Development of testing apparatus for investigating electromagnetic dynamics of contactors: A pilot study

Abstract

It is easy to find electromagnetic contactors in modern electromechanical devices owing to their advantages, which encompass a simple structure, ease of use, and low cost. However, these devices also have inherent drawbacks, including heat dissipation, contact erosion, and inefficient power consumption during long-term operation. This has sparked interest in contact soft-landing, which aims to reduce issues like contact bounces, contact welding, and arcing. This paper presents the development of a testing apparatus for investigating the electromagnetic dynamics of contactors or mechanical relays, aimed at developing an open-loop model-based controller for contact soft-landing. Theoretical equations based on physical theorems are derived to describe the behavior of the electromagnetic coil under varying factors. Additionally, a pilot study was conducted using the proposed testing apparatus to explore the relationship between heat dissipation, flowing current, air gap, and the Lorentz force produced by exposing ferromagnetic material to the magnetic field surrounding the electromagnetic coil. The experimental and simulation results showed good fitting, with a normalized root mean squared error ranging from 2.5% to 4.5% for various scenarios. Notably, it was found that the flowing current passing through the electromagnetic coil can be controlled by changing the duty cycle of the pulse width modulation signal driving the conductivity of the MOSFET. However, the results suggest that a modulation frequency greater than 5 kHz is not suitable for driving the electromagnetic coil.

Keywords:

• Electromagnet
• Lorentz force
• soft-landing
• electromagnetic contactor

Introduction

Electromagnetic contactors serve as essential components in various industrial applications, encompassing switches, protective circuits for high-power loads,^[1] motors, power distribution,^[2] electric heating resistors,^[3] and electric vehicle batteries.^[4] These contactors offer multiple advantages, such as ease of use, bidirectional current flow capability, isolation of the control stage from the power stage in electrical circuits, high current conduction, durability, and cost-effectiveness. However, these benefits are accompanied by inherent challenges that can impact contactors’ lifespan and operational quality, including contact erosion, arcing, heat generation, and safety concerns.^[5,6] Of particular concern are significant collisions leading to sparks and substantial heat generation, potentially resulting in material melting at contact points.^[7] As a result, research on soft landing has emerged as a vital area of interest, demanding a meticulous investigation to ensure enhanced efficiency.

To deal with this issue, the field of soft-landing research has seen numerous studies addressing the challenges associated with contactors.^[8,9] Some studies explore feedback mechanisms for controlling contactors,^[10,11] while others focus on closed-loop feedback systems,^[12–15] addressing magnetic flux intensity,^[16] energy control,^[17,18] speed regulation,^[19,20] and even sensorless closing control.^[21–23] However, implementing and analyzing such feedback systems can be complex, involving expensive sensors,^[24] simulation tools, and specialized circuit design.^[25,26] Furthermore, existing studies have not thoroughly investigated other relevant factors, such as heat dissipation, passage current in the electromagnetic coil, and Lorentz forces during soft landings.

This study takes a holistic approach to address these limitations, aiming to comprehensively analyze the factors influencing the Lorentz force of the electromagnet, which directly affects the soft-landing process. An innovative testing apparatus is developed to conduct experimental tests, exploring the influence of various factors on the electromagnet, including current control methods, modulation frequency, and the Lorentz force. These tests yield valuable insights into the interplay of these factors. In addition, simulation data based on a computational model of these factors is validated for accuracy and reliability by comparing it with experimental data using the normalized root mean squared error. Through pilot studies, an established equation is derived, describing the relationship between the Lorentz force produced by the electromagnetic coil and the applied voltage, controlled by the duty cycle in the form of pulse width modulation, which facilitates soft-landing research. The motivation for this paper lies in the novel insights gained from experimental investigations and the potential improvements in the performance and reliability of electromagnetic contactors, contributing to a deeper theoretical understanding of electromagnetic dynamics.

System architecture

Mechanical design

The ferromagnetic plate exposed electromagnet test apparatus is specifically designed to assess the relationship between distance, surface area, current intensity, and their impact on the Lorentz force. The apparatus operates on the principle of translational motion, utilizing a lead screw mechanism slider to adjust the distance between the ferromagnetic plate and the electromagnetic coil.

Figure 1 presents a comprehensive overview of the apparatus designed for experimental investigations of the electromagnetic contactor’s characteristics. The apparatus comprises a stationary electromagnet mounted on a base, which generates a magnetic field directed toward a ferromagnetic plate. The ferromagnetic plate is securely fixed to the head of a dynamometer, a specialized device capable of measuring the electromagnetic force within a range from 0 to 200 $N.$

Figure 1. Design structure of electromagnetic contactor testing apparatus.

To enable smooth and adjustable vertical translational movement, the dynamometer is bonded to a slider. This slider is guided by a screw and linear slide mechanism, allowing for a displacement range of 180 $\mathit{\text{mm}}.$ The translational motion can be manually regulated using a spoked handwheel. A potentiometer measures the displacement and distance between the ferromagnetic plate and the electromagnet. Once the initial position of the ferromagnetic plate is set, a handle screw is employed to fix the slider, ensuring stability during the measurement and recording processes conducted by the dynamometer.

Electrical design

The electrical block diagram is depicted in Figure 2, featuring a custom-designed microcontroller unit (MCU) with the ATMEGA2560 chip. The MCU emits digital control signals via pulse-width modulation (PWM) to regulate the MOSFET-based driver’s conductivity, precisely controlling the current in the electromagnetic coil. To assess the coil’s heating, a negative temperature coefficient (NTC) sensor is directly mounted on it and linked to the MCU's analog-to-digital interfaces. The potentiometer and a shunt resistor acting as a current sensor are both connected to a dedicated analog-to-digital (ADC) 12-bit resolution chip, establishing a connection with the MCU through the serial peripheral interface (SPI). The dynamometer records the Lorentz force produced by the electromagnet, and this device is communicated to the MCU using the universal asynchronous receiver/transmitter (UART) protocol. For data acquisition, the MCU connects to a personal computer (PC) via UART to USB conversion.

Figure 2. Electrical block diagram for the testing apparatus.

Delay compensation

The generation of a magnetic field by the electromagnetic coil is achieved through the flow of current, which is controlled by an N-channel MOSFET, as depicted in Figure 3. The MOSFET is driven by a PWM signal from the MCU to its gate. To dissipate the back electromotive force of the electromagnetic coil, a flyback diode is employed. This configuration allows for the precise adjustment of current flow in the electromagnetic coil by modulating the voltage applied to the MOSFET gate.

Figure 3. Schematic of MOSFET-based driver for switching the electromagnetic coil.

When transmitting the PWM signal into the MOSFET gate using a pulse generator, the waveform signal can be observed on an oscilloscope at both the MOSFET gate and drain, as depicted in Figure 4. Channel 1 represents the voltage level at the gate pin of the MOSFET, while channel 2 provides that of the drain pin. It is noticeable that the phase of the waveforms is reversed due to the inherent properties of the N-channel MOSFET, and there is a delay time of approximately 30 $\mathit{\text{ns}},$ resulting in a phase shift at the moment of logic transition. This delay is known as the propagation delay, defined as the time it takes to change the input logic edges of the gate to affect the voltage drop across the drain-source junction. The delay in turning a MOSFET on or off occurs because of the time needed to charge or discharge the gate capacitance and is influenced by factors such as gate resistance, parasitic capacitance, and intrinsic characteristics. To ensure the accuracy of the percentage of duty cycle in PWM form, compensating for this propagation delay becomes essential. This consideration can be expressed by the following equation: (1) $$D_O=\{\begin{array}{c}0\\ D_I+t_d{f}_{\mathit{\text{PWM}}}\mathrm{ }\\ 1\end{array}\mathrm{ }\begin{array}{c}{D}_I=0\\ \mathrm{ }0<D_I+t_d{f}_{\mathit{\text{PWM}}}\le 1\\ \mathrm{ }{D}_I+t_d{f}_{\mathit{\text{PWM}}}>1,\end{array}$$(1) where $D_O$ represents the actual duty cycle of the PWM signal transmitted by the MCU; $D_I$ represents the desired duty cycle; $t_d$ represents the propagation delay, and $f_{\mathit{\text{PWM}}}$ is the modulation frequency. It should be noted that the value of $D_O$ is limited and saturated to a constraint of the full cycle.

Figure 4. Waveforms of the MOSFET gate-drain.

Methods and theoretical basis

Lorentz force

Figure 5 depicts a kinematic diagram of a contactor consisting of a ferromagnetic plate playing the role of mechanical contact, and an electromagnet producing a magnetic field to attract the ferromagnetic plate. This configuration is commonly found in various devices such as contactors, mechanical relays, and circuit breakers. The magnetic circuit features the air gap $x,$ defined as the distance between the ferromagnetic plate and the electromagnet, the flowing current $i$ passing through the electromagnetic coil, and the Lorentz force $F$ produced by exposing the ferromagnetic plate to the magnetic field induced by the surrounding electromagnet. It is assumed that the cross-sectional area of the ferromagnetic plate is denoted by $A.$ Let the number of turns in the winding be represented as $n;$ the magnetomotive force (MMF), also known as ampere-turns, is the product of $n\times i.$ The effective mean length of the magnetic flux path through the air gap is determined to be $2x$ because the flux passes through both the left and right gaps, each having a length of $x.$^[27] Thus, the reluctance of the magnetic circuit can be approximated by: (2) $$R=\frac{2.x}{\mu .A}$$(2) where $\mu$ represents the magnetic permeability of air. The magnetic flux $\varphi$ passing through the electromagnetic core and the air gap is expressed in terms of the reluctance $R$ and the magnetomotive force $\mathit{\text{MMF}}$ as follows:^[28](3) $$\varphi =\frac{\mathit{\text{MMF}}}{R}$$(3)

Figure 5. Kinematic diagram of an electromagnet and ferromagnetic plate.

According to Faraday’s law,^[29] recalling the relationship between flux density $B$ and the magnetic flux $\varphi$ as $B=\varphi /A,$ and combining Eqs. (2)(2) $$R=\frac{2.x}{\mu .A}$$(2) and (3)(3) $$\varphi =\frac{\mathit{\text{MMF}}}{R}$$(3) , one obtains: (4) $$B=\frac{n.i.\mu }{2.x}$$(4)

By assuming a uniform magnetic field produced surrounding the electromagnet, the Lorentz force $F$ acting on the cross-sectional area $A$ of the ferromagnetic plate can be simplified as:^[29](5) $$F=\frac{{A.B}^2}{\mu }$$(5)

Substituting Equation (5)(5) $$F=\frac{{A.B}^2}{\mu }$$(5) into Equation (4)(4) $$B=\frac{n.i.\mu }{2.x}$$(4) , it yields (6) $$F=\frac{n^2.i^2.\mu .A}{4x^2}$$(6)

Equation (6)(6) $$F=\frac{n^2.i^2.\mu .A}{4x^2}$$(6) reveals that the Lorentz force exhibits a direct proportionality to the cross-sectional area of the ferromagnetic plate and the square of the current passing through it. Conversely, it demonstrates an inverse proportionality to the square of the air gap. Additionally, the Lorentz force is influenced by the electromagnet’s structure, including its magnetic permeability material and the number of turns. This paper focuses on investigating factors that can be manipulated without altering the fundamental structure of the electromagnet. In other words, the study aims to explore the impact of varying the amperage and distance on the Lorentz force of the electromagnet.

Dynamic characteristics of electromagnet

An electromagnet can be represented as an $\mathit{\text{RL}}$ circuit in series, where $R$ denotes the DC resistance of the electromagnetic coil, and $L$ represents its inductance. According to Kirchhoff’s voltage law, the applied voltage $u$ powered to the electromagnet can be expressed as: (7) $$\mathit{\text{Ri}}+L\frac{\mathit{\text{di}}}{\mathit{\text{dt}}}=u$$(7) where $i$ is the flowing current in the electromagnetic coil.

The electrical characteristic of an electromagnet is its inductive property, which opposes any changes in current. Consequently, when the power is supplied to an electromagnetic coil, the flowing current does not immediately reach its maximum level but instead increases steadily until limited by the DC resistance of the coil. In the steady state, the current in the electromagnetic coil can be approximated as: (8) $$i=\frac{V_{\mathit{\text{DC}}}}{R}\times D_O$$(8) where $V_{\mathit{\text{DC}}}$ is the supply voltage.

Heat rising

The continuous power supply to the electromagnetic coil leads to heat dissipation and an increase in temperature. Several factors influence the coil’s temperature in the contactor, including ambient temperature, self-heating of the coil, and the temperature generated by the electricity-conductive mechanical contact. As the coil heats up, its resistance increases. The resistance (R) of the coil at a specific temperature (T) is represented by the following equation:^[12](9) $$R=R_0[1+k_{\mathrm{R}}(T-20\left)\right]$$(9) where $R_0$ is the resistance of the electromagnetic coil at the ambient temperature 20 °C, $k_R$ is the thermal coefficient, and $T$ is the electromagnetic coil temperature. One crucial observation is that the current-turns ratio and the Lorentz force of a given coil remain constant under any conditions. Consequently, as the coil heats up, its resistance increases according to Equation (9)(9) $$R=R_0[1+k_{\mathrm{R}}(T-20\left)\right]$$(9) with the same initial applied voltage. This leads to a constraint on the current flowing through the coil, resulting in a reduction of the Lorentz force.

Normalized root mean squared error

This study introduces computational models that describe parameters affecting the Lorentz force and electromagnet performance. Model accuracy is assessed by comparing them with experimental results, using the normalized Root Mean Squared Error (nRMSE) as a metric. This metric is an extension of RMSE that normalizes error values, enabling comparison across different datasets. A lower nRMSE value signifies higher model accuracy. Zhi Li et al. also demonstrated that the distribution is highly concentrated and nearly unbiased, with an overall NRMSE of 5.76%.^[30] In this study, an NRMSE of less than 5% is deemed highly accurate. However, it’s important to note that the NRMSE value has several limitations when assessing a wide range of measurements. The formula to calculate nRMSE is as follows: (10) $$\mathit{\text{nRMSE}}=\frac{1}{O_{\mathrm{\text{max}}}-O_{\mathrm{\text{min}}}}\sqrt{\frac{\sum {\left(P_i–O_i\right)}^2\mathrm{ }}{m}}$$(10) where $P_i$ represents the simulated value at the $i^{\mathit{\text{th}}}$ instance, $O_i$ represents the experimental value at the $i^{\mathit{\text{th}}}$ instance, $O_{\mathrm{\text{max}}}$ represents the maximum experiment value, $O_{\mathrm{\text{min}}}$ represents the minimum experiment value, and $m$ is the total number of samples.

Results and discussion

The experimental setup, depicted in Figure 6, includes a ferromagnetic plate mounted on the dynamometer head, aligned with and facing the electromagnet. The dynamometer’s position is measured by a potentiometer and adjusted to set a predetermined gap between the ferromagnetic plate and the electromagnet. The amplitude of the Lorentz force induced in the electromagnet is precisely controlled by the current through the MOSFET-based driver, which is managed by the microcontroller unit. A lithium battery serves as the current source to power the entire apparatus. The effectiveness of the Lorentz force on various factors was validated, and the experimental data were recorded on a personal computer, with a minimum of 400 logging data samples for each test.^[21] After each test, the ferromagnetic plate is demagnetized in preparation for the next test. Several system parameters are listed in Table 1.

Figure 6. Experimental setup for investigating the electromagnetic contactor.

Table 1. Parameters of testing apparatus for electromagnetic contactors.

Parameter	Unit	Value
Electromagnet dimension (L x W x H)	mm	80 × 38 x 50
Wire diameter	mm	0.2
Number of turns ($n$)	Turn	150
Internal resistance of electromagnet at $20°\mathrm{C} (R_0)$	Ohm	400
Total inductance of electromagnet ($L$)	mH	268
Ferromagnetic plate dimension (L x W x H)	mm	30 × 50 x 10
Magnetic flux of ferromagnetic plate ($\varphi$)	Tesla	2.0
Supply voltage ($V_{\mathit{\text{DC}}}$)	V	0 to 95
Battery capacity	Ah	20
Thermal coefficient of copper	1/K	0.00404

Strength of Lorentz force

Initially, the air gap between the ferromagnetic plate and the electromagnet is set to 90 mm as shown in Figure 7, with the electromagnet de-energized to prevent attraction. To eliminate the influence of the gravity force on the ferromagnetic plate, the dynamometer is zero-returned. Subsequently, a stable magnetic field capable of attracting the ferromagnetic plate is generated by regulating a constant current through the electromagnet. The dynamometer provides a measured value indicating the Lorentz force exerted by the magnetic field on the ferromagnetic plate. After each test, the air gap is gradually decreased by 0.1 mm increments for the next test. For comparison with experimental results, a theoretical simulation using Equation (6)(6) $$F=\frac{n^2.i^2.\mu .A}{4x^2}$$(6) is performed on MATLAB.

Figure 7. Relationship between Lorentz force of the electromagnet and the ferromagnetic plate at different air gaps.

As shown in Figure 7, the magnetic field surrounding the electromagnet significantly increases as the air gap decreases, with the experimental curve closely matching the simulation (nRMSE = 3.5%). This validates Equation (6)(6) $$F=\frac{n^2.i^2.\mu .A}{4x^2}$$(6) as an appropriate representation of the Lorentz force exerted by the electromagnet on the ferromagnetic plate.

Existing literature on the Lorentz force emphasizes the strong relationship between the current through the electromagnet and the induced Lorentz force. To address this effect, we sequentially set the air gap to 1 mm and 1.5 mm. This distance allows for the Lorentz force observed to change gently at this distance without abruptly overshooting. For each gap, the electromagnet is driven by a regulated current to generate the Lorentz force, which is then measured by the dynamometer. After each test, the current through the electromagnet is gradually increased with an interval of 10 mA by increasing the voltage accordingly via the MOSFET-based driver. The simulation results obtained using Equation (6)(6) $$F=\frac{n^2.i^2.\mu .A}{4x^2}$$(6) and the experimental data are depicted in Figure 8, with the solid line representing simulation data and the dotted markers indicating experimental results.

Figure 8. Relationship between Lorentz force and flowing current in the electromagnet.

With the air gap held constant, the Lorentz force produced by the magnetic field increases exponentially as the excitation current flowing through the electromagnet develops. The fitting levels (nRMSE) between the simulation and experimental data are 3.3% for the air gap of 1 mm and 3.1% for the air gap of 1.5 mm. Hence, the established model Equation (6)(6) $$F=\frac{n^2.i^2.\mu .A}{4x^2}$$(6) accurately represents the Lorentz force and can reliably simulate this force in practical applications.

Heat dissipation

When the electromagnet is energized, it generates heat due to internal resistance, eddy currents, and hysteresis losses in the electromagnetic coil. Failure to manage this heat generation properly can lead to a temperature increase, negatively impacting the electromagnet’s performance and lifespan. Excessive temperature can cause insulation material degradation, alter coil resistance, and even result in demagnetization. To address the heat dissipation problem, analyzing the relationship between temperature and operational time is crucial. A graph illustrating the relationship between thermal dissipation over time provides valuable insights into the heat dissipation characteristics of the electromagnet, as shown in Figure 9.^[31]

Figure 9. Variation of dissipated heat on the electromagnet over time and its relationship to the internal resistance.

The dissipated temperature of the electromagnet, measured using a thermal camera, exhibits a linear increase over time. This indicates that maintaining the flowing current in the electromagnet for an extended period can cause overheating, posing a threat to the electromagnetic coil’s lifespan. Notably, the internal resistance of the electromagnetic coil is directly proportional to the dissipated temperature.

Additionally, simulation results based on Equation (9)(9) $$R=R_0[1+k_{\mathrm{R}}(T-20\left)\right]$$(9) for the dissipated heat concerning internal resistance closely match the experimental results, with an nRMSE of 2.5%. This highlights the reliability of the constructed model for heat dissipation and underscores the thermal risks to the behavior and operation of the electromagnet. Moreover, fluctuations in resistance lead to alterations in current intensity within the conducting wire. As resistance increases, following the well-known formula $I=U/R,$ there is a reduction in current, consequently leading to a decrease in the Lorentz force under the constant applied voltage, as depicted in Figure 10. The fitting level between simulation data and experimental data is nRMSE = 4.5%. These negative effects, occurring over prolonged periods, may even impact the physical parameters of the electromagnet irreversibly. Based on these evaluations, it is evident that implementing heat dissipation power control methods is crucial to mitigate the risk of excessive temperature rise and prevent associated performance degradation.

Figure 10. Relationship of the Lorentz force with temperature.

Change of flowing current

Equation (9)(9) $$R=R_0[1+k_{\mathrm{R}}(T-20\left)\right]$$(9) reveals that the DC resistance of the electromagnetic coil changes with the rising dissipated temperature. However, for a short period with minimal temperature increase, the internal resistance can be assumed to be constant. Consequently, the current flowing into the electromagnet can be controlled by adjusting the pulse width, which regulates the conductivity of the MOSFET and, in turn, the applied voltage to the electromagnetic coil. Two potential factors that may affect the flowing current are the duty cycle and modulation frequency. The actual flowing current passing through the electromagnet is measured using a current sensor, while simulation data is obtained using Equation (1)(1) $$D_O=\{\begin{array}{c}0\\ D_I+t_d{f}_{\mathit{\text{PWM}}}\mathrm{ }\\ 1\end{array}\mathrm{ }\begin{array}{c}{D}_I=0\\ \mathrm{ }0<D_I+t_d{f}_{\mathit{\text{PWM}}}\le 1\\ \mathrm{ }{D}_I+t_d{f}_{\mathit{\text{PWM}}}>1,\end{array}$$(1) , and Eqs. (6–8). Figure 11 depicts the relationship between the duty cycle and the Lorentz force at 1 kHz (Figure 11(a)), 5 kHz (Figure 11(b)), 10 kHz (Figure 11(c)), and 50 kHz (Figure 11(d)).

Figure 11. Relationship between the duty cycle and the flowing current.

Figure 11 illustrates the significant impact of PWM signal frequency on the operation of the electromagnet, especially at high frequencies. At modulation frequencies of 1 kHz and 5 kHz, the Lorentz force generated by the electromagnet, which is directly related to the current flowing through the coil as indicated in Equation (6)(6) $$F=\frac{n^2.i^2.\mu .A}{4x^2}$$(6) , shows a linear correlation with the duty cycle controlling the MOSFET conductivity. This study tested frequency values from 1 kHz to 100 kHz in 1 kHz increments.

The data presented in Figure 11 follows a typical pattern: at 1 kHz, there’s a proportional relationship, at 5 kHz, sigmoidal behavior begins, at 10 kHz, the sigmoidal change increases, and at 50 kHz, the correlation plot saturates. As the PWM signal frequency increases, the inductor may not fully discharge between pulses, resulting in decreased average current at low-duty cycles and increased current at high-duty cycles.

Additionally, the impedance of the equivalent circuit of the electromagnet, which includes the inductor and resistor, varies with frequency, causing a significant increase in circuit impedance at high frequencies. These findings emphasize the importance of carefully selecting the PWM frequency and duty cycle to optimize the performance of the electromagnet. Ideally, the PWM frequency should be maintained at a certain value where the relationship between the current and duty cycle remains linear. The limitations of PWM frequency depend on the characteristics of each electromagnetic coil. For the electromagnetic coil in this study, it was concluded that a PWM frequency lower than 5 kHz is preferable.

Using Equation (6)(6) $$F=\frac{n^2.i^2.\mu .A}{4x^2}$$(6) , Equation (8)(8) $$i=\frac{V_{\mathit{\text{DC}}}}{R}\times D_O$$(8) , and Equation (9)(9) $$R=R_0[1+k_{\mathrm{R}}(T-20\left)\right]$$(9) , the Lorentz force can be expressed as follows: (11) $$F=\frac{n^2.\mu .A}{4.x^2}.{\left(\frac{V_{\mathit{\text{DC}}}.D_O}{R_0[1+k_{\mathrm{R}}(T-20\left)\right]}\right)}^2$$(11)

The experimental validation of Equation (11)(11) $$F=\frac{n^2.\mu .A}{4.x^2}.{\left(\frac{V_{\mathit{\text{DC}}}.D_O}{R_0[1+k_{\mathrm{R}}(T-20\left)\right]}\right)}^2$$(11) is depicted in Figure 12 with an air gap of 1.5 mm, the supply voltage $V_{\mathit{\text{DC}}}=24\mathrm{V},$ and $f_{\mathit{\text{PWM}}}=1 \mathit{\text{kHz}},$ and other parameters are listed in Table 1. The experimental result closely aligns with the simulation results obtained using Equation (11)(11) $$F=\frac{n^2.\mu .A}{4.x^2}.{\left(\frac{V_{\mathit{\text{DC}}}.D_O}{R_0[1+k_{\mathrm{R}}(T-20\left)\right]}\right)}^2$$(11) with nRMSE = 1.5%, confirming the accuracy of the computational model. This powerful framework enables precise calculation, design, and control of electromagnets, enhancing their applicability across various fields and opening new prospects for future advancements in this area.

Figure 12. Relationship between applied voltage to the electromagnetic coil, induced temperature, and produced Lorentz force.

Conclusion

In this study, the study designed and implemented a dedicated apparatus to investigate the Lorentz force of electromagnets and contactors. The primary objective was to propose an approach for suppressing sparking resulting from the shock vibration of mechanical contacts. During the pilot study, this paper exposed a ferromagnetic plate to the magnetic field produced by the electromagnet. The experimental results yielded several key findings:

• The Lorentz force exhibited an exponential increase as the air gap between the ferromagnetic plate and the electromagnet decreased, particularly when the gap was less than 10 mm.

• The temperature of the electromagnet gradually increased over time, reaching up to 65 degrees Celsius after approximately 900 seconds of operation. This rising temperature caused an increase in the internal resistance of the electromagnetic coil, resulting in reduced current flow and degradation of the Lorentz force.

• This study also explored the use of pulse-width modulation (PWM) to adjust the current passing through the electromagnetic coil. However, the experimental results indicated that the modulation frequency strongly influenced the amplitude of the current. Specifically, at a modulation frequency of 50 kHz and a duty cycle of 20%, there was no current flowing in the electromagnetic coil.

Additionally, the simulation results, based on the provided computational models, are closely aligned with the experimental findings from the apparatus tests. This alignment suggests the feasibility of developing an active driving controller for the electromagnet.

This paper recommends further investigation into developing a current controller for the electromagnet. This research aims to optimize power consumption, minimize heat dissipation, and maintain a sufficient Lorentz force to attract ferromagnetic material in specific contactors.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number TX2023-20b-01. We acknowledge the support of time and facilities from National Key Laboratory of Digital Control and System Engineering (DCSELab), Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for this study.