself if you feed excessive voltage into it.

If you are going to be using a brushed DC motor along with a controller, it is highly likely it will use PWM technique to do so. In such a case, you will need a somewhat modified formula . Additionally, we also need the following extra data

P_C = Pulse Width Modulation Cycle [in %]
V_D = Max Voltage Drop Across Controller

V_L = (V₀/N₀)*(N_L + (DN/DM)*M_L/P_C) + V_D [V]

So if I had a controller with say an 85% PWM cycle and a 3 V voltage drop across the controller,

V_L = 124.6 V

You will need to make sure that your controller is designed to accept this much voltage. If not, you will likely damage it if you feed this voltage into it.

This calculated voltage and the nominal value of current of a given motor together will better guide your motor search/selection.

[Important: The calculations are meant for approximate 'ball parking' of the required power supply only. If you want the exact values, you will need to consult your motor's manufacturer's specs or technical support. Please also note that the actual numerical values used here are for illustration purposes only and do not represent the prototype.]