Ž . Sensors and Actuators 81 2000 297–300 www.elsevier.nlrlocatersna Magnetic field analysis of a resolver with a skewed and eccentric rotor K. Masaki a , K. Kitazawa a , H. Mimura a , M. Nirei b , K. Tsuchimichi c , H. Wakiwaka c, ) , H. Yamada c a Tamagawa Seiki, 1879 Oyasumi, Iida 395-8515, Japan b Nagano National College of Technology, 716 Tokuma, Nagano 381-8550, Japan c Shinshu UniÕersity, 500 Wakasato, Nagano 380-8553, Japan Abstract Factory automation applications such as machine tools, etc., with high precision motion control require a feedback sensor with low speed-ripple for precise velocity control. The resolver is one of feedback sensors widely used in automation applications. Distorted signal-output related to speed fluctuations of the resolver result from permeance ripples, etc., produced by eccentricity of the rotor and stator slots in which coils are installed, and of the rotor itself. Although the permeance method has been used to analyze and determine the optimal magnetic design of a resolver, it remains an imperfect solution. This paper proposes a new magnetic field analysis method which offers the means to produce better analysis. The most significant feature of our method is that the skewed resolver rotor is divided into segments and the induced voltages of each segments are calculated and combined. Therefore, the analysis of the skew affect and the Ž . eccentricity of the rotor becomes possible by using the 2-D FEM two-dimensional finite element method with magnetic vector potential. The analyzed results of the spectrum in the induced dual phase voltage waveforms indicate the possibilities of close agreement with the measured values. These results confirm the validity of this method. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Resolver; Skewed rotor; Eccentricity; 2-D FEM; Revolution angle; Spatial spectrum 1. Introduction A resolver is a sensor similar to a rotary transformer, which converts a revolution angle into an electric signal, and has been known for some time. The resolver is widely used in diverse environments as a result of its robust structure and wide range of operation temperature and is particularly favored as the sensor for robot servo control because of its reliability. These circumstances are demand- ing the most appropriate designing method of resolvers due to the need for precise velocity control. The principal causes of resolver errors are magnetic designs, coil instal- lations, and spatial harmonics in the output voltage as a result of manufacturing errors in these parts. Although the use of an analysis method for permeance harmonics based on slot combinations and winding methods which reduce specific harmonics has been proposed in the past, the ) Corresponding author. Tel.: q 81-26-226-4101 ext. 2501; Fax: q 81- 26-223-7754; E-mail: wakiwak@gipwc.shinshu-u.ac.jp application of such a method has been difficult to imple- wx ment in practice 1 . We have shown how the short-circuit winding of a resolver reduces the angular error due to the wx rotor eccentricity 2 . This paper describes a magnetic field analysis method to determine an optimal magnetic design Ž which eliminates harmonics, using 2-D FEM two-dimen- . wx Ž. sional finite element method in the following way 3 : 1 Ž. use the 2-D FEM method including skew effects; 2 determine the magnetic flux distribution of the analysis Ž. model including eccentricity; and 3 determine the limits of analysis accuracy from the difference between the mea- sured data and the calculated data. 2. Fundamental principals and structure of the resolver Ž. Fig. 1 a shows the structure of a brushless resolver. Ž. Fig. 1 b shows the schematic diagram of the resolver windings. The dual-phase windings effectively 908 apart are spaced at the stator side which is opposed to the exciting winding inside the rotor. Assuming that the input voltage e s i 0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. Ž . PII: S0924-4247 99 00179-X