Designing with Linear Motor

June 1, 2001
Working around linear motor shortcomings is the safest and most effective way to tap into their advantages

Industrial linear motors offer design engineers the possibility of constructing machines in new ways. Fast, simple, and flexible, linear motors are easy to install and in many cases come with integrated sensors and bearings. Successful applications, however, require precise drive planning and a design that’s appropriate for linear motors.

Advantages of linear motors

From a technical point of view, an industrial linear motor is nothing more than a traditional servo motor that produces a linear movement instead of a rotational one. Accordingly, all parameters of this movement can be controlled right down to position if the proper feedback signals are available.

With the help of modern servo amplifiers, linear motors can trace out nearly any motion profile (position, speed, acceleration) by simply expressing it in software. In contrast, traditional linear actuators such as pneumatic cylinders can perform but one type of move over which they offer little control.

Linear motors are not only more programmable than traditional actuators, they also have the dynamics to deliver a wider range of responses. In addition, they eliminate the need for many components (end sensors, dampers, tubing) and their slim cylindrical shape, consisting of two mechanical parts, is very accommodating.

Physical limits

Linear motors also have weaknesses. The greatest disadvantage undoubtedly lies in their limited power and force densities. As with every electromagnetic drive, this limit is determined by magnetic saturation effects and the ohmic resistance in the electrical wiring (copper or aluminum).

Similarly, a linear motor with a particular volume can never produce the same force as a pneumatic or hydraulic cylinder of the same size. This comparison is not quite fair, however, as both the pneumatic and the hydraulic solutions require either an additional external compressed air source or oil preparation. Linear motors, on the other hand, represent an entirely electric solution.

Compared to rotating electrical motors, the power density of linear motors is basically the same. For many applications with rotary drives, however, step-down gears are often used. Speed is sacrificed for increased torque or higher force by using an additional spindle or belt. A high force can be produced, yet the dynamics are lost and all the additional disadvantages of mechanical conversion gears must be accepted.

Drive design for linear motors

The Achilles tendon of linear motors is that only a limited amount of force is available, which makes drive design extremely important. Today, modern design programs help with all necessary calculations, so that anyone can design a linear motor system.

Mechatronic design method

The suggested mechatronic construction method is not — on completion of the mechanical design — to simply select any old motor from any old catalog that is able to move the mechanics. It should not happen that the construction must be subsequently strengthened just because a more powerful (and heavier) motor had to be chosen. On the contrary, basic drive technology considerations must be part of the design process and should always aim to reduce the direct as well as indirect costs of the drive system.

Importance of mass in motion

The in-motion mass (gripper and working load) has, via the formula F = ma, a direct influence on the required driving force. A reduction of the mass in motion not only reduces the required driving power but, in general, also leads to simpler guiding systems and constructions. While the working load is dictated by either the process or the job at hand, most of the room to maneuver can be found in the areas of design and choice of materials for tool carriers, grippers, or other equipment in motion. Specific densities of several materials will need to be considered: steel — 7.9kg/dm3; aluminum — 2.7 kg/dm3; and Delrin/POM — 1.4 kg/dm3.

In most cases, one of the aims of using linear motors is to produce fast movement. Because of the higher acceleration needed, mass has a larger “weighting” — as a result of the formula F = ma — than in more slowly running applications, such as in older machines. The reduction of in-motion mass is therefore very important.

It is not only a question of minimizing motor force and size, but also that the force F produced by the linear motor must be taken up by the motor’s mounting, which can mean that complex mounting systems must be designed. If the importance of the sequence of events is realized — heavy gripper, high drive force necessary, powerful and heavy motor, heavy motor mounting — it is then easy to understand why fighting for every gram of in-motion mass is part of clever drive design.

For vertical applications, direct-acting drives like linear motors are not retained by friction. In such cases, this otherwise advantageous property means that a stationary linear motor must permanently produce a retention force corresponding to Fh = mx9.8 m/sec2. Consequently, a reduction of in-motion mass is even of great importance for slowly running vertical applications.

Movement times

When figuring cycle time, the starting point is once again F = ma. The force required depends on the acceleration needed, which depends to a large extent on the movement’s time restrictions.

During the acceleration itself, the relationships s(t) = 1/2at2 or a = 2s/t2 are applicable. Due to the quadratic relationship between required acceleration and given time, it is worth fighting for every millisecond, in particular for short-stroke movements. Linear motor properties important during the optimization process include exact synchronization, fitting motion profiles, and the possibility of any asymmetric movement.

Any asymmetric movement possible

For linear motors, there is no particular reason to carry out movement symmetrically. For example, for a linear displacement from A to B, the forward movement without load can be allocated a different amount of time than the return movement with a load connected. In figure 1, such a movement is computed for the symmetrical (each direction of the motion taking 100 msec) and the asymmetrical case.

In the asymmetric case, movement with load mass was assigned 116 msec and that without load mass just 84 msec. The result is an approximately 26% lower peak force and a 15% lower average force (RMS force) for the same process cycle-time.

Exact synchronization

Linear motors are controlled in closed loop mode. This means that from the first to last repetition the movements are independent of temperature, age, and environmental factors and are always identical.

Consequently, intermeshing movements can be carried out without large safety margins. Follow-up movement can already be started while the first movement is still being carried out. As a result, either more time is available for the actual movement, or the process cycletime can be reduced (see figure 2).

Fitting motion profiles

Modern linear motor systems offer a choice of various optimized motion profiles. Depending on the particular application or movement, optimization with regard to freedom of shock, acceleration behavior, and speed is possible and thus various load conditions can be taken into account.

Why use a design program

If the relationships may be simply explained by the formula F = ma, why use a design program for linear servo motors? For exact drive design, certain additional limiting conditions must be considered during calculation:

• The maximum feeding force produced by a linear motor is speeddependent and is influenced by the servo amplifier’s properties. As in the case of rotational servomotors, where maximum torque is reduced with increasing rotation, linear motors suffer a reduction in maximum force with increasing speed due to the countervoltage. (Figure 1 shows how the design program computes this force limit depending on current speed in the force/time relationship and shows it as a border line in the diagram.)
• Long-stroke movements usually result in the drives running into a force limit during the acceleration and braking phases, where otherwise the limiting factor is maximum speed.
• For estimating whether or not a motor will overheat under given conditions, the continuous force required (RMS force) must be calculated.
• The choice of a suitable motor is an iterative process, as the mass of the part of the motor in motion is included in the total mass in motion.

From an academic point of view, it can be very interesting to consider these factors in drive design. For most users, however, it is more sensible to invest time in design considerations and leave mathematical calculations to a program.

Design program basics

Using a design program (figure 3) is divided into four steps:

• Segmentation and definition of movement
• Input of global and segment-specific data
• Choice of the linear motor on the basis of computed force
• Testing of static and dynamic relationships (limits)

During the segmentation of movement, the complete motion is subdivided into individual integral movement sections, such as fast run-in, slow lowering, fast lifting, etc. Next, global data like mass of the gripper or the configuration (vertical, horizontal) are entered and then enhanced, as required, with local data such as load masses or counter-forces during individual movement segments.

Starting with this information, the program computes the required drive data, and the first drive may be freely chosen. The ratings, peak force, and RMS force computed are then used to select a suitable motor on the basis of the motor characteristics available. A subsequent look at the dynamic limits helps determine the correct servo controller. Depending on the application, this process must be run iteratively until the best solution is found.

A design program should not only be used to select a drive, but also to promote an integral way of looking at things: What happens if the load mass can be reduced by 10%? What effect does a reduction or increase of the movement times of individual segments have? Which movement profile is optimal for this application? These questions may be computed for different solution variants and displayed graphically by the design program in a few minutes.

Dr. Ronald Rohner is an engineering manager at NTI Ltd./LinMot, Rogers, Minn. and Zurich, Switzerland.

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