Jerad P. 10/1/015 Motor Thermal Limits on Torque Production (Frameless Motor Level)
Jerad P. 10/1/015 The theory of operation of a frameless permanent magnet motor (PMM) and its thermal limitations is essential to an understanding of the physical constraints of torque generation and power conversion in a mechatronics system. This understanding allows the mechatronics system designer to realize the trade offs that exist between size and torque, speed operating points and gain a more intuitive sense for the ratings communicated in motor data sheets. This document focuses on rotary PMMs, however the concepts presented can be extended to linear motors, stepper motors, reluctance motors, as well as generators. Figure 1. Frencken America Manufactured otor (left) and Stator (right) At the simplest level, a PMM is an power transfer device. This power transfer occurs in the interaction between the stator and rotor (Figure 1). The stator and rotor are both made from magnetically permeable steel to keep magnetic fields within the volume of the frameless motor and minimize stray fields. The stator is stationary and comprised of multiple tooth / slot combinations and a multi winding, usually copper, embedded in the stator slots. The rotor, as the name implies, is free to rotate and is populated with multiple permanent magnets (poles) of alternating polarity mounted in a surface permanent magnet (SPM) or internal permanent magnet (IPM) configuration. Although a complete motion control system consists of many other components such as a mechanical housing to enclose the stator, a shaft to transmit torque from the rotor to the outside world, bearings to keep the shaft and rotor centered to the stator, a position or velocity feedback mechanism, as well as complex drive electronics and motion control software, these can be ignored for the moment. The main focus will be electrical power in (stator), mechanical power out (rotor), and power loss (stator) as shown in Figure. Figure depicts the power balance that exists at the frameless motor level. Input power in the form of voltage and current is supplied to the stator at the winding terminals. Output power in the form of torque and angular velocity is generated by the magnetic interaction between the rotor and dynamic stator fields. This produces useful power to a mechatronic Figure. Power Balance in a Frameless Motor
Jerad P. 10/1/015 system in the form of torque and angular velocy (speed). Power loss can be attributed to several different mechanisms in the stator and rotor, but the most substantial is typically ohmic loss, a product of the motor current squared and the stator resistance. If the entire motion control system is considered, additional losses can be found, including bearing, seal, and drive electronics losses. Some of these system level losses are very significant, but for now system losses will be ignored as we focus on ohmic losses in the stator, which takes the form of dissipated heat. This heat is converted to internal energy of the motor components and a rise in temperature of the stator and rotor. Table 1. Functional Temperature Limits of Various Materials All materials in the stator and rotor have a thermal limit. For example, at a certain temperature, the stator and the windings insulation materials start to break down, at some point eventually causing shorts. otor magnets will permanently lose magnetism, disabling the electromagnetic phenomena that generates torque. Epoxies will lose their bond strength at a certain temperature, jeopardizing the mechanical bond between the rotor and magnets. Thermal limits for various motor components, most commonly the stator, are classified according to several different industry standards, e.g. ASTM D 307, IEC 60085, and NEMA MG 1. Because numerous materials such as magnet wire, insulations, epoxies and varnish are used together in motor construction, the thermal class of the motor is determined by the lowest rated component. Table 1 lists typical materials that are used in the construction of stators along with their associated maximum temperatures. In order to determine the thermal performance limit of a motor, a link has to be made between the heat dissipation from the power balance previously described and the temperature rise of individual motor components. As long as the temperature limits are not exceeded based on the properties of the individual motor materials, the motor is operating in a thermally safe region. The motor component of greatest consideration is the stator. This is typically the hottest component of a motor and is where most of the heat is generated through ohmic losses. Lumped Parameter Transient Convection Stator Model. A lumped capacitance model of the stator is one of the simplest thermal models and can be applied if the thermal resistance to conduction within the stator core is small relative to the thermal resistance to convection at the convection fluid interface. This condition can be tested through analysis of the Biot number given in (1), where h is the convection coefficient between the stator and the fluid interface, L c is the characteristic length of the stator (volume divided by area where convection takes place), and k is the thermal conductivity of the
Jerad P. 10/1/015 stator. Typically, if Bi < 0.1 the temperature distribution within the stator, designated as T stator in Figure 3, can be considered mostly uniform, justifying the use of the lumped capacitance model. Figure 3. Lumped Capacitance Thermal Model The lumped capacitance model assumes two modes of energy transfer: an input in the form of internally generated heat from the coil windings (q in = P loss,) and an output in the form of convection (q out = q conv ). Additionally, there is a mode of power transfer to the stator mass as the bulk temperature of the stator rises. This is represented in Figure 3 and the power balance equations are given in () (3) and (4). The solution to this differential equation is given in (5), which is plotted in Figure 4 and demonstrates a first order response between ohmic power loss and the stator temperature rise above ambient. From this expression of stator temperature as a function of time, we can see that the maximum amplitude of depends on the thermal resistance of the system (7), the inverse of the product of the convection coefficient and convection area. The thermal time constant of the response (8) is also a function of these parameters, as well as mass and specific heat of the stator. The significance of thermal resistance is that it gives a direct relationship between power input in the form of heat and temperature rise for the lumped thermal mass. Thermal resistance, although it can be Figure 4. Thermal esponse of Lumped Capacitance Thermal Model derived approximately, is typically determined empirically and published for a standard motor, usually accompanied with the assumption of mounting to a heat sink of a specific
Jerad P. 10/1/015 size and material. NEMA ICS 16 (011) contains detailed procedures relating to the determination of thermal resistance and thermal time constant. Figure 5 shows the temperature response from an equivalent test performed at Frencken America on a production sample size of four motors. The thermal resistance and thermal time constant are derived from the temperature response and are, shown in Table. Figure 5. Motor Temperature esponse Measurement Table. Measurement of Thermal esistance and Thermal Time Constant Knowing the thermal resistance is extremely beneficial since it allows the mechatronics system designer to define an allowable temperature rise from a known ambient operating condition and determine acceptable power loss in the form of heat which is distributed throughout the stator. Figure 6. esolution of Individual Phase Ohmic Losses into Constant Power Dissipation Once a thermally acceptable heat dissipation from ohmic losses is known, we can look closer at the mechanism that creates ohmic losses or heat in a stator with balanced three currents with the purpose of relating total ohmic loss to motor current. Each stator will contribute ohmic losses of a periodic nature (proportional to the squared sine function), however when the three s are added together, the result is a constant (Figure 6). The relationship between currents, resistances, and ohmic losses are summarized in (10) (16) and
Jerad P. 10/1/015 finally, this is related to the maximum continuous motor torque in (17) by introducing the torque constant of the motor. This equation can be further simplified by introducing the motor constant in (18). Higher motor constants, higher allowable stator temperature rises, and smaller thermal resistances all contribute to higher continuous torque in the motor. P loss, ohmic assuming balanced 3 currents and resistances i lineline peak a i P i i b loss, ohmic a, peak c 3 MS, continuous a, if torque constant k i continuous if motor constant k continuous i i k (assuming k a a, k i b, peak 3i MS ims P 3 T MS, continuous M M i 3 i b, i loss, ohmic lineline T M max therm b b, c, peak c, i 3 linelinei q 3 is in units k T i max is defined as c c, MS MS lineline Nm A MS max 3 lineline therm lineline does not change with motor temperature) max 3 k T lineline therm (10) (11) (1) (13) (14) (15) (16) (17) (18) Intermittent Duty Performance. Knowledge of the thermal time constant allows motor use cases other than continuous duty to be analyzed. When continuous duty cycle is not required, higher (peak) torques and currents are possible because the stator does not have an opportunity to reach the full possible value of before cooling begins. The larger the thermal time constant, the slower a motor will react to a heat input and the lower the change in temperature will be. Ten different types of electric motor duty cycles (S1 S10) are defined extensively in IEC 60034 1 and this duty rating system can be used to specify in great detail the exact loading scenario for an electric motor. One example shown in Figure 7 is the S6 continuous operation periodic duty, shown along with the corresponding temperature response. Acceptable currents from a thermal limitation perspective can be analyzed in a similar manner as the continuous duty case. First, temperature rise needs to be correlated to power loss amplitude and Figure 7. IEC 60034 1 Duty Type S6
Jerad P. 10/1/015 the other parameters defining the periodic operation. Then, the relationship between currents and torque limitations are tied to the power loss amplitude. Figure 8. Torque Derating due to NdFeB Magnet Temp Figure 9. elative esistance of Copper Higher fidelity thermal models. Although a knowledge of the rotor temperature is necessary to determine derating in a motor's torque constant, note that the lumped capacitance method mentioned previously only focuses on the temperature of a single body, the stator. Predictions of rotor and magnet temperature rely on more accurate models and validation through empirical testing. Two primary means of improving the fidelity of the lumped capacitance thermal model are the multi node lumped capacitance model and thermal FEA. The multi node lumped capacitance model is similar to the simple lumped capacitance model described Secondary effects to consider. Equation (18) assumes that k M does not change with motor temperature, however there are actually temperature dependencies within k M that are important and can contribute to derating or improved performance of the motor. The first is the temperature dependence of magnet strength, on k T, which is an inverse linear relation up to the point where demagnetization occurs. The derating of k T is shown for a motor with Neodymium magnets in Figure 8. The second effect is that of temperature on resistance, Figure 9, which is a direct linear relationship. Both these effects work to reduce the motor constant at elevated temperatures beyond the room temperature assumption in (18). These combined effects were compared to theory by Frencken America for a spaceflight operation motor application where the frameless motor had to operate at extreme temperatures. Torque constant and power draw at a given torque were found to be very close to theoretical predictions, as shown in Figure 10. Figure 10
Jerad P. 10/1/015 previously, however in place of a single thermal mass, multiple masses within the model are considered to be able to store heat energy in the form of distinct temperatures. Each of the possible paths of heat from one thermal mass to the other is captured as well. The FEA approach, Figure 11, evaluates the temperature distribution within a given geometry based on a defined m esh of nodes, many more so than a multinode lumped capacitance model. Both approaches can typically model effects s uch as heat sources, thermal boundary conditions, and the heat transfer modes of conduction and radiation in addition to convection, to varying levels of accuracy. The results of the thermal models should always be validated through testing to ensure accuracy. Figure 1 shows one such test performed in a thermal vacuum chamber and used to validate predictions of thermal resistance of a motor in a vacuum when the primary means of heat dissipation is radiation instead of convection. Figure 11. Thermal FEA Motor Model Figure 1. Thermal Vacuum Motor Test Conclusion. In this document, the theory of motor performance thermal limitations have been described in detail. The typical method of heat transfer in a motor and the heat transfer equations have been developed and related to torque output. The importance of the dependency between torque required of a motor, the size of the motor, and the method of heat transfer in the motor cannot be overstated and requires careful attention in order to ensure proper sizing of a motor for a given application.
Jerad P. 10/1/015 Description of the Figures: Figure 1. Image of a Frencken America Manufactured Stator and otor Figure. Image of power balance: Input, Power, and Loss in a motor. Figure 3. Image of the stator heat balance equation and the heat transfer equations use Figure 4. Plot of a stator thermal response Figure 5. Motor Temperature esponse Measurement Figure 6. Plot of summation of squares of three power showing constant power dissipated as heat. Figure 7. Image taken from IEC 60034 1 showing motor duty cycles. Figure 8. kt dependence on temperature Figure 9. dependence on temperature Figure 10. OCO3 bi directional torque measurements Figure 11. FEA thermal model method for determining temperature distribution in a motor (Motorsolve Thermal Module) Figure 1. OCO3 thermal vacuum testing photo. Table 1. Thermal limits of common materials. [ref YES paper where this came from] Table. Measurement of Thermal esistance and Thermal Time Constant