Chapter 6: Efficiency and Heating. 9/18/2003 Electromechanical Dynamics 1

Transcription

1 Chapter 6: Efficiency and Heating 9/18/2003 Electromechanical Dynamics 1

2 Losses As a machine transforms energy from one form to another there is always a certain power loss the loss is expressed as heat, causing a temperature increase there is a reduction in efficiency Types of losses mechanical speed dependent frictions found in bearings and brushes speed dependent windage and turbulence electrical conductor I 2 R losses (copper losses) brush voltage drop losses magnetic iron losses 9/18/2003 Electromechanical Dynamics 2

3 Electrical Losses Conductor losses are a function of the wire resistance and the carried current L R = ρ ρ = ρ0 1+ A R = resistance of conductor L = length of conductor A = cross sectional area ρ = resistivity at temperature t ρ 0 = resistivity at 0 C ( α t) α = temperature coefficient of resistance at 0 C t = temperature of conductor For designers, it is more useful to relate losses as a function of the conductor mass 1000 J P c = ζ ρ P c = specific conductor power loss J = current density [A/mm 2 ] ρ = resistivity at temperature t [nω m] ζ = density of the conductor [kg/m 3 ] 2 9/18/2003 Electromechanical Dynamics 3

4 Electrical Losses For copper conductors the acceptable current densities range from 1.5A/mm 2 to 6A/mm 2 the corresponding losses vary from 5 W/kg to 90 W/kg In brushes, a voltage drop develops as a function of brush materials used, the applied pressure, and brush current the drop varies from 0.8V to 1.3V Iron losses are due to hysteresis and eddy currents dependent on the magnetic flux density, speed of rotation, steel quality, and armature size typical values are 0.5 W/kg to 20 W/kg iron losses impose a mechanical drag on the armature similar to mechanical friction 9/18/2003 Electromechanical Dynamics 4

5 Load Influenced Losses Fixed losses a dc motor running at no-load develops no useful power some power is consumed to rotate the motor shaft no-load power must overcome friction, windage, iron losses, and copper losses in the shunt field windings Variable losses armature copper losses are a function of the motor loading Losses contribute to the temperature rise in a machine thermal limits control the total amount of power the machine can deliver (rated or nominal power) an overloaded motor will overheat and have a loss of useful life 9/18/2003 Electromechanical Dynamics 5

6 Efficiency Curve The machine efficiency varies for different loadings the efficiency rises sharply as loading increases for a broad range of power the efficiency is rather flat at higher loading the efficiency slowly falls Example 10 kw, rpm, 230 V, 50 A dc motor losses: mechanical losses = 290 W iron losses = 420 W shunt filed copper losses = 120 W armature copper losses at fullload = 595 W calculate the losses and efficiency at 0%, 25%, 50%, 75%, 100%, and 150% of nominal loading 9/18/2003 Electromechanical Dynamics 6

7 Life Expectancy The life expectancy of electrical apparatus is limited by the temperature of its insulation higher temperatures result in shorter life the service life diminishes by half for each 10 C rise in temperature Factors that contribute to insulation deterioration are heat, humidity, vibration, acidity, oxidation, and time insulators become hard and brittle insulation cracks result in short-circuit failures Most organic insulators have a life expectance of 8 to 10 years at 100 C 9/18/2003 Electromechanical Dynamics 7

8 Thermal Classifications of Insulators Established by standards maximum operating temperatures: 105 C, 130 C, 155 C, 180 C, 220 C maximum ambient temperature for design purpose: 40 C allows performance guarantees normal life expectancy of 20,000 hours to 40,000 hours Thermal insulator design influences size and costs The machine temperature varies from point to point all machines have some place that is the warmest the hot-spot temperature must not exceed the maximum allowable temperature the location is usually not known the machine s average temperature is always less than the hot-spot temperature average temperature is easier and more accurate to measure 9/18/2003 Electromechanical Dynamics 8

9 Temperature Rise Hot spot temperature limits compared to average machine temperature limits temperature rise is the temperature difference between limits and maximum ambient temperature rise permits relative comparisons Example machine with Class F insulation full-load test at ambient T = 32 C hot spot T = 125 C does it meet standards? 9/18/2003 Electromechanical Dynamics 9

10 Temperature Rise Calculations The hot-spot temperature is difficult to measure the location is somewhere inside the winding thermocouples can be used, but costs can only be justified for large machines Average winding temperature is an acceptable alternative simple to measure determined by measuring the winding resistance R2 t2 = ( 234Cu + t1 ) 234Cu { or 228Al} R1 R 1 = cold resistance R 2 = hot resistance t 1 = cold winding temperature t 2 = hot winding temperature with the hot temperature, the temperature rise can be found 9/18/2003 Electromechanical Dynamics 10

11 Resistance Method Example a machine is cold with an ambient temperature of 19 C shunt-field resistance is 22 ohms build with class B insulation at full load and stabilized operating temperature, the field resistance is 30 ohms the operating ambient temperature is now 24 C calculate the average full-load temperature the full-load temperature rise does the motor meet temperature standards 9/18/2003 Electromechanical Dynamics 11

12 Machine Size The maximum allowable temperature rise establishes the nominal power rating of a machine The physical size depends on the rated power and speed of rotation for a fixed power output, a lower speed machine is always bigger than a high speed machine the size of a machine depends uniquely upon its torque low-speed motors are more costly for a fixed output power Consider a 100 kw, 2000 rpm, 250V machine Suppose one builds another machine having the same power and voltage but runs at half speed need to double the number of armature conductors or double the pole flux typically increase both, causing an increase in size A 10 kw, 2000 rpm machine is about the same size of a 100 kw, 2000 rpm machine 9/18/2003 Electromechanical Dynamics 12

13 Homework 6-9, 6-17, 6-20 and /18/2003 Electromechanical Dynamics 13