Fig. 1. 3D surface mesh of a claw-pole machine.

Electro-mechanical devices populate the average home, from the hair dryer blower, to the washing machine, to the cordless drill. However, electro-mechanical devices are not limited to power generation or power conversion. Sensors, such as speed sensors, proximity detectors, and magnetic couplers are used to detect motion or position information. All of these devices use primarily a combination of electromagnetic fields and some kind of motion.

Electro-mechanical devices have been around for many years, but the way they are designed has changed dramatically over the last 15 years. With the introduction of high level design and analysis computer programs, guesswork has been all but eliminated. From the “back-of-the-envelope” initial design concept to the released product, each idea can be virtually prototyped on the computer, leading to more efficient, more reliable, high performance devices.

Design programs based on scientifically developed empirical formulae are perhaps the most widely used tools to size electro-mechanical devices. With these tools, designs are easy to set up, simulations are computed quickly, and solutions have a reasonable accuracy. Design has indeed come a long way, but in an era when all the qualities of the materials must be used effectively to operate highly saturated magnetic circuits, more sophisticated analysis is necessary. For example, the nonlinear behavior of the steels used in a device, and the induced effects due to motion or varying fields can dominate the behavior of devices, so much more rigorous evaluations are required now.

Fig. 2a. Line plot of the cogging torque vs. magnet shape.

Finite element computational tools have become the cornerstone of design because these tools address the full manifestation of device behavior. Additionally, interface technology makes it increasingly easier to parameterize the shape of each component or to create basic objects and then combine them into different device models. The meshing of the problem domain, which used to induce nightmares for the best design engineer, is now a breeze. Fig. 1 shows a 3D mesh for a claw pole structure. Some tools offer 2D translating or rotating motion, but the more advanced tools feature rotating, translating and pivoting motion, all in a 3D environment—complex but absolutely necessary to study linear machines and actuators.

Fig. 2b. 3D surface plot of the cogging torque vs. magnet shape.

In a first phase of the design, once the initial sizing is done, the Finite Element Method (FEM) computation focuses on optimizing the lamination and characterizing the device. For permanent magnet machines, the cogging, torque (in rotating motion machines) or the force (in translating motion devices) is often a key element of the design. The sensitivity of the device’s response to any geometric feature can be readily computed.

Fig. 3. Line plot of the flux linkage in a switched-reluctance machine.

Fig. 2 shows the variation of the cogging torque of a brushless machine when the shape of the magnet is modified. It is easy to review the results and select the configuration that minimizes the cogging torque.

Fig. 4. Line plot of the induced voltage (back-EMF) in a 3-phase spindle motor.

Flux linkages used by design tools are obtained through parameter sweeps of the input current and the position. In this case, information is given to the program to solve for a range of currents and a range of positions. The output is the curve of flux linkage versus currents for the different positions. These curves contain all the nonlinear characteristics of the static problem; they can be considered multi-static images of the device. These types of curves are also used to devise control schemes. The curves can be imported into system simulation tools for the design of the power supply and the drive. For a switched-reluctance machine, Fig. 3 shows the curve of flux linkage in one coil versus the current for positions of the rotor versus the stator ranging from unaligned to aligned.

There are several elegant ways to include solid-body motion in an electromagnetic FEM tool, but for the pairing of solid-body motion with external circuit connections, the number of available packages is dramatically reduced. The preferred way is to use a moving frame scheme in which the rotor is physically moving versus the stator. This technique seems to be fairly universal, with very few computational and technical limitations.

Fig. 5. Surface plot of the flux-density distribution for a speed sensor.

With motion, the computation is then performed in a transient mode, according to a time sampling. Any result at the current time sample is dependent upon the results from the previous time sample. Such a computation is widely available for 2D geometries with rotating motion. The number of modeling tools featuring this type of computation for 3D geometries is much smaller. Translating and pivoting motions for 3D geometries are reserved to a few select tools. Fig. 4 shows the 3D computation of the back EMF in a three-phase spindle motor.

The most robust computation can be performed by considering the mechanical equation of the solid body motion, as well. An inertia or a mass can be assigned to the moving parts. Friction can also be included. Advanced packages let the user link an external mechanical set, such as a spring or any variable external load, inertia or friction. Any change in these quantities changes the load case being solved.

These tools can also be used to characterize a speed sensor, for instance. The motion is applied to the inducing part of the sensor, most likely a toothed wheel. The result is an induced voltage on the sensor coil that is representative of the character of the motion. For a change in the material characteristics, the effect of the resistivity and the permeability of the material of the inducing part of the sensor is seen in the output of the voltage. Besides optimizing and characterizing the sensor, the designer can study misalignment, tolerances and their effect on the performance of the device. Fig. 5 shows the flux density distribution for one position of the sensor wheel.

In addition to the optimization of the shape and the performances of the machine, the design engineer today must evaluate the effects of failures. A combination of mechanical input, physical properties, geometric parameters and external circuit connections allows the user to describe any possible feature, from short circuit to misalignment, from internal fault to external fault.

In a few advanced FEM packages, a link between the package and Matlab/Simulink opens a whole new world of possibilities for full system analysis. Today, with the use of Flux and its connection to Matlab/Simulink, the electro-mechanical part of the computation is embedded inside the Matlab/Simulink tool to provide a transient co-simulation. This provides the capability to test advanced controls of the full system, drive and device, including all of the nonlinear behaviors of the system that could be induced by eddy current and motion induced effects.

The question that begs answering is how fast can all this be accomplished. Given the speed of CPUs found in common computers today, as well as the improvements in the formulations, computations that required weeks of CPU time a few years ago now require only a few hours. The simulation of the response of a brushless machine takes an average of one hour for a 2D geometry, 4 hours for a 3D geometry. Of course, the computation time is dependent on the complexity of the problem, but these computations can now be automated and controlled by optimization tools: the user defines the initial design and a set of critical target functions, and then lets the software compute. An optimized structure is produced without any further user intervention. The designer is free to think of the next generation of design.