Selecting a Motor: Motor Selection Calculation Formulas

The following explains the required formulas for controlling a stepper motor or servo motor based on pulse signal.

Operating Pattern

For stepper motors, the pattern for acceleration/deceleration operation in the figure on the left is commonly used as operating patterns on pulse speed. The pattern for self-start operation (rectangular operation) in the figure on the right can be used when the operating speeds are low and the load inertia is small.

f₁

Starting Pulse Speed [Hz]

f₂

Operation Pulse Speed [Hz]

A

Number of Operating Pulses

t₀

Positioning Time [s]

t₁

Acceleration (Deceleration) Time [s]

Formula for the Number of Operating Pulses A [Pulse]

The number of operating pulses is expressed as the number of pulse signals that add up to the angle that the motor must rotate to get the load from point A to point B.

• *For geared motors, this is the step angle (resolution) of the gearhead output shaft

Formula for Operation Pulse Speed f₂ [Hz]

The operation pulse speed can be obtained from the number of operating pulses, the positioning time, and the acceleration (deceleration) time.

① For Acceleration/Deceleration Operation

While the length of the acceleration (deceleration) time is an important point, this is not easy to decide as it depends on the acceleration torque and acceleration/deceleration rate.
Initially, as a reference, calculate the acceleration (deceleration) time at roughly 25 % of the positioning time. (The calculation must be adjusted before the final decision can be made.)

② For Self-Start Operation (Rectangular operation)

Formula for Acceleration/Deceleration Rate T_R [ms/kHz]

The acceleration/deceleration rate indicates the degree of acceleration of pulse speed and is calculated using the formula shown below.

• Calculate the pulse speed using full step conversion.
• For this formula, the unit for speed is [kHz] and the unit for time is [ms].

Conversion Formula for Converting Operation Pulse Speed f₂ [Hz] to Operating Speed N_M [r/min]

Calculation of Load Torque

Refer to this formula.

Formula for Acceleration Torque T_a [N·m]

If the motor speed is varied, the acceleration torque or deceleration torque must always be set.
The basic formula is the same for all motors. However, use the formulas below when calculating the acceleration torque for stepper motors on the basis of pulse speed.

[Common Basic Formula for All Motors]

\(\begin{align} T_a= \frac{\left((J_0 + J_1) \cdot i^2 + J_L\right)}{9.55} \cdot \frac{N_M}{t_1} \end{align}\quad\quad\)

J₀

Rotor Inertia [kg·m²]

J₁

Electromagnetic Brake Inertia [kg·m²]

J_L

Total Load Inertia [kg·m²]

N_M

Operating Speed [r/min]

t₁

Acceleration (Deceleration) Time [s]

i

Gear Ratio

[When Calculating the Acceleration Torque for Stepper Motors on the Basis of Pulse Speed]

① For Acceleration/Deceleration Operation

② For Self-Start Operation (Rectangular Operation)

• *For geared motors, this is the step angle (resolution) of the gearhead output shaft

Formula for Required Torque T_M [N·m]

The required torque is calculated by multiplying the sum of load torque and acceleration torque by the safety factor.

Formula for Effective Load Torque T_rms [N·m]

Calculate the effective load torque when selecting the servo motors and BX Series brushless motors.
When the required torque for the motor varies over time, determine if the motor can be used by calculating the effective load torque.
The effective load torque becomes particularly important for operating patterns such as fast-cycle operations where acceleration/deceleration is frequent.