Analysis of Magnetic Circuit Structure of Magnetic Suspension Bearing and Method of Establishing Mathematical Model
Abstract: The composition and working principle of the magnetic suspension bearing system are introduced, and the magnetic suspension bearing is compared and analyzed from the properties of the control current, the controlled degrees of freedom, the way of generating the suspension force, the way of the acting force, and the arrangement of the magnetic poles. The method and steps for establishing the mathematical model of the levitation force of the magnetic suspension bearing based on the equivalent magnetic circuit method provide a reference for the design of the magnetic circuit structure of this type of bearing and the establishment of the mathematical model.
Magnetic bearing is a new type of bearing that utilizes magnetic field force to levitate the rotor without contact and the levitating position can be controlled by the control system. Compared with traditional bearings, magnetic bearing has many advantages such as no friction and wear, no lubrication, high speed, high precision and long life, and is widely used in machinery industry, aerospace, robotics, computer, energy transportation and life sciences and other fields . Analyzing the magnetic circuit structure and establishing the mathematical model of the levitation force is the key to designing a magnetic bearing system with excellent performance.
1 The composition of the magnetic bearing system and its working principle
A complete magnetic suspension bearing system consists of rotor, electromagnet, controller, power amplifier, displacement detection circuit with displacement sensor, etc. [2-3]. Figure 1 shows the composition and working principle of the single-degree-of-freedom active DC magnetic bearing differential control system. The magnetic suspension bearing system is controlled by 2 electromagnets with 1 degree of freedom. The bias current of the electromagnet is i0. Assuming that the rotor is disturbed and deviated from the equilibrium position by a small distance x0, the sensor detects x0, and the position controller will This displacement is transformed into a control signal id, and the control current ic+=i0+id of the electromagnet a is obtained by driving the power amplifier. As the control current increases, the air-gap magnetic flux increases, so the magnetic attraction force Fm+ generated by the electromagnet a increases; similarly, the control current ic-=i0-id of the electromagnet b, because the control current decreases, the air-gap magnetic flux decreases Therefore, the magnetic attraction force Fm- generated by the electromagnet b decreases, and the resultant force Fres=Fm+-Fm- on the rotor is directed upward, so that the rotor returns to the equilibrium position, and the current id=0 at this time. Similarly, when the rotor is deflected upwards, the 2 electromagnets will generate a downward synthetic levitation suction, returning the rotor to the equilibrium position.
2 Classification and characteristics of magnetic suspension bearings
2.1 Classification according to the nature of control current
According to the nature of the control current, magnetic bearings can be divided into DC magnetic bearings and AC magnetic bearings. The DC maglev bearing uses a DC power amplifier for power drive, and at least one bipolar DC power amplifier or two unipolar DC power amplifiers are required for one degree of freedom. The AC maglev bearing adopts AC power inverter for power drive [4-5]. Due to the high price, large size and high power consumption of the DC power amplifier, and the mature technology, low price and low power consumption of the AC power inverter, the AC magnetic bearing can use the AC power inverter.
2.2 Classification by controlled degrees of freedom
According to the controlled degrees of freedom imposed by the magnetic bearing on the suspended rotor, it can be divided into axial single-degree-of-freedom magnetic bearing, radial two-degree-of-freedom magnetic bearing and radial-axial three-degree-of-freedom magnetic bearing [3,6]. The axial single-degree-of-freedom magnetic suspension bearing mainly realizes the stable control of the rotor in the axial direction; the radial two-degree-of-freedom magnetic suspension bearing mainly realizes the suspension stability control of two radial degrees of freedom at one end of the rotating main shaft; the radial-axial three-degree-of-freedom magnetic suspension The bearing integrates an axial single-degree-of-freedom magnetic suspension bearing and a radial two-degree-of-freedom magnetic suspension bearing. Different combinations of the above types of magnetic suspension bearings can form a four-degree-of-freedom magnetic suspension support system and a five-degree-of-freedom magnetic suspension support system. The four-degree-of-freedom magnetic suspension support system consists of two radial two-degree-of-freedom magnetic suspension bearings, and the five-degree-of-freedom magnetic suspension support system consists of two radial two-degree-of-freedom magnetic suspension bearings plus an axial single-degree-of-freedom magnetic suspension bearing or a radial two-degree-of-freedom magnetic suspension bearing. The degree of freedom magnetic suspension bearing is composed of a radial-axial three-degree-of-freedom magnetic suspension bearing.
2.3 Classification according to the way of generating suspension force
According to the way of electromagnetic force generation, it can be divided into active magnetic bearing, passive magnetic bearing and hybrid magnetic bearing [1,6].
(1) Active magnetic suspension bearing, also known as electromagnetic suspension bearing, the suspension force is all generated by the control coil, the position of the rotor is detected by the displacement detection system, and then the control system performs active control to realize the stable suspension of the rotor.
(2) Passive magnetic suspension bearing, also known as permanent magnetic suspension bearing, the suspension force is only generated by permanent magnets or superconductors, and is equipped with auxiliary mechanical devices to realize the support and control of the rotor.
(3) Hybrid magnetic suspension bearing, also known as permanent magnetic and electromagnetic hybrid magnetic suspension bearing, its mechanical structure includes permanent magnet or superconductor and control coil, permanent magnet or superconductor is used to provide static bias magnetic flux, when the rotor is subjected to external disturbance or When under load, the control magnetic flux required to return the rotor to the equilibrium position is generated by the control coil, which has the advantages of passive magnetic suspension bearing to provide static suspension force and active control when it is disturbed.
2.4 Classification by force
According to the acting force, it can be divided into attraction type and repulsion type. Attractive type uses the principle of “opposites attract each other”, and repulsive type uses the principle of “same-sex repulsion”. The maglev trains designed by Germany are based on the Attractive Suspension System (EMS), while those represented by Japan use the Repulsive Suspension System (EDS). The “normally conductive magnetic suction type” is also an attractive type.
2.5 Classification by magnetic pole arrangement
According to the magnetic pole arrangement, it can be divided into homopolar magnetic bearing (HeteropolarMagneticBearing) and heteropolar magnetic bearing (HomopolarMagneticBearing) . The magnetic flux circuit of the homopolar magnetic suspension bearing is perpendicular to the axis of the rotor, while the magnetic flux circuit of the heteropolar magnetic suspension bearing is parallel to the axis of the rotor. The homopolar magnetic bearing has high precision, small axial size, large levitation force, small eddy current loss, and the disadvantage is that the hysteresis loss is large; the main feature of the heteropolar magnetic bearing is that the rotor always rotates under the same magnetic field polarity, and the magnetic hysteresis The loss is small, and the disadvantage is that the axial size is large and the space utilization rate is low.
2.6 Other categories
In addition, according to the contact mode, it can be divided into complete non-contact type and partial contact type; according to the structure, it can be divided into vertical type, horizontal type, inner rotor type and outer rotor type.
3 Magnetic circuit structure analysis
3.1 Single-degree-of-freedom magnetic bearing
Figure 2a shows a schematic diagram of the magnetic circuit structure of a single-degree-of-freedom active magnetic suspension bearing, which consists of a stator, a suction disk, a control coil and a rotating shaft. Magnetic circuit. When the control coil is energized, the control current is adjusted to make the electromagnet generate a controllable magnetic flux, so as to adjust the size of the left and right magnetic attraction of the suction plate, and the suction plate is suspended in the middle equilibrium position under the action of the left and right magnetic attraction . Figure 2b shows a schematic diagram of the magnetic circuit structure of a single-degree-of-freedom hybrid magnetic suspension bearing , which is mainly composed of a stator, a permanent magnet ring, a control coil, a rotor and a rotating shaft. The radially magnetized permanent magnet ring is used to provide static bias magnetic flux. When there is no external disturbance or load, the rotor is only stably suspended in the equilibrium position under the action of the permanent magnet ring; when there is disturbance or load, the control coil current is adjusted , the control magnetic flux is superimposed with the static bias magnetic flux generated by the permanent magnet ring to generate the bearing capacity required to withstand disturbances or loads. The magnetic suspension bearing structure only relies on permanent magnets to generate bias magnetic flux, which greatly reduces the ampere-turns of the control coil, reduces the power consumption of the power amplifier, reduces the volume of the magnetic suspension bearing, and reduces the mass of the magnetic suspension bearing.
3.2 Radial two-degree-of-freedom magnetic bearing
Figure 3a shows the schematic diagram of the magnetic circuit structure of the DC radial two-degree-of-freedom active heteropolar magnetic suspension bearing . It consists of control coil, rotor and shaft. The magnetic flux generated after each pair of magnetic pole coils is energized forms a circuit through the stator, the air gap and the rotor. Figure 3b shows a schematic diagram of the magnetic circuit structure of a DC radial two-degree-of-freedom hybrid heteropolar magnetic suspension bearing . Three permanent magnets are embedded in three separated stator magnetic poles, and control coils are wound on the other three magnetic poles; A magnetic isolation aluminum block is used for magnetic isolation every 2 magnetic poles. Both the bias magnetic flux produced by the permanent magnet and the control magnetic flux produced by the control coil flow through each pair of magnetic poles to form a loop with the rotor.
Figure 3c shows the schematic diagram of the magnetic circuit structure of the DC radial two-degree-of-freedom hybrid homopolar monolithic quadrupole magnetic suspension bearing, which is composed of a stator (4 magnetic poles), an auxiliary stator, a permanent magnet and a laminated rotor. The control magnetic flux at the air gap and the bias magnetic flux provided by the permanent magnet are superimposed in one direction and subtracted in the opposite direction to generate a controllable levitation force . Figure 3d shows an AC radial two-degree-of-freedom active heteropolar magnetic suspension bearing . The three pairs of magnetic poles are evenly distributed along the circumference at 120° in space, which simplifies the structure of the magnetic suspension bearing with four pairs of magnetic poles. The biggest advantage of 3 pairs of magnetic poles is that 3 sets of coils can provide a three-phase AC excitation control current through a three-phase power inverter to generate a synthetic rotating magnetic field. Through the closed-loop control method of current and displacement feedback, the synthetic magnetic flux can be directed to the rotor. The position is shifted in the opposite direction, so that the radial suspension force can be generated to return the rotor to the equilibrium position, and the rotor can be supported at the equilibrium position, which can greatly reduce the cost and volume of the magnetic suspension bearing power amplifier.
3.3 Radial-axial three-degree-of-freedom magnetic suspension bearing Figure 4a shows a DC radial-axial three-degree-of-freedom hybrid magnetic suspension bearing , which consists of an axial stator, an axial control coil, a radial stator, and a radial control coil. , annular permanent magnet, rotor and shaft, etc. The annular permanent magnet provides axial and radial bias magnetic flux at the same time, and two axial coils and two radially opposite coils are connected in series as control coils for related degrees of freedom. The structure has the characteristics of compact structure and large bearing capacity; however, it needs 3 bipolar DC power amplifier circuits, and its power loss is relatively large.
Figure 4b shows the schematic diagram of the magnetic circuit structure of the AC-DC radial-axial three-degree-of-freedom hybrid magnetic suspension bearing . The axial direction is driven by a DC switching power amplifier, and the radial direction is driven by a three-phase inverter. The magnetized annular permanent magnet is provided with a static bias magnetic flux both axially and radially. This AC-DC three-degree-of-freedom hybrid magnetic bearing integrates the advantages of three-phase AC drive, permanent magnet bias and axial-radial joint control, reduces the volume of the magnetic bearing system, greatly reduces the loss of the power amplifier, and has the advantages of High efficiency and low cost.
Figure 4c shows the radial-axial three-degree-of-freedom tapered roller type magnetic suspension bearing structure. The rotor is made into a conical shape within the bearing range, and the magnetic force generated by the magnetic flux perpendicular to the conical surface can be decomposed into axial and radial Suspension force, thereby controlling the axial and radial degrees of freedom. Due to the mutual coupling between its degrees of freedom, the control difficulty is increased. In addition, the system has poor anti-interference performance, and the use of DC drive, the power amplifier is large in size, large in power consumption, and high in cost .
In summary, to design a magnetic suspension bearing system with better performance, the following aspects should be mainly studied.
(1) The hybrid magnetic suspension bearing that uses permanent magnets to provide static bias magnetic flux is small in size and has a large bearing capacity. When the magnetic suspension bearing system has no load or external disturbance, the magnetic suspension bearing can achieve stable suspension completely by relying on permanent magnets; The rare earth resources used to manufacture permanent magnets are abundant, so the permanent magnetic bias hybrid magnetic suspension bearing will be a research hotspot for a long time in the future.
(2) The AC magnetic bearing uses an AC power inverter to drive the control coil, and one AC power inverter can completely drive 2 degrees of freedom in the radial direction. Compared with the traditional DC magnetic bearing, its power loss is greatly reduced, and it can Effectively reduce the cost of the magnetic suspension bearing system, so the AC magnetic suspension bearing will receive more and more attention from domestic and foreign magnetic suspension bearing researchers.
(3) The three-degree-of-freedom hybrid magnetic bearing that integrates the axial and radial directions is more compact in structure than the traditional one radial two-degree-of-freedom magnetic bearing and one axial single-degree-of-freedom hybrid magnetic bearing , and will greatly reduce the volume of the magnetic suspension bearing, which is bound to become an important direction of future magnetic suspension bearing research.
(4) In some special fields, the magnetic suspension bearing needs to be rotated externally, which makes it necessary to study the outer rotor magnetic suspension bearing. The magnetic circuit structure design of the outer rotor magnetic suspension bearing will be a very important research direction. With this technology The research will expand the magnetic bearing technology to more application fields.
4 Build a mathematical model
At present, most of the methods for establishing the mathematical model of the levitation force of the magnetic bearing use the equivalent magnetic circuit method. The basic idea of the equivalent magnetic circuit method is to use the resistance to replace the magnetic permeability at each air gap and the iron core magnetic resistance, and use the electric field to represent the magnetic resistance of each air gap. The magnetic field produced by the coil and the magnetic field produced by the permanent magnet. Because the stator and rotor core of the magnetic suspension bearing are made of high magnetic permeability materials, which have the phenomenon of magnetic saturation and hysteresis, it is very difficult to carry out accurate mathematical analysis of the magnetic field of the magnetic suspension bearing. Considering that some factors have little influence on the system model, before establishing the mathematical model, in order to simplify the problem, the main factors should be considered, only the reluctance of the working air gap should be considered, and the magnetism of the stator and rotor cores of the magnetic suspension bearing is ignored. Resistance, hysteresis, eddy current loss and magnetic flux leakage, etc. [4-9]. The main steps of using the equivalent magnetic circuit method to establish the mathematical model of the levitation force of the magnetic bearing are as follows:
(1) According to the magnetic circuit generated by the magnetic suspension bearing, the equivalent magnetic circuit method is used to obtain its equivalent magnetic circuit diagram;
(2) According to the equivalent magnetic circuit diagram, the air gap permeability G at each suspended air gap is obtained;
(3) According to Kirchhoff’s law of magnetic circuit ∑F=0 and ∑Φi=0, solve the magnetic flux Φ of each branch;
Through the comparative analysis of the magnetic circuit structure and characteristics of various magnetic suspension bearings, the key research directions of magnetic suspension bearings are prospected, and the mathematical model of the magnetic suspension force mathematical model based on the equivalent magnetic circuit method is expounded. The research on its control system provides a reference.