Velocity profile equations, Plotter Router Fresadora CNC, alciro

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1. MOTOR STEP BY STEP (STEP MOTOR)

1.1. Permanent magnet motors
1.2. Stepper motors, variable reluctance

1.3. Hybrid Stepper Motors

1.3.1. Hybrids of two and four phases
1.3.2. Hybrids of three and five stages

1.4. Comparison of different types of stepper motors

2. CHARACTERISTICS OF STEPPER MOTORS

2.1. Static characteristics

2.1.1. Holding torque (Holding torque)
2.1.2. Static position error

2.1.3. Excitation sequences

2.1.3.1. Variable reluctance motors
2.1.3.2. Hybrid engines
2.1.3.3. Microstep sequence

2.2. Dynamic Characteristics

2.2.1. Curves / torque / frequency
2.2.2. Relationship between the dynamic torque and static torque
2.2.3. Mechanical Resonance
2.2.4. Compensating mechanical inertia (dampers)

2.2.5. High speed operation

2.2.5.1. Model of a hybrid stepper motor
2.2.5.2. Calculation of dynamic torque (pull out)

4. ENGINE POWER STEP BY STEP

4.1. Excitation sequences

4.1.1. Sequence of two active phases (full step)
4.1.2. Sequence of an active phase (wave-wave excitation)
4.1.3. Half-step sequence (half step)
4.1.4. Excitation sequence for a variable reluctance motor
4.1.5. Excitation sequence in microstep stepper motors

4.2. Stepper motor bipolar and unipolar

4.2.1. Relationship between torque and bipolar and unipolar excitation
4.2.2. Stepper Motors 8-wire

4.3. Power amplifiers (Drivers)

4.3.1. Problems with Drivers

4.3.1.1. Suppression circuits

4.3.2. Constant voltage feeding

4.3.2.1. Improvement additional resistance voltage feeding

4.3.3. Stepper motor control for power

4.3.4. Bipolar chopper control in H-bridge

4.3.4.1. H-bridge for a two-phase motor.
4.3.4.2. Chopper phase and inhibition

4.3.5. Choosing the type of chopper

4.3.5.1. Ripple Current
4.3.5.2. Losses in the motor
4.3.5.3. Dissipation in the bridge
4.3.5.4. Minimum current

4.3.6. Types of current control

4.3.6.1. Pulse width modulation (Pulse Width Modulation)
4.3.6.2. Fixed stop time (Frequency Modulation switching control)

5. TORQUE CHARACTERISTICS AND PULSE INTERVALS

5.1. Dynamic equations and acceleration

5.1.1. Dynamic equations
5.1.2. Friction torque

5.1.3. Acceleration of stepper motors

5.1.3.1. Slowdown in stepper motors
5.1.3.2. Limitations of the analysis of acceleration
5.1.3.3. Need to optimize acceleration

5.1.4. Optimal velocity profile

5.1.4.1. Velocity profile equations
5.1.4.2. Example of calculating the velocity profile
5.1.4.3. Considerations of the velocity profile

5.1.5. Loads connected to the engine through transmission elements

5.1.5.1. Transmitted by belts and gears
5.1.5.2. Lifting
5.1.5.3. Moving objects using tape
5.1.5.4. Linear motion by worm and gear

5.1.6. Performance of a screw
5.1.7. Friction, torque and inertia
5.1.8. Example of calculating the torque in linear system
5.1.9. Example of calculating torque motor pull-in start

5.2. Determination of time and pulse interval

5.2.1. Considerations on the characteristics of pull-in
5.2.2. Theory of linear acceleration pulse intervals

6. STAGE OF POWER AND CONTROL CIRCUIT

6.1. Amplifier

6.1.1. Driver

7. ALGORITHMS AND CONTROL PROGRAM

7.1. Instructions and communication

7.1.1. Control Commands

7.1.1.1. Command parameters control
7.1.1.2. Shares of control commands

Technical Datasheets

5.1.4.1. Velocity profile equations

$T(f)\ =\ T_L(f)+J*\left( \frac{\partial^2 \theta }{\partial t^2} \right)$ (5.15)

For an n-phase motor with the rotor teeth and p the length of steps is 2 * π / n * p, and the ratio of steps is related to the speed of the rotor:

$\frac{\partial \theta }{\partial t}\ =\ \frac{2*\pi *f}{n*p}$ (5.16)

substituting equation 5.15 in the 5.15

$T(f)\ =\ T_L(f)+\left( J*\frac{2*\pi }{n*p}\right)*\frac{\partial f}{\partial t}\\ \frac{\partial f}{\partial t}\ =\ \left[ T(f)-T_L(f) \right]*\frac{n*p}{2*\pi *J}$ (5.17)

This equation can be integrated to find the time t needed to reach the ratio of f steps, when the engine accelerates.

$\frac{n*p}{2*\pi *J}\int_{0}^{t}\partial t\ =\ \frac{n*p*t}{2*\pi *J}\ =\ \int_{0}^{f}\frac{\partial f}{T(f)-TL(f)}$ (5.18)

In general this integral can be implemented graphically, as the functions T (f) and T _L (f) are not analytical functions. Figure 5.7 (b) shows the function 1 / [T (f)-T _L (f)] in the shaded area A _1, corresponding to the integral of this function with respect to the ratio of steps between 0 and f _1. The time t ₁ for the ratio of steps f ₁ can be obtained from equation 5.18:

$t_1\ =\ \frac{2*\pi *J*A_1}{n*p}$ (5.19)

The full velocity profile for acceleration can be obtained by repeating this process for a range of reason given steps to reach the ratio of pull-out f _m. The process can be simplified if T (f) and T _M (f) can be approximated to an analytic function, such as the following example.

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