Choosing A Motor Part 2

In the last edition we discussed torque, speed, area of activity, steepness, and load cases as considerations in choosing a motor. In the second part of the extract we will continue with the motional profiles and the transmission ratio.

The Motional Profiles:

A profile is generated by the digital control system of a machine. The abundance of tasks within the control systems leads to a preference for the simplest profiles. The simplest consists of three combinations of a point in time and the acceleration that must apply from this point in time. In the table below the speed and the position have been added for information. In order that the distance S is covered within the time Ts the following must apply:

This profile is called the triangular profile. Use is also made of the trapezoidal profile and the third order profile; they are all shown below:

For the trapezoidal profile we have a time division of 1/3 acceleration, 1/3 constant speed and 1/3 deceleration. The background to this breakdown of time is the minimisation of the dissipation in the motor; the proof comes from the following.

Imagine that the time interval within which there is acceleration or deceleration is equal to T1. Since the distance S

must be covered within the time Ts, the acceleration that applies for this is

For the dissipation in the motor we have is Ws:

By differentiating to T1 it follows from the above formula that minimum dissipation occurs at T1 = Ts / 3

For the third order profile the same time division applies as for the trapezoidal profile, but the acceleration and deceleration are built up and cut down in 1/9 part of Ts.

The condition that the distance S must be covered in the time Ts leads to a lot of calculations for the third order profile that can be reduced by making use of the formulas shown below.

If we now insert:

a_max as the maximum acceleration, Tc as the time within which the acceleration is equal to a_max or - a_max T1 as the time within which the acceleration rises, then the maximum speed vmax occurring is:

The connection between a_max, S, T1, Cand Ts is:

The consequences of changes in T1, Tc and amax can be identified with this quadratic formula. If the time profile is fixed, this holds likewise for the force required (or the torque required) as a function of the time if the properties of the mechanics are fixed. Appendix 4 shows how the amplifier specification then comes about.

These time profiles can be compared relatively with one another, using the starting point that the distance S has to be covered within the time Ts, and that friction and damping are absent. This gives us the following table, in which it is assumed that there is a transmission between the linearly moving load and the motor, which converts a rotation into a linear movement.

Compared with the triangular profile the trapezoidal profile has the advantage of a lower dissipation. But the peak current ((:) with the acceleration ) that the amplifier has to deliver is 13% higher.

The third order profile has the characteristic that the acceleration is built up gradually, as a result of which resonance in the drive circuit is excited to less of a degree. This is an advantage if the load has to follow the motional profile offered as closely as possible. A drawback of the third order profile is the greater current. Compared with the triangular profile this can lead to an amplifier that must be capable of delivering more than twice the power of a second order profile.

The aforementioned interval of time of the third order profile can of course be changed to produce a better adjustment to the amplifier properties. Another argument may be the suppression of an oscillation that has developed by way of the acceleration. The oscillation can be struck ¨dead¨ by the right choice of the point in time of the start of the deceleration.

In summary, we can say that the nature of the motional profile has an impact on the load of both the motor and the amplifier.

The Transmission

As previously mentioned, the choice of transmission ratio is a means by which, with a given load and motional profile, the motor load can be optimised. In this section we shall be taking a brief look at the most common transmissions.

What you want from the transmission will depend on your point of view. For control engineering purposes the preference is for a transmission with no friction and no play. The attainable bandwidth of the control depends on the lowest (mechanical) natural frequency in the drive circuit. This value is connected with the stiffness of the transmission, which should therefore preferably be as great as possible and preferable independent of the position of the load.

Examples of natural frequency are frame and torsional resonances. Which is why the performance of calculations on mechanical dynamic behavior of the system is one of the first activities to be carried out. As far as the motor is concerned, we shall have to look at the natural frequencies of:

--The rotor (hollow rotor motors!) --The motor suspension --The coupling between the tacho and the motor --The couplings and transmissions to the load.

The presence of self-braking capability in the transmission can be desirable for safety reasons or the presence of external forces, such as the force of gravity. Maintenance must of course be minimal and increasingly the evaluation criteria include noise emissions.

Divergences in the wish list can lead to the preference for a drive in which the load and the motor are connected directly to one another. What we have then is a direct drive. But if we do opt for a transmission, then the most common are:

1) the screwed spindle and (circulating ball) nut.

This form of transmission can be found in both many processing machines and CD players and is used to effect the conversion from a rotation to a translation. If a high mechanical natural frequency of the mechanical system is desirable, a large diameter screwed spindle, whose torsional stiffness level is high, must be chosen. Here torsional stiffness means the ratio between the torque on the spindle and the angular displacement between the motor and the point of application of the load; with the screwed spindle this depends on the load position. With a high stiffness level we have to accept a large moment of inertia. If we go for a play-free version, then allowance must be made for increased friction.

2) geared-belt transmission

Both the rotation-rotation conversion and the rotation-translation conversion can be made with greared-belt transmission. An additional positive property of the geared belt/gear wheel contact is that the play that exists is passed through under friction. This reduces the potential for difficulties with the stability of the control. It is likewise true of the transmission that with a high mechanical natural frequency we have to accept a large moment of inertia of the gear wheels and the belt. Additionally, the value of the natural frequency depends on the load position in the case of a rotation - translation conversion.

3) gear transmission

Rotation-rotation conversions and rotation-translation conversions can be effected via gear whells, or via the combination of gear wheel/gear wheel and gear wheel/gear rack. The high load-bearing capacity of metal gear wheels allows a small construction- volume. A weakness is the play between the gear wheels, which comes to the fore if the torque reverses direction. Pretensioned gear wheels can eliminate the play, but this concept is not widely available.

Each transmission has a moment of inertia, its own friction and a certain stiffness. The consequence is that these properties must be taken into account when optimising the transmission ratio!