Abstract: This paper presents a topology for an axial permanent magnet vernier motor with low-speed, high-torque characteristics for a small direct-drive system driven by a lens. This structure employs a toroidal permanent magnet and concentrated windings to accommodate limited motor installation space and torque output requirements. The design utilizes an analytical model of the permanent magnet motor's magnetic circuit and finite element analysis to evaluate and compare the motor's main steady-state characteristics, verifying the proposed motor's operating characteristics at low speeds of 0-100 rpm. This provides a basis and experience for the design of this type of motor.
1 Introduction
In lens drive systems, the following categories are generally classified according to the installation position of the drive motor: body drive type, lens drive type and body-lens dual drive type. Among them, the lens drive type (the type in which the drive motor is directly installed in the lens) reduces the setting of reducer and flexible linkage mechanism. Its motor performance is generally superior to that of the body drive motor, but it requires the use of a direct drive motor that can achieve low speed and high torque. At present, most direct drive applications achieve low speed and high torque drive through reduction device. Although the traditional precision speed change device is relatively mature, it is usually large in size, noisy and inefficient. Therefore, a low speed and high torque direct drive motor that does not require a speed change device is urgently needed [1]-[3]. Applying the direct drive motor to a small lens drive system can directly convert electromagnetic energy and mechanical energy, reducing energy loss. At the same time, the traditional electromagnetic motor can also learn from the mature motor control strategy and compare it with the ultrasonic motor [4] driver that uses piezoelectric ceramics to achieve precise and stable control of the motor.
The permanent magnet vernier motor is a popular axial magnetic field type permanent magnet synchronous direct drive motor. Due to its multi-pole design, it has the characteristics of a low-speed, high-torque "magnetic gear" [5]-[6], which overcomes many shortcomings of the traditional permanent magnet synchronous motor in direct drive applications and has good application and research prospects. The mechanism of the vernier motor is more complex than that of the traditional permanent magnet motor, but its unique design principle allows it to have low-speed, high-torque characteristics without relying on reduction gears, so it is widely used in direct drive systems. Although the permanent magnet vernier motor is still lagging behind the magnetic gear composite motor in terms of torque density, the amount of permanent magnets used is reduced by nearly half, and the torque density is greatly improved compared with the traditional permanent magnet motor. At the same time, reasonable pole number design and tooth slot optimization can make the high torque characteristics of the vernier motor reach the optimal level, and the disc axial air gap magnetic field design of the same power level can further reduce the motor volume and improve the torque density compared with the radial magnetic field design [7].
Therefore, this paper focuses on the application of small lens drive systems and, with reference to the existing installation method of ring ultrasonic motors, proposes a design scheme using an axial permanent magnet vernier motor structure. The steady-state characteristics of the motor in the low-speed region are evaluated by magnetic circuit analysis and three-dimensional finite element simulation. The paper explores and summarizes the operating characteristics and optimization schemes of low-speed, high-torque electromagnetic motors under such working conditions.
2 Motor Design and Analysis
2.1 Axial Permanent Magnet Motor Structure
The proposed axial permanent magnet vernier motor (Figure 1) features a parallel stator-rotor structure and an axial air gap magnetic field. Its main advantages include small size, light weight, good speed regulation performance, and high reliability, meeting the requirements of high-load lenses for drive motor installation size and high torque output. The motor's single-layer air gap is designed to be 0.3-0.5mm. The main structure consists of a stator and a rotor. The stator includes a stator core and windings, while the rotor includes a rotor core and a ring-shaped permanent magnet. To reduce eddy current losses in the magnetic circuit and improve motor efficiency, the core is generally made of cold-rolled silicon steel sheets. While silicon steel sheets for radial motors can be directly stamped, axial motors have an axial magnetic circuit in the core and cannot directly use pressed silicon steel sheets. Instead, the rolled-up thin layer of silicon steel is typically axially cut with the required toothed structure. Simultaneously, the ring-shaped permanent magnet design effectively reduces magnetic leakage, improves the air gap magnetic field strength and magnetic circuit utilization, and the reduced losses improve motor efficiency.
Table 1 lists the main parameter requirements for motor operation. When powered by battery, the average torque output should be higher than 200 gf.cm. At the same time, the vibration and noise during the focusing process should not be too large, which is quantified as the noise at the rated speed of 50 rpm being lower than 40 dB.
2.2 Equivalent Magnetic Circuit Analytical Method
To clearly describe the relationships between the parameters, Figure 2 shows a schematic cross-sectional view of the proposed axial motor and provides definitions for some of the motor parameters. Furthermore, for ease of analysis, the following basic assumptions are made:
1) The permeability of the stator and rotor cores is infinite;
2) The relative permeability of the permanent magnet is taken as its actual permeability, and the relative permeability of the air region between the poles of the permanent magnet is the same as that of the permanent magnet.
3) The analysis region is in a two-dimensional plane, and end effects are neglected;
4) The stator slots are radially open slots, and the current density is uniformly distributed on each coil side within the slot.
To solve for the magnetomotive force distribution of the unloaded air gap magnetic field, according to Ampere's circuital law, neglecting the magnetomotive force of the stator and rotor cores, the magnetic field lines loop in Figure 2 are used to obtain...
Where Fg is the air gap magnetomotive force, Fmag is the permanent magnet magnetomotive force, Br is the remanence of the permanent magnet, gm is the axial thickness of the permanent magnet, μm is the permeability of the permanent magnet, and g is the actual length of the air gap. The above magnetomotive forces are their respective fundamental amplitudes. Taking into full account the magnetic flux density distribution at different locations in the air gap magnetic field, the expression of the air gap magnetomotive force can be extended to:
Where Fg1 is the fundamental amplitude, θm represents the rotor position angle with the stator as a reference, θ represents the mechanical angle between a certain position on the stator and the reference axis, Zr is the number of permanent magnet pole pairs, and n represents the harmonic order of the air gap magnetomotive force. In surface-mounted permanent magnet motors, calculating the equivalent permeability of the air gap can be simplified to calculating the air gap permeability per unit area. The slotted structure is approximated as shown in Figure 3, where the air gap permeability is calculated in two parts: P0 (between the slotless surface and the rotor) and P1 (between the slotted surface and the rotor). The derivation of the equivalent permeability of the air gap per unit area is as follows:
Where P0 is the air gap permeability from the slotless surface of the stator to the rotor, P1 is the air gap permeability from the slotted surface of the stator to the rotor, Pm is the m-th harmonic component of the air gap permeability, μ0 is the vacuum permeability, b0 is the slot width, ts is the tooth pitch, m is the harmonic order, Zs is the number of stator slots, and j is the number of slots deviating from the short-pitch winding (j=0 in the full-pitch winding). ge is the equivalent length of the air gap. Since the permeability of the permanent magnet is close to the space and is surface-mounted, the permanent magnet can be treated as air when calculating the permeability. β is defined as a compensation coefficient [8], where the ratio of β to the slot width/air gap length has the relationship shown in Figure 4:
The air gap magnetic field strength BPM = P(θ)F(θ) gives the expressions for the back electromotive force e(t) and electromagnetic torque T(r).
Where λ is the flux linkage per phase, N is the number of coil turns, Dg is the average diameter of the air gap, l is the radial length of the air gap, ω is the mechanical angular velocity, α is the angle corresponding to the stator tooth pitch, kT is the motor torque coefficient, Irms is the effective value of the winding line current, Ri is the inner diameter of the air gap, Ro is the outer diameter of the air gap, and r represents the radius at a certain position in the air gap. Furthermore, to effectively improve the smoothness of motor operation, the cogging torque under this structure needs to be minimized to the greatest extent possible. The relationship between motor design parameters affecting the magnitude of the cogging torque is explored. Based on the analytical relationship of the above magnetic field parameters, the cogging torque can be expressed analytically as follows:
Where W represents the energy of the magnetic field generated by the permanent magnet in the main air gap when unloaded.
2.3 Three-dimensional finite element simulation and comparison
During motor operation, there is a magnetic field generated by both the permanent magnet and the armature current. Figure 5 shows the magnetic field strength distribution after the armature is energized. The maximum magnetic field strength is around 1.7T. There is no risk of core saturation, and a certain overload operation is allowed, which meets the motor design requirements.
Figure 6 compares and analyzes the steady-state characteristics of the axial permanent magnet vernier motor at 50 rpm obtained by the magnetic circuit analysis method and the three-dimensional finite element simulation method. The figures show the electromagnetic torque curve, no-load back EMF curve and its harmonic analysis, and cogging torque curve and its harmonic analysis. In the equivalent magnetic circuit method, the motor and material parameters in the spatial dimension are constant, therefore the electromagnetic torque calculated by the numerical relationship is a constant value, as shown in Figure 6(a). However, the equivalent magnetic circuit method cannot set the BH curve characteristics of the core material and infinite harmonic orders, thus failing to reflect the magnetic circuit saturation characteristics. The resulting back EMF waveform is more idealized and sinusoidal than that obtained by the finite element method, as shown in Figure 6(b).
Table 2 summarizes the comparison of the steady-state performance of the motor obtained by the magnetic circuit analysis method and the three-dimensional finite element analysis method. Due to the generation of magnetic saturation effect, the effective value of the no-load back electromotive force of the two methods differs by 7.6%, and the average value of the electromagnetic torque differs by 1.5%. In both sets of results, the peak-to-peak value of the cogging torque is lower than 7.5% of the average electromagnetic torque, indicating that the magnetic circuit analysis method has little deviation in evaluating the motor performance, and the accuracy can be improved by setting more compensation coefficients.
3. Conclusion
This paper focuses on the application of small direct drive systems and designs an axial permanent magnet vernier motor that meets the requirements for lens installation. The motor is analyzed by finite element method (FEM) calculation from aspects such as magnetic field distribution, back electromotive force, cogging torque, electromagnetic torque, and torque fluctuation. The results are compared with analytical modeling results to illustrate the steady-state characteristics of the motor and verify the reliability of the magnetic circuit analytical model, providing a basis and experience for the design of this type of motor.
