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Design and analysis of the static lateral edge effect of linear motors Zhang Guangyi (four industrial colleges, four 644) to ask questions. The conformal transformation method is applied to study the distribution of the lateral edge of the no-load magnetic field of a linear motor. It is proposed to introduce a third air-gap coefficient in the electromagnetic design of the linear motor, so as to improve the calculation accuracy. The experiment is basically consistent with the calculation, indicating that the analysis is correct.
1 Introduction Linear motors are motors that produce linear motion directly.
It can be seen as an evolution from a rotating electric motor. It is envisaged that the rotary motor is cut radially and the circumference is developed into a straight line, and a flat-plate linear motor with a wide range of applications is obtained, as shown in FIG.
The radial, circumferential and axial directions of the rotating electrical machine correspond to the normal, longitudinal and transverse directions of the linear motor.
Since the core of the linear motor has both longitudinal and lateral ends, a so-called edge effect is produced, which is the main difference between the linear motor and the rotary motor. The vertical and horizontal edge effects are divided into static and dynamic, respectively. The edge effect when only the primary current (no load) is used is called the static edge effect. The effect of the longitudinal and lateral edges on the magnetic field when there is relative motion between the secondary and primary or the current (load) in the secondary is called dynamic edge effect. In this paper, the static lateral edge effect is analyzed, and on this basis, the third air gap coefficient is introduced into the electromagnetic design of the linear motor, which improves the accuracy of electromagnetic calculation.
2 Distribution of no-load air gap magnetic field and introduction of the first and second air gap coefficients The flat-plate linear motor only places the primary on the side of the secondary guide, which is called a single-sided type. If a primary is placed on each side of the secondary guide, it is called a bilateral type. The bilateral type can eliminate the unilateral magnetic pull force (when both the primary and secondary have iron core), and the secondary material utilization rate is also high. Figure 2 shows the distribution of the no-load air gap magnetic field for a bilateral structure and its effects on longitudinal and lateral edge effects. The air gap magnetic field is evenly distributed along the y direction (lateral direction) and is a forward traveling wave along the x direction (longitudinal direction), as shown in Fig. 2a. Like a rotating electric machine, the actual air gap g is replaced by the slotless equivalent air gap g, that is, the discontinuous slot current is regarded as a slice current continuously transmitted to the surface of the core, and the fundamental magnetic potential generated by the two is the same, such as Figure 2b shows. The effect of the notch is equivalent to the first air gap coefficient K.
The static lateral edge effect of a linear motor is calculated according to the theoretical formula of a rotating electric machine (for a semi-closed groove): (for a bilateral type) (for a single-sided type) where t is the pitch of the primary core and b is the width of the notch. The two-dimensional magnetic field of Figure 2b can be progressively reduced to an equivalent dimensional magnetic field. According to the theoretical analysis of the two-dimensional magnetic field: B is the complex amplitude of the x-axis component and the y-axis component of the air gap magnetic density, J is the complex amplitude of the equivalent plate current density, and the amplitude distribution of the α= magnetic field component is shown in Fig. 3. Shown.
In the middle of the air gap, ie z = 0, where: F is the amplitude of the fundamental magnetic potential. Equation (6) shows that there is only a z-axis component in the cross section in the air gap, and its amplitude B is proportional to the magnetic potential. If the order is obtained from equation (6), it can be regarded as a coefficient introduced by considering the uneven distribution of the magnetic field along the z-axis direction, which is called the second air gap coefficient, and g is the equivalent air gap considering the influence. Thus the two-dimensional field of Figure 2b is simplified to the dimensional field of Figure 2. The magnetic field has only the z-axis component, which produces a magnetic field distribution whose current should be a body current density uniformly distributed along the z-axis: the calculation for the unilateral linear motor K is still the same as equation (7).
3 Distribution of static lateral edge effect analysis. Apply the conformal transformation (coordinates are shown in Fig. 5, ξ=y is obtained by equations (12) and (13). Different y values ​​can be used to obtain the distribution of B. The lateral width of the secondary guide is equal to the primary core width. It can be seen that the magnetic flux will decrease in the range of l. If the flux reduction is ΔΥ1, then dy can be obtained by equation (12), where u is the value of u when y =0. The average magnetic density in the range of l is such that the air gap magnetic potential is the equivalent air gap after considering the static lateral edge effect, and K is called the third air gap coefficient.
3.2 The lateral width of the secondary guide is greater than the primary core width. l Set the lateral width of the secondary guide to extend the primary core on each side.
In this case, the magnetic flux will be reduced in the range of l, and the effective magnetic flux entering the secondary guide will increase in the lateral direction to the both ends y = 0 to the range, and the effective thrust will be generated, especially when /g and g When it is larger, the increase in magnetic flux is more significant. Therefore, the two effects of the lateral edges should be considered together.
1 , the value can be obtained by the formula (12). A simplified calculation of the amount of flux increase (both sides) entering the secondary guide from 0 to the range is approximated, and the equation is a comparison of K (the g can be seen to be very close when calculated).
Theoretical calculation value and approximate calculation value comparison theoretical calculation K Approximate calculation K The coefficient K g3 introduced by considering the influence of the static lateral edge magnetic field of the linear motor, the value of which can be greater than 1, or equal to or less than 1.
4 Conclusion The lateral edge magnetic field is the part of the traveling wave magnetic field. It participates in energy transfer and conversion with the traveling wave magnetic field in the core, and produces effective electromagnetic thrust. In the electromagnetic design of linear motors, the introduction of the third air gap coefficient according to the analysis of this paper will improve the calculation accuracy. Table 2 compares the calculated and measured values ​​of electromagnetic quantities (short-circuit test) with and without K =1). It can be seen from Table 2 that the calculated value after considering K is more consistent with the measured value.
The measured value of the seven-pole linear motor of the project is considered K. The calculated value deviation is not considered K. The calculated value deviation is measured by the six-pole linear motor. The calculated value deviation is not considered K. The calculated value deviation is 2 Shanghai University of Technology. Linear Asynchronous Motor [ ] . Beijing: Mechanical Industry Press, 3 Wang Jianzhong. Electromagnetic design features and calculation examples of linear asynchronous motor [J].Small and medium-sized motor technical information, 1977 (4) Research on static lateral edge effect of linear motor