A long secondary linear traction motor analysis based on electromagnetic-thermal-fluid coupling

The temperature analysis of the motor is critical for its functioning and durability as it has a significant impact on enhancing its efficiency. The purpose of this paper is to design a rational water cooling system for the Double-sided Linear Flux Switching Permanent Magnet motor (DLFSPM), thereby reducing the adverse effects of temperature rise. This paper conducts electromagnetic fluid and thermal analyses of DLFSPM. It also designs a rational cooling structure to reduce the temperature rise while running thereby contributing to its operation reliability. The electromagnetic-thermal-fluid coupling model provides a feasible solution for reducing the temperature increase of the DLFSPM motor under rated operating conditions, thereby enhancing its overall performance.


Introduction
The Double-sided Linear Flux Switching Permanent Magnet motor (DLFSPM) has a wide range of potential applications in areas such as precision processing, urban railway transportation and linear generators.However, the heating issue of the motor has been gaining critical attention as it poses significant safety risks.As a result, it is imperative to identify effective approaches for mitigating the increase in motor temperature [1].
Currently, significant progress has been made in the study of temperature fields with the thermal network method and numerical analysis being the two main approaches for analyzing these fields [2][3].The thermal circuit method has several advantages including simple modeling, smaller calculation size and quick calculation of motor temperature during the optimization of motor parameters.Nonetheless, this approach may not adequately capture the temperature distribution of internal points within the motor [1].The finite element analysis (FEA) is a prevalent numerical analysis method that can simulate infinite complexities with finite elements to analyze the calculation results.However, this method often requires a considerable amount of time and is slow to calculate.
In [4], the obtained losses from electromagnetic analysis were utilized as heat source inputs for thermal analysis.Numerical calculations of temperature distribution in different regions were conducted by using a three-dimensional finite element method.In [5], the temperature distribution of two distinct heat dissipation models was analyzed by using the thermal network analysis model.Meanwhile, the cooling results of water-cooled motors were compared.The response surface method was also employed to analyze the EM characteristics of the water-cooled motor.A sensorless temperature estimation method is proposed in a study [6] where the thermal network model of an induction motor is created.The losses are incorporated into an equivalent thermal network model to estimate the temperature of the induction motor.This approach provides a foundation for the rational design of cooling systems in induction motors.
This study primarily focuses on the electromagnetic-fluid-thermal coupling analysis in the DLFSPM motor.Thermal simulation results are obtained based on the specific heating source of the DLFSPM motor.Subsequently, a motor cooling system is designed to mitigate temperature rise.Finally, a comparative analysis is conducted to assess the cooling effectiveness of the water cooling system about the initial model.

Electromagnetic field model of dlfspm
The linear motor can be viewed as an expansion along the radius of a rotary motor, as it is a derivative of the latter.To improve the precision of analyzing electromagnetic characteristics, a 2D finite element model is constructed to simulate the original structure of the DLFSPM motor.Figure 1 illustrates the 2D representation of the motor in the model.Analyzing the air gap magnetic field is a crucial step and of non-negligible part of the process of electromagnetic characterization.The primary and secondary of the DLFSPM are positioned in parallel with each other.During flux switching, the flux primarily travels through the primary teeth, air gap and secondary teeth.It also exits the motor.
To mitigate the temperature rise of the motor, perforations were made on the stator and stator yoke, precisely targeting the center of the double-H movers where the flux and magnetic density distributions were comparatively lower [ [6]]. Figure 2 shows the flux and magnetic density distribution of the DLFSPM motor under no load before and after drilling the stator.The change in air gap magnetic flux density of the DLFSPM motor due to perforations is presented in Figure 3.The results indicate that the peak air gap magnetic flux density after drilling reaches 1.82 T, which is comparable to the initial model's 1.78 T. Consequently, the impact of perforations on magnetic flux density in the air gap can be considered insignificant.

Motor loss calculation
Electric motors convert energy but experience losses in the process, leading to heat generation.The motor's electromagnetic losses include core loss, solid loss and stranded loss.
Core loss is generated when the primary and secondary cores of the motor are magnetized by alternating currents.More specifically, the core loss of the stator teeth can be expressed by the following equation: , whose value can be identified by the type of silicon steel sheet.The average mag net flux density at the stator teeth is denoted by t B .G represents the weight of the stator.The eddy current density within the permanent magnets can be defined as follows: where J represents the current density; S strands for the cross-sectional area of the PM;  refers to the material conductivity;  refers to the motor operating frequency; r  is the effective penetration depth;  is the magnetic flux;  is the volume; PM P is the solid loss of the PM.
When current flows through the wingding, the stranded loss is generated in the winding wires.Based on Joule's law, this loss is equivalent to the product of the square of the winding current and the resistance, which reflects the power dissipated by the current flowing in the winding.The equation is expressed as: where the number of phases is denoted by m , the valid value of the winding current in the primary winding of the DLFSPM is denoted by I , and the resistance of the primary winding of the DLFSPM is denoted by R .
Based on the finite element analysis, various types of electromagnetic losses were obtained and depicted in Figure 4. From the figure, it can be observed that the winding loss represents a significant portion of the total losses while the motor is operating under load.

Figure 4
The various types of electromagnetic losses.
The heat generation rate is an essential parameter used to calculate the motor temperature field, representing the heat produced by each component's volume in the motor.The heat generation rate is typically used to determine the motor's heat-generating capacity, which is calculated as follows: where p represents the loss of motor components W; V represents the volume of each loss- generating component.

Mathematical model
The mathematical formulation representing the temperature distribution of the DLFSPM adheres to the core principles of heat transfer and can be articulated as follows: ( ) where the thermal conductivities of the motor material in the    、 、 respectively.The motor temperature is described by T .The specific heat capacity is described by c .The component density is described by  .The motor heat source density is described by Q . 1 S is the surface of the insulation boundary.2 S is the thermal convection surface.0 T is the surrounding medium temperature.

Design of the cooling structure
Core-back cooling is a conventional water-cooling technique for linear motors, which entails embedding a water-cooled pipe in the back of the core.Low-temperature water flows into the inlet of the pipe and the water flowing through the pipe carries away heat, resulting in high-temperature water flowing out of the outlet to cool the motor.The cooling structure of the motor is presented in Figure 5. and Figure 6.

Fluid field analysis
When analyzing the heat-flow coupled field of DLFSPM, it is commonly assumed that fluid flow and temperature fluctuations do not exert a reciprocal influence on each other.This paper utilizes a simplified model to compute the distribution of both the flow field and temperature increase.This approach greatly reduces the analysis time and lessens the computational burden of heat-flow coupling.
After fluid field calculation, a cross-sectional velocity distribution diagram and velocity flow line diagram in the pipe are obtained, as presented in Figure 7.The inlet boundary condition selects the velocity inlet.The pressure outlet is picked as the outlet boundary condition.The thermal-fluid coupled field calculation uses the finite element volume method when the winding passes at 10 A/mm 2 , the motor will generate electromagnetic losses.As shown in Figure 8 below, at the pipe entrance, the surrounding stator has better cooling performance as the water temperature is relatively low and the flow velocity is high.As water flows through the latter part of the pipe, the water temperature increases, resulting in a lower cooling effect on the stator.Overall, the cooling effect has been significantly improved.

Multi-physics field simulation
Table 1 presents the final values of the surface convective heat transfer coefficients for DLFSPM components obtained through the analysis mentioned above.Air convection is the main heat transfer mode under natural cooling.The 2D model is preferred over the 3D model due to its light computation load, making it more convenient for obtaining results.The ambient temperature is set to 22°C.The transient temperature distribution in the motor during typical operation under its rated working conditions is solved and analyzed by using FEA software.
Figure 9 demonstrates that the temperature rise during normal operation of the motor reaches 167°C with the coil winding exhibiting the highest temperature.The stator, which has a large contact area with air, exhibits a relatively low-temperature rise.From the aforementioned analysis, it can be inferred that the primary source of heat generation in the motor is attributed to the losses in the winding.Figure 10 depicts the temperature rise of the motor with an added water-cooling structure, revealing a maximum temperature of 103.4°C.The laying of the water channel in the stator is not only beneficial to the reduction of the temperature rise of the stator but also influences the thermal distribution of the winding and movers, which reduces the temperature rise of the whole machine compared to the natural cooling.

Conclusion
In this paper, the design and analysis of a water-cooling structure for the DLFSPM motor were conducted.The electromagnetic analysis model for the DLFSPM was first established and the installation position of the cooling water channel was determined considering the reducing impact on the magnetic density distribution.The heat source distribution and size of the motor were obtained, which were applied to the magnetic-thermal coupling analysis.In the second part, the feasibility of IOP Publishing doi:10.1088/1742-6596/2728/1/0120027 the cooling system was validated through simulation calculations of the pressure, flow velocity and velocity flow line in the water channels.The temperature rise distribution within the motor stator resulting from the presence of the water channels was provided.Finally, by integrating the results of magnetic field analysis, flow field analysis and thermal analysis, it was demonstrated that the watercooling system has a substantial influence on reducing the motor's temperature increase with a decrease of nearly 64℃.The motor dissipates more internal heat so that the temperature rise of all parts of the motor falls within a standard and reasonable range to ensure efficient motor operation.

Figure 2
Figure 2 Results of electromagnetic simulation.

3 Figure 3
Figure 3 Comparison of magnetic flux density in the air gap of two structures.

Figure 5
Figure 5 Core-back cooling structure of DLFSPM.Figure 6 Installation diagram of the cooling structure.

Figure 7 .
Figure 7.The result of fluid field calculations.

Figure 8 .
Figure 8.The Stator temperature distribution with Core-back cooling structure.

Figure 9
Figure 9 Motor temperature distribution under natural cooling.

Figure 10
Figure 10 Motor temperature distribution under water cooling.

Table 1
Surface heat dissipation coefficient of the DLFSPM components.