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Plotter Router Fresadora CNC

 Technical Datasheets

5. TORQUE CHARACTERISTICS AND PULSE INTERVALS

5.1. Dynamic equations and acceleration

5.1.1. Dynamic equations

When a stepper motor is synchronized with the control pulse train, the torque produced by the motor is equivalent to the load torque that opposes the motion. This is the amount of torque needed to accelerate the rotor / load inertia and friction torque. The expression that defines it is determined by the fundamental dynamic equations:

T_M\ =\ J*\frac{\partial \omega }{\partial t}+D*\omega +T_f (5.1)

where

T M = torque produced by motor
J = inertia of the rotor and load combination
Ω = angular velocity of rotor
D = viscous friction constant
T f = friction load torque independent of speed

The motor torque T M is a function of speed, magnetomotive forces, the torque angle and other parameters related to static torque machine discussed in section 3.2.

If you use the equation 5.1 has to assume: (1) not used mechanical compensating inertia, (2) the engine torque does not have the oscillating components, and only considers the speed range. The first term on the left is the torque needed to accelerate the inertia of the rotor and load combination. When the rotor torque load is transmitted through gears or pulleys, the inertia J is the inertia of the load by itself, but the amount is reflected as a function of the diameter ratio.

Figure 5.1. Friction and viscous load torque depending on speed

When considering the terms of control, is convenient to express the dynamic equation based on the relationship of steps f (Hz Steps * s -1) and the equation for this case is expressed as:

T_M\ =\ \theta _s*J*\frac{\partial f }{\partial t}+\theta _s*D*f +T_f (5.2)

where

Θ s = pitch angle (radians)
f = frequency step (steps s -1)

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