Formulas Index:

Synchronous Speed: Frequency: Number of Poles: Horsepower: Motor Slip: Calculating Motor Speed, RPM:
=V-(Tt/Kt+I0)/Ke×Rt ಏ 1000

Where: V= supply voltage, V; Tl = load torque, oz-in.; Kt = motor torque constant, oz-in./A; I0 = motor no-load current, A; Rt = motor terminal resistance, Ohms; Ke = motor voltage constant, V/1,000 rpm. It is possible to solve for an unknown quantity (voltage or current) when speed is known.

Determining Speed and Current Flow:

W = (VS – I x Rmt) / KE and I = TL / KT + INL

Where: W = Speed, VS = Supply Voltage, Rmt = Motor Terminal Resistance, I = Current, T = Load Torque, KE = Back – EMF Constant

Output Power = Torque*(No load speed)/1351.2
Rated Current = Torque/Torque Constant
Back EMF = V/KRPM
Efficiency: Motor Efficiency = Pout/Pin, Pout = (Vin - Iin * Rm) * (Iin - Io)
V = Voltage
Pout = Output power
Pin = Input power

Torque is generated by force acting on a rotating body; it is the product of an acting force and the effective length of its lever arm.
The formula is:
T = F*r
T Torque [Nm]
F Force [N]
r Lever arm [m]

The above equation describes the relation between the force and the length of the lever arm. With Motor Couplings, a certain torque can either be achieved with a large outer diameter of the Motor Couplings and a low acting force, or with a small outer diameter and a high acting force. But in practice this relationship will be a proportional increase.

The relationship between the encoder CPR frequency and the speed of the motor (RPM) is given by the following equation:

f = (cycles/rev)*(rev/sec)/1000 = kHz

RPM = Revolution per Minute
CPR = Cycles per Revolution

Distance Conversion:
(PPR) / (2*pi*radius of shaft) = pulses per inch
(Pulses per inch)^-1 = inch per pulse

Motor Torque x Gear Ratio = Torque at the Wheel

Input Shaft Speed (RPM) / Gear Ratio = Output Shaft Speed

Gear Ratio = Teeth on one gear : Teeth on a second gear

Example: If one gear has 60 teeth and a second gear has 20 teeth the gear ratio would be 3:1

Step angle calculation:

φ=( (N_s-N_r)/(N_s*N_r ))*360°
φ = Step Angle
Ns = Number of teeth on stator
Nr = Number of teeth on rotor

Steps per second = rpm * steps per revolution
60