17 Motion
Introduction
This chapter covers the topic of motion control through the PLC to stepper and servo motor devices. It is not exhaustive in the sense that all motion subjects will be discussed but rather that the student will be given experiences with two of the more popular single axis control concepts, stepper and servo control.
Stepper motors are used traditionally for low torque applications with no feedback. The servo on the other hand can handle higher torque applications and requires a feedback device.
Mechanical Conversions and Moving a Device
A review of mechanical devices follows with some basic formulas for conversion of energy into rotating or linear motion, in this case, controlled motion. Both applications in this chapter involve motion projects that are considered controlled motion. The device does not need to coordinate with any other axis but must produce a controlled motion to specification. In general, motors do not provide this level of control. That is, dc motors and ac motors do not provide acceleration and constant speed control at a designated level repetitively. They do not hold a position at zero speed unless there is no torque on the motor shaft.
In general, motors have the following characteristics: For rotating objects:
EQ
For objects in linear motion:
EQ
Objects such as pumps, fans, blowers and conveyors require HP ratings for running based on the physical characteristics of the device. General formulas for torque and the relationship between torque and horse power are given in the following:
Torque Formulas:
Eq. 17.3
Eq. 17.5
Torque also has been defined in vector notation. If a force F is not perpendicular to the rotating arm, the component perpendicular produces torque.
Fig. 17.1
A lever arm rotates with a force F is applied. The torque T = r × F has magnitude T = |r| |F⊥| = |r| |F| sinθ with direction out of the page.
The cross product is an example of the right-hand rule in which the fingers curl in the direction of the force from the lever arm. Then the thumb points in the direction of the torque. This can be expressed in terms of:
T = rFsinθ or T=rF⊥ Eq. 17.6
Torque is also related to angular momentum L via the following equation:
Eq. 17.7
where L is angular momentum and t is time.
Also, for angular ration about a fixed axis:
L = Iω Eq. 17.8
where I is moment of inertia and ω is the angular velocity.
Also derived:
Eq. 17.9
The term α is the angular acceleration of the body with units rad/s2.
These formulas are not inclusive and are not to be committed to memory or used except after checking with a manufacturer to verify the accuracy of the specific formula with their equipment. Formulas developed from these basic formulas exist to size the motor for an application. Torque is especially valuable in sizing the servo or stepper motor applications. While progressing through the following applications, remember that the proper sizing of the motor and motor controller are an integral part of the overall proce