1. Field of the Invention
This invention relates to a stepping motor having two sets of stator yoke units, and in particular to the adjustment of cogging torque.
2. Related Background Art
Referring to FIG. 10 of the accompanying drawings which shows the structure of stator yoke units used in a stepping motor according to the prior art, stators 1 and 2 having stator poles 1a and 2a, respectively, constructed in the form of comb teeth form a stator yoke unit. Stator yoke units constructed of entirely the same stators as the pair of stators and 2 are disposed back to back on their respective stators 2 and constitute the stator assembly of the stepping motor. The two sets of stator yoke units are such that circular bosses 2b and holes 2c are formed in each of the respective stators 2 so that the phases of the stator poles deviate from each other by 1/4 pitch.
Referring now to FIG. 11 of the accompanying drawings which is a perspective view of the stepping motor constructed in the manner described above, the reference numeral 12 designates a rotor shaft, and a cylindrical rotor magnet 13 is fixed coaxially with the rotor shaft 12 for rotation about the rotor shaft. The rotor magnet 13 has formed on the peripheral surface thereof opposed to the stator poles 1a, 2a, 1a, 2a the same number of magnetic poles as the number of the stator poles on one set of stator yoke units. That is, the number of one set of stator poles in FIG. 11 is 24, and in this case, the number of the magnetic poles of the rotor is 24 because each of N poles and S poles is counted as one, and is 12 if counted in terms of the number of pairs of magnetic poles. The reference numerals 14 and 15 denote coils wound on the respective stator yoke units in the form of bifilar turns and led out of the stators through cut-away portions 1f, 1f, 2f and 2f.
FIG. 12 of the accompanying drawings is a diagram of the driving circuit of the stepping motor, and FIG. 13 of the accompanying drawings is a time chart of 2-phase excitation driving pulses applied to the driving circuit of FIG. 12.
FIG. 14a of the accompanying drawings is a developed view of stator poles and a rotor magnet of the stepping motor of FIG. 11. Two sets of stator yoke units are designated by a (comprising stators 1a.sub.1 and 2a.sub.1) and b (comprising stators 1a.sub.2 and 2a.sub.2), respectively, and the magnetic poles of the rotor are denoted by 13a.
Here, description will be made of the stationary position of the rotor and the cogging torque when the coils are not excited.
Description will first be made of the cogging torque acting between the stator yoke unit a and the rotor.
In considering the torque acting between the stator yoke unit a comprising one set of stators and the rotor, a two-pole stepping motor shown in FIG. 15 of the accompanying drawings is adopted as a model. This two-pole stepping motor corresponds to one pitch of the stepping motor of FIG. 11.
If in FIG. 15, the coordinates x, y are defined as shown, the point at which the torque acting on the rotor 16 is zero is the point at which the center of the magnetic pole coincides with the center of the stator pole and therefore, .theta.=0, .pi., 2.pi., . . . , n.pi..
Also, when ##EQU1## the torque acts equally on the rotor 16 between the right and left stators 17 and 18 and therefore, again in this case, the torque is zero. Assuming that the torque varies in the fashion of sine, EQU Ta=a.sub.1 sin 2.theta. (1)
and the torque varies at a period of 1/2 of the period 2.pi. of the stator poles.
If the number of the pairs of magnetic poles of the stator and the rotor is p, the equation (1) becomes EQU Ta=a.sub.1 sin 2p.theta.. (2)
If p.theta. =.alpha., EQU Ta=a.sub.1 sin 2.alpha.. (3)
The equation (2) is a case represented by mechanical angle, and the equation (3) is a case represented by electrical angle. Description will hereinafter be made by the use of .alpha..
A curve Ta in FIG. 16 of the accompanying drawings represents the cogging torque acting between the stator yoke unit a and the rotor. On the other hand, the torque acting between the stator yoke unit b and the rotor is represented as ##EQU2## because the stator yoke unit b deviates in phase by 1/4 pitch relative to the stator yoke unit a. On the other hand, in terms of electrical angle, That is, in contrast with Ta, the sign has only changed. The curve Tb of FIG. 17 of the accompanying drawings represents the above equation with p as p =1.
Here, the cogging torque To as the stepping motor can be represented by the sum of cogging torques acting on the two stator yoke units a and b and the rotor and therefore is ##EQU3## The curve To of FIG. 16 shows the characteristic of the cogging torque when a.sub.1 &gt;b.sub.1, and the cogging torque To of the stepping motor does not differ from the cogging torque acting between a single stator yoke unit and the rotor, in the number and positions of the points at which the torque is zero, and the peak value thereof only becomes small. If a.sub.1 =b.sub.1, the cogging torque becomes zero. Also, if a.sub.1 and b.sub.1 can be controlled arbitrarily, the magnitude of the cogging torque can be set to any magnitude.
Consider now a case where deviation exists in the circumferential direction with respect to the rotor shaft 12, that is, a case where the stator yoke unit a and the stator yoke unit b are disposed with phase deviation of 1/4 pitch and the stator yoke unit b deviates from this position by an angle error .alpha.k (electrical angle).
Assuming that the position of the rotor when the point at which the center of the magnetic pole of the rotor and the center of the magnetic pole of the stator yoke unit coincide with each other is regarded as the reference angle .theta. (mechanical angle), and assuming that the magnitude of the torque produced in the stator yoke unit a is Tk and the magnitude of the torque produced in the stator yoke unit b is Tk+.DELTA.T, the cogging torque T1 acting on the two stator yoke units a and b and the rotor is represented as ##EQU4## and therefore, if it is resolved and put in order, the following is obtained: ##EQU5## But high-order components are not taken into consideration.
Usually, the cogging torque refers to the maximum value of the above equation and therefore, T1Max=-.sqroot..sub.(2Tksin.alpha.kcos.alpha.k) 2.sub.+(2TKsin.alpha.k+.DELTA.T) 2 is the cogging torque. Accordingly, the cogging torque has its magnitude determined by the angle error .alpha.k and the non-uniformity of the magnitude of the cogging torque between the stator yoke units.
Here, assuming that .DELTA.T =0 and examining the influence of only the angle error .alpha.k upon the production of the cogging torque, the maximum value of the cogging torque is T1Max=2Tksin.alpha.k and the influence is as shown in the table of FIG. 18 of the accompanying drawings In calculation, one period of the electrical angle has been calculated with respect to a mechanical angle of 30.degree., i.e., a case where the stator has twelve poles, and assuming that the deviation of the mechanical angle is .theta.k, 2k =12.theta.k. From this result, it is seen that if the two sets of stator yoke units are in a right position, no cogging will occur, but is the stator yoke units deviate by 0.5.degree., there will occur cogging corresponding to 20% of the magnitude of the cogging torque produced by one set of stators.
Description will now be made of the relation between the stationary position of the rotor and the position in which the cogging torque To is zero.
Generally, between the magnetic energy W by the rotor magnet of a stepping motor and the cogging torque, there is the following relation: ##EQU6## Thus, the magnetic energy W can be represented by ##EQU7##
FIG. 17 shows the relation between the magnetic energy of the above equation and the rotor position. Here, the rotor 13 tries to come to a standstill at a location whereat the magnetic energy is smallest and therefore, in the position of .alpha.=.pi./2, 3.pi./2 . . . . (2.sub.n-1).pi./2, the cogging torque becomes zero and thus, originally, the rotor tries to come to a standstill in this position, but since the magnetic energy W is high, the rotor becomes unstable and does not come to a standstill (the time when the rotor stably comes to a standstill is the time when frictional force is great). After all, it is in the position of .alpha.=0, .pi., 2.pi., . . . , n.pi. that the rotor stably comes to a standstill.
That is, the rotor stably comes to a standstill in a position in which the cogging torque curve changes from the negative to the positive, and the rotor does not stably come to a standstill in a position in which the cogging torque changes from the positive to the negative.
As is apparent from the foregoing description, the stationary position of the rotor of the stepping motor in a state in which the coil is not excited is .alpha.=0, .pi., 2.pi., . . . , n.pi. (n being an integer).
The operation when the rotor rotates by an amount corresponding to one pitch of the stator poles when the coils of the stepping motor shown in FIG. 12 are excited as shown in FIG. 13 will now be described with reference to the developed view of FIG. 14a showing the stator poles and rotor magnetic poles of the stepping motor.
As already described, when the coils are not excited, the rotor 13 is in the position of .alpha.=0. When the phase A and phase B are subsequently excited, the magnetic poles 13a come to the position of 1/8 pitch intermediate of the stator poles 1a, 1a, i.e., the position of .alpha.=.pi./4. In the next phase B and phase A, the magnetic poles come to the position of 3/8 pitch intermediate of 1/2 pitch and 1/4 pitch (.alpha.=3.pi./4). In the next phase A and phase B, the magnetic poles come to the position of 5/8 pitch intermediate of 1/2 pitch and 3/4 pitch (.alpha.=5.pi./4). In the next phase B and phase A, the magnetic poles come to the position of 7/8 pitch intermediate of 3/4 pitch and 1 pitch (.alpha.=7.pi./4). Subsequently, in the phase A and phase B, the same thing as the beginning is repeated.
In a stepping motor wherein two yoke members each provided with a plurality of pole teeth parallel to a rotor shaft on the inner surface thereof are combined into one pair and which has two pairs of yokes, welding and fixing each pair of yokes when assembling the yokes is described and shown in Japanese Laid-Open Patent Application No. 59-53079.
The stationary angle error of the rotor in the excited condition of the coils of the stepping motor will now be described with reference to FIG. 14b. In this figure, the solid line shows the cogging torque To =(a.sub.1 -b.sub.1) sin 2.alpha., and the plus side which is the upper half of the torque of the vertical axis is a torque for returning the rotor with respect to the direction of movement of the rotor, and the minus side which is the lower half is a torque for advancing the rotor.
In the non-excited condition, the rotor is stationary in the position of .alpha.=0.
Now, since the first step of excitation excites the phases A and B, the exciting torque of dotted line 19 acts and tries to advance the rotor 13 to the position of .alpha.=.pi./4 in which the exciting torque is zero. On the other hand, in the position of .alpha.=.pi./4, a cogging torque which is a.sub.1 -b.sub.1 is acting. This cogging torque acts in a direction to return the rotor to the position of .alpha.=0 and therefore, after all, the rotor comes to a standstill in a position wherein the torque which returns the rotor by the cogging torque and the torque which advances the rotor by the torque exciting the phases A and B are balanced with each other. This position is the position of .alpha.=.alpha.1 in FIG. 14b, and is on this side of the position of .alpha.=.pi./4 which is the stationary position of the rotor which should originally be obtained. At the second step, the phases A and B are excited, and the exciting torque of dotted line 20 acts and tries to advance the rotor to the position of .alpha.=3.pi./4 in which the exciting torque is zero.
On the other hand, in the position of .alpha.=3.pi./4, a cogging torque which is -(a.sub.1 -b.sub.1) acts. This cogging torque acts in a direction to advance the rotor and therefore, after all, the rotor comes to a standstill in a position wherein the torque which advances the rotor by the cogging torque and the torque which returns the rotor by the torque exciting the phases A and B are balanced with each other. This position is the position of .alpha.=.alpha.2 in FIG. 14b, and is advanced with respect to the position of .alpha.=3.pi./4 which is the stationary position of the rotor which should originally be obtained.
At the next third steps, the same thing as the first step happens and the rotor comes to a standstill in a position .alpha.3 which is on this side of the position of .alpha.=5.pi./4 which is the original stationary position of the rotor. Further, at the fourth step, the same thing as the second step happens and the rotor comes to a standstill in a position .alpha.4 advanced with respect to the position of .alpha.=7.pi./4 which is the original stationary position of the rotor. If the angle error of the rotor relative to the position which should originally be obtained is plotted on the vertical axis and the number of steps of the stepping motor is plotted on the horizontal axis, there is obtained the characteristic of FIG. 14c of the accompanying drawings. In the case of the two-phase excitation system, usually the angle error of the rotor has its sign reversed at each step. That is, the amount of angular movement of the rotor changes to small, great and small at each step, and this has led to the important disadvantage that a uniform accurate amount of movement is not obtained.
Also, in the rotating condition of the motor, the fluctuation of the cogging torque can be regarded as the fluctuation of an extraneous load applied to the motor, and this has also led to the disadvantage that when an attempt is made to utilize the stepping motor as a multipole brushless DC motor, it is difficult to drive the motor smoothly so that there occurs no fluctuation of the number of rotations, by speed control in a state in which these load fluctuations corresponding to one half of the number of excitation change-overs exist during one full rotation.
As regards a motor of small cogging torque, there has been the disadvantage that where the motor is used for positioning or the like, when the driving current of the motor is cut off, the retained torque is small and therefore the set position is liable to deviate due to external factors.