THERMAL ANALYSIS OF AN INDUCTION MOTOR BY HYBRID MODELING OF A THERMAL EQUIVALENT CIRCUIT AND CFD Thiago Voigdlener, voigdlener@gmail.com Daniel Jochelavicius, danieljoche@gmail.com Federal University of Santa Catarina, Mechanical Engineering Department, Florianópolis, SC, Brazil Marco A. Peretti, peretti.marcoa@gmail.com Whirlpool Corporation, Joinville, Brazil Abstract. The constant pressure over manufacturers for the production of smaller, more efficient and less expensive motors motivates a thermal analysis simultaneous to an electromagnetic project. In this context, this paper presents a Thermal Network model of a monofasic induction motor with permanent capacitor used in domestic applications. The transient solution and modeling are made with Modelica programing language. The heat transfer convective coefficients are determined by computacional fluid dynamics modeling. Hence, this paper presents a hybrid model which provides fast and accurate results in steady or transient states and for different flow states: turbulent forced convection and natural convection. The model has been validated with experimental data. Keywords: induction motors modeling, thermal network, computacional fluid dynamics, Modelica 1. INTRODUCTION Electric induction motors are broadly employed and represent about 80% of the electric motors in operation. Due to their large use, it is estimated that induction motors are responsible for 38% of the total world electric consumption (Yonn and Kauh, 2002). Because of their life expectancy of 15 to 20 years, the running costs of general motors usually exceed their purchase price and the higher efficiency becomes of fundamental importance. The efficiency of an electric motor represents the machine energetic behavior during conversion of electric power in mechanical power. The difference of these two powers is the total motors losses which represents motor efficiency. Generally all losses depend on temperature which is directly related to the integrity of the winding insulation. Therefore, the ability to predict the temperature distribution of spinning electric machines is very important in motor design (Bonnet, 1994). In this context, this paper presents a Thermal Network (TNW) model of a permanent split-phase capacitor (PSC) induction motor used in domestic applications. The transient solution and modeling are made with Modelica programing language. The heat transfer convective coefficients are determined by computacional fluid dynamics (CFD) modeling. Hence, this paper presents a hybrid model which provides fast and accurate results in steady or transient states and for different flow states: turbulent forced convection and natural convection. The model has been validated with experimental data. 2. FLUID DYNAMIC ANALYSIS Due to PSC motor complex geometry as well as difficulties to find empiric correlations in literature which allows to estimate heat transfer by convection for all motor surfaces, numeric-computational models have been used to solve motor airflow and heat transfer problem. The solution of this problem require the handling of Navier-Stokes equations, highly non linear, coupled to mass and energy conservation equations (Maliska, 1995). Thus, global heat transfer coefficients have been obtained Fluent-Ansys comercial code. These parameters obtained from CFD are area-weighted-average coefficients of discretized surfaces, used on TNW model are presented hereafter. In order to simplify the solution of the hybrid model presented above, prescribed temperatures are used as boundary
conditions, avoiding the need to solve the conduction problem on solid bodies. The joule losses derived from electromagnetic dynamic are also not considered on CFD. Both inputs that were neglected on the CFD model are then accounted on the TNW model. Air is assumed as newtonian fluid, incompressible and it s properties are calculated at 313 K. Steady state is considered and gravity field actuating on vertical-down direction. Natural convection effect in motor low speeds is modeled with Boussinesq approximation. For high spinning velocities κ-ε model is used to model turbulence. The boundary conditions for momentum conservation are no wall slipping and no penetration on walls. A constant rotational velocity is prescribed for fluid intern cells. The SIMPLEC model was used to couple pressure and velocity by it s fast convergence. The first order UPWIND discretization scheme was used to interpolate velocity, temperature, turbulent kinetic energy and turbulent kinetic energy dissipation fields. PRESTO method was used to interpolate pressure field. Due to it s complexity, a non structured mesh with 1,543,557 elements was built. The rotor spin was considered using rotational reference planes over two distinct regions stator-static and rotor-rotational. Figure 1. Mesh of motor bench. 3. THERMAL NETWORK A TNW is constructed by means of thermal-electric analogy between heat diffusion and electric charge conduction. As an electrical conductance is associated to electric conduction, a thermal conductance can be associated to heat conduction. The components used to model thermal circuits are presented below: Thermal nodes: Regions of punctual temperature whereby the connection between different elements is made; Thermal capacitance: Represents the capacity of determined body to stock energy as heat; Conduction: Governs the heat flux through a solid or between different solids; Convection: Responsible for the heat flux between solid surface and it s adjacent fluid; Prescribed heat flux: Source of heat, in this model represents motor joule losses. A general cylindric component was used to model motor solid components in which heat conduction was discretized axially and radially neglecting multiaxis effects. Axial and radial conduction were considered equal in all componets, except rotor and stator core which are made by pressed plates generating severe differences between both conductions by the significant accumulation of contact resistances.
3.1 Convection Coefficients The average on area heat transfer coefficients were calculated at three motor speeds: 1,600; 1,000 and 600 rpm and also no speed (pure natural convection). Doing this the computational effort is reduced by simulating only four cases on steady state. Observing the continuity of the Average Heat Transfer Coefficients (AHTC) as function of motor speed it is possible to adjust polynomial equations to interpolate discrete simulated values. An AHTC can be calculated for each discrete solid surface, which will be used on TNW model later. These adjust provides great model agility keeping good model final answers. 3.2 Joule Losses For present model prescribed joule losses, obtained from experimental data, are used on stator and rotor windings and other losses are not considered. This methodology is used for thermal model validation, which can be easily substituted by and electromechanical model coupling. 4. SYSTEM MODEL AND EQUATIONS Modelica languange by OpenModelica opensoftware can be used to model the system, coupling more then 1,500 equations. Modelica is a simulation language that incorporates multiple physics domains, such as electrical, mechanical, and thermal domains, based on algebraic and ordinary differential equations (Fritzon, 2004). Physic components libraries and simulation packages can be used, allowing programmer to focus on physics modeling and saving debugging time. The concepts of a TNW are used to create elements and their connections, observing heat fluxes paths between motor discretized components. As Modelica is an object-oriented language then it is reasonable to reuse components just changing some parameters values. In order to preserve model order different motor parts are separated in classes. Figure 2 shows TNW model of stator core which is lately connected to other components respecting heat flux considered paths. For only one component that separation may be questioned. But for a system with more than 1,500 equations, this rigorous and discretized classes separation is justified. Figure 2. Stator core TNW model.
5. MODEL PERFORMANCE AND EXPERIMENTAL VALIDATION Experimental measurements have been realized to get electric currents and motor speed (inputs to thermal model) in a 4,000 seconds test and also to validate thermal results. The tested motor is a small induction motor used for domestic applications, with permanent split-phase capacitor, squirrel cage rotor, IV poles, 184 W of power, 127 V, 60 Hz, 45 µf capacitor, 1,625 rpm with F class insulation. Measured characteristics were investigated by mechanical coupling of the PSC motor to dynamometer. The motor was start-up at nominal load torque and was turned of at time of 1,800 seconds. Thereafter, Joule losses are zero and install the regime of natural convection. Figure 3. Experimental motor bench: (1) Dynamometer; (2) PSC induction motor and (3) System control and data acquisition. Figure 4 shows the Joule losses in the stator windings used as inputs to the model. Through the experimental values, the Joule losses were obtained by the product of the resistance and the square of the current. Figure 4. Joule losses in the stator windings.
The performance of proposed thermal model is done by comparison between model predicted and experimental temperatures. Measurements has been done with thermocouples (type T) installed on motor interior looking for points which better represent the average temperature of each part along test time. Figure 5 shows the comparison between computational predicted temperatures by the model and experimental temperatures of model at 100% of load. It s evident that the model has foreseen the temperature throughout the geometry, as both analytical and experimental data follow the same tendency. Also, main winding temperature is higher than the auxiliary one which is higher than stator temperature, in model and experimental, with 5 K maximum deviation on stator core, a thermal element of greater mass and dimensions. At 1,800 seconds of test the motor has been shut down, then pure natural convection regime settles in, and model keeps a good accuracy. Figure 5. Experimental validation. 6. CONCLUSION This article presented the development and aplication of a TNW model of a permanent split-phase capacitor induction motor used in domestic applications. The model is based on thermal-electric analogy and utilized geometric parameters, thermophysical properties and heat transfer characteristics through conduction and convection (forced and natural). Then, the model proved to be capable of predicting temperatures of motor different parts through time operation. The evaluation of motor convection heat transfer coefficients has been related on literature showing thath those coefficients vary as function of position, surface geometries, flow direction velocity and fluid characteristics. Due to this airflow complexity correlations give only aproximated results. A detailed investigation has been done in order to predict those coefficients with precision by the solution of fluid dynamics over convection surfaces. Modelica language was used to model and solve TNW facilitating the construction, accelerating the transient simulation with an easy changing of parameters values (which allow to compare different setup and operation conditions). It is also possible to couple this model with other models related to it, as electric and mechanical.
7. REFERENCES Bonnet, A.H., 1994. An update on ac induction motor efficiency. IEE Trans. Ind. Apllicat., Vol. IA-16, pp. 1362 1372. Fritzon, P., 2004. Principles of object-oriented modeling and simulation with modelica 2.1. NJ: IEEE Press. M. K. Yonn, C.S.J. and Kauh, S.K., 2002. Efficiency increase of an induction motor by improving cooling performance. IEE Trans. Energy Conversion, Vol. 17, pp. 1 6. Maliska, C.R., 1995. Transferência de calor e mecânica dos fluidos computacional. LTC, Rio de Janeiro, Brazil.