COMPUTER AIDED DESIGN OF SWITCHED RELUCTANCE MOTORS FOR USE IN ROBOTIC ACTUATORS

Transcription

1 COMPUTER AIDED DESIGN OF SWITCHED RELUCTANCE MOTORS FOR USE IN ROBOTIC ACTUATORS PRADEEPKUMAR ASHOK, Research Associate; PROF. DELBERT TESAR, Director; ROBOTICS RESEARCH GROUP THE UNIVERSITY OF TEXAS AT AUSTIN, AUSTIN, TEXAS, U.S.A. ABSTRACT The Switched Reluctance Motor (SRM) is emerging as a strong contender to the permanent magnet synchronous motor as a prime mover of choice in robotic actuators. This paper describes a design synthesis tool for switched reluctance motors. First, a review of the currently existing design tools is presented. The paper then details a parametric design synthesis procedure that requires the formulation of analytical relationships that involve SRM performance and design parameters. The analytical relationships (rules of thumb for design) thus developed can be used along with parametric reduction techniques to work towards an optimal design. KEYWORDS: Switched Reluctance Motor, Computer Aided Design, Synthesis, Robot, Actuator. 1. INTRODUCTION A new SRM design synthesis tool was needed to facilitate the development of Standard Actuator Building Blocks (SABB) [1] as the driver of open architecture machines assembled on demand. The SABB is a new concept that is not seen in present-day robotics where most mechanical systems are designed as one-off systems. Non-standardization means that robot structures--design, manufacture, maintenance and repair--are expensive and time consuming. On the other hand, the SABB calls for a standardized open architecture in the design, manufacture and operation of these complex structures. Tesar proposes ten basic classes of actuators that meet most actuator application requirements. The ten classes are shown in Fig 1. When scaled, these actuators meet requirements varying from those appropriate for microsurgery to the high powered/high torque applications that are needed in airplanes, ships, and submarines. A set of about 300 standardized actuators would enable the designer to configure on demand any type of active mechanical system. If these 300 or so actuators could be mass manufactured, this would result in modular low cost automation. However, before they can be manufactured, the actuators need to be designed. Designing a single actuator presently requires excess personnel resources and time, primarily due to the fact that no single commercial entity can master Figure 1. Actuator design tool components. and commercialize the design and production of all of the individual components that go into an actuator (Fig. 1 also shows the ten basic internal components for the SABB). This, therefore, gives rise to the need for a comprehensive design tool. The tool has to be able to do both design synthesis and analysis. The science base needed for the creation of such a

2 design tool is large, complex and constantly being expanded and refined. We start this process by creating a design synthesis tool for an emerging prime mover, namely the SRM. Various tools have been built to aid in the design of the SRM. Krishnan [2] describes one such tool that consists of two modules; the design module and the analysis module. The design module is very basic and helps in initial sizing based on the power equation. About the same time, Miller and his colleagues at the University of Glasgow prepared commercial SRM analysis software called PC- SRD TM. PC-SRD TM has been in the market for more than a decade now and is a specialized calculating tool that assists the design engineer with initial sizing and preliminary design of the SR motor. A SRM analysis tool with piece-by-piece break up of the various computational modules was also presented by Tang [3]. Tang integrated geometric modeling, FEA, simulation, and control into the package. The same FEA core is used for magnetic, mechanical, and thermal calculations. Where time is critical, he has substituted analytical or empirical solutions as alternatives to the FEA methodology. Another tool that deserves mention is SRDAS TM. This tool is primarily an analysis software developed by Rasmussen [4] to test control strategies. The internal structure of this software resembles that of PC-SRD TM. This software has a couple of additional computational modules that help analyze vibration and sound. All of the above tools are primarily for design analysis and simulation. Given a set of design parameters, they can be used to calculate the desired performance characteristics. (This process, however, is the reverse of design synthesis, where the user inputs performance specifications and gets machine parameters as output from the design procedure). These tools can be used effectively only by people familiar with switched reluctance motors, their design parameters and control techniques. Note that even though some of the above tools take performance specifications as inputs they do not use all of them during initial sizing. The initial sizing is always done using the power output relation. The rest of the parameters are extracted from these initial parameters and the actual optimization is done by the user, judiciously adjusting the design parameters. This may not be the best approach to take when designing actuators. These tools also do not cover the wide spectrum of geometric options available.. 2. OBJECTIVE The desired features in an SRM design synthesis tool are as follows: completely modular architecture; this is to ensure that certain computational and operation modules of the system can later be reused for the design of other components (for example components like gear trains, brakes, clutches, etc., that go into the design of a modular actuator) interactive, frequently providing the user with valid and pertinent information. The tool should help the user better describe his requirements and constraints. The tool should in effect be a study/design tool. use analytical descriptions of user requirements in terms of the design parameters to algebraically eliminate some parameters from the core design process. This synthesis approach greatly reduces the scale of the design process [5], [6]. 3. PROPOSED APPROACH The proposed design synthesis module is a two-layered structure (Fig 2). An inner layer built on rules, data, and strategies supports the top layer consisting of the User Input Check, Search, Extrapolate and Generate modules. 3.1 User Inputs A design process always starts with the user specifying his requirements. The requirements can be broadly classified into performance specifications and design constraints.

3 3.1.1 Performance Specifications The characteristics that are most often used to describe the performance of an SR motor are: Torque speed profile, Torque/Speed/Thermal Performance User Input Trade - Off limits, Power density, Torque density, Rules Acceleration characteristics, Step size, Torque per ampere, Stiffness, Efficiency, User Input Torque ripple, Rotary inertia, Acoustic Check emission, Electromagnetic emission, Database Database Reliability and Manufacturing cost. For each of the above performance specifications, the Search Design user sometimes provides actual numerical Inference Synthesis Inference Engine Output values that he desires and at other times just Engine simply wants some parameter optimized Extrapolate without any constraint on what the value of Design Design that parameter is. For example, the user could Rules Rules be specific enough to say give me torque Generate ripple <.001Nm, or be vague and just say minimize torque ripple. Figure 2. The design synthesis module Design Constraints In addition to the above performance specifications the user may have additional inputs that constrain the solution space. These can be broadly classified as: 1) Power supply constraints: this could be in the form of supply voltage available, amperage limitations, number of phases or supply frequency. 2) Type of motor: cylindrical field, axial field, multi-tooth are some of the choices 3) Geometric characteristics: these kinds of inputs could be length/diameter ratio, length, diameter, volume, air gap thickness, or even the lamination template. 4) Material characteristics: the inputs could be with regards to the kind of material to use for the core, shaft, permanent magnet, wiring, insulation, etc. 5) Controller characteristics: voltage control, current control, average voltage control, and three level control are some of the probable input choices. 3.2 User Input Check The user does not necessarily have to specify all performance specifications. The more specifications and constraints the user is able to specify, the less time it takes for the design module to converge on a design. However unless the user is familiar with the science behind the working of a SRM, he will not be in a position to supply the design tool with all the required information. This is the impetus for the User Input Check module. This module checks the information supplied by the user for both sufficiency and consistency. To ensure sufficiency of user inputs, the module depends on previously developed performance trade-off rules. These rules are shown to the user as trade-off plots among performance parameters to better enable the user to define their requirements. For example, let us say the user wants 98% efficiency for his design, but does not specify the base speed of the motor, he is shown a trade-off plot similar to the one shown in Fig. 3 and asked to suggest a value for speed. The tool thus prompts the user to come up with an informed decision and this accelerates the design process by reducing the number of free (unspecified) variables.

4 The user, of course, has the option of not suggesting a value, in which case the design synthesis proceeds to create all the designs possible. A closely associated problem is the selection of the motor geometry. This is one of the user inputs that falls into the design constraints category. The different geometric configurations for a SRM are the standard SRM, inside/out SRM, multi-tooth SRM, inside/out multi-tooth SRM, drag Cup SRM, inside/out drag cup SRM, single field axial SRM, dual field axial Mechanical loss (O) / Electrical Loss ( ) Speed Figure 3. Example of a performance trade-off design rule. As an example, the generalized torque equation is given by SRM, radial and axial field SRM and hypocycloidal SRM. There has not been a great deal of work in the literature comparing the performances characteristics of this range of SRMs based on these different configurations. Hatcher and Tesar [7] compare 5 different SRM geometries. This tool uses independent generalized performance relations to compare geometries. T V S 1 = K A A D 2 g V G m (1) where K is the configuration coefficient, g is the airgap, A V is the volumetric electric loading, A G is the airgap area, and D m is the torque moment arm. These relations form good rules of thumb that could be presented to the user during the initial stages of the design so that he can make a better decision as to what geometry is most appropriate for his application. These rules are termed configuration selection design rules. In addition to checking for sufficiency, this module also does a check for consistency. An example situation occurs when the user mistakenly inputs a continuous torque requirement value that is higher than the peak torque he wants. However, not all inconsistencies may be identifiable at this stage. Some of them may be evident only when the generate module fails to produce a solution. In such cases, the generate module will prompt the user to selectively free one of the parameters that is causing conflict. After the user input is checked, the tool queries the user as to the approach he would like to take to arrive at the design. He is allowed to go through the entire sequence, which is Search Extrapolate Generate or jump straight on to Generate. The user might choose the second option if he desires a new concept and does not want the tool to be biased by past designs. The next three sections will detail the three modules Search, Extrapolate and Generate. 3.3 Search This module primarily accepts inputs after they have been checked for consistency and then queries the database trying to find a match between the user specifications and past designs. The database typically consists of motors previously designed and optimized by the tool and commercially available motor design whose performance characteristics are proven and available. If a match is found, then the design and the performance characteristics are immediately made available to the user. The success of this module depends on the way data is stored and searched. The database will have to be flexible and store data in various forms. An object oriented data handling structure for a similar system is described by Gerbaud, et al [8]. 3.4 Extrapolate Realistically, the odds of finding a perfect match are slim. The next logical step is to extrapolate from a current design. This requires a design rule database that relates the performance characteristics of the SRM to the important design parameters that governs them.

5 These design rules are called performance parameter design rules (Fig. 4). One of the rules we will use is For a given level of output power, the volume of a SR motor is inversely proportional to the rotor speed. Or in other words For a given power output, the torque is Volume proportional to the volume. Now assume that the user wants a design for a 40 Nm motor with a particular power output. Also assume that we have a motor in the design database that has the same power output but is only rated for a continuous torque of 20 Nm. Now using the design rule stated before, one can immediately converge to a design that is double the volume of the previous motor. This saves considerable amount of time. The coarse design thus identified will of course have to be transferred to a design analysis module to confirm that it meets all performance specifications which will, then, result in a refined set of design parameters. 3.5 Generate Now assuming that a design could not be generated using either the Search or the Extrapolate methodology, the Generate module is used (Fig. 5). The first step is identification of the parameters involved. The minimum set of parameters that describe the system is generated. The nonlinear relationships between the performance parameters and the design parameters are identified. This is followed by a systematic procedure of eliminating redundant parameters [5]. This requires that design rules be established among the design parameters. These design rules are called design parameter design rules. Once the reduced set of relationships is obtained, an optimization procedure is used to arrive at the values of the design parameters. Note here that the more parameters we are able to eliminate, the easier it becomes to find an optimal solution (by orders of magnitude). Table 1. lists some of design rules documented by the authors [9]. Torque and Current Torque and Speed Torque and Length /Diameter Torque and Air Gap Speed and Length/Diameter Speed and Length/Diameter Speed and Length/Diameter Speed and Voltage Speed Figure 4. Example of a performance parameter design rule. Torque varies as the square of the current until saturation, after which the increase is linear. Torque is initially constant until we reach base speed. After that the torque speed curve exhibits constant power characteristics. After this portion, the curve follows the relation Tω 2 = constant. Torque and diameter follow a quadratic relation, while torque only increases linearly with increase in length. (Standard SRM) Torque is quadratically inversely proportional to the air gap. Hoop stress is proportional to the square of the diameter and directly proportional to the length. Critical Speed is proportional to the square of the diameter and inversely proportional to L ( 3/2). Inertia varies as the fourth power of the diameter and linearly with regards to the length. For a higher base speed, opt for a higher supply voltage. Design Parameter Design Rules Identification of Parameters Reduction of Parameters Solution / Optimization Figure 5. Processes inside the "Generate" module. Speed and Volume For the same power output, volume of motor is quadratically inversely proportional to speed. Voltage and Current For more torque increase the current, and for a higher base speed opt for higher voltage. Power loss and Current The electrical power loss increases as the square of the current. Power loss and Speed 2.76 The mechanical loss follows the relation : PTm ω = Pbe + Pw K5ω + K6ω 2 and the electrical loss follows the relation : PTe ω = Pe + Ph K3ω+ K4ω Table 1. Design rules for SRM.

6 3.6 Design Analysis The output from the design synthesis module is generally a completely defined SR motor. This is then fed to an analysis module which uses FEA and simulation tools, to check the performance output against the initial performance requirements. The difference in the two will be used to fine-tune the design synthesis tool. 3.7 Design Example The design procedure outlined in this paper was used to design a motor for an actuator for an advanced weapons elevator [10] on an aircraft carrier. The performance requirement was to produce a continuous torque of 36ft-lb at a base speed of 3600 rpm. It was also required that the motor be rugged and easy to maintain and torque dense. No other requirements were specified. The constraints were that it had to operate on the ship s 440 volt supply and be accommodated in a volume that measured 11 inches in diameter and 4.5 inches in axial length. There was no similar design in the database. So, the search and extrapolate methodology could not be used. Therefore it was decided to generate a new design. In order to arrive at a first set of motor parameters, design rules were used. These design rules were generated from the SRM design literature. Table 2. highlights some of the many considerations. Configuration selection design rules Performance trade-off design rule Performance parameter design rule Design parameter design rules Axial Field SRM Versus Radial Field SRM Ruggedness Versus Torque Density Torque versus Air gap Stator and rotor pole angles Table 2. Design rule table. Once the design rules were in place, the empirical relation formulated by Radun [11] was used to arrive at a first set of design parameters. where I T = nser 0.9 N p Bsat lstk STF Rg I 2 I sat g B = µ N o sat p sat (2) (3) Here nser refers to the number of pole windings in series, N p refers to the number of turns per pole, lstk refers to the stack length, STF is the stacking factor, R g is the radius of the air gap, I is the current and I sat is the current at which saturation starts. In the second equation, g refers to the airgap, B sat refers to the saturation flux density of the material and µ refers to the permeability of air. A FEA o analysis was done on the design thus generated to arrive at the final values. The motor designed was a 3 phase 6/4 SRM with a stator pole angle of 30 degrees and a rotor pole angle of 32 degrees. It was designed to operate at 440 volts at a base current of 58 amps. The lamination material was Permendur. The nominal torque output was 36ft-lb and the peak 57 ft-lb. (Fig. 6). It weighed 70 lbs and had an efficiency of 90.94%. Figure 6. Torque vs. Rotor position for various current levels (max. 79A)

7 4. CONCLUSIONS The aim of this paper is to lay the foundation for the development of a design synthesis procedure for SRMs. The science base needed for the methodology was identified as sets of design rules, the rules [9] being: Performance trade-off design rules, Performance parameter design rules, Design parameter design rules, and Configuration selection design rules. The design rules help design synthesis by reducing the number of the free design parameters needed to arrive at a design. The methodology was used to generate a motor design for an elevator actuator which was later refined and optimized using FEA analysis. This methodology can also be used for designing other components within the actuator like gears, bearings etc. 5. ACKNOWLEDGEMENTS This work was supported by U.S Department of Defense grant #N REFERENCES [1] D. Tesar, Electro-Mechanical Actuator Architecture, Report, Robotics Research Group, The University of Texas at Austin, June [2] R. Krishnan, A.S. Bharadwaj and P.N Materu, Computer-Aided Design of Electrical Machines for Variable Speed Applications, IEEE Transactions on Industrial Electronics, Vol. 35, No. 4, November [3] Y. Tang, Characterization, Numerical Analysis and Design of Switched Reluctance Motors, IEEE Transactions on Industry Applications, Vol. 33, No. 6, November/December [4] P.O. Rasmussen, Design and Advanced Control of Switched Reluctance Motors, Dissertation, Aalborg University, Denmark, Jan [5] T.R. Waskow, D. Tesar, Algebraic Elimination Techniques for Design in Mechanical Systems, University of Texas at Austin Report to the DOE, August [6] B. Donoso, D, Tesar, Parametric Modeling and Design of Robot Transmissions using a New Binary Matrix Solution Methodology, University of Texas at Austin Report to the DOE, May [7] E.L Hatcher, D. Tesar, Conceptual Redesign of an Advance Prime Mover for Direct Drive Robotics and Automation Applications, University of Texas at Austin Report to the DOE, May [8] L. Gerbaud, J. Bigeon, G. Champenois, Expert System Bases to Automate Selection of Drive, Proceedings of the International Conference on Industrial Electronics, Control and Instrumentation, Pages(s): , Vol.1, [9] P. Ashok, D. Tesar, Design Synthesis Framework for Switched Reluctance Motors, University of Texas Report to the U.S. Department of Energy and U.S. Navy, August [10] D. Tesar, M. Pryor, J. Banks, J. Janardhan, P. Ashok, S. Park, S. Shin, S. Kang, G. Krishnamoorthy, S. Vaculik, J. Yoo, P. Hvaas, S. Woei, Design of a ¼ Scale Actuator for an Advanced Weapons Elevator, University of Texas at Austin Report to the DOE, Grant #N , April, [11] V. Radun, Design Considerations for the Switched Reluctance Motor, IEEE Transactions on Industry Applications, Vol. 31, No. 5, September / October 1995.