The linear stepper motor analysis often uses the field-circuit method. It can combine the accuracy of the field calculation with the simplicity of the calculation of the road to ensure that the calculation has a certain degree of accuracy and is more convenient to use. In the field-circuit integration method, the calculation of the tooth-to-layer permeability is mainly based on the assumption that the magnetic densities outside the tooth layer are evenly distributed, and the tooth layer area is divided separately to solve the local field.
In the calculation of the stepping motor, the traditional air gap model is based on the assumption that the magnetic densities in the various parts of the core are uniformly distributed: the stator and the moving core are equal magnetic planes, respectively. Actual stepper motor cores have teeth on the surface, and the teeth are often saturated. Therefore, the air gap ratio is inconsistent with the actual situation and the calculation error is large. In the 1980s, domestic scholars proposed that the tooth layer method can more accurately reflect the magnetic field distribution within the motor than the magnetic permeability method.
In the tooth-to-layer permeability comparison model, a tooth pitch unit is defined within a tooth pitch range, and a parallel line is formed at a position one-times after the tooth roots of the stator and the mover, and it is considered to be an equipotential line. Different degrees of saturation of different stator and rotor teeth are used to solve the local field, and the specific permeability of the tooth layer is calculated.
The concept of the tooth layer is similar to the concept of magnetic permeability and air gap ratio permeance, but there are qualitative differences between the two: First, the air gap is only a function of position compared with the magnetic permeability, and the tooth layer is also related to the magnetic pressure drop of the tooth layer than the magnetic permeability. Secondly, the air gap ratio magnetic flux is calculated on the assumption that the surface of the iron core of the stator and the mover is equal to the magnetic plane. This assumption corresponds to an infinite magnetic permeability of the iron core and a large error when the iron core is saturated. The tooth layer method takes into account the non-uniformity of the magnetic field distribution in the stator and the mover teeth and the nonlinearity of the magnetization curve, and can accurately reflect the complex magnetic field distribution in the tooth layer of the stepper motor.
When calculating the magnetic field of a linear stepper motor, the boundary conditions of the teeth at the two ends of each pole are different from those at the middle of the pole, and there is an edge effect. When the number of teeth per pole is large, the edge effect can be ignored.
However, the prototype calculated by this paper only has 3 teeth per pole, and the number of teeth is very small. We must consider the edge effect and use a sub-polar tooth layer as the research object to solve it. In order to compare these two conditions, the calculations are performed here. Figure 1 shows the calculation model of the magnetic field of the tooth layer.
1. 1 Computational Model Considering a Pitch A linear stepper motor considers a tooth pitch model as shown in Fig. 1a, where x is the staggered distance between the centerline of the stator tooth and the centerline of the mover tooth. The solution area is ABCDA. When vector-bit analysis is used, the motor boundary value problem can be expressed as: (5) The tooth flux in the unit core when adding a pitch range is calculated. v—permeability L reciprocal.
1. 2 Considering a pole-computing model Linear stepper motor Considering a calculation method for a lower pole tooth When the problem of the boundary value of a motor tooth layer can be expressed as: J——The average value of the current density along the z direction in the coil - The vector magnetic bit value (a constant) at the boundary.
1a model of a pitch 1b of a model of a pole 2 of a model of the tooth than the calculation of the permeability of the ANSYS calculation of the tooth layer than the permeability using the large finite element software developed by the American company ANSYS 5. 01 [7], calculated in vector The magnetic position is an unknown function, and a free mesh subdivision unit is used to calculate the tooth layer specific permeability at different relative positions of the stator and rotor teeth and at different saturation levels. Figures 2a, 2b are calculated field maps of Model 2 at several different locations (enlargement of the imaginary box A′′ portion in Figure 1b), and Figures 2c, 2d are the calculated field maps of Model 1.
3 Computed values ​​for the permeance of the per-orthodontic layer calculated for the two models. It can be seen from Figure 3 that the tooth layer is the largest at the magnetic permeability and the smallest at x = S/2. As the saturation degree increases, the change of the tooth layer relative to the magnetic permeability is less and less obvious.
3a Model 1 Computed tooth layer permeability 3b Model 2 Computed tooth layer permeability analysis For each tooth layer specific permeability, the tooth specific magnetic flux per tooth pitch is multiplied by the number of teeth per pole [ 8], Figure 3 is the result of a pitch-to-pitch tooth ratio multiplied by 3.
Harmonic analysis of the results of the two model calculations shows that when the number of teeth in the motor is small, the effect of the edge end tooth (model 2) is calculated and compared with the permeance and the one-tooth model (model 1). : When the motor is not saturated, the higher harmonics can be neglected, and the constant flux and the fundamental wave permeability change little, so the conventional method can still be used to calculate the saturation of the tooth layer when compared with the magnetic conductive machine. Although the constant flux does not change much, However, the proportion of the second harmonic wave increases, and the fundamental wave changes greatly. At this time, the calculation of the tooth layer ratio magnetic flux must be calculated with the whole pole.
In summary, the more saturated the motor is, the more severe the edge effect is. The error of the calculation of the tooth layer ratio of the different models is greater, and the harmonic variation of different times is also different. In general, since the hybrid linear stepper motor operates in a relatively saturated condition, in the case of the tooth layer ratio magnetic permeability solution, when the number of teeth per pole is small, the edge effect should be considered in order to obtain an accurate solution.
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