A Pragmatic Approach for Comparative Analysis of Linear and Rotary Generators
This paper identifies the need for consolidating analysis techniques for the purpose of designing linear electrical generation systems. Additionally, it identifies a need for concise system development tools that help designers make practical comparisons between linear
and rotary machines.
The basic principles for converting mechanical energy to electrical energy have been known for over a century. It would seem that after this much time, advancements in electrical generation should have reached their limits; however, up to the late 1980’s and early 90’s the use of linear generators for the generation of electricity has not been seriously considered  .
Linear generators and motors are classified as linear motion electromagnetic systems (LMESs) . LMESs that are used as electric generators function by directly utilizing the translational (back and forth or up and down) thrust from mechanical systems to generate electricity as opposed to the more conventional generation approach
of rotational mechanical energy conversion.
For an engineer to determine the feasibility of using a linear electric generator in a system’s design many comparisons between rotary and linear machines must be made. Several points to consider when making this comparison include: practicality of using linear power generation for that particular system, cost to build and design, total system efficiency, role of modern day power electronics, type of driving force (linear or rotational) applied to the generator system, system power factor, force density and force ripple on the drive components, cost to maintain, and the system’s reliability. The relative weights of these considerations will vary from one system to the next. The motivation behind this question was the decision on whether to use a linear or rotary generator on a buoy driven, ocean wave electrical generator project . During this decision process, many opinions and assumptions between these competing systems were made, but finding hard data that compared the two methods was not readily available. Taking the time to thoroughly evaluate the electrical and mechanical technical aspects of this choice (rotary vs. linear) conflicted with the tight scheduling requirements of the project. This situation forced the team to make a best approximation based on limited experience instead of a deliberate and thoroughly evaluated approach.
WHY LINEAR GENERATORS ARE USED
Electrical energy generation is being expanded by creative innovation, and linear generators are a large part of this trend. In Livermore, California at Sandia National Laboratories, an innovative and practical use for linear generators is being developed. The system being studied is an internal combustion engine with a single free piston inside of a double-ended two-stroke cylinder. The free piston is embedded with permanent magnets and the outside of the aluminum cylinder has armature coils wrapped around it. As each cylinder alternates firing, the piston is driven back and forth causing the permanent magnet’s field to cross the alternator coils and generate electricity. In this application the generator’s electric demand is controlled by electronics in order to develop controlled loading to the piston and controlled back-pressure to the cylinder. This refined combustion process results in compression ratios of about 30:1 and thermal efficiencies as high as 56%, depending on the type of fuel used. In this study eight different fuels were tested with very low emissions (NOx emissions <10ppm). The application of this device is to eliminate drive train losses and reduce emissions in vehicles by efficiently generating electrical energy directly from the piston’s motion. This electricity is then stored and used to drive electric motors at the vehicle’s wheels. An important consideration when evaluating linear systems is the translational speed of the driving force, in this case the driven piston speed was approximately 1.1 meters per second. 
Furthermore, research to find the best generator design for low speed and high thrust applications is occurring. One noteworthy study “Linear Generators for direct-drive wave energy conversion” is intended to select the best type of generator to be used in the Archimedes Wave Swing (AWS) ocean energy pilot plant . The AWS is a very large underwater power plant; it has a 9m diameter upper floater that is driven by the varying wave mass above it. This research compared five different types of linear electric generators. Each generator was specified to operate under the AWS’s driving thrust of 1MN (That’s 10^6 N!) at translational speeds of approximately 2.2m/sec. These numbers suggest a peak mechanical driving power of 2.2MW to the AWS’s electric generator . Predicted material costs for these generators ranged from 138,000 to 287,000 Euros ($167,000 to $342,000 US) and output efficiency loss predictions that ranged from 260 kW to 672kW . In conclusion, the study recommended that a three-phase transverse flux permanent magnet generator (TFPM) should be used. It was also recommended that due to a low power factor of 0.3, the generator must be overrated by a factor of three or be used with more expensive and complex power converter electronics .
LINEAR vs. ROTARY
In systems that have lower translational speeds such as ocean wave driven electric generators, it is necessary to somehow couple the low speed and high thrust of the wave into useable electric power. The induced voltage in a generator, according to Faraday’s Law, is E= N dФ/dt (where E = induced voltage in the generator windings, N = number of turns in the coil, and dФ/dt = the time rate of change of magnetic flux in the magnetic circuit) . As seen by Faraday’s Law, to increase the induced voltage in a generator, it is necessary to either increase the relative speed of the magnetic field or increase the amount of magnetic flux. Rotary machines use a high speed of rotation, large rotor diameter or high flux to achieve a high dФ/dt. When slow linear motion is used in a rotary machine, a gearbox that converts the slow translational force into high-speed torque is required. Linear generators can use complex linear gear drives or stronger magnetic flux to achieve a high dФ/dt. Increasing the flux of any electric machine has practical limits due to the magnetic saturation of materials, maximum limits on magnetic sources, mechanical clearance requirements that increase the air gap (reducing the magnetic flux), and high costs associated with creating higher fluxes. 
When considering rotary generators for electrical power generation in linear motion applications, the gearbox consequences must be considered. LMES sources identify the comparative advantages of linear machines over rotary machines by identifying efficiency losses, low reliability, and more frequent maintenance requirements with a gearbox driven machine . In some system designs these consequences may carry significant weight, while in other applications they will not.
The AWS and the free piston generator are fine examples showing that practical applications exist for linear generators. Due to their limited use to date, linear electric generators are more expensive than rotary generators. Furthermore, given the other variables discussed, it is a difficult process for a system designer to know when to use linear and when to use rotary. Adding to the complexity of this decision is the fact that no practical source for an off the shelf linear generator is available. Even if a linear generator appears to be preferred in a specific application, it must be designed, simulated, built and tested. Because of the unknown quantities that exist in linear generator applications an investment in this technology exposes a company or investor to financial risk.
Linear electric power generation has obvious advantages in specific applications. These advantages may be out weighed by their high cost. In order for this technology to take hold, it is imperative that a quantitative and accurate means of evaluating these systems be developed. Such a study should consolidate measurements, expectations, and predictions of: efficiency, cost to build, reliability, power factor, power electronics, cost to operate, cost to maintain, and reliability. Additionally, due to the effect of system size on both cost and efficiency, these considerations should be evaluated over a complete range of system output power and mechanical driving speeds.
One approach for this very ambitious goal is to design, evaluate and predict the performance of many system designs using the previously mentioned considerations. Each system can be tested and evaluated on the same platform under various real world conditions. A good starting point for this approach would be the further development of the air gap wound permanent magnet generator being developed for an ocean wave, buoy driven energy conversion project .
By making a study with this extent of information available in one single reference “Comparative Analysis
of Linear and Rotary Generators”; time to evaluate and judge the merits of linear electrical generation systems can be reduced. A resource created by this type of research can provide a baseline for sound engineering decisions, and linear electric generation can find its niche in electrical power generation.
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