the induction machine handbook chuong (12)

Chapter 12 THERMAL MODELING AND COOLING 12.1. INTRODUCTION Besides electromagnetic, mechanical and thermal designs are equally important. Thermal modeling of an electric machine is in fact more nonlinear than electromagnetic modeling. Any electric machine design is highly thermally constrained. The heat transfer in an induction motor depends on the level and location of losses, machine geometry, and the method of cooling. Electric machines work in environments with temperatures varied, say from –20 0 C to 50 0 C, or from 20 0 to 100 0 in special applications. The thermal design should make sure that the motor windings temperatures do not exceed the limit for the pertinent insulation class, in the worst situation. Heat removal and the temperature distribution within the induction motor are the two major objectives of thermal design. Finding the highest winding temperature spots is crucial to insulation (and machine) working life. The maximum winding temperatures in relation to insulation classes shown in Table 12.1. Table 12.1. Insulation classes Insulation class Typical winding temperature limit [ 0 C] Class A 105 Class B 130 Class F 155 Class H 180 Practice has shown that increasing the winding temperature over the insulation class limit reduces the insulation life L versus its value L 0 at the insulation class temperature (Figure 12.1). T b aLLog +≈ (12.1) It is very important to set the maximum winding temperature as a design constraint. The highest temperature spot is usually located in the stator end connections. The rotor cage bars experience a larger temperature, but they are not, in general, insulated from the rotor core. If they are, the maximum (insulation class dependent) rotor cage temperature also has to be observed. The thermal modeling depends essentially on the cooling approach. © 2002 by CRC Press LLC© 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… Figure 12.1 Insulation life versus temperature rise 12.2. SOME AIR COOLING METHODS FOR IMs For induction motors, there are four main classes of cooling systems • Totally enclosed design with natural (zero air speed) ventilation (TENV) • Drip-proof axial internal cooling • Drip-proof radial internal cooling • Drip-proof radial-axial cooling In general, fan air-cooling is typical for induction motors. Only for very large powers is a second heat exchange medium (forced air or liquid) used in the stator to transfer the heat to the ambient. TENV induction motors are typical for special servos to be mounted on machine tools etc., where limited space is available. It is also common for some static power converter-fed IMs, that operate at large loads for extended periods of time at low speeds to have an external ventilator running at constant speed to maintain high cooling in all conditions. The totally enclosed motor cooling system with external ventilator only (Figure 12.2b) has been extended lately to hundreds of kW by using finned stator frames. Radial and radial-axial cooling systems (Figure 12.2c, d) are in favor for medium and large powers. © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… However, axial cooling with internal ventilator and rotor, stator axial channels in the core, and special rotor slots seem to gain ground for very large power as it allows lower rotor diameter and, finally, greater efficiency is obtained, especially with two pole motors (Figure 12.3). [2] a.) zero air speed smooth frame end ring vents b.) finned frame external ventilator internal ventilator c. ) d. ) Figure 12.2 Cooling methods for induction machines a.) totally enclosed naturally ventilated (TENV); b.) totally enclosed motor with internal and external ventilator c.) radially cooled IM d.) radial – axial cooling system The rotor slots are provided with axial channels to facilitate a kind of direct cooling. © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… axial channel internal ventilator axial rotor channel axial rotor cooling channel rotor slots Figure. 12.3 Axial cooling of large IMs The rather complex (anisotropic) structure of the IM for all cooling systems presented in Figures 12.2 and 12.3 suggests that the thermal modeling has to be rather difficult to build. There are thermal circuit models and distributed (FEM) models. Thermal circuit models are similar to electric circuits and they may be used both for thermal steady state and transients. They are less precise but easy to handle and require a smaller computation effort. In contrast, distributed (FEM) models are more precise but require large amounts of computation time. We will define first the elements of thermal circuits based on the three basic methods of heat transfer: conduction, convection and radiation. 12.3. CONDUCTION HEAT TRANSFER Heat transfer is related to thermal energy flow from a heat source to a heat sink. In electric (induction) machines, the thermal energy flows from the windings in slots to laminated core teeth through the conductor insulation and slot line insulation. On the other hand, part of the thermal energy in the end-connection windings is transferred through thermal conduction through the conductors axially toward the winding part in slots. A similar heat flow through thermal conduction takes place in the rotor cage and end rings. There is also thermal conduction from the stator core to the frame through the back core iron region and from rotor cage to rotor core, respectively, to shaft and axially along the shaft. Part of the conduction heat now flows through the slot insulation to core to be directed axially through the laminated core. The presence of lamination insulation layers will make the thermal conduction along the axial direction more difficult. In long stack IMs, axial temperature differentials of a few degrees (less than 10 0 C in general), (Figure 12.4), occur. © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… circumpherential flow shaft rotor core radial flow stator core stator frame Figure 12.4 Heat conduction flow routs in the IM So, to a first approximation, the axial heat flow may be neglected. Second, after accounting for conduction heat flow from windings in slots to the core teeth, the machine circumferential symmetry makes possible the neglecting of circumferential temperature variation. So we end up with a one-dimensional temperature variation, along the radial direction. For this crude approximation defining thermal conduction, convection, and radiation, and of the equivalent circuit becomes a rather simple task. The Fourier’s law of conduction may be written, for steady state, as () qK =θ∆−∇ (12.2) where q is heat generation rate per unit volume (W/m 3 ); K is thermal conductivity (W/m, 0 C) and θ is local temperature. For one-dimensional heat conduction, Equation (12.2), with constant thermal conductivity K, becomes: q x K 2 2 = ∂ θ∂ − (12.3) A basic heat conduction element (Figure 12.5) shows that power Q transported along distance l of cross section A is AlqQ ⋅⋅≈ (12.4) with q, A – constant along distance l. The thermal conduction resistance R con may be defined as similar to electrical resistance. [] W/C KA l R 0 con = (12.5) © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… Area A Q 2 Q Q 1 x=0 θ=θ 1 x=l θ=θ 2 l stack b h s s ∆ ins fA Figure 12.5 One dimensional heat conduction Temperature takes the place of voltage and power (losses) replaces the electrical current. For a short l, the Fourier’s law in differential form yields [] 2 W/mdensity flowheat f ; x Kf − ∆ θ∆ −≈ (12.6) If the heat source is in a thin layer, A p f cos = (12.7) p cos in watts is the electric power producing losses and A the cross-section area. For the heat conduction through slot insulation ∆ ins (total, including all conductor insulation layers from the slot middle (Figure 12.5)), the conduction area A is ( ) stator/slotsN ;Nlbh2A ssstackss −+= (12.8) The temperature differential between winding in slots and the core teeth ∆θ Co is AK R ;Rp ins conconcosCos ∆ ==θ∆ (12.9) In well-designed IMs, ∆Θ cos < 10 0 C with notably smaller values for small power induction motors. The improvement of insulation materials in terms of thermal conductivity and in thickness reduction have been decisive factors in reducing the slot insulation conductor temperature differential. Thermal conductivity varies with temperature and is constant only to a first approximation. Typical values are given in Table 12.2. The low axial thermal conductivity of the laminated cores is evident. © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… Table 12.2. Thermal conductivity Material Thermal conductivity (W/m 0 C) Specific heat coefficient C s (J/Kg/ 0 C) Copper 383 380 Aluminum Carbonsteel 204 45 900 Motor grade steel 23 500 Si steel lamination – Radial; – Axial 20 – 30 2.0 490 Micasheet 0.43 - Varnished cambric 2.0 - Press board Normex 0.13 - 12.4. CONVECTION HEAT TRANSFER Convection heat transfer takes place between the surface of a solid body (the stator frame) and a fluid (air, for example) by the movement of the fluid. The temperature of a fluid (air) in contact with a hotter solid body rises and sets a fluid circulation and thus heat transfer to the fluid occurs. The heat flow out of a body by convection is θ∆= hAq conv (12.10) where A is the solid body area in contact with the fluid; ∆θ is the temperature differential between the solid body and bulk of the fluid, and h is the convection heat coefficient (W/m 2 ⋅ 0 C). The convection heat transfer coefficient depends on the velocity of the fluid, fluid properties (viscosity, density, thermal conductivity), the solid body geometry, and orientation. For free convention (zero forced air speed and smooth solid body surface [2]) () ( ) () ( ) () ( ) Cm W/- horizontal 67.0h Cm W/-down l vertica496.0h Cm W/- up l vertica158.2h 0 2 25.0 Co 0 2 25.0 Co 0 2 25.0 Co θ∆≈ θ∆≈ θ∆≈ (12.11) where ∆θ is the temperature differential between the solid body and the fluid. For ∆θ = 20 0 C (stator frame θ 1 = 60 0 C, ambient temperature θ 2 = 40 0 C) and vertical – up surface () ( ) CmW/5.44060158.2h 0 2 25.0 Co =−= When air is blown with a speed U along the solid surfaces, the convection heat transfer coefficient h c is () ( ) UK1huh Co 0 C += (12.12) © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… with K = 1.3 for perfect air blown surface; K = 1.0 for the winding end connection surface, K = 0.8 for the active surface of rotor, K = 0.5 for the external stator frame. Alternatively, () ( ) 5m/sfor U Cm W/ L U 77.1uh 0 2 25.0 75.0 C >= (12.13) U in m/s and L is the length of surface in m. For a closed air blowed surface – inside the machine: () () () a air Co c C a ;2/a1UK1hUh θ θ =−+= (12.14) θ air –local air heating; θ a –heating (temperature) of solid surface. In general, θ air = 35 – 40 0 C while θ a varies with machine insulation class. So, in general, a < 1. For convection heat transfer coefficient in axial channels of length, L (12.13) is to be used. In radial cooling channels, h c c (U) does not depend on the channel’s length, but only on speed. () ( ) Cm/WU11.23Uh 0 275.0 c c ≈ (12.15) 12.5. HEAT TRANSFER BY RADIATION Between two bodies at different temperatures there is a heat transfer by radiation. One body radiates heat and the other absorbs heat. Bodies which do not reflect heat, but absorb it, are called black bodies. Energy radiated from a body with emissivity ε to black surroundings is ()()()() 21 2 2 2 121 4 2 4 1rad AAq θ−θθ+θθ+θσε=θ−θσε= (12.16) σ–Boltzmann’s constant: σ = 5.67⋅10 -8 W/(m 2 K 4 ); ε – emissivity; for a black painted body ε = 0.9; A–radiation area. In general, for IMs, the radiated energy is much smaller than the energy transferred by convection except for totally enclosed natural ventilation (TENV) or for class F(H) motor with very hot frame (120 to 150°C). For the case when θ 2 = 40° and θ 1 = 80°C, 90°C, 100°C, ε = 0.9, h rad = 7.67, 8.01, and 8.52 W/(m 2 °C). For TENV with h Co = 4.56 W/(m 2 , °C) (convection) the radiation is superior to convection and thus it cannot be neglected. The total (equivalent) convection coefficient h (c+r)0 = h Co + h rad ≥ 12 W/(m 2 , °C). The convection and radiation combined coefficients h (c+r)0 ≈ 14.2W/(m 2 , °C) for steel unsmoothed frames, h (c+r)0 = 16.7W/(m 2 , ° C) for steel smoothed frames, © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… h (c+r)0 = 13.3W/(m 2 , °C) for copper/aluminum or lacquered or impregnated copper windings. In practice, for design purposes, this value of h Co , which enters Equations (12.12 through 12.14), is, in fact, h (c+r)0 , the combined convection radiation coefficient. It is well understood that the heat transfer is three dimensional and as K, h c and h rad are not constants, the heat flow, even under thermal steady state, is a very complex problem. Before advancing to more complex aspects of heat flow, let us work out a simple example. Example 12.1. One – dimensional simplified heat transfer In an induction motor with p Co1 = 500 W, p Co2 = 400 W, p iron = 300 W, the stator slot perimeter 2h s + b s = (2.25 + 8) mm, 36 stator slots, stack length: l stack = 0.15 m, an external frame diameter D e = 0.30 m, finned area frame (4 to 1 area increase by fins), frame length 0.30m, let us calculate the winding in slots temperature and the frame temperature, if the air temperature increase around the machine is 10°C over the ambient temperature of 30°C and the slot insulation total thickness is 0.8 mm. The ventilator is used and the end connection/coil length is 0.4. Solution First, the temperature differential of the windings in slots has to be calculated. We assume here that all rotor heat losses crosses the airgap and it flows through the stator core toward the stator frame. In this case, the stator winding in slot temperature differential is (12.3) () C 83.3 15.0058.036.00.2 6.0500108.0 lbh2NK l l 1p 0 3 stacksssins coil endcon 1Coins cos = ⋅⋅⋅ ⋅⋅⋅ = +         −∆ =θ∆ − Now we consider that stator winding in slot losses, rotor cage losses, and stator core losses produce heat that flows radially through stator core by conduction without temperature differential (infinite conduction!). Then all these losses are transferred to ambient through the motor frame through combined free convection and radiation. () () () C 758.74 1/43.030.02.14 300400500 Ah q 0 frame0rc total aircore = ⋅⋅⋅π⋅ ++ ==θ−θ + with θ air = 40°, θ ambient = 30°, the frame (core) temperature θ core = 40 + 74.758 = 114.758 ° C and the winding in slots temperature θ cos = θ core + ∆θ cos = 114.758 + 3.83 = 118.58°C. In such TENV induction machines, the unventilated stator winding end turns are likely to experience the highest temperature spot. However, it is not at all simple to calculate the end connection temperature distribution. © 2002 by CRC Press LLC Author: Ion Boldea, S.A.Nasar………… ……… 12.6. HEAT TRANSPORT (THERMAL TRANSIENTS) IN A HOMOGENOUS BODY Although the IM is not a homogenous body, let us consider the case of a homogenous body – where temperature is the same all over. The temperature of such a body varies in time if the heat produced inside, by losses in the induction motor, is applied at a certain point in time–as after starting the motor. The heat balance equation is () () radiation ,conduction ,convectionthrough body thefrom transfer heat 0 )conv( cond body in the onaccumulati heat 0 t in W time unitper losses loss TThA dt TTd McP −+ − = (12.17) M–body mass (in Kg), c t –specific heat coefficient (J/(Kg⋅ 0 C)) A–area of heat transfer from (to) the body h–heat transfer coefficient Denoting by       === KA l R; Ah 1 R and McC cond (rad) convtt (12.18) equation (12.17) becomes ()() t 00 tloss R TT dt TTd CP − + − = (12.19) This is similar to a R t , C t parallel electric circuit fed from a current source P loss with a voltage T – T 0 (Figure 12.6). p loss R C T T 0 tt τ =C R t tt T -T max 0 T-T 0 t Figure 12.6 Equivalent thermal circuit For steady state, C t does not enter Equation (12.17) and the equivalent circuit (Figure 12.6). The solution of this electric circuit is evident. () tt t 0 t 0max eTe1TTT τ − τ − +         −−= (12.20) © 2002 by CRC Press LLC [...]... TRANSIENTS The ultimate detailed thermal equivalent circuit of the IM should account for the three dimensional character of heat flow in the machine Although this may be done, a two dimensional model is used However we may break the motor axially into a few segments and “thermally” connect these segments together To account for thermal transients, the thermal equivalent circuit should contain thermal... – thermal resistance from core to air in ventilation channel Rt6 – thermal resistance towards the air inside the end connections (it is ∞ for round conductor coils) Rt7 – thermal resistance from the frontal side of end connections to the air between neighbouring coils Rt8 – thermal resistance from end connections to the air above them Rt9 – thermal resistance from end connections to the air below them... convention, through the circulating air in the machine Areas of heat transfer A6 – A9 depend heavily on the coils shape and their arrangement as end connections in the stator (or rotor) For round wire coils with insulation between phases, the situation is even more complicated as the heat flow through the end connections toward their interior or circumferentially may be neglected (R6 = R7 = ∞) As the air temperature... torque The duty cycle d may be defined as d= t ON t ON + t OFF (12.31) Complete use of the machine in intermittent operation is made if, at the end of ON time, the rated temperature of windings is reached Evidently the average losses during ON time Pdis may surpass the rated losses Pdisn, for continuous steady state operation By how much depends both on the tON value and on the machine equivalent thermal... source (W) Thermal Thermal resistance capacitor (0C/W) (J/ 0C) I Figure 12.11 Thermal circuit elements with units A detailed thermal equivalent circuit–in the radial plane–emerges from the more realistic thermal circuit of Figure 12.9 by dividing the heat sources into more components (Figure 12.12) The stator conductor losses are divided into their in-slot and overhang (endconnection) components The same... optimization method, the parameters of the equivalent circuit In essence, the squared error between calculated and measured (after filtering) temperatures is to be minimum over the entire time span In Reference 6 such a method is used and the results look good As some of the thermal parameters may be calculated, the method can be used to identify them from the losses and then check the heat division from its center... the machine is already hot at, say, 1000C, ∆θendcon = 1550 – 1000 = 55 C So the time allowed to keep the machine at stall is reduced to 0 (∆t )100 →155 0 C = 55 ⋅1⋅ 380 = 20.9 seconds 1000 The equivalent thermal circuit for this oversimplified case is shown on Figure 12.7a On the contrary, for long stacks, only the winding losses in slots are considered However, this time some heat accumulated in the. .. conductor insulation The machine is designed for lower winding temperatures at full continuous load To simplify the problem, let us consider two extreme cases, one with long end connection stator winding and the other a long stack and short end connections For the first case we may neglect the heat transfer by conduction to the winding in slots portion Also, if the motor is totally enclosed, the heat transfer... inside the machine was considered uniform, the stator and rotor equivalent thermal circuits as in Figure 12.10 may be treated rather independently (pFe = 0 in the rotor, in general) In the case where there is one stack (no radial channels), the above expressions are still valid with ns = 1 and, thus, all heat transfer resistances related to radial channels are ∞ (R4 = R5 = ∞) 12.10 A DETAILED THERMAL... heat transfer and thermal capacitances Cti (J/0C) stand for heat absorption in the various parts of the motor The heat sources plossi(W) represent current sources in the equivalent circuit Thermal resistances decrease with cooling air speed The windings have the highest temperature spots, in general It has been shown that, at least in small power IMs, about 80% of the heat (loss) in the stator coils . applications. The thermal design should make sure that the motor windings temperatures do not exceed the limit for the pertinent insulation class, in the worst. situation. Heat removal and the temperature distribution within the induction motor are the two major objectives of thermal design. Finding the highest winding