§01 magnetism Iron runner

   One A small plastic toy will make people feel very magical , It consists of three discs . One of the discs is evenly embedded 16 A small round magnet , Their magnetic poles are staggered .

   The other is evenly embedded with four large round magnets , Their magnetic polarity They are also staggered .

   The plastic disc in the middle is fixed on the base , Fix it evenly 10 individual Iron nut . Then use a metal shaft to fix the three discs together . The disks on both sides can rotate .

   The following is the most magical phenomenon , You move a gear , You will find that the gear on the other side rotates in the opposite direction . The ratio of the rotation speed of the two gears is exactly equal to the reciprocal ratio of the number of embedded magnets . Inlaid with 16 A small magnet wheel rotates for a circle , The wheel inlaid with four magnets rotates around .

   This kind of magnet gear has the maximum magnetic moment due to interaction , So it has a natural locked rotor saturation effect , Similarly, there is no contact , There will be no wear , No lubrication required . In wind power generators 、 This kind of magnetic variable speed gear has been applied in inertial energy storage equipment .

§02 work How it works

   that So how to explain the working principle of magnetic variable speed gear ？ A relatively simple method can be explained by the signal sampling theorem .

   For convenience , Through coordinate transformation , Arrange the position of the magnet according to the angle , Form a straight line . Because the circumference is circular , This array of magnets changes from 0 Increase to form periodic arrangement structure .

   Because the arrangement of magnets is magnetic polarity, the polarity is wrong , Therefore, the magnetic field intensity in front of the magnetic pole fluctuates . For the sake of simplicity , We assume that this fluctuation presents a sinusoidal signal change , Inlaid with 16 The turntable of a small magnet fluctuates eight times a week , We remember that the spatial fluctuation frequency is 8Hz, Then there is 4 The magnetic field fluctuation frequency of the turntable of a large magnet is 2Hz.

   Here we are , We still don't know the function of the intermediate iron nut . Because the iron nut has strong magnetic conductivity , So we can regard nut as discrete sampling of magnetic field , The nut has 10 individual , So the spatial sampling frequency is 10Hz.

   Next, let's assume that the large magnet rotary table is pushed to rotate forward , Then its magnetic field is sampled by the nut , Whether the ten discrete magnetic field signals generated above will push the small magnet turntable to rotate in the opposite direction ？

   Intuitively , If you push the small magnet to rotate in the opposite direction , There is a magnetic field component in the magnetic field corresponding to ten nuts , Its spatial frequency is also 8 Hz, Angular velocity is negative （ reverse ）, Only in this way can the small magnet turntable be attracted to rotate in the opposite direction .

   therefore , The question becomes ： For a frequency of 2Hz The signal of , use 10Hz In the discrete signal obtained by sampling frequency , Is there a The frequency is -8Hz The signal ？ Be careful , The negative frequency here can be understood as the spatial angular velocity is in the opposite direction .

   For in Signals and systems For those who have studied signal sampling and recovery in this course , The above conclusion is obvious . As shown in the figure below ： original 2Hz The signal of , after 10Hz After sampling , The discrete signal formed is the left and right periodic extension of the original signal spectrum , The extension period is 10Hz.

   In the spectrum after periodic extension , You can see stay ±8Hz Presence at means 8Hz Two spectral lines of sinusoidal signal . especially , This 8Hz The spectral line of is left blue and right red , With the original 2Hz The left and right spectral lines of are exactly opposite , It means that its corresponding frequency is negative , The rotation direction of the corresponding space is the same as the original 2Hz Space rotates in the opposite direction .

※ total    junction ※

   benefit Using the same method, it can also be analyzed that the large magnet disk will also feel the magnetic field from the small magnet disk after sampling 2Hz The magnetic field in the opposite direction , You can try to analyze . Through this analysis , It can be seen that the existence of the intermediate nut is essential .

   Using the method of signal spectrum analysis , It makes it easier for us to see its internal essence through complex phenomena .

● Related chart Links :

• chart 1.1 The embedded 16 A small magnet disk
• chart 1.2 A disc with four large magnets embedded
• chart 1.3 The embedded 10 A disc of iron nuts
• chart 1.4 The two magnet gears will reverse
• chart 1.5 Magnetic variable speed gear
• chart 2.1 Arrange the magnetic poles in a straight line along the circumferential angle
• chart 2.2 The magnetic field intensity signal above the magnetic pole is equivalent to sinusoidal wave
• chart 2.4 The magnetic field signal that drives the small magnet turntable to rotate
• chart 2.5 Bilateral spectrum of magnetic field sampling signal