Motor control device

Abstract

A motor control device drives a two-phase synchronous motor. The motor control device includes a control current waveform generation unit that generates a control current waveform by superimposing a basic sinusoidal wave with a reluctance torque correction waveform that suppresses fluctuations in the reluctance torque of the two-phase synchronous motor, and a current control signal generation unit that generates a current control signal for supplying current to the windings of the two-phase synchronous motor based on the control current waveform generated by the control current waveform generation unit. The reluctance torque correction waveform may be a waveform obtained by full-wave rectifying an original waveform having a frequency twice that of the basic sinusoidal wave and matching its phase to the basic sinusoidal wave, to have the same sign as or a different sign from the basic sinusoidal wave.

Description

Technical Field

[0001] The present invention relates to a motor control device for driving a two-phase synchronous motor. Background Art

[0002] A typical example of a two-phase synchronous motor is a two-phase stepping motor.

[0003] When a two-phase stepping motor is driven with a sinusoidal current, conditions exist for generating rotational vibration. Specifically, the natural frequency is determined by the sum of the rotor inertia and the load inertia, as well as the motor's generated torque. Rotational vibration occurs when the frequency of the sinusoidal current driving the motor is half or one-quarter the rotational speed relative to this natural frequency.

[0004] Furthermore, in stepping motors, when the motor is stopped by exciting the windings with a constant current, the stopped position may deviate from the theoretical stop position. This is called "stationary angle error."

[0005] These rotational vibration and static angle error issues are particularly pronounced in hybrid stepper motors, especially small hybrid stepper motors. Slot magnet stepper motors, which have magnets inserted between stator and / or rotor teeth, also suffer from significant rotational vibration and static angle error.

[0006] Patent Document 1 discloses a method of suppressing vibration by forming an excitation current through micro-stepping driving of triangular wave pulses and changing the third and fifth harmonic components of higher harmonics obtained by Fourier transforming the triangular wave pulses.

[0007] Patent Document 2 points out that vibration is generated by higher harmonics of the back electromotive force of the motor, and discloses a method of suppressing the higher harmonics of the back electromotive force by excitation phase compensation.

[0008] Non-Patent Document 1 points out that the cause of motor vibration is cogging torque, and discloses a method of suppressing the cogging torque by compensating the excitation phase.

[0009] Prior art literature

[0010] Patent Literature

[0011] Patent Document 1: Japanese Patent Application Laid-Open No. 2003-9592

[0012] Patent Document 2: Japanese Patent Application No. 2019-516339

[0013] Non-patent literature

[0014] Non-Patent Literature 1: Takemura Hidetaka, et al., "Study on Vibration Reduction of Cogging Torque Compensators in Stepping Motor Drive Systems," Proceedings of the Japan Society of Mechanical Engineers (Edition C), Vol. 78, No. 785 (January 2012), pp. 74-81 Summary of the Invention

[0015] Technical problem to be solved by the invention

[0016] One embodiment of the present invention provides a novel motor control device capable of suppressing vibration of a two-phase synchronous motor based on a different perspective from the above-mentioned conventional technology.

[0017] Furthermore, one embodiment of the present invention provides a motor control device capable of reducing a stationary angle error of a two-phase synchronous motor.

[0018] Technical means for solving technical problems

[0019] One embodiment of the present invention provides a motor control device for driving a two-phase synchronous motor. The motor control device includes a control current waveform generator that generates a control current waveform by superimposing a basic sinusoidal wave with a reluctance torque correction waveform that suppresses fluctuations in the reluctance torque of the two-phase synchronous motor. The motor control device also includes a current control signal generator that generates a current control signal for supplying current to a winding of the two-phase synchronous motor based on the control current waveform generated by the control current waveform generator.

[0020] With this configuration, a reluctance torque correction waveform that suppresses reluctance torque fluctuations is superimposed on the basic sine wave to generate a control current waveform, which is then used to drive the two-phase synchronous motor. This suppresses vibrations caused by reluctance torque fluctuations.

[0021] The inventors of this application discovered that the origin of rotational vibration and static angle error in a two-phase synchronous motor can be explained by the fact that the waveform (θ-T waveform) of the torque's rotor angle dependence relative to the excitation phase, caused by the motor current value, fluctuates, leading to the present invention. In particular, they discovered that the sum of the reluctance torque, previously thought to be negligible in prior theories regarding stepping motors, affects the fluctuations in the θ-T waveform. Therefore, one embodiment of the present invention utilizes a control current waveform obtained by superimposing a reluctance torque correction waveform that suppresses the fluctuations in reluctance torque (more precisely, the fluctuations that depend on the excitation phase) on a basic sine wave. This allows for both suppressing rotational vibration and improving static angle error. In other words, this control current waveform suppresses or prevents the fluctuations in the reluctance torque waveform (θ-T waveform) relative to the excitation phase. By using this control current waveform, smooth, low-vibration drive can be achieved when driving a motor in an open-loop system for motors with significant reluctance torque.

[0022] The motor control device may also drive the two-phase synchronous motor by open-loop constant current control. The open-loop control may be control without either position feedback or speed feedback.

[0023] In one embodiment of the present invention, the reluctance torque correction waveform comprises a waveform obtained by full-wave rectification of an original waveform having a frequency twice that of the basic sine wave and a phase matching that of the basic sine wave, to a waveform having the same sign or a different sign as the basic sine wave. Phase matching does not necessarily mean strict phase matching. While strict phase matching is possible, it is possible to intentionally introduce a slight phase offset to enhance the vibration reduction effect. Therefore, the purpose of phase matching here is to allow for a phase offset within a range that suppresses fluctuations in the excitation phase that are dependent on the reluctance torque.

[0024] In one embodiment of the present invention, the original waveform is a sinusoidal waveform.

[0025] In one embodiment of the present invention, the reluctance torque correction waveform has a waveform obtained by full-wave rectification of the original waveform to have the same sign as the basic sine wave when the amplitude of the angular differential of the self-inductance of the two-phase synchronous motor is greater than the amplitude of the angular differential of the mutual inductance of the two-phase synchronous motor; and has a waveform obtained by full-wave rectification of the original waveform to have a different sign from the basic sine wave when the amplitude of the angular differential of the self-inductance is less than the amplitude of the angular differential of the mutual inductance.

[0026] In one embodiment of the present invention, the reluctance torque correction waveform is a waveform calculated using a ratio between an amplitude of an angular differential of a self-inductance and an amplitude of an angular differential of a mutual inductance of the two-phase synchronous motor.

[0027] In one embodiment of the present invention, the reluctance torque correction waveform is a waveform that changes according to the motor current supplied to the two-phase synchronous motor.

[0028] In one embodiment of the present invention, the two-phase synchronous motor is a stepper motor. The stepper motor may be a hybrid type or a slot magnet type.

[0029] In one embodiment of the present invention, the control current waveform has a waveform obtained by superimposing the basic sine wave, the reluctance torque correction waveform, and a magnet torque correction waveform for compensating for nonlinearity of magnet torque with respect to current.

[0030] The nonlinearity of magnet torque relative to current can contribute to motor rotational vibration. Therefore, by superimposing a magnet torque correction waveform on the control current waveform, the motor's rotational vibration and static angle error can be further improved. This current correction for magnet torque nonlinearity is particularly effective in hybrid stepping motors.

[0031] In one embodiment of the present invention, the magnet torque correction waveform is a waveform that changes according to a motor current supplied to the two-phase synchronous motor.

[0032] In one embodiment of the present invention, the magnet torque correction waveform has a waveform that amplifies the amplitude of the peak portion of the basic sine wave when superimposed on the basic sine wave.

[0033] The above and other objects, features and effects of the present invention will become more apparent from the following description of the embodiments with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 3 is a waveform diagram showing the θ-T waveform of the ideal magnet torque.

[0035] Figure 2 It is a waveform diagram showing the relationship between the magnet torque, inductance and its angular differential and the rotor angle.

[0036] Figure 3A and Figure 3B This is a diagram for explaining the relationship between the state of a stepping motor and its self-inductance.

[0037] Figure 4A 3 is a waveform diagram showing a θ-T waveform associated with the reluctance torque when the amplitudes of the angular differentials of the self-inductance and the mutual inductance are equal.

[0038] Figure 4B is a waveform diagram showing a θ-T waveform associated with the reluctance torque when the amplitudes of the angular differentials of the self-inductance and the mutual inductance are unequal.

[0039] Figure 5A and Figure 5B This is a waveform diagram for explaining a current waveform for suppressing fluctuations in the θ-T waveform corresponding to the excitation phase of the reluctance torque.

[0040] Figure 5C and Figure 5D This is a waveform diagram for explaining the inversion of the superimposed waveform according to the magnitude relationship of the amplitudes of the angular differentials of the self-inductance and the mutual inductance.

[0041] Figure 6 This is a waveform diagram for explaining that the fluctuation of the θ-T waveform of the reluctance torque can be eliminated by current correction.

[0042] Figure 7 : is a characteristic diagram showing the torque-current characteristics of the hybrid stepping motor.

[0043] Figure 8 This is a waveform diagram for explaining an example of current correction for compensating for nonlinearity of magnet torque with respect to current.

[0044] Figure 9 This is a waveform diagram for explaining an example of current correction for compensating for nonlinearity of magnet torque with respect to current.

[0045] Figure 10 This is a perspective view for explaining a configuration example of a two-phase hybrid stepping motor.

[0046] Figure 11 It is an exploded perspective view for explaining the structure of the stator and rotor of the hybrid stepping motor.

[0047] Figure 12 This is a diagram showing the structure of the stator as viewed along the rotation axis.

[0048] Figure 13 This is a block diagram for explaining an example of an electrical configuration related to control and drive of a stepping motor.

[0049] Figure 14 An example of a control block related to the control of a stepping motor is shown.

[0050] Figure 15 : is a diagram showing an example of measuring the rotational vibration of the stepping motor.

[0051] Figure 16 : is a diagram showing an example of measuring the rotational vibration of the stepping motor.

[0052] Figure 17 This is a perspective view for explaining a structural example of a two-phase slot magnet type stepping motor.

[0053] Figure 18 It is an exploded perspective view for explaining the structure of the stator and rotor of the slot magnet type stepping motor.

[0054] Figure 19 This is a partially enlarged cross-sectional view showing the rotor teeth and stator teeth of the slot magnet type stepping motor in an enlarged manner.

[0055] Figure 20A and Figure 20B This figure shows the results of magnetic analysis of θ-T waveforms of slot magnet type stepping motors with gap ratios of 4 and 8.

[0056] Figure 21A and Figure 21B This is a graph showing analysis results of the self-inductance and mutual inductance of a slot magnet type stepping motor having a gap ratio of 4.

[0057] Figure 22A and Figure 22B This is a graph showing the torque analysis results of a slot magnet type stepping motor with a gap ratio of 4 times.

[0058] Figure 23A and Figure 23B This is a diagram showing the results of analyzing the self-inductance and mutual inductance of a slot magnet type stepping motor having a gap ratio of 8.

[0059] Figure 24A and Figure 24B This is a graph showing the torque analysis results of a slot magnet type stepping motor with a gap ratio of 8 times.

[0060] Figure 25 3 is a waveform diagram showing an example of the waveforms of the A-phase sinusoidal current and the B-phase sinusoidal current when the d-axis is excited with the rated current.

[0061] Figure 26 This is a waveform diagram showing the angular differential value of the inductance obtained from the inductance analysis results of the slot magnet type stepping motor.

[0062] Figure 27 This waveform diagram shows a superposition of θ-T waveforms of reluctance torque obtained by calculation and analysis for a slot magnet type stepping motor.

[0063] Figure 28 This is a diagram showing a measurement example (without correction) of rotational vibration related to a slot magnet type stepping motor.

[0064] Figure 29 1 is a diagram showing a measurement example of rotational vibration related to a slot magnet type stepping motor (during current correction).

[0065] Figure 301 is a waveform chart showing actually measured values ​​of motor current in a slot magnet type stepping motor.

[0066] Figure 31A and Figure 31B This figure shows the measurement results of the static angle error when the slot magnet type stepping motor is driven in full steps.

[0067] Figure 32A and Figure 32B This figure shows the measurement results of the static angle error when the slot magnet type stepping motor is driven by microstepping. DETAILED DESCRIPTION

[0068] The inventors of this application discovered that the motor current value causes fluctuations in the rotor angle dependence of torque (θ-T characteristic) with respect to the excitation phase, which can explain the deterioration of rotational vibration and / or static angle error. Specifically, they discovered that the nonlinearity of the current value with respect to the generated torque affects the fluctuations in the θ-T waveform representing the relationship between rotor angle and torque. Furthermore, the reluctance torque, previously considered negligible in stepping motor theory, also affects the fluctuations in the θ-T waveform. Based on these findings, the present application provides the following embodiments.

[0069] Specifically, this embodiment provides a current waveform that prevents fluctuations in the reluctance torque waveform relative to the excitation phase, thereby reducing rotational vibration and / or improving static angle error. This allows for smooth, vibration-free open-loop operation of motors with significant reluctance torque.

[0070] [Study on the ideal magnetic torque]

[0071] In synchronous motors with low angular dependence of motor inductance, such as surface magnet motors, hybrid stepping motors, and some embedded magnet motors, the torque generated by the motor is primarily due to the magnets. This torque is called "magnet torque."

[0072] The magnet torque T of the two-phase motor M It can be represented by the synthesis of the θ-T waveforms of phase A and phase B. The θ-T waveform of phase A can be represented by the A phase current I A The product of the rotor position (specifically, the rotor angle θ) and sin(θ) is I A ·Sin(θ) is used to represent the θ-T waveform of phase B. The θ-T waveform of phase B can be expressed as the current I B The product of the rotor position function cos(θ) I B ·cos(θ). Therefore, the magnet torque T M It can be expressed as the sum of these as shown in the following formula (1): where the torque constant is assumed to be 1.

[0073] T M =I A sin(θ)+I B ·cos(θ) (1)

[0074] It is known that the relationship between magnet torque and current in stepping motors is not linear. Therefore, we introduce a second-order term for the current and set its coefficient to p, which can be written as the following equation (2). In the case of ideal magnet torque, p = 0, as shown in equation (1).

[0075] T M =I A (1-pI 2 A )sin(θ)+I B (1-pI 2 B )cos(θ) (2)

[0076] Here, we consider the case of ideal magnet torque, that is, the case of p = 0. In addition, we consider the case where the current changes with time at an ideal sinusoidal waveform with an angular velocity ω, I A (t)=cos(ωt),I B (t)=-sin(ωt) (where t represents time) Therefore, the above formula (2) is as follows.

[0077] [Mathematical formula 1]

[0078] TM(t, θ)=cos(ωt)sin(θ)-sin((ωt)cos(θ)=-sin(ωt-θ) (3)

[0079] In this case, the θ-T waveform is Figure 1 Specifically, assuming ω=1, the θ-T waveforms at t=0, π / 4, and π / 2 are shown.

[0080] from Figure 1 As can be seen, the θ-T waveform maintains its shape while moving in parallel, and under any constant load, torque does not pulsate. Therefore, the vibration force in the rotational direction caused by torque pulsation does not act, and the motor's rotation does not vibrate.

[0081] [Study on reluctance torque]

[0082] Even without a magnet, electromagnetic force is generated between the cores due to the magnetic flux generated by the coils. This electromagnetic force generates torque. This is called "reluctance torque." Reluctance torque originates from the θ dependence of the motor's inductance. Let the sum of the magnetic energy be U and the self-inductance of phases A and B be L. A 、L B, when the mutual inductance is M, the reluctance torque T r It can be written as the following formula.

[0083] [Mathematical formula 2]

[0084]

[0085] For example, a hybrid stepping motor includes: a rotor having a plurality of small teeth (rotor teeth) arranged at equal intervals at a certain small tooth pitch on the circumference; and a stator arranged opposite the rotor. More specifically, the rotor has two rotor segments that are offset by half the small tooth pitch around the rotating axis, and these two rotor segments are fixed to the rotating axis. One rotor segment is magnetized to the south pole, and the other rotor segment is magnetized to the north pole. On the circumference of each rotor segment, a plurality of (for example, 50) small teeth are arranged at equal intervals at a fixed small tooth pitch. The stator has a plurality of main poles, each of which has a plurality of small teeth (stator teeth) arranged at the same small tooth pitch as the rotor.

[0086] A two-phase stepper motor has an A phase, a B phase offset by 90 degrees relative to A, a / A phase offset by 180 degrees relative to A, and a / B phase offset by 180 degrees relative to B. The stator has multiple main poles, each of which has windings supplying currents for the A, B, / A, and / B phases. Each main pole is equipped with stator teeth that face the rotor. While the stator teeth on the A phase main pole face the rotor teeth, the stator teeth on the B phase main pole are offset by one-quarter of a pitch (90 degrees electrical angle) relative to the rotor teeth. The stator teeth on the / A phase main pole are offset by two-quarters of a pitch (180 degrees electrical angle) relative to the rotor teeth. The stator teeth on the / B phase main pole are offset by three-quarters of a pitch (270 degrees electrical angle) relative to the rotor teeth.

[0087] Consider the state where phase A is excited to the N pole and phase / A is excited to the S pole. Figure 2 As shown in (a), the magnet torque T at this time M It can be represented by a sinusoidal function of the rotor angle θ. Figure 3A As shown, the stator main pole S of phase A A The state where the small tooth of the stator and the small tooth of the rotor R (more specifically, the S-pole rotor segment) are facing each other is the excitation stable point (electrical angle 0 degrees). / A The small teeth of the rotor R (more specifically, the S-pole rotor segment) are offset by only half the pitch (180 degrees in electrical angle). A From this state, the rotor R is rotated 90 degrees in electrical angle (1.8 degrees in mechanical angle when the number of rotor teeth is 50). Figure 3B In the state shown, the magnet torque T M At this time, the self-inductance of phase A is L ATherefore, it can be assumed that the self-inductance of phase A is L A The phase of Figure 2 (b) shows that the self-inductance of phase A is L A The magnet torque T M Therefore, it can be assumed that the self-inductance L of phase A is A The angular differential dL A The phase of / dθ is as follows Figure 2 (c) In other words, it can be assumed that the magnet torque T M By similarly examining the self-inductance L of phase B, B And the mutual inductance M, the following relationship can be derived.

[0088] [Mathematical formula 3]

[0089]

[0090] Therefore, let the self-inductance L A and L B The amplitude of the angle differential is LΔ, and the amplitude of the angle differential of the mutual inductance M is MΔ, then the reluctance torque T r (t,θ) can be written as the following formula.

[0091] [Formula 4]

[0092]

[0093] When MΔ=LΔ, the reluctance torque T is when the current waveform is an ideal sine wave. r like Figure 4A The figure shows the magnetic reluctance torque T when t = 0, π / 8, π / 4, 3π / 8, π / 2. r It can be seen that the θ-T waveform is related to the magnet torque T M The same direction and speed are maintained while the waveform is maintained. Therefore, when MΔ=LΔ, if the motor is rotated by an ideal sinusoidal current, the magnet torque T M and reluctance torque T r The waveform of the combined total torque is constant in time, and the translational speed of the waveform is uniform (specifically, a certain translational speed is achieved when ω is constant). Therefore, the motor does not behave in a vibratory manner.

[0094] On the other hand, when MΔ=LΔ / 2, the reluctance torque T is when the current waveform is an ideal sine wave. r like Figure 4B The figure shows the magnetic reluctance torque T when t = 0, π / 8, π / 4, 3π / 8, π / 2. rThe relevant θ-T waveform. It can be seen that the reluctance torque T r The total torque will fluctuate over time, and thus generate a vibration force. Figure 4B It can be seen that the intervals between the zero torque points in the θ-T curve corresponding to the equally spaced times t = 0, π / 8, π / 4, 3π / 8, and π / 2 are unequal. This indicates that even in the absence of a load, an excitation force and corresponding vibration are generated.

[0095] Therefore, for any values ​​of the amplitude parameters LΔ and MΔ, the reluctance torque T r The θ-T waveform is the motor current that does not change in time. Therefore, the reluctance torque T r A two-variable function T that does not require t and θ r (t,θ), but rather like the magnet torque T M Similarly, the univariate function T bracketed by (ωt-θ) r (ωt-θ) can be expressed. That is, it can be expressed as T r (t,θ)=T r (ωt - θ) is sufficient. This means that the waveform at any time t does not change, but only shifts by ωt, while the waveform at time t = 0 remains unchanged. The advection equation is a known differential equation that provides this solution, and it can be applied as follows.

[0096] [Formula 5]

[0097]

[0098] When the above-mentioned formula (6) is substituted into the left side of formula (7), the following is obtained.

[0099] [Formula 6]

[0100]

[0101] Since it needs to be zero at any θ, we can get the following formula.

[0102] [Formula 7]

[0103]

[0104] Thus, the following formula is obtained.

[0105] [Formula 8]

[0106]

[0107]

[0108] Combining them, we can get the following formula.

[0109] [Formula 9]

[0110]

[0111]

[0112] After solving these, the following is obtained: Where A1, A2, δ1, and δ2 are constants.

[0113] I A I B =A1cos(2ωt+δ1) (15)

[0114] I A 2 -I B 2 =A2cos(2ωt+δ2) (16)

[0115] to I A Solving it, we can get the following formula.

[0116] [Formula 10]

[0117]

[0118] Likewise, for I B Solving it, we can get the following formula.

[0119] [Mathematical formula 11]

[0120]

[0121] The I of formula (17) and (18) A , I B Substitute into formula (6) to obtain the reluctance torque T r , determine the unknown coefficients so that T r = -αsin(2(ωt-θ)), the following is true.

[0122] [Mathematical formula 12]

[0123]

[0124] Substituting it into equations (17) and (18), the phase A current I A and B phase current I B It can be obtained as follows.

[0125] [Mathematical formula 13]

[0126]

[0127]

[0128] I A and I B is a real number, so the square root must always be positive, and the solution for a net current of zero during one cycle of the current is the following equation.

[0129] [Mathematical formula 14]

[0130]

[0131]

[0132] Phase A current I when MΔ=LΔ / 2 A and B phase current I B The waveforms are respectively Figure 5A The curve 512 and Figure 5B As shown in the curve 522. Here, ω = 1, LΔ = 1. In the above equations (22) and (23), since α is the amplitude of the reluctance torque, it is set here as α = 1. The amplitude of the current is approximately

[0133] Phase A current when MΔ=LΔ and B phase current The waveforms are respectively Figure 5A The curve 510 and Figure 5B 520. These are sinusoidal waveforms. Figure 5A The sine wave current waveform shown in the curve 510 is the same as the phase A current I A The difference between the waveforms (curve 512) is called the "superimposed waveform", Figure 5A The phase A current I shown in curve 512 is obtained by superimposing the superimposed waveform of curve 511 on the sinusoidal current waveform of curve 510. A Similarly, Figure 5B The sinusoidal current waveform shown in the curve 520 is the same as the B-phase current I B The difference between the waveforms (curve 522) is called the "superimposed waveform", Figure 5B The phase B current I is shown by curve 521. By superimposing the superimposed waveform of curve 521 on the sinusoidal current waveform of curve 520, the phase B current I shown by curve 522 is obtained. B The superimposed waveforms (curves 511 and 521) are obtained by rectifying a sinusoidal waveform having a period twice that of the sinusoidal current waveform (curves 510 and 520) corresponding to the case where LΔ=MΔ to have the same sign as the sinusoidal current (curves 510 and 520).

[0134] Figure 6 In the figure, the case of MΔ=LΔ / 2 and the reluctance torque T are shown.r The figure shows the θ-T waveform related to the reluctance torque T when t=0, π / 8, π / 4, 3π / 8, π / 2. r The relevant θ-T waveform. It can be seen that the reluctance torque T r The waveform and Figure 4B Unlike the case of a motor driven by a sinusoidal current, its shape does not change with time.

[0135] When the motor is excited, the amplitudes LΔ and MΔ of the angular differential of the inductance depend on the motor current. Therefore, it is preferable to include the changes in the amplitudes LΔ and MΔ that depend on the motor current when calculating the currents of each phase supplied to the motor. However, in actual applications, since the square root processing of formulas (22) and (23) is too cumbersome, a basic superimposed waveform with constant amplitudes LΔ and MΔ is tabulated in advance. By adjusting the amplitude of the basic superimposed waveform according to the motor current, a basic superimposed waveform to be superimposed on the basic sine wave ( Figure 5A and 5B The superimposed waveform ( Figure 5A and 5B In this case, the stepping motor can be sufficiently reduced in vibration. When LΔ<MΔ, the sign of the superimposed waveform can be reversed (see Figure 5A 、 5B curves 511a, 521a).

[0136] As mentioned above, the superimposed waveform does not necessarily have to have a strict waveform as derived from equations (22), (23), etc. Figure 5A and Figure 5B As shown in curves 511 and 521, the superimposed waveform has a waveform of a higher harmonic with a frequency twice that of the basic sine wave (curves 510 and 520) as the original waveform, and has a waveform obtained by full-wave rectification of the original waveform to have the same sign as the basic sine wave. Considering the waveform (original waveform) before full-wave rectification of the superimposed waveform, it is a sine wave, but not a strictly sinusoidal waveform. Therefore, to be precise, the superimposed waveform is a waveform that can be obtained by full-wave rectification of the higher harmonic waveform of the basic sine wave (original waveform) to have the same sign as the basic sine wave. Of course, as the superimposed waveform, a waveform obtained by full-wave rectification of a strictly higher harmonic waveform with a frequency twice that of the basic sine wave to have the same sign as the basic sine wave can also be used. Even in this case, a certain vibration reduction effect can be expected.

[0137] When LΔ<MΔ, due to Figure 5A and Figure 5B In the case of curves 511 and 522, the sign of the superimposed waveform is reversed (see Figure 5A 、 5B511a, 521a), so the superimposed wave characteristics in this case have the waveform of the higher harmonics of twice the frequency of the basic sine wave (to be precise, the waveform like the higher harmonics) after full-wave rectification into a waveform with a different sign from the basic sine wave.

[0138] The reason why the superimposed waveform is reversed when the magnitude relationship between LΔ and MΔ is reversed is explained.

[0139] In the A phase current I A In the above formula (22), LΔ / MΔ=β, and when the second term in the double root is subjected to a Maclaurin expansion, the double root of formula (22) is expressed as follows.

[0140] [Mathematical formula 15]

[0141]

[0142] The first term is the solution when β = 1, which is a sine wave with a period of ωt. The second term is the correction term for the part that deviates from β = 1. The second term when β = 1.1 (MΔ < LΔ) and β = 0.9 (LΔ < MΔ) is Figure 5C The solid and dotted lines are shown in the figure respectively. Figure 5C The waveform when β = 1.1 (MΔ < LΔ) represented by the solid line corresponds to Figure 5A The superimposed waveform is represented by curve 511. Figure 5C The waveform when β = 0.9 (LΔ < MΔ) indicated by the dotted line is inverted relative to the waveform when β = 1.1 (MΔ < LΔ) (solid line). The waveform at this time corresponds to Figure 5A The superimposed waveform shown by the middle curve 511a is the reverse waveform of the curve 511.

[0143] Similarly, consider the B-phase current. B In the above formula (23), LΔ / MΔ=β, and when the second term in the double root is subjected to a Maclaurin expansion, the double root of formula (23) is expressed as follows.

[0144] [Formula 16]

[0145]

[0146] The second term when β=1.1(MΔ<LΔ) and β=0.9(LΔ<MΔ) is Figure 5D The solid and dotted lines are shown in the figure respectively. Figure 5D The waveform when β = 1.1 (MΔ < LΔ) represented by the solid line corresponds to Figure 5B The superimposed waveform is represented by curve 521. Figure 5DThe waveform when β = 0.9 (LΔ < MΔ) indicated by the dotted line is inverted relative to the waveform when β = 1.1 (MΔ < LΔ) (solid line). The waveform at this time corresponds to Figure 5B The superimposed waveform shown by the middle curve 521a is the reverse waveform of the curve 521.

[0147] As described above, when the magnitude relationship between LΔ and MΔ is reversed, the response can be achieved simply by reversing the superimposed waveform.

[0148] [Magnetic torque considering nonlinearity]

[0149] Considering the current correction when the magnet torque is nonlinear with respect to the current, it is known that in stepping motors, there occurs a phenomenon where the torque is not nonlinear with respect to the current. Figure 7 An example of the torque-current characteristics of a two-phase hybrid stepping motor is shown in FIG. The torque characteristic relative to the input current is a nonlinear torque curve. A quadratic polynomial is used to fit the torque curve, and the first-order coefficient is set as the torque constant k. t , set the second-order coefficient to p·k t , then the nonlinear magnet torque with respect to the current is expressed as follows by taking into account the torque constant in equation (1).

[0150] [Mathematical formula 17]

[0151]

[0152] If we solve the problem in the same way as in the case of reluctance torque, we get the following result.

[0153] [Mathematical formula 18]

[0154]

[0155]

[0156] According to Cardano's formula, x 3 A solution for -px-q=0 is as follows.

[0157] [Mathematical formula 19]

[0158]

[0159] Where D = 4p 3 -27q 2 , p≠0

[0160] Comparing with the cubic equation (22) to be solved, the coefficients are placed and solved as follows, which gives equations (27) and (28). Where δ = δ1 or δ2.

[0161] [Mathematical formula 20]

[0162]

[0163]

[0164]

[0165] Here, based on the analogy of the current phase in the case of the ideal magnetic torque described above, in order to set the magnetic torque to a sine wave, δ1=0 and δ2=-π / 2.

[0166] I in formula (27) and (28) A comp and I B Comp is substituted into I of formula (24) A and I B , we can get the following formula.

[0167] T M =αk t (cos(ωt)sin(θ)-sin(ωt)cos(θ))=-αk t sin(ωt-θ)(29)

[0168] α is the amplitude of the input current. When the discriminant D < 0, that is, the solution of the following equation has an imaginary part.

[0169] [Mathematical formula 21]

[0170]

[0171] The final current solution is shown below, which is obtained by adding the real part Re and the imaginary part Im to obtain a continuous form.

[0172] I A =Re(I A comp)+Im(I A comp) (31)

[0173] I B =Re(I B comp)+Im(I B comp) (32)

[0174] As an example, consider Figure 7 Current correction in the case of torque constant k t = 0.2745 (N·m / A), the quadratic coefficient of torque is p = 0.095 (N·m / A 2 ). When D=0, the excitation current α is as follows, and the current waveform at this time is as follows Figure 8This is shown as curve 802 in FIG. From a phenomenological perspective, it can be explained that in order to compensate for the reduction in torque during one-phase excitation, the current value at the current peak increases, and the excitation current waveform approaches a triangular wave.

[0175] [Mathematical formula 22]

[0176]

[0177] Figure 8 Curve 800 represents the pre-correction sinusoidal current waveform (α·sinωt). Here, ω = 1. Curve 801 represents the superimposed waveform corresponding to the difference between curve 802 and curve 800. By superimposing the superimposed waveform of curve 801 with the sinusoidal current waveform of curve 800, the corrected current waveform of curve 802 is obtained.

[0178] As an example in the case of D>0, the correction current waveform when the excitation current α=1.8 (A) is given by Figure 9 As shown in curve 902. Figure 9 Curve 900 represents the sinusoidal current waveform (α·sinωt) before correction. Curve 901 represents the superimposed waveform corresponding to the difference between curve 902 and curve 900. By superimposing the superimposed waveform of curve 901 with the sinusoidal current waveform of curve 900, the corrected current waveform of curve 902 is obtained. It can be seen that as the excitation current increases, the current value at the peak portion must be further increased.

[0179] The superimposed waveforms (curves 801 and 901 ) for compensating for the nonlinearity of the magnet torque have waveforms that amplify the amplitude of the peak portion of the sinusoidal current waveforms (curves 800 and 900 ).

[0180] As a specific example, the application of the above correction method to a two-phase hybrid stepping motor will be described. In this hybrid stepping motor, lower vibration levels can be achieved by using the above-mentioned current correction method to correct the reluctance torque. Furthermore, if current correction is combined with the correction method to correct the nonlinearity of the magnet torque, even lower vibration levels can be achieved.

[0181] Figure 10 This is a perspective view for explaining a configuration example of a two-phase hybrid stepping motor. A stepping motor 1 includes a stator 2 , a rotor 3 , a motor flange 4 , a bracket 5 , and a pair of bearings 6 and 7 .

[0182] The stator 2 includes a stator core 21 and a winding 22. A motor flange 4 and a bracket 5 are fixed to both ends of the stator core 21, respectively, and they constitute a motor housing 8.

[0183] A rotor 3 is rotatably disposed about a rotation axis 10 within a motor housing 8. The rotor 3 includes a rotation shaft 30 disposed along the rotation axis 10 and a rotor core 31 supported by the rotation shaft 30. The rotation shaft 30 is rotatably supported by a pair of bearings 6 and 7. One bearing 6 is mounted on the motor flange 4, and the other bearing 7 is mounted on the bracket 5.

[0184] Figure 11 This is an exploded perspective view for explaining the structure of the stator 2 and the rotor 3. The rotor 3 includes a rotating shaft 30 arranged along the rotation axis 10 (see FIG. Figure 10 ), a disk-shaped permanent magnet 40 supported on the rotating shaft 30, and a pair of rotor segments (iron cores) 41 and 42 fixed on either side of the permanent magnet 40. The permanent magnet 40 is magnetized along the rotating axis 10. The permanent magnet 40 is sandwiched between the pair of rotor segments 41 and 42.

[0185] A plurality (e.g., 50) of pole teeth (small teeth, i.e., rotor teeth) 33 are formed on the circumferential surface of each rotor segment 41, 42 at regular intervals along a circumferential direction 11 around the rotation axis 10 at a predetermined rotor tooth pitch. Each rotor tooth 33 forms a protrusion extending parallel to the rotation axis 10. The protrusions of the rotor teeth 33 may be slightly inclined relative to the rotation axis 10.

[0186] The pair of rotor segments 41 and 42 have substantially the same structure. They are fixed to the rotating shaft 30 with an offset of half the rotor tooth pitch. Therefore, when viewed along the rotation axis 10, the rotor teeth 33 of the other rotor segment 42 are positioned between the rotor teeth 33 of the one rotor segment 41.

[0187] Figure 12 The structure of the stator 2 (stator core 21) as viewed along the rotation axis 10 is shown. When viewed along the rotation axis 10, the stator 2 is roughly formed into a quadrilateral frame shape. The stator 2 is divided into a rotor accommodating space 32 in the center, in which the rotor 3 is arranged. The rotor accommodating space 32 is formed into a cylindrical shape centered on the rotation axis 10. The stator 2 has a frame-shaped back yoke 27 and a plurality of (8 in this example) main poles 28 (magnetic poles) protruding from the back yoke 27 toward the rotation axis 10. The plurality of main poles 28 are arranged at intervals along the circumferential direction 11 around the rotation axis 10. Each main pole 28 forms a protrusion parallel to the rotation axis 10.

[0188] Each main pole 28 has a support portion 28a whose base end is connected to the back yoke 27 and an opposing portion 28b connected to the front end of the support portion 28a. The opposing portion 28b faces the rotor accommodating space 32, that is, faces the rotor 3, and extends to both sides of the support portion 28a in the circumferential direction 11. Therefore, a winding slot 29 is formed between each main pole 28 and another main pole 28 adjacent to it in the circumferential direction 11. The winding 22 (see Figure 10) are arranged in these winding slots 29. More specifically, the winding 22 is wound on each main pole 28, and the winding 22 is accommodated in the winding slots 29 between adjacent main poles 28. The opposing portion 28b has an opposing surface opposing the rotor 3. A plurality of stator teeth 23 (small teeth) protruding toward the rotation axis 10 are formed on the opposing surface. Each stator tooth 23 is composed of a protrusion along the rotation axis 10. The plurality of stator teeth 23 are arranged at equal intervals along the circumferential direction 11 at a prescribed stator tooth pitch. In the case where the rotor teeth 33 are arranged obliquely with respect to the rotation axis 10, the stator teeth 23 are also arranged obliquely with respect to the rotation axis 10 accordingly.

[0189] Figure 13 This is a block diagram illustrating an example of an electrical structure related to the control and drive of a stepping motor. Power from a DC power supply 50 is supplied to the stepping motor 1 via a drive circuit unit 55. The drive circuit unit 55 is an example of a motor control device and includes a PWM inverter 51, a current detector 52, and a control device 60. The PWM inverter 51 supplies power from the DC power supply 50 to the stepping motor 1. The PWM inverter 51 is controlled by the control device 60. The PWM inverter 51 includes a multi-phase bridge circuit 511 corresponding to the multi-phase windings of the stepping motor 1, and a pulse width modulation pattern generator 512 that generates a PWM (pulse width modulation) control signal for turning on / off the switching elements (power devices) that constitute the bridge circuit 511. The control device 60 applies a voltage command to the PWM inverter 51. The pulse width modulation pattern generator 512 generates a PWM control signal based on the voltage command. The current detector 52 detects the current (motor current) flowing through each phase of the stepping motor 1.

[0190] The control device 60 monitors the detection signal of the current detector 52 and controls the stepping motor 1 with a constant current. More specifically, the control device 60 drives the stepping motor 1 through open-loop constant current control without position feedback and speed feedback. The control device 60 typically includes a processor 61 (CPU) and a memory 62, and the processor 61 is configured to implement multiple functions by executing programs stored in the memory 62. The memory 62 can be composed of one or more storage media. The memory 62 preferably includes a storage medium that can be written and can retain data even when the power is cut off. The processor 61 can perform calculations while exchanging data with the memory 62, and generate a voltage command for controlling the PWM inverter 51. The processor 61 controls the PWM inverter 51 based on the drive current amplitude command and position command (or speed command) provided from the outside or generated internally to achieve the drive of the stepping motor 1 corresponding to the drive current amplitude command and position command (or speed command).

[0191] Figure 14FIG. 6 is a diagram showing an example of a control module of a control device 60 related to the control of a stepping motor. The processor 61 executes a program stored in the memory 62, thereby realizing Figure 14 Thus, the control device 60 substantially includes a basic sine wave generator 70, a reluctance torque correction waveform generator 71, a magnet torque correction waveform generator 72, a coefficient setter 73, a first adder 76, a second adder 77 and a current feedback controller 78.

[0192] The basic sine wave generator 70 generates a basic sine wave (basic sine wave current waveform) for driving the stepping motor 1 with a sine wave. The basic sine wave generator 70 may include a table representing a basic waveform for generating the basic sine wave, and the table may be stored in the memory 62. The basic waveform has a sine wave waveform. The basic sine wave is generated by multiplying the basic waveform by the basic sine wave coefficient set by the coefficient setter 73. The basic sine wave is equivalent to Figure 5A 、 Figure 5B 、 Figure 8 and Figure 9 The waveforms are shown as curves 510, 520, 800, and 900. The basic sine wave generator 70 determines a frequency based on a position command (or a rotation speed command) and generates a basic sine wave of the frequency.

[0193] The reluctance torque correction waveform generator 71 generates a reluctance torque correction waveform for current correction related to the reluctance torque. The reluctance torque correction waveform is Figure 5A and Figure 5B The superimposed waveforms are shown as curves 511 and 521 in FIG. The reluctance torque correction waveform generator 71 may include a table representing basic correction waveforms for the superimposed waveforms, which may be stored in the memory 62. The basic correction waveforms are multiplied by the reluctance torque correction coefficients set by the coefficient setter 81 to generate reluctance torque correction waveforms corresponding to the superimposed waveforms (curves 511 and 512). The reluctance torque correction waveform generator 71 determines a frequency based on a position command (or speed command) and generates a reluctance torque correction waveform at that frequency.

[0194] The magnet torque correction waveform generator 72 generates a magnet torque correction waveform for current correction related to the nonlinear term of the magnet torque. This magnet torque correction waveform is equivalent to Figure 8 and Figure 9 The superimposed waveforms are shown as curves 801 and 901 in FIG. The magnet torque correction waveform generator 72 generates magnet torque correction waveforms corresponding to the superimposed waveforms (curves 801 and 901) based on the magnet torque correction coefficients set by the coefficient setter 81. The magnet torque correction waveform generator 72 determines a frequency based on a position command (or a speed command) and generates a magnet torque correction waveform having that frequency.

[0195] The coefficient setting device 73 generates various coefficients based on the drive current amplitude command. Specifically, the coefficient setting device 73 generates a basic sine wave coefficient for determining the amplitude of the basic sine wave generated by the basic sine wave generator 70.

[0196] The coefficient setter 73 also generates a reluctance torque correction coefficient for determining the amplitude of the reluctance torque correction waveform generated by the reluctance torque basic correction waveform generator 71 based on the drive current amplitude command. By generating the reluctance torque correction coefficient based on the drive current amplitude command, it is possible to generate an appropriate reluctance torque correction waveform according to the motor current to reduce the influence of the fluctuation of the reluctance torque. Specifically, the reluctance torque correction coefficient is equivalent to By multiplying by (LΔ / MΔ-1) (equivalent to (β-1) in the above equations (22a) and (23a), the sign of the reluctance torque correction coefficient is reversed according to the magnitude relationship between the amplitude LΔ and MΔ of the angular differential of the inductance. For example, the reluctance torque basic correction waveform generator 71 generates a value equivalent to Figure 5A and Figure 5B In the case of the basic correction waveform of the superimposed waveform of the curves 511 and 521 in FIG, when LΔ≥MΔ, a positive reluctance torque correction coefficient is generated, and when LΔ<MΔ, a negative reluctance torque correction coefficient is generated.

[0197] The amplitudes LΔ and MΔ of the angular differential of the inductance vary depending on the motor current, and the values ​​that vary with current are determined by the design of the individual stepping motor 1. Therefore, the values ​​of LΔ and MΔ that vary with the motor current can be determined in advance based on design analysis of the stepping motor 1 or based on measurements after the stepping motor 1 is manufactured. Based on the determined values ​​of LΔ and MΔ, the value of the reluctance torque correction factor for the motor current can be determined, and this value can be tabulated in advance. This allows the generation of a reluctance torque correction factor that appropriately varies with the motor current. Of course, a table of LΔ and MΔ for the motor current can be generated in advance, and based on this table, the reluctance torque correction factor corresponding to the drive current amplitude command (substantially consistent with the motor current) can be calculated.

[0198] The coefficient setter 73 also generates a magnet torque correction coefficient for correcting the nonlinear term of the magnet torque based on the drive current amplitude instruction. Specifically, the coefficient setter 73 generates α and p in equations (27) and (28) as magnet torque correction coefficients and provides them to the magnet torque correction waveform generator 72. The magnet torque correction waveform generator 72 generates a magnet torque correction waveform (equivalent to Figure 8 and Figure 9 801, 901 in the superimposed waveforms).

[0199] The first adder 76 and the second adder 77 respectively superimpose the reluctance torque correction waveform and the magnet torque correction waveform on the basic sine wave generated by the basic sine wave generator 70 to generate a control current waveform. Figure 14 In the example, the basic sine wave is superimposed with the reluctance torque correction waveform, and then the magnet torque correction waveform is superimposed on this superimposed waveform. However, the order of superposition can be changed, and the magnet torque correction waveform can be superimposed on the basic sine wave first, and then on the reluctance torque correction waveform. Of course, the reluctance torque correction waveform and the magnet torque correction waveform can also be superimposed first, and then on the basic sine wave. Thus, the control current waveform generation unit is configured to include a basic sine wave generator 70, a reluctance torque correction waveform generator 71, a magnet torque correction waveform generator 72, a coefficient setter 73, and adders 76 and 77.

[0200] The current feedback controller 78 generates a voltage command based on the control current waveform and supplies this voltage command to the PWM inverter 51. More specifically, the current feedback controller 78 performs constant current control by feeding back the difference between the command current based on the control current waveform (in which the correction waveform is superimposed on the basic sine wave) and the detection current detected by the current detector 52 as the voltage command. Alternatively, vector control can be performed in a rotor rotation coordinate system or a position command coordinate system. In this case, the basic sine wave and the superimposed waveform can be superimposed on the DC axis.

[0201] The pulse width modulation pattern generator 512 included in the PWM inverter 51 is an example of a current control signal generating unit that generates a PWM control signal (current control signal) for causing each phase current having a control current waveform to flow through the winding of each phase of the stepping motor 1. The switching elements included in the bridge circuit 511 of the PWM inverter 51 are controlled based on the PWM control signal.

[0202] In addition, the features of the current correction related to the nonlinear terms of the magnet torque can be omitted. In this case, Figure 14 In the structure, the magnet torque correction waveform generator 72 and the second adder 77 can be omitted, and the addition result in the first adder 76 can be directly (or after necessary modification) provided to the current feedback controller 78.

[0203] exist Figure 15 and Figure 16 Shown in Figures 10 to 15 The stepping motor 1 to be measured has a mounting angle dimension of 28 mm, a motor length of 32 mm, a maximum excitation static torque of 0.1 N·m, and a rotor inertia moment of 9.2×10 -7 kg·m 2 , two-phase hybrid stepping motor with 50 rotor teeth. Figure 15 Curve 150 shows the relationship between the rotational speed and the rotational vibration level when no current correction related to the reluctance torque and the magnet torque described above is performed. Figure 15 A curve 151 shows the relationship between the rotational speed and the rotational vibration level when the current correction related to the reluctance torque and the magnet torque described above is performed. Figure 16 Curves 161 and 162 show the relationship between the rotational speed and the rotational vibration level when the above-mentioned current correction is performed. Curve 161 shows the measurement result when operating at the rated current, and curve 162 shows the measurement result when the operating current is set to 50% of the rated current.

[0204] In the absence Figure 15 In the case of the correction shown in curve 150, it can be seen that the rotational vibration is large at speeds of 60 rpm and 120 rpm. The frequency component of the vibration at this time has a peak value of 200 Hz, which is the natural vibration frequency of the rotor. When the speed is 60 rpm, the frequency of the motor current fundamental wave is 50 Hz, and when the speed is 120 rpm, the frequency of the motor current fundamental wave is 100 Hz. The vibration around 60 rpm occurs when the frequency of the current fundamental wave reaches one-quarter of the rotor's natural vibration frequency (fourth-order vibration). In addition, the vibration around 120 rpm occurs when the frequency of the current fundamental wave reaches one-half of the rotor's natural vibration (second-order vibration).

[0205] like Figure 15 As shown in the curve 151, by applying the current correction, the rotation vibration level can be greatly reduced. Figure 16 As shown, by changing the current correction value according to the operating current, it can be found that the vibration is reduced even if the operating current is changed.

[0206] As another specific example, the application of the above-mentioned correction to a slot magnet stepping motor will be described. In this slot magnet stepping motor, low vibration levels can be achieved by using the above-mentioned current correction to correct the reluctance torque. Current correction to correct the nonlinear term of the magnet torque is not necessarily required in slot magnet stepping motors, and low vibration levels can be achieved even if it is omitted.

[0207] Figure 17 The following shows an example of the structure of a slot magnet type stepping motor. Figure 10 The same reference numerals are used for corresponding parts of the structures shown in the drawings, but this does not mean that the parts with the same reference numerals are substantially the same.

[0208] The stepping motor 1 includes a stator 2 , a rotor 3 , a motor flange 4 , a bracket 5 , and a pair of bearings 6 and 7 .

[0209] The stator 2 includes a stator core 21 and a winding 22. A motor flange 4 and a bracket 5 are fixed to both ends of the stator core 21, respectively, and they constitute a motor housing 8.

[0210] A rotor 3 is rotatably disposed about a rotation axis 10 within a motor housing 8. The rotor 3 includes a rotation shaft 30 disposed along the rotation axis 10 and a rotor core 31 supported by the rotation shaft 30. The rotation shaft 30 is rotatably supported by a pair of bearings 6 and 7. One bearing 6 is mounted on the motor flange 4, and the other bearing 7 is mounted on the bracket 5.

[0211] Figure 18 It is an exploded perspective view for explaining the structures of the stator 2 and the rotor 3 .

[0212] Rotor teeth 33 are formed on the outer circumferential surface of rotor core 31 at regular intervals in circumferential direction 11 at a predetermined tooth pitch. Each rotor tooth 33 extends parallel to rotation axis 10. However, rotor teeth 33 may be inclined relative to rotation axis 10.

[0213] Rotor slots 34 are formed between adjacent rotor teeth 33. Rotor slot magnets 35 are inserted into the rotor slots 34. Rotor slot magnets 35 are hard magnetic inserts (typically permanent magnet pieces) extending in a rod-like shape along the rotor slots 34. Rotor slot magnets 35 are fixed to the rotor slots 34 using, for example, an adhesive.

[0214] The stator core 21 includes a frame-shaped back yoke 27 and a plurality of main poles 28. The plurality of main poles 28 extend from the back yoke 27 toward the rotor core 31 and are arranged around the rotor core 31 at intervals in the circumferential direction 11. Thus, the plurality of main poles 28 divide the rotor housing space 32, which is substantially cylindrical and centered on the rotation axis 10. The winding 22 (see FIG. 2 ) is a substantially cylindrical rotor housing space 32. Figure 17 . Figure 18 (not shown in the figure) is wound around each main pole 28.

[0215] Each main pole 28 includes a support portion 28a coupled to the back yoke 27 and a facing portion 28b coupled to the front end of the support portion 28a. The facing portion 28b faces the rotor accommodation space 32 and therefore faces the rotor core 31. The facing portion 28b extends on both sides of the support portion 28a in the circumferential direction 11. Consequently, winding slots 29 are formed between each main pole 28 and another main pole 28 adjacent in the circumferential direction 11. The windings 22 are arranged in these winding slots 29. The facing portion 28b has a facing surface that faces the rotor core 31. A plurality of stator teeth 23 are formed on this facing surface, projecting toward the rotation axis 10. The plurality of stator teeth 23 are arranged at equal intervals along the circumferential direction 11 at a predetermined tooth pitch. Each stator tooth 23 extends along the rotation axis 10 to match the rotor teeth 33. If the rotor teeth 33 are arranged at an angle relative to the rotation axis 10, the stator teeth 23 are also arranged at an angle relative to the rotation axis 10.

[0216] Stator slots 24 are formed between adjacent stator teeth 23. Stator slot magnets 25 are inserted into the stator slots 24. Stator slot magnets 25 are hard magnetic inserts (typically permanent magnet pieces) extending in a rod-like shape along the stator slots 24. Stator slot magnets 25 are fixed to the stator slots 24 using, for example, an adhesive.

[0217] The rotor slot magnets 35 and the stator slot magnets 25 are magnetized in radial directions from the rotation axis 10. The radial directions from the rotation axis 10 are directions perpendicular to the rotation axis 10. Therefore, the rotor slot magnets 35 are magnetized in the depth direction of the rotor slots 34. Furthermore, the stator slot magnets 25 are magnetized in the depth direction of the stator slots 24. With respect to the radial directions from the rotation axis 10, the magnetization directions of the rotor slot magnets 35 and the stator slot magnets 25 are the same. Therefore, when the rotor slot magnets 35 and the stator slot magnets 25 face each other, the magnetic poles of the rotor slot magnets 35 and the magnetic poles of the stator slot magnets 25 facing each other are magnetic poles of opposite polarity.

[0218] Figure 19 It is a partially enlarged cross-sectional view showing the rotor teeth 33 and the stator teeth 23 in an enlarged manner.

[0219] The rotor teeth 33 are protrusions extending in a direction intersecting the circumferential direction 11, which serves as the direction of movement. The rotor teeth 33 project outward (away from the rotation axis 10) with a substantially constant width in radial directions within a cross-section perpendicular to the rotation axis 10. Each rotor tooth 33 has a top surface 33a facing away from the rotation axis 10. The top surface 33a extends along the circumferential direction 11 around the rotation axis 10. In a cross-section perpendicular to the rotation axis 10, the multiple rotor teeth 33 have substantially identical cross-sectional shapes and are arranged at equal intervals at a constant rotor tooth pitch Pr. The rotor slots 34 formed between adjacent rotor teeth 33 are defined by a pair of substantially parallel side surfaces 34b and 34c defined by the rotor teeth 33, and a bottom surface 34a formed between these side surfaces 34b and 34c, resulting in a substantially rectangular cross-sectional shape. The bottom surface 34a extends along the circumferential direction 11 around the rotation axis 10. The distance from the bottom surface 34 a of the rotor slot 34 to the top surface 33 a of the rotor tooth 33 , that is, the height of the rotor tooth 33 is referred to as “rotor tooth height Hr”.

[0220] The rotor slot magnet 35 is made of a hard magnetic material and is a rod-shaped insert (typically a permanent magnet sheet) extending along the rotation axis 10. In this embodiment, the rotor slot magnet 35 has a generally rectangular cross-section perpendicular to the rotation axis 10. The rotor slot magnet 35 has a bottom surface 35a facing the bottom surface 34a of the rotor slot 34, a top surface 35d (opposing surface) located on the opposite side of the rotation axis 10 from the bottom surface 35a, and a pair of side surfaces 35b and 35c formed between the bottom surface 35a and the top surface 35d. The bottom surface 35a and the top surface 35d are chamfered to form a curved surface with an arc-shaped cross-section between the side surfaces 35b and 35c. The bottom surface 35a of the rotor slot magnet 35 is bonded (fixed) to the bottom surface 34a of the rotor slot 34, for example, using an adhesive.

[0221] The top surface 35d of the rotor slot magnet 35 is the surface facing the stator 2. In this embodiment, the top surface 35d is located set back toward the rotation axis 10 relative to the imaginary cylindrical surface defined by connecting the outer peripheral surfaces (top surface 33a) of the plurality of rotor teeth 33. Specifically, the distance between the bottom surface 35a and the top surface 35d, i.e., the magnet thickness (rotor magnet thickness) MTr, is less than the depth of the rotor slot 34 (= rotor tooth height Hr). As a result, the entire rotor slot magnet 35 is accommodated within the rotor slot 34. The top surface 35d is substantially parallel to this imaginary cylindrical surface. Strictly speaking, the top surface 35d can be a flat surface, and this plane can be parallel to the plane formed by connecting the opening edges of the corresponding rotor slots 34. In this embodiment, the plurality of rotor slot magnets 35 inserted into the plurality of rotor slots 34 have substantially the same shape and size.

[0222] The stator teeth 23 are projections extending in a direction intersecting the circumferential direction 11, which serves as the direction of movement. They extend parallel to the rotor teeth 33. Within a cross-section perpendicular to the rotation axis 10, the stator teeth 23 project radially inward (in a direction approaching the rotation axis 10) with a substantially constant width. Each stator tooth 23 has a top surface 23a facing the rotation axis 10. Top surface 23a extends along the circumferential direction 11 around the rotation axis 10. Within a cross-section perpendicular to the rotation axis 10, the multiple stator teeth 23 have substantially identical cross-sectional shapes and are arranged at equal intervals at a constant stator tooth pitch Pr. The stator slots 24 formed between adjacent stator teeth 23 are defined by a pair of substantially parallel side surfaces 24b and 24c defined by each stator tooth 23, and a bottom surface 24a formed between these side surfaces 24b and 24c. These slots have a substantially rectangular cross-sectional shape. The bottom surface 24a extends along the circumferential direction 11 around the rotation axis 10. The distance from the bottom surface 24 a of the stator slot 24 to the top surface 23 a of the stator tooth 23 , that is, the height of the stator tooth 23 is referred to as a “stator tooth height Hs”.

[0223] The stator slot magnet 25 is made of a hard magnetic material and is a rod-shaped insert (typically a permanent magnet sheet) extending along the rotation axis 10. In this embodiment, the stator slot magnet 25 has a generally rectangular cross-section perpendicular to the rotation axis 10. The stator slot magnet 25 has a bottom surface 25a that faces the bottom surface 24a of the stator slot 24, a top surface 25d (opposing surface) located on the rotation axis 10 side relative to the bottom surface 25a, and a pair of side surfaces 25b and 25c formed between the bottom surface 25a and the top surface 25d. The bottom surface 25a and the top surface 25d are chamfered to form a curved surface with an arc-shaped cross-section between the side surfaces 25b and 25c. The bottom surface 25a of the stator slot magnet 25 is bonded (fixed) to the bottom surface 24a of the stator slot 24, for example, using an adhesive.

[0224] The top surface 25d of the stator slot magnet 25 is the surface facing the rotor 3. In this embodiment, the top surface 25d is located set back from the imaginary cylindrical surface defined by connecting the inner circumferential surfaces (top surface 23a) of the plurality of stator teeth 23, moving away from the rotation axis 10. Specifically, the distance between the bottom surface 25a and the top surface 25d, i.e., the magnet thickness (stator magnet thickness) MTs, is less than the depth of the stator slot 24 (= stator tooth height Hs). Thus, the entire stator slot magnet 25 is accommodated within the stator slot 24. The top surface 25d is substantially parallel to this imaginary cylindrical surface. Strictly speaking, the top surface 25d can be a flat surface, and this plane can be parallel to the plane formed by connecting the opening edges of the corresponding stator slots 24. In this embodiment, the plurality of stator slot magnets 25 inserted into the plurality of stator slots 24 have substantially the same shape and size.

[0225] The rotor slot magnets 35 and the stator slot magnets 25 may have substantially the same shape and size.

[0226] When the rotor teeth 33 and stator teeth 23 face each other, a fixed gap (air gap) is formed between them, relative to their opposing direction, i.e., the radial direction (the depth direction of the slots 34 and 24). This gap is referred to as "iron gap ΔF." When the rotor slots 34 and stator slots 24 face each other, a fixed gap is formed between the rotor slot magnets 35 and stator slot magnets 25, relative to their opposing direction, i.e., the radial direction (the depth direction of the slots 34 and 24). This gap is referred to as "magnet gap ΔM."

[0227] Slot-magnet stepping motors generally offer significantly higher holding torque than hybrid-type stepping motors. However, the ratio of self-inductance to mutual inductance varies significantly depending on the shape and configuration of the magnets, exacerbating rotational vibration and static angle error. In particular, the ratio of the magnet gap ΔM (inter-magnet gap), the air gap between the stator slot magnets 25 and the rotor slot magnets 35, to the iron gap ΔF (inter-iron gap), the air gap between the stator 2 and the rotor 3 (rotor core) (hereinafter referred to as the "gap ratio ΔM / ΔF") plays a significant role.

[0228] Figure 20A and Figure 20B This is the result of magnetic analysis of the θ-T waveform of a slot magnet type stepping motor. Assuming the current is a sine wave, the rotor angle dependence of the torque is calculated when the excitation is at specific electrical angles of π / 8, π / 4, and 3π / 8. Figure 20A and Figure 20B In order to visually understand the fluctuation of the waveform, the zero point of the torque is expressed as the same as the zero point of the electrical angle. The analysis object is a mounting angle size of 60mm, a motor length of 40mm, and a rotor inertia moment of 370×10 -7 kg·m 2 , a two-phase slot magnet type stepping motor with 50 rotor teeth. Slot magnet type motors are designed to handle two motors with greatly different characteristics by changing the magnet thickness MTr and MTs. One motor has a gap ratio ΔM / ΔF of 4 times, and its characteristics are Figure 20A The other has a gap ratio ΔM / ΔF 8 times greater than that shown in Figure 20B The holding torque of the former is 2.0 N·m, and that of the latter is 1.3 N·m. The holding torque of a hybrid stepping motor of the same size is, for example, 1.1 N·m.

[0229] from Figure 20A and Figure 20B A comparison shows that for slot magnet motors with a gap ratio ΔM / ΔF of 8, the waveform fluctuates significantly depending on the excitation phase. This results in increased rotational vibration and worsening of the static angle error.

[0230] Figure 21A The following shows the analysis results of the self-inductance L and the mutual inductance M when the rotor of a slot magnet type motor with a gap ratio ΔM / ΔF of 4 is slowly rotated in a non-excited state. Figure 21B The following shows the analysis results of the self-inductance L and the mutual inductance M of the same motor when the rotor is slowly rotated with the d-axis current at the rated current value and the q-axis current at zero. Figure 22A Shown corresponding to Figure 20A (no excitation state) torque analysis results. In addition, Figure 22B Shown corresponding to Figure 20B (d-axis rated current excitation) torque analysis results. Figure 22A ) is the braking torque.

[0231] from Figure 21A and Figure 21B It can be seen that the self-inductance L and the mutual inductance M have an angular dependence of 2θ with respect to an electrical angle. In particular, when the d-axis is excited with the rated current, the amplitude of the mutual inductance M becomes larger than when there is no excitation. When the angular differential values ​​of the inductances L and M are proportional to the reluctance torque, but when the inductances L and M can be regarded as sine waves, the amplitudes of the inductances L and M are roughly equal to the amplitudes of their angular differential values. That is, in general, it can be considered that the amplitude of the inductance itself acts on the reluctance torque. Therefore, for LΔ and MΔ used in formula (6), the values ​​of the amplitude of the self-inductance L and the amplitude of the mutual inductance M are used respectively. From Figure 22B It can be seen that torque ripple is generated when the rated current is excited. This corresponds to Figure 20A and Figure 20B The torque at the ideal stable point is not zero, which is the excitation force.

[0232] Figure 23A The following shows the results of analyzing the self-inductance L and the mutual inductance M of a slot magnet type motor having a gap ratio ΔM / ΔF of 8 when the rotor rotates slowly in a non-excited state. Figure 23B The following shows the analysis results of the self-inductance L and the mutual inductance M of the same motor when the rotor is slowly rotated with the d-axis current at the rated current value and the q-axis current at zero. Figure 24A Shown corresponding to Figure 23A (no excitation state) torque analysis results. In addition, Figure 24B Shown corresponding to Figure 23B (d-axis rated current excitation) torque analysis results. Figure 24A ) is the braking torque.

[0233] It can be seen that the ratio of self-inductance L to mutual inductance M during de-energization is significantly different compared to a slot magnet motor with a gap ratio ΔM / ΔF of 4. While the braking torque is lower than that of a motor with a gap ratio ΔM / ΔF of 4, the torque ripple during excitation is approximately doubled. This suggests that when driven with an ideal sine wave, the motor with a gap ratio ΔM / ΔF of 8 exhibits greater vibration. Furthermore, this suggests that the braking torque has no direct effect on rotational vibration.

[0234] When the d-axis is excited with the rated current, the A-phase sinusoidal current and the B-phase sinusoidal current are as follows: Figure 25 As shown. Based on the inductance analysis results of a slot magnet motor with a gap ratio ΔM / ΔF of 8 times ( Figure 23B ) to find the angle differential, such as Figure 26 As shown, the self-inductance L of phase A is obtained A The angle differential value dL A / dθ、B phase self-inductance L B The angle differential value dL B / dθ, and the angular differential value dM / dθ of the mutual inductance M. Based on this, the reluctance torque T is calculated according to formula (4): r , and the torque analysis results ( Figure 24B ) for comparison, such as Figure 27 The value calculated by equation (4) is basically consistent with the torque analysis result, including the absolute value. Therefore, the torque ripple component can be said to be generated by the reluctance torque.

[0235] In fact, if Figure 23B As shown in the figure, the inductance L and M depend on the motor and are waveforms containing some high-order harmonics. Figure 23B In the case of , the self-inductance L is a waveform containing a harmonic component with a period twice the period of the self-inductance L, and the mutual inductance M is a waveform containing a harmonic component with a period three times the period of the mutual inductance M. Due to such harmonic components, the angular differential waveforms of the inductances L and M will also be deformed from sine waves. Therefore, in equations (17) and (18), it is hoped that the amplitudes LΔ and MΔ (i.e., coefficients A1 and A2) of the angular differential of the inductance and the phase components δ1 and δ2 of the harmonic current will be effectively changed according to the inclusion method of the harmonics. More specifically, compared with making the phase of the reluctance torque correction waveform completely consistent with the basic sine wave, performing phase matching with some small phase offsets set may achieve a better vibration suppression effect.

[0236] The electrical structure for driving the slot magnet type stepper motor is the same as that of the hybrid type stepper motor, such as Figure 13 and Figure 14As shown in the figure, in slot magnet stepping motors, vibration can be reduced by performing current correction for the reluctance torque and the nonlinear term related to the magnet torque, as in hybrid stepping motors. However, compared to hybrid stepping motors, the need for current correction for the nonlinear term related to the magnet torque is less, so this correction can be omitted.

[0237] Figure 28 and Figure 29 The following table shows an example of measuring rotational vibration. The stepping motor 1 to be measured has a mounting angle dimension of 60 mm, a motor length of 40 mm, and a rotor inertia moment of 370 × 10 -7 kg·m 2 、Two-phase slot magnet type stepping motor with 50 rotor teeth (refer to Figures 18 and 19 ) and hybrid stepping motors of the same size (see Figures 10 to 12 ). For a two-phase slot magnet type stepping motor, measurement results are shown for a motor having a gap ratio ΔM / ΔF of 4 times and a motor having a gap ratio ΔM / ΔF of 8 times.

[0238] Figure 28 The relationship between the rotational speed and the rotational vibration level is shown when the current correction related to the reluctance torque and the magnet torque described above is not performed (when the vehicle is driven with a non-corrected sine wave). Figure 29 The relationship between the rotational speed and the rotational vibration level is shown when the current correction related to the reluctance torque is performed and the current correction related to the magnet torque is omitted.

[0239] Figure 30 The figure shows the measured value of the motor current for a slot magnet type stepping motor having a gap ratio ΔM / ΔF of 8 times. Figure 30 The basic current waveform before correction (sine wave. Corresponding to Figure 5A and Figure 5B Curves 510, 520), and the reluctance torque correction current waveform superimposed thereon (corresponding to Figure 5A and Figure 5B Curves 511, 521) and the corrected current waveform (corresponding to Figure 5A and Figure 5B The corrected current waveform is a waveform obtained by superimposing the reluctance torque correction current waveform on the basic current waveform. However, the reluctance torque correction current waveform is superimposed with an amplitude adjusted according to the motor current.

[0240] When driving with uncorrected sinusoidal current ( Figure 28), both the slot magnet type stepping motor and the hybrid type stepping motor with a gap ratio ΔM / ΔF of 4 and 8 times exhibit significant secondary and quartic rotation vibrations. In contrast, it can be seen that when current correction is performed ( Figure 29 ) under the same conditions, the vibration is greatly reduced regardless of the type of motor.

[0241] Figure 31A and Figure 31B The following table shows the measurement results of the static angle error when a slot magnet motor with a gap ratio ΔM / ΔF of 4 is driven in full steps (1.8° / pulse). Figure 31A The measurement results are shown when the stopping current is set to the rated current. Figure 31B The measurement results are shown when the stop current is set to 50% of the rated current. In each figure, the measurement results are shown when the current correction related to the above-mentioned reluctance torque is performed and when it is not performed. In the past, it was believed that the static angle error of full-step drive was determined by the mechanical accuracy of the small teeth. However, if the reluctance torque is taken into consideration, it is not limited to this, and the static angle error during full-step drive can also be improved by current correction. In addition, from Figure 31A and Figure 31B It can be seen that even if the stop current is different, the effect of improving the static angle error can be obtained by current correction, which remains unchanged.

[0242] Figure 32A and Figure 32B These are the measurement results of the static angle error when a slot magnet type stepping motor was driven at microstepping speed (0.36° / pulse). Figure 32A The measurement results are shown when the stopping current is set to the rated current. Figure 32B The following diagram shows the measurement results when the stall current is set to 50% of the rated current. Each figure shows the measurement results when the current correction related to the reluctance torque described above is performed and when it is not performed. It can be seen that the current correction effect is maintained even in microstepping drive, and the improvement in the static angle error is maintained even when the stall current is changed.

[0243] While the embodiments of the present invention have been described above, the present invention can also be implemented in other forms. For example, while the above embodiments primarily describe stepping motors, the present invention can also be applied to other types of two-phase synchronous motors, such as surface magnet motors and embedded magnet motors.

[0244] Furthermore, the above-described embodiment primarily describes an example in which current correction related to reluctance torque fluctuations and current correction related to nonlinearity of magnet torque are performed. However, even if current correction related to nonlinearity of magnet torque is omitted, a vibration reduction effect can still be achieved. Furthermore, even if current correction related to reluctance torque fluctuations is omitted and only current correction related to nonlinearity of magnet torque is performed, a certain vibration reduction effect can still be achieved.

[0245] Furthermore, various design changes can be implemented within the scope of the matters described in the claims.

[0246] In the following, regarding the correction of the nonlinearity of the magnet torque, features extracted from this specification and the accompanying drawings can be noted.

[0247] 1. A motor control device for driving a two-phase synchronous motor, comprising:

[0248] a control current waveform generating unit that generates a control current waveform obtained by superimposing a basic sine wave and a magnet torque correction waveform for compensating for nonlinearity of current with respect to magnet torque of the two-phase synchronous motor; and

[0249] A current control signal generating unit generates a current control signal for supplying a current to the winding of the two-phase synchronous motor according to the control current waveform generated by the control current waveform generating unit.

[0250] 2. In the motor control device according to item 1, the magnet torque correction waveform is a waveform that changes according to a motor current supplied to the two-phase synchronous motor.

[0251] 3. The motor control device according to item 1 or 2, wherein the magnet torque correction waveform has a waveform that amplifies the amplitude of a peak portion of the basic sine wave when superimposed on the basic sine wave.

[0252] 4. The motor control device according to any one of items 1 to 3, wherein the two-phase synchronous motor is a stepping motor.

[0253] 5. The motor control device according to item 4, wherein the stepping motor is a hybrid type or a slot magnet type.

[0254] The embodiments of the present invention have been described in detail, but these are merely specific examples used to clarify the technical content of the present invention. The present invention should not be construed as being limited to these specific examples, and the scope of the present invention is defined only by the appended claims.

[0255] This application claims priority based on Japanese Patent Application No. 2020-082561 filed on May 8, 2020, and incorporates all the contents of that application into this application.

[0256] Label Description

[0257] 1 stepper motor

[0258] 2 stator

[0259] 3 rotors

[0260] 21 stator core

[0261] 22 Winding

[0262] 23 stator teeth

[0263] 24 stator slots

[0264] 25 stator slot magnets

[0265] 28 Main Pole

[0266] 29 winding slots

[0267] 30 Rotation axis

[0268] 31 rotor core

[0269] 33 rotor teeth

[0270] 34 rotor slots

[0271] 35 rotor slot magnets

[0272] 40 permanent magnets

[0273] 41 rotor segments

[0274] 42 rotor segments

[0275] 50 DC power supply

[0276] 51 PWM Inverter

[0277] 512 Pulse Width Modulation Pattern Generator

[0278] 52 Current detector

[0279] 55 drive circuit unit

[0280] 60 Control Device

[0281] 70 Basic Sine Wave Generator

[0282] 71 Reluctance torque correction waveform generator

[0283] 72 Magnet torque correction waveform generator

[0284] 73 Coefficient Setter

[0285] 76 First Adder

[0286] 77 Second adder

[0287] 78 Current Feedback Controller

[0288] Hr rotor tooth height

[0289] MTr rotor magnet thickness

[0290] Hs stator tooth height

[0291] MTs stator magnet thickness

[0292] ΔF Iron gap

[0293] ΔM Magnet gap

Claims

1. A motor control device for driving a two-phase synchronous motor, characterized in that: Include: a control current waveform generating unit that generates a control current waveform obtained by superimposing a basic sine wave and a reluctance torque correction waveform that suppresses fluctuations in the reluctance torque of the two-phase synchronous motor; as well as a current control signal generating unit for generating a current control signal for supplying a current to the winding of the two-phase synchronous motor according to the control current waveform generated by the control current waveform generating unit; The reluctance torque correction waveform comprises a waveform obtained by full-wave rectification of an original waveform having a frequency twice that of the basic sine wave and a phase matching that of the basic sine wave to a waveform having the same or different sign as the basic sine wave. The reluctance torque correction waveform has the following characteristics: when the amplitude of the angular differential of the self-inductance of the two-phase synchronous motor is greater than the amplitude of the angular differential of the mutual inductance of the two-phase synchronous motor, the original waveform is full-wave rectified into a waveform with the same sign as the basic sine wave; when the amplitude of the angular differential of the self-inductance is less than the amplitude of the angular differential of the mutual inductance, the original waveform is full-wave rectified into a waveform with a different sign from the basic sine wave.

2. The motor control device according to claim 1, wherein The original waveform is a sinusoidal waveform.

3. The motor control device according to claim 1, wherein The reluctance torque correction waveform is a waveform calculated using a ratio between an amplitude of an angular differential of a self-inductance and an amplitude of an angular differential of a mutual inductance of the two-phase synchronous motor.

4. The motor control device according to claim 1, wherein The reluctance torque correction waveform is a waveform that changes according to a motor current supplied to the two-phase synchronous motor.

5. The motor control device according to claim 1, wherein The two-phase synchronous motor is a stepping motor.

6. The motor control device according to claim 5, wherein: The stepper motor is of hybrid type or slot magnet type.

7. The motor control device according to any one of claims 1 to 6, wherein: The control current waveform has a waveform obtained by superimposing the basic sine wave, the reluctance torque correction waveform, and a magnet torque correction waveform for compensating for nonlinearity of magnet torque with respect to current.

8. The motor control device according to claim 7, wherein: The magnet torque correction waveform is a waveform that changes according to a motor current supplied to the two-phase synchronous motor.

9. The motor control device according to claim 7, wherein: The magnet torque correction waveform has a waveform that amplifies the amplitude of a peak portion of the basic sine wave when superimposed on the basic sine wave.

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