summary
Researchers Li Ruyao and Yang Wenying from the School of Electrical Engineering and Automation at Harbin Institute of Technology and Guizhou Zhenhua Qunying Electric Co., Ltd. published an article in the 2018 supplement 2 of the Journal of Electrical Engineering Technology (titled "Numerical Algorithm for Temperature Field of High Voltage DC Relay Coil"). They pointed out that high voltage DC high-power relays are key components in fields such as new energy vehicles, and the multi-turn densely wound electromagnetic coil is a key component in the magnetic circuit. Its operating temperature rise will seriously affect the electromagnetic parameters of the relay.
These types of coils operate at high and uneven temperatures for extended periods or when they reach steady state. Previous studies have mostly treated them as a single component or a region with uniform temperature distribution, which does not match the actual large temperature differences. This fails to provide accurate reference values such as the maximum temperature for thermal design, which is a critical step affecting the lifespan and reliability of relays.
This paper proposes a numerical calculation method for the temperature field of multi-turn closely wound coils, combining an equivalent thermal resistance network and finite difference finite element method. Considering the material properties of the copper wire, insulating varnish, and air inside the winding, as well as the influence of dimensional parameters such as wire diameter, varnish thickness, and inter-wire distance on heat transfer, the method can quickly calculate the temperature field inside the coil. Comparison with the finite element method and experimental measurements demonstrates the feasibility and high computational efficiency of this method, providing a basis for relay heating design and a theoretical reference for accurate temperature calculation in multi-field coupled simulations of relays.
With the widespread adoption of new energy sources, high-power DC relays are increasingly used in electric vehicles, charging stations, and other applications requiring high current flow. Multi-turn, tightly wound coils are frequently used in relays, contactors, and other switching devices as the source of electromagnetic drive force. These coils typically have over a thousand turns. Due to the tight winding of the enameled wire and the continuous flow of current, the multi-turn coil is often one of the main heat sources in these mechanisms, resulting in significant temperature rise after prolonged operation. As the power requirements of these DC relays increase, the temperature rise problem becomes increasingly pronounced.
Higher temperatures affect coil resistance and the properties of ferromagnetic materials, which in turn affect the electrodynamic force of the electromagnetic coil, significantly impacting the operating characteristics of the equipment. With the improvement of computer performance and the higher demand for simulation accuracy, the effects of multiphysics coupling are beginning to be considered in the dynamic characteristic simulation of electromagnetic mechanisms. Among these factors, temperature, which affects the electrical, magnetic, and mechanical properties of materials, is a relatively important factor that needs to be calculated as accurately as possible.
Excessive temperature rise can also affect the insulation performance and lifespan of the enameled wire insulation layer, leading to inter-turn short circuits and other issues, thus impacting its lifespan and reliability. The experimental results in this paper show that the temperature distribution inside a multi-turn, densely wound coil is non-uniform. This indicates that previous assumptions about uniform internal temperature distribution, made due to the difficulty in measuring the internal temperature of the coil, and the assumption that the coil windings were made of pure copper, are inapplicable. The various application environments of high-power DC relays place higher demands on their environmental temperature resistance and thermal design. More accurate methods for calculating coil temperature rise are crucial for multi-field coupling simulation and thermal design of relays.
Extensive research and calculations on coil temperature have been conducted in fields such as motors and electrical appliances, ranging from the earlier thermal circuit method to the now widely used finite element method. Xi Jianzhong and Huang Linmin respectively used the Newtonian temperature rise method and the thermal circuit method to calculate the temperature rise of electromagnet coils, but both methods treat the coil as a single component, calculating a value for the coil as a whole, and failing to obtain the temperature distribution.
References [3-5] used the thermal resistance network method to calculate the temperature of the motor stator and rotor, respectively. Both methods treated the coil section as a uniform whole, neglecting the internal structure of the coil. References [5-12] used the finite element method to calculate the temperature of relays, motor stators, and other components. These articles primarily focused on heat loss calculations, ignoring the complexity of heat dissipation within the coil. Their coil windings were considered a uniform whole, and the thermal conductivity of the materials in these regions was set to high values, some even directly to the thermal conductivity of copper, resulting in almost no temperature difference within the winding sections.
The simulation results from these papers show that the temperature difference in the coil section is less than 1℃, and in some cases even less than 0.1℃, which does not conform to the larger temperature difference distribution inside the actual coil. The lack of attention to the temperature distribution difference in the coil is related to the difficulty in obtaining its internal temperature. Furthermore, the main material in the coil winding is copper, which has a very high thermal conductivity, easily leading to the subjective impression that its overall internal thermal conductivity is also high, while ignoring the influence of the enameled wire enamel layer with very low thermal conductivity and the internal air.
References [13,14] considered the temperature distribution of the coil section when calculating the overall temperature of the device, but the method used was to calculate the overall thermal conductivity according to the proportion occupied by the material layers. Their layering model did not consider the internal structure of the winding, such as the varnish and air. References [15,16] estimated the internal temperature of the coil by measuring the change of coil current with temperature, but the result was also an average value, not the actual measured value.
Previous methods using thermal circuit analysis, thermal resistance network analysis, and finite element analysis to obtain coil temperatures were primarily average temperatures. This was mainly because they did not consider the influence of the coil winding's internal structure and material distribution on temperature distribution, assuming instead that the internal material contained high and uniform thermal conductivity. However, the maximum temperature and other parameters required for heating design differ significantly from the average temperature. Measuring the internal temperature of multi-turn coils is difficult, especially during actual electrical operation. Therefore, a method for calculating the internal temperature distribution of multi-turn coils is urgently needed.
This paper, based on the distribution of copper, enamel, and air within a multi-turn winding, and considering material properties and dimensional parameters, constructs a finite difference matrix equation using the concept of a thermal resistance network. This allows for a relatively fast and accurate calculation of the winding's temperature field. Furthermore, the temperature rise data inside the coil, measured using an embedded sensor probe, matches the values obtained by the calculation method, confirming the feasibility of the proposed approach. This method can provide more reliable data for relay thermal design and lays the foundation for accurate temperature field calculations in multi-field coupling of relays.
Figure 1. Schematic diagram of the overall structure and coil cross-section of the DC high voltage relay.
Figure 2. Coil winding and probe placement process
Figure 3 Temperature measuring device
in conclusion
This paper addresses the temperature rise problem of multi-turn densely wound coils in high-power DC relays. It employs a method combining the equivalent thermal circuit concept and the finite difference method to solve the temperature matrix, thus obtaining the temperature field of the multi-turn densely wound coil. The calculated temperature difference between the highest and lowest steady-state temperatures of the winding portion inside the example coil exceeds 50℃, which better reflects the actual operating conditions of the coil. Compared with measured results, the calculation accuracy ranges from 1.75% to 8.01%.
This method, which uses an aligned coil arrangement to calculate the temperature field, more accurately reflects actual coil temperature rise measurements than an interleaved arrangement, and offers better versatility. The calculation time is less than 1 second, demonstrating high computational efficiency compared to the finite element method. It is suitable for multiphysics simulation calculations involving temperature in high-power DC relay products and for designing product environmental temperature resistance and lifespan.
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