Electro-mechanical converters are key driving components of electro-hydraulic proportional control elements. They can continuously and proportionally convert externally input voltage signals into reciprocating linear displacements, generate 2.5 times the electromagnetic force of structures of the same size, and have attracted widespread attention due to their high linearity and low hysteresis characteristics.
In traditional coil assemblies, eddy currents easily form within the magnetic material during movement, reducing the electromagnetic force generated by the coil. Furthermore, the inherent characteristics of the coil assembly limit its response time and speed. Developing electro-mechanical converters with high response and high thrust is a growing trend in electro-hydraulic proportional control technology. Many scholars and research institutions both domestically and internationally have conducted research in this area. This paper focuses on current-carrying coils, employing a novel coil segmentation method and comparing it with series-parallel combinations. By altering the resistance and time constant to reduce the loading response time at both ends of the coil, the response characteristics and output electromagnetic force of the moving-coil electro-mechanical converter can be significantly improved.
Structure and Principle
The proposed moving-coil electromechanical converter mainly consists of a permanent magnet, a current-carrying coil, a thrust coil frame, an armature, a housing, a guide pin, a protective cover, and an output shaft, as 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 within the ring-shaped permanent magnets and is fixed to one end of the housing with screws. The current-carrying coil is wound around the thrust coil frame and connected to the output shaft. It floats in the air gap between the permanent magnets and the armature via a guide pin and is isolated from the outside environment by a sealing bowl.
1 – Permanent magnet; 2 – Housing; 3 – Screw; 4 – Armature; 5 – Terminal; 6 – Coil;
7 – Protective cover; 8 – Coil frame; 9 – Sealing bowl; 10 – Output shaft; 11 – Guide pin
Figure 1. Structure diagram of a moving-coil linear motor
The control principle is shown in Figure 2. The input signal voltage ui is processed by an amplifier and then applied to the control coil. Together with the thrust coil frame, it is subjected to an electromagnetic force Fcd in the constant magnetic field provided by the permanent magnet, resulting in a displacement xc, which in turn drives the output shaft to move. The moving 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 ui as a correction voltage ue to ensure that the moving 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.
Figure 2 Control principle of electromechanical converter
Coil group design
Currently, the commonly used coil winding method is the single-coil type, which has limited improvement in response speed and electromagnetic thrust, making it difficult to meet the current requirements for energy conservation, environmental protection, high efficiency, and speed. This paper proposes dividing the original coil into multiple equal segments to form a parallel coil assembly, which can significantly reduce coil energy consumption and meet the requirements for high output force and high-frequency response.
With a constant input current I in a single coil, the response time t of the electromagnet is:
t=-T1n（1-RI/U） (1)
Where I is the current (A); U is the voltage (V); R is the coil resistance (Ω); L is the coil inductance (H); and T = L/R is the time constant (s).
Since the resistance and inductance of the coil affect the time constant and current magnitude of the entire circuit when the input voltage is constant, the output force and response time of the electromechanical converter can be adjusted by changing the resistance and inductance.
By analyzing the relationship between coil size and coil impedance, it can be seen that coil inductance is directly proportional to the length, diameter, and square of the number of turns of the motor coil (winding part). To achieve high response, coil inductance must be reduced during the design phase.
Inductance Li represents the inherent characteristic of the coil itself and is independent of the current magnitude. Its expression is as follows:
Li=CiN2Dix10-3 (2)
Where Ci is a coefficient, which is related to the length li and diameter Di of the coil (wound part); Nc is the number of turns of the coil; and Di is the diameter of the coil, in meters.
By dividing a long coil into a short coil group, while keeping the motor size parameters constant, the coil resistance value and electrical time constant are adjusted by changing the number of turns of the coil.
The motor control circuit board drives the motor via input control signals to control the connection and disconnection of electronic switches S1, S2, S3, and S4 in the series and parallel circuits, thereby realizing the series and parallel operation of the combined coils. Figure 3 shows an analysis of the inductance L and resistance R of the coils in the entire circuit after switching of this electromechanical converter device.
Figure 3 Schematic diagram of coil circuit
In a series circuit, as shown in Figure 3(a) under series conditions, assume:
①S1 circuit: Switches K1, K2, K3, and K4 are closed; inductor LS1; resistor RS1.
②S2 circuit: Switches K1, K3, and K4 are closed, K2 is open, inductor LS2, resistor RS2;
③S3 circuit: Switches K1 and K4 are closed, K2 and K3 are open, inductor LS3, resistor RS3;
④S4 circuit: Switch K1 is closed, K2, K3, and K4 are open, inductor LS4, resistor RS4;
In a series configuration using parallel winding, the coupling coefficient between the two coil groups is 1. The inductance L and resistance R of the series coil groups are respectively:
(3)
In a parallel circuit, as shown in Figure 3(b) under parallel conditions, assume:
①P1 circuit: switch K1 is closed, switches K2, K3, and K4 are open, inductor LP1, resistor RP1;
②P2 circuit: Switches K1 and K2 are closed, switches K3 and K4 are open, inductor LP2, resistor RP2;
③P3 circuit: Switches K1, K2, and K3 are closed, switch K4 is open, inductor LP3, resistor RP3;
④ P4 circuit: Switches K1, K2, K3, and K4 are closed; inductor LP4; resistor RP4.
Figure 4. Transfer function flowchart
In a parallel environment using a parallel winding method, neglecting mutual inductance, the inductance L and resistance R of the coil group are respectively:
(4)
The impedance of a coil assembly connected in series increases after being divided into equal parts, while the impedance of a coil assembly connected in parallel decreases.
Modeling and Simulation of Step Response Analysis
Within the working air gap, based on the force experienced by the current-carrying control coil in a uniform magnetic field, the no-load force characteristics of the moving coil assembly can be obtained as follows:
(7)
Where Ki is the current gain coefficient (N/A); i is the coil current (A); Bg is the air gap magnetic flux density (T); Dc is the average diameter of the coil (m); and Nc is the number of turns of the coil winding.
Given that, by combining formula (5), we can obtain:
(8)
In series connection:
(9)
Parallel connection:
(10)
Where Di is the diameter of the i-th coil assembly; ρ is the resistivity of the coil assembly; and A is the cross-sectional area of the conductor of the coil assembly. Combining the above formula, the transfer function block diagram shown in Figure 4 can be established. A voltage U = 1V is applied to both ends of the four series-connected coil groups, and the characteristic curves of each coil group are obtained through MATLAB simulation. Figure 5 shows the voltage variation curves across the four series-connected coil groups over time, where tr is the time when the response reaches its maximum value: tr1 = 1.02ms, tr2 = 2.03ms, tr3 = 3.06ms, and tr4 = 4.21ms. Among them, S1 has the fastest response speed, and S4 has the slowest response speed, but both eventually reach the same steady state and remain unchanged.
Figure 5 shows the voltage variation curves across the series coil group.
Figure 6 shows the Ampere force variation curves of four series coil groups with different series connection structures over time. As can be seen from the figure, the Ampere force F(t) of the four series coil groups exhibits different rate changes. Specifically, at tr1 = 1.02 ms, F1 = 17.2 N, F2 = 16.6 N, F3 = 15.2 N, and F4 = 13.6 N. It is evident that S1 has the fastest response speed, while S4 has the slowest, but ultimately all four series structures essentially reach a maximum value of 17.3 N.
Figure 6. Electromagnetic force variation curve of series coil group
Figure 7 shows the acceleration response a(t) of four series coil groups as a function of time. As can be seen from the figure, S1 has the fastest response speed, reaching an acceleration value of 1.72g (1.02ms); S4 has the slowest response speed, eventually reaching a steady state and maintaining it at around 1.73g (3.06ms). Specifically, when tr1 = 1.02ms, a1 = 1.72g, a2 = 1.66g, a3 = 1.52g, and a4 = 1.36g, which is consistent with the analysis results in Figure 6.
Figure 7. Acceleration variation curve of the series coil group
Similarly, the characteristic curves of their respective parallel coil groups were obtained. The voltage U(t) across the parallel coil groups of the four structures varied with time. Within the allowable error range (less than 0.2×10－3s), the curves of voltage change with response time of the four different parallel coil groups were fitted, and their rise time tr was basically consistent with the response time curve of a single coil group.
in conclusion
With the response time remaining constant, in a series environment, the current-carrying response time of a uniformly segmented coil assembly increases by approximately three times when the number of coil assemblies in series increases from one to four. In a parallel environment, the number of parallel coil assemblies increases to four, the total resistance decreases, the length of the resistance coil increases, and the current increases. With the coil loading response speed being basically the same as that of a single-turn coil assembly, theoretically, the electromagnetic force increases to 16 times the original, and the acceleration reaches 27.64g, which can achieve high response characteristics and high thrust control effect.
