电机翻译

According to their source origins, these flux densities can be divided into B,,, B,,,, Bd4 and BICd. BflPM1 B,(pM) and are obtained in a no-load condition (with PM source only), and BN4 ,,, are obtained in a loaded condition without magnetized PMs, modeling PMs as air. Fig. 2 shows radial
11. ANALYSIS OF TORQUE AND TORQUE RIPPLE!
1-
Mccbvnul mp* Ic 1 dm
Fig.2 Radial flux densities of the motor
TOSCA, a nonlinear FEM solver for magnetic field, was used to calculate the flux density of 4-pole, 6-tooth PM motors in Fig. l. A half model of the motor with quadratic elements (39820 nodes) is sufficient, using periodic geometry and symmetric boundary condition. According to the Maxwell stress method, the torque is T (9)=
Abstmct-For permanent magnet (PMf brushless DC motors, torque ripple, is an important origin of vibration, acoustic noise and speed fluctuation. In this paper, the output torque profiie of a PM motor with one phase energized is decomposed into the commutation torque, the reluctance torque and the armature reaction according to their source origins. It verifies that the output torque profile is qualitatively equivalent to the BEMF profile for low reluctance motors. This paper discusses the effect of magnet pole shaping and magnet arc length on the output torque and torque ripple. A magnet edge shaping is proposed to design a trapezoidal BEMF motor without torque ripple, with minimal sacrifice of the maximum output torque.
h -I Po
r B, * BI&
r
= h C Ansin (ne ‘y.)
*I
+
(1)
where po,T,r,Br,B, and h are the permeability of air, integration contour, radius, radial flux density, tangential flux , density and axial height respectively, and 4, and Y, are the amplitudes of Fourier series coefficients and the corresponding phase shifts. These densities are the nonlinear sum of two magnetic sources, PMs and armature winding or coil, i.e. B,),,, and BflpH+,. Equation (1) can be rewritten as:
unnotched motor
1.5 1 ..
notched motor Fig. 1 4-pole. 6-teeth permanent manet motors.
I. INTRODUCITON
Torque ripple, defined by the difference between the minimum and maximum torque divided by the maximum torque, consists of two components: the electromagnetic torque fluctuation and the reluctance torque. The reluctance torque is extensively discussed by Hwang and Lieu [l], with the sensitivity analysis and design techniques. In this paper, our discussion is focused on the former torque ripple generated by the electromagnetic torque fluctuation originating from the interaction between the PMs and the armature current. Reduction of electromagnetic torque fluctuation has been studied by a number of investigators. For example, Carlson et al. [2] and Ishikawa and Slemon [3] studied the torque ripple caused by electro-motive force, using attenuation method such as stator slot skewing or PM shifting. In PM DC motors, the most popular design type is the trapezoidal back electro-motive force (BEMF) motor, where DC is commutated properly to the flat portion of the trapezoidal BEMF in each phase. Any fluctuation of BEMF during the commutation range will appear as torque ripple, and induce vibration. This torque ripple can be virtually eliminated if the BEMF of the motor is perfectly trapezoidal. Since experimentally measuring the BEMF for different designs is costly and time consuming, modeling of the BEMF in PM motors should be pursued. In this paper, the output torque profile of a PM motor with one phase energized, is calculated using FEM analysis of magnetic field and Maxwell stress method. After decomposing the output torque by its characteristics, it shows that the output torque profde is qualitatively equivalent to the BEMF profile and can be used to design a trapezoidal BEMF motor without torque ripple. Finally, design methods, magnet pole shaping, changing of magnet arc length and magnet edge shaping, are presented to design a trapezoidal BEMF motor, with minimal sacrifice of the maximum output torque.
0 1995 IEEE
0018-9464/95$04.00
3738
motor geometry since both the armature reaction and the output torque are the same function of loading current and magmtic circuit for a given motor. The BEMF torque is about 80% of the magnitude, and also has the same characteristic shape as the output torque, which makes it possible for the output torque profile to be used for designing the BEMF shape. It is also noticed that the sum of three torque components is neady equivalent to the output torque, which implies that the motor is operated below the saturation.