How to design a linear machine

In this blog I will take a look at the design of linear machines, where advanced material models are being used in order to investigate the effects of hysteresis on the machine characteristic.

Linear machines are electrical motors or generators which transform mechanical energy into electrical energy and vice versa, through the use of linear motion.

An electromagnetic field produced by coils or permanent magnets on a stator interacts with a fields on a moving part, sometimes called a plunger. By switching the phase currents on and off, the plunger advances along the field lines.

Actuators are devices similar to linear machines, used primary in applications where accurate positioning is required. Actuators can be hydraulic, pneumatic or mechanical, as well as electrical. The electrical actuator has the advantage of being more efficient, environmentally clean and precise, compared to the other types.
With the advent of more electrical transportation systems, especially in aeronautics where weight is a significant constraint, more and more electrical actuators are being developed with an aim of improved efficiency and reliability.

A significant number of applications require linear motion to be produced, either in order to provide traction or accurate positioning. The range of movements vary significantly, from the nano-scale in the semiconductor industry to meters in the case of industrial applications, all while maintaining very small resolutions.
Recovering energy from linear motion is also becoming more and more interesting, with the advent of green energy generation, like tidal wave generators.

Some of these applications use a standard, rotating electrical motor and a mechanism for converting between circular and linear motion, like screw, rack and pinion, chain / belt drive, etc.

This is not an efficient method for transferring the power, since mechanical losses will add up and reduce the efficiency of the system.

Linear machines and actuators are much more adequate for this type of application, providing accuracy, efficiency and reliability. The efficiency and performance of linear machines and actuators needs to be considered from the design stage. Advanced modelling techniques are required in order to accurately simulate these devices.

Electromagnetic effects need to be considered together with mechanical, thermal and circuit coupling. Material behaviours, like saturation, demagnetization and hysteresis can also be significant contributors to the performance of the device. The optimization process of the linear device needs to be able to include all of these considerations and be solved in a reasonable amount of time.

Opera can use rigid body dynamics equations to calculate movement at every timestep using the user defined mass, applied force, friction and speed varying force, or viscosity. Linear motion can be applied along any of the 3 axes and can also be applied to all 3 axes at the same time. Both linear and rotational motion can be defined in a model, and eddy currents produced by both types of movement can be simulated.

We will now look at an example of a cylindrical actuator and the effects that including advanced material models can make on the accuracy of the results obtained.

As well as modelling non-linear magnetic effects using an anhysteretic magnetic curve, Opera also provides solver technology that allows the simulation of non-linear effects using a full hysteresis loop of the materials.

The performance and characteristic of the device will depend in this case on previous history of the magnetic circuit. The inclusion of the full hysteresis curve allows computation of hysteresis losses and latching forces which would be non-existent in the simulations using anhysteretic material models. The method used in the Opera solvers is a trajectory-based algorithm and it was developed by Peter Kirby et al in 2009. It only requires data for the major loop in quadrants 1 through 3, much less than other hysteresis models. The solver calculates the energy lost due to hysteresis, adding up the losses generated over a number of cycles: