Many scholars and research institutions both domestically and internationally have studied moving-coil linear motors, but most research has focused on the structure and materials of permanent magnets, optimization of the overall motor structure, and the design of control circuits and chips incorporating efficient control strategies. However, research on the power-to-force ratio and the time delay from start-up to steady state is still limited. This paper delves into these aspects in depth.
Moving-coil linear motors can continuously and proportionally convert externally input voltage signals into reciprocating linear displacement, generating approximately 2.5 times the electromagnetic force of a structure of the same size. They have attracted widespread attention due to their high linearity and low hysteresis characteristics. However, in traditional single-coil coil assemblies, eddy currents are easily generated within the magnetic material during operation, reducing the electromagnetic force produced by the coil. Furthermore, the inherent impedance characteristics of the coil assembly limit its response time and speed. Developing moving-coil linear motors with high output electromagnetic force and high response is a development trend in the electrical engineering field.
To address this, this paper proposes a novel bidirectional reversible controllable moving-coil linear motor. A novel coil segmentation and parallel combination method is employed for its current-carrying coil. By changing the resistance and time constant, the loading response time at both ends of the coil is improved. A PWM pulse width modulation control method is used to control the magnitude and direction of the coil current. This not only achieves stable and disturbance-free motor switching control but also enables the device to achieve large electromagnetic force output and high-frequency response characteristics.
Structure and Principle
The structure of the moving-coil linear motor is shown in Figure 1. Several ring-shaped permanent magnets are fixedly connected to the circumference of the inner wall of the housing. The armature is located inside the ring-shaped permanent magnets and is fixed to one end of the housing with screws. The current-carrying coil is wound on the electromagnetic force coil frame and connected to the output shaft. It floats in the air gap between the permanent magnets and the armature through a guide pin and is isolated from the outside by a sealing bowl. A physical picture of this novel ring-shaped moving-coil linear motor is shown in Figure 2.
The control principle is shown in Figure 3. First, the input signal voltage ui is processed by an amplifier and then applied to the control coil. The current-carrying control coil, along with the electromagnetic force coil frame, is in a constant magnetic field provided by the permanent magnet and is subjected to the electromagnetic force Fcd, resulting in a displacement xc, which in turn drives the shaft core to move. The coil assembly's position error is detected by a displacement sensor and then converted into a signal voltage, which is used to compensate for the input signal ur as a correction voltage ue to ensure that the coil assembly remains in the required correct position. The magnitude and direction of the electromagnetic force depend on the magnitude and direction of the control current i in the coil. By changing the direction of the input voltage signal, the direction of the electromagnetic force Fcd is changed, thereby achieving bidirectional motion. In this way, the system is controlled by a closed loop, which also improves its control accuracy and response speed.
The electromagnetic force Fcd is always proportional to the armature current i, while the induced electromotive force E is always proportional to the mover velocity vc. These proportionality constants are called the electromagnetic force constant and the back electromotive force constant, respectively, and their values differ slightly. The armature reaction has a similar effect, approximately equal to the product of the air gap magnetic induction intensity Bg and the effective winding length la. Furthermore, it requires no commutation within its travel range, and the coil inductance remains essentially constant within the travel range; therefore, this moving-coil linear motor exhibits good controllability.
Composite coil design
The coil is a key component of a moving-coil linear motor, its main function being to convert electrical energy into mechanical energy. It is widely used in fields such as actuator control. Currently, the commonly used coil winding method is a single-coil combination, which has limited response speed and electromagnetic force, low conversion efficiency, and fails to meet current requirements for energy conservation, environmental protection, and high efficiency. This paper divides the original coil into multiple equal segments and connects them in parallel. This not only significantly reduces the weight and energy consumption of the coil and lowers material losses, but also meets the requirements for large electromagnetic force and high-frequency response.
Under the same voltage, a single-coil series circuit can reduce response time and increase response speed, but it is difficult to achieve a large electromagnetic force output. Only by maintaining the length of the coil acting in the magnetic field can the large electromagnetic force output of the device be guaranteed. This can be achieved by increasing the length of the energized coil in the circuit through parallel coil groups, without increasing the back electromotive force compared to a single coil group. Using uniformly divided parallel moving-coil coils can reduce the device's resistance and inductance, thus amplifying the current and significantly improving the electromagnetic force output; however, because its inductance is relatively small, it has little impact on the response of the moving-coil linear motor.
If the current is too large, the generated magnetic field will interact with the air gap magnetic field, causing nonlinear limitation of the magnetic field; if a large current is applied for a long time, the operating temperature will rise rapidly, leading to overheating and damage, and the operating time and life of the motor will be limited to a certain extent; the presence of coil inductance means that the operating current always easily reaches a steady state.
Figure 4 is a schematic diagram of three sets of coil circuits, with the following assumptions:
(1) In the circuit of group A shown in Figure 4(A), switch S1 is closed, and the inductance is LS1 and the resistance is RS1. It is called: the group A coil in series;
(2) In the circuit of group B shown in Figure 4(B), switches S1 and S3 are closed, and the inductor is LS2 and the resistor is RS2. It is called: a single-group group B coil;
(3) In the circuit of group C shown in Figure 4(C), switches S1, S2, and S3 are closed, and the inductor is LS3 and the resistor is RS3. It is called: the parallel group C coil;
In the formula: Inductance represents the inherent characteristic of the coil itself and is independent of the current magnitude. Its expression is as follows:
Since the input voltage is constant, the resistance and inductance of the coil affect the time constant and current magnitude of the entire circuit. With a constant input current I in a single coil, the response time t of the electromagnet is:
By analyzing the relationship between the moving coil size and the coil impedance, it can be seen that the coil inductance is directly proportional to the length, diameter, and square of the number of turns of the motor coil (winding part). In order to achieve high response, the coil inductance must be reduced during the design. The inductance L and resistance R of the coil group were measured using the DT-9935 LCR digital measuring instrument shown in Figure 5, as shown in Table 1.
The unique feature of the moving-coil linear motor described in this paper is that it increases the working time and response speed of the working coil by dividing the coil, and then uses PWM control to combine the coils in parallel to improve the electromagnetic force of the working coil. For the current-carrying coil, a new coil division and series/parallel combination method is adopted, and PWM pulse width modulation control is used to control the magnitude and direction of the coil current.
In the PWM control loop, the coil's cyclic operation is mainly controlled by using a D flip-flop to input a cyclic operation signal. The current magnitude is primarily controlled by pulse width modulation (PWM), i.e., by controlling the duty cycle of the control signal to control the current magnitude, thereby altering the magnitude of the electromagnetic force. Simultaneously, the control signal and the control pulse oscillation signal are used in a gate circuit to alternately turn on and off two corresponding driver transistors, controlling the transistors to output pulse width modulated pulses with a 180° phase difference, satisfying the frequency requirements of the entire device, as shown in Figure 6.
In this paper, to keep the motor size parameters constant, the long coil can be divided into short coil groups to change the number of turns and adjust the coil inductance and electrical time constant.
Modeling and Simulation
Within the working air gap, based on the force formula for the current-carrying control coil (moving coil) in a uniform magnetic field, the no-load force characteristics of the motor's moving coil assembly can be obtained as follows:
In the formula, Ki is the current-force gain of the moving-coil motor converter (N/A); i is the coil current (A); Bg is the air gap magnetic induction intensity (T); and la is the effective winding length of the coil (m).
The dynamic equation for the coil terminal voltage is: (4)
In the formula, u - coil terminal voltage (V); Ku - amplifier gain; ui - signal voltage (V); Rc - coil resistance (Ω); rp - amplifier internal resistance (Ω); L - coil inductance (H); Ke - coil velocity induced back electromotive force constant; E - induced electromotive force (V); vc - mover velocity (m/s); xc - coil assembly displacement (m).
With a stable input at both ends of the coil circuit, the dynamic equation of the coil assembly is:
In the formula, Mc is the mass of the coil assembly (kg); Bc is the viscous damping coefficient of the coil assembly (N·s/m); and Kc is the elastic damping coefficient of the coil assembly (N/m).
Combining formulas (3), (4), and (5), we obtain the relationship between the input voltage ur and the displacement xc.
Third-order transfer function:
By performing a Laplace transform on the above-mentioned dynamic equations of the motor, a block diagram of the transfer function of a moving-coil linear motor with signal voltage ur as input and coil assembly speed vc as output can be given, as shown in Figure 7.
Displacement step response analysis
From the transfer function block diagram shown in Figure 7, the mathematical model of the motor can be obtained as follows:
Using the parameters shown in Table 2, the dynamic step response curve of the motor displacement was obtained through MATLAB simulation analysis for equation (7), as shown in Figure 8.
As can be seen from Figure 8, for a unit step signal input, group A lines
After analysis, the dynamic step response curve of the motor displacement was obtained, as shown in Figure 8.
As shown in Figure 8, for a unit step signal input, the displacement amplitude changes of coils A and B are relatively small, eventually stabilizing at 0.8 mm, with rise times tr of 26.6 ms and 14.6 ms respectively. The amplitude change of the parallel coil C is relatively large, eventually stabilizing at 7.5 mm, with a rise time tr of 0.112 s. Under unit signal control, when the displacement Xc of coil C is 1 mm, tXc = 9.94 ms. Therefore, under unit signal control, using parallel coils can improve the displacement characteristics, reducing the response time to 9.94 ms.
in conclusion
Under the same voltage conditions, compared with series connection of moving coil components, a single moving coil assembly has lower circuit resistance and inductance, which can reduce response time and improve response speed, but it is difficult to achieve a large electromagnetic force output. Only by maintaining the length of the coil acting in the magnetic field can the large electromagnetic force of the device be guaranteed. Increasing the length of the energized coil in the circuit by connecting coil groups in parallel increases the electromagnetic force without increasing the back electromotive force compared to a single coil. This paper verifies that by using a parallel design, the time for a uniformly segmented coil assembly to reach a displacement step response of approximately 1 mm is reduced from more than 14.6 ms to less than 9.94 ms, more than doubling the response speed; the electromagnetic force increases from 10.8 N to 93.2 N, and the acceleration is also increased eightfold. Combined with PWM control, higher frequency response control can be achieved, reducing the response time to reach the maximum electromagnetic force to 0.688 ms, greatly improving the high-frequency response characteristics of the entire device and achieving the characteristics of short output displacement response time and large electromagnetic force. This moving-coil linear motor can be widely used in various automatic control systems that require high response speed, such as direct-drive CNC products, and has a promising future.
By Luo Liangwei, Zhang Gong, Liang Jimin, Wang Weijun, Xu Zheng, Gu Xing, Guo Yunpeng, and Liang Songsong, Guangzhou Institute of Advanced Technology, Chinese Academy of Sciences; School of Mechanical and Electrical Engineering, Guangdong University of Technology; and Shenzhen Institutes of Advanced Technology
