Discussion
The fundamental purpose of the vast majority of the world's electric motors is to electromagnetically induce relative movement in an air gap between a stator and rotor to produce useful torque or linear force.
According Lorentz force law the force of a winding conductor can be given simply by:
\mathbf{F} = I \boldsymbol{\ell} \times \mathbf{B} \,\!
or more generally, to handle conductors with any geometry:
\mathbf{F} = \mathbf{J} \times \mathbf{B}
The most general approaches to calculating the forces in motors use tensors.[81]
Power
Where rpm is shaft speed and T is torque, a motor's mechanical power output Pem is given by,[82]
in British units with T expressed in foot-pounds,
P_{em} = \frac {rpm \times T}{5252} (horsepower), and,
in SI units with shaft speed expressed in radians per second, and T expressed in newton-meters,
P_{em} = {speed \times T} (watts).
For a linear motor, with force F and velocity v expressed in newtons and meters per second,
P_{em} = F\times{v} (watts).
In an asynchronous or induction motor, the relationship between motor speed and air gap power is, neglecting skin effect, given by the following:
P_{airgap}=\frac{R_r}{s} * I_r^{2}, where
Rr - rotor resistance
Ir2 - square of current induced in the rotor
s - motor slip; ie, difference between synchronous speed and slip speed, which provides the relative movement needed for current induction in the rotor.
According Lorentz force law the force of a winding conductor can be given simply by:
\mathbf{F} = I \boldsymbol{\ell} \times \mathbf{B} \,\!
or more generally, to handle conductors with any geometry:
\mathbf{F} = \mathbf{J} \times \mathbf{B}
The most general approaches to calculating the forces in motors use tensors.[81]
Power
Where rpm is shaft speed and T is torque, a motor's mechanical power output Pem is given by,[82]
in British units with T expressed in foot-pounds,
P_{em} = \frac {rpm \times T}{5252} (horsepower), and,
in SI units with shaft speed expressed in radians per second, and T expressed in newton-meters,
P_{em} = {speed \times T} (watts).
For a linear motor, with force F and velocity v expressed in newtons and meters per second,
P_{em} = F\times{v} (watts).
In an asynchronous or induction motor, the relationship between motor speed and air gap power is, neglecting skin effect, given by the following:
P_{airgap}=\frac{R_r}{s} * I_r^{2}, where
Rr - rotor resistance
Ir2 - square of current induced in the rotor
s - motor slip; ie, difference between synchronous speed and slip speed, which provides the relative movement needed for current induction in the rotor.
Gassing Station | EV and Alternative Fuels | Top of Page | What's New | My Stuff