White Paper. 201-White Paper Series Linear Motors David J. Carroll 10/01/07

Transcription

1 Linear Motor Heat Sink 201- Series Linear Motors David J. Carroll 10/01/07 ISO 9001:2000

2 Introduction Airex Corporation provides linear motor sizing information to system designers to insure maximum motor performance and identify any requirement for cooling in the motor application. With modeling information on thermal design and heat rise information specific to the application, designers can optimize the linear motor to their system requirement. The Linear motor, like many devices, must be optimized in its operating environment to insure a long and service free life. The system integrator or designer with system responsibility is tasked with the proper application of cooling by first determining the effect of heating in operation. Complex Linear motor applications can employ a variety of cooling solutions, and with each method come benefits and tradeoffs. For any given system this includes; liquid cooling, forced air convection or conduction cooling. The minimum required thermal resistance for the cooling can be determined by subtracting the motor thermal resistance from the total system thermal resistance. The primary focus of this document is to discuss air-cooling via the application of a heat sink. Background and Linear Motor Features The Linear motor coil temperature increases with increasing power applied to the coil. The force produced by the motor is the current times the motor force constant and the power to be dissipated is the applied current squared times the resistance. Note: In this paper, resistance denotes electrical resistance. Thermal resistance will always be detailed separately. The motor force (F) is: F I Kf Where: F Motor force I Current K f Force constant The motor power to be dissipated (P) is measured in Watts and is calculated using the following equation: Where: P I 2 R R Resistance October 1, 2007 Page 2 of Linear Motor-Heat Sink

3 The resistance of the coils in the motor is specified in Ohms at 20 C. The coil resistance varies with the temperature of the copper coils. The following formula can be used to determine the resistance of the copper coils at a specific temperature: R Ri ( i ( T f T )) Where: R Coil Resistance Ri Coil Resistance Specified at 20 C T f Final Coil Temperature T i Initial Coil Temperature An example of the resistance change due to temperature follows: A motor coil has a delta resistance of 7.57 Ohms at 20 C and is to be installed in a 70 C ambient temperature (see definitions below) environment. Find the resistance of the coil due to the warm environment. R 7.57Ohms ( (70 C 20 C) 9. 06Ohms As power is applied to the motor coils, heat is generated, which warms the copper coils, thus increasing the coil resistance. This increase in resistance further increases the power to be dissipated. The heat generated in the motor coils must be dissipated fast enough or the coils will continue to heat up to a point of failure. By design, heat is conducted from the active portions of the coil to the mounting bracket, where the heat must be removed by external means. Using equation 2 and the conditions from the above example; the power to be dissipated as heat when 2.5 Amps is applied continuously to the motor is: 2 P 2.5Amps 9.06Ohms 56. 6Watts If the motor in the above example were running at its maximum rating of 125 C, the resistance would be about 10.7 Ohms. The power dissipated with a 2.5 Amp motor current would be just over 66 Watts. The heat to be dissipated, can be conducted into the structure of a system, transferred to another system via a liquid cooled heat exchanger, or dissipated by an air-cooled heat sink. October 1, 2007 Page 3 of Linear Motor-Heat Sink

4 The Airex Linear motor design (shown in Figure. 1 below), improves performance by optimally using the coil structure to distribute and transfer heat to the mounting bracket. Heat is transferred longitudinally across adjacent end-turns by the motor heat sink cap, which is located opposite the mounting bracket, allowing heat to flow into the core of the motor. The motor coil assembly sides are insulated to minimize the heating of the surrounding magnets. In most cases, less than 10% of the motor heat is dissipated into the magnet track, minimizing magnet heating, thus maximizing magnet track flux production at high motor power levels. Figure1: Linear Motor Sectional View Motor Coil Mounting Bracket Magnet Track Thermal Insulation Motor Coils Heat Sink Cap October 1, 2007 Page 4 of Linear Motor-Heat Sink

5 A Little Thermodynamics Heat is transferred by conduction, convection and radiation. Conduction relies on good physical contact between a warm object and a cooler one to transfer heat. Conduction is the most efficient means for transferring heat at the temperatures normally encountered in Linear motor applications. Convection is the process of transferring heat to a fluid or a gas such as air, where the fluid is self-displacing (it moves) due to density change. Heat is also transferred by emitted radiation. The heat escapes as electromagnetic radiation and can transmit heat from a warm object to cooler surroundings. Radiant transfer of heat depends on temperature difference and the properties and orientation of the object surfaces. Radiation of heat is proportional to 5.7E-8 times the difference between the fourth power of temperatures ( Kelvin) of the motor and the fourth power of the temperature of the surrounding objects. Radiation works best with great differences in temperature such as between the sun and the earth, or between a person and a fire in the fireplace. Only small amounts of heat can be removed from the motor coil by radiation at normally expected motor temperatures. The conduction of heat from a hot object to a cooler object is not instantaneous; the thermal resistance of the materials in the path limits the flow of heat. Similar to an electrical circuit, the total thermal resistance of a system is the sum of the series elements in the path. The thermal resistance of an object is defined as the heat rise across an element in the circuit when a given amount of heat is flowing through the path. The element is bounded at each end by an isothermal. An isothermal is an interface where the temperature is assumed to be constant across the entire surface of the interface. The thermal resistance R T has units of C/W: Where: T R T P T Temperature difference between the two isothermals P Power (Heat) flowing through object Doubling the thickness of a material in a series path doubles the thermal resistance of the material. A table shown below lists the thermal resistance of some common materials. Some tables of material thermal properties list thermal conductance, which is the inverse of thermal resistance. Materials such as silver, copper and aluminum have very low thermal resistances and are good conductors of heat. Steel (especially stainless steel) can have thermal resistances more than 10 times higher than copper. Materials such as G11 or air have very high thermal resistances and are often referred to as thermal insulators. October 1, 2007 Page 5 of Linear Motor-Heat Sink

6 Every system has a maximum thermal resistance, which is calculated for the total thermal drop in the system the power dissipated in the system. The maximum thermal resistance is also called the system thermal resistance limit RS has units of C/W: Where: R S T P October 1, 2007 Page 6 of Linear Motor-Heat Sink S T S Difference temperature across the system P Power (Heat being dissipated) Many Linear motor applications are cooled by convection via an attached heat sink. The typical heat sink uses fins to greatly increase the surface area to improve the efficiency of heat transfer to the air. Air is a relatively poor medium for transferring heat. It is a thermal insulator and has fluidic properties that limit close interaction with fin surfaces thus limiting heat transfer. Forced air movement can greatly enhance the effect of convection. With convection cooling, heat from the motor flows from the warm motor coil-mounting bracket into the core of the heat sink, where the heat sink surface area is cooled by air through convection. For our purposes the heat sink calculations shown here apply to air at sea level pressure. Only radiation and conduction will directly move heat in a vacuum. There are many buzzwords and terms used when discussing motor performance and heat. The essential definitions follow: Ambient Temperature - The maximum temperature of the air that generally surrounds the Linear motor coil and magnet track, measured in degrees Celsius ( C). Generally the maximum ambient temperature for the Linear motor coils, commutation devices, cables, and magnet tracks is 90 C. Heat Sink A device with large surface area used to dissipate heat from a warm object into the surrounding air. Maximum Temperature The temperature limit or rating of an object, specified in C. If the maximum temperature is exceeded, the operational life of the device will be shortened. The maximum temperature for the Linear motor coil is 125 C, measured as an average throughout the coil. Power The amount of heat to be dissipated in Watts. Resistance The opposition of electric current in a conductor. Measured in Ohms. System Thermal Resistance Limit The temperature rise seen in a system when a given level of heat (power) is being transferred. Calculated as the temperature rise divided by the dissipated power. The sum of the thermal resistance drops in the system must be less than the system resistance limit.

7 Temperature Rise An increase in temperature of an object above a reference temperature. The temperature rise is measured as the average coil temperature minus the ambient temperature. The maximum temperature rise generally specified for the Linear motor is 105 C. Thermal Capacity The ability of an object to absorb heat per unit temperature rise. Thermal capacity aids in the ability of a motor to handle peak power demands without exceeding its specified ratings. Thermal Resistance The temperature rise seen in an object when a given level of heat (power) is being transferred through the object, Stated as the temperature rise divided by the dissipated power. Thermistor A resistive device embedded in the Linear motor coil, used to evaluate the coil thermal performance. This device can be selected to have a negative temperature coefficient (NTC) or a positive temperature coefficient (PTC). Thermostat A temperature sensitive switch, embedded in the motor bracket. A thermostat is a device that signals the system that the motor bracket is over temperature. Typical System Configurations: o In moving magnet track applications, the coil can be directly attached to a substantial machine base, which can often provide the highest level of cooling through direct conduction. The system designer can select the appropriate mounting material such as aluminum, as well as a sufficient volume of material to easily conduct heat away from the coil and dissipate it into the surroundings. Other cooling means such as liquid cooled heat exchangers or large heat sinks are easily integrated to the fixed coil. The weight of any heat spreading or dissipating device such as a cooling loop has no impact on the motion problem. The key advantages to stationary coil configurations include the possibility of very high levels of cooling, the elimination of moving cables / cooling hoses and a possible reduction in moving mass. When the coil is part of the moving member, similar to the system shown on the cover page or in Figure 2, it is necessary to critically evaluate the heat removal means. The heat removal means has moving mass and can impact other system components. A moving coil system can exhibit the highest levels of motion performance, due to low moving mass. Some motion problems with a low duty cycle can maintain a safe operating temperature, by carefully managing the thermal capacity of the motor. The system designer must review the motion profile and duty cycle in light of the cooling requirement. Some systems move fast enough and far enough to make convection cooling efficient through sufficient movement of air over the heat sink. A Linear motor magnet track and coil can be side mounted to reduce the overall height of a motion platform. In the configuration shown in Figure 2, good design October 1, 2007 Page 7 of Linear Motor-Heat Sink

8 practices must be used to minimize the loss in heat transfer efficiency due to the longer thermal path between the coil mounting bracket and the heat sink. The number of material interface boundary crossings also impacts cooling effectiveness. The following slide configuration minimizes these issues by using a wide adaptor block to transport motor heat to the table, which is acting as the heat sink. Also note the lip on the adaptor block, which overlaps the side of the motor mounting bracket to remove a few extra watts of heat. Heat sink grease must be used on all mating surfaces to minimize losses in the thermal path. Figure 2. Low profile slide application, heat flow shown with red arrows Some systems localize the heat dissipation by isolating the motor and heat sink combination from the remainder of the system. The motor/heat sink combination is mechanically attached to system via a thermal barrier such as a block or strip of G11. This approach minimizes conduction of heat from the hot components into the rest of the system. In addition to isolating conducted heat from the system, the warm air from the heat sink may need to be deflected away from thermally sensitive components. Encoders and bearings can be especially sensitive to heat in some applications due to differential thermal expansion, thermal drift, or the use of low melting point materials. Linear Motor Thermal Resistance The Linear motor thermal resistance is specified and verified at the factory. The specification of thermal resistance elements allows the system designer to budget the thermal requirements of the system. The process of thermal resistance and continuous power rating testing begins with the measurement of electrical resistance to establish the initial test parameters. The motor bracket is mounted to a heat sink (typically less than 0.06 C/W thermal resistance). The motor is energized to an initial power level and the motor power and temperatures are monitored and the power is gradually increased. The thermal drop between ambient and the heat sink temperature is maintained by airflow to be October 1, 2007 Page 8 of Linear Motor-Heat Sink

9 less than 10 degrees C. The test power is gradually increased until the motor is at the maximum operating limits. The thermal limit is reached when either the average coil temperature reaches 125 C or the temperature rise exceeds 105 C. The coil described in above examples was tested at a power level of 169 Watts with a temperature rise of 105 C. Using equation 4 above, the thermal resistance of this Linear motor plus the attached heat sink R TH is: R TH T P 105 C 169Watts 0.62 C/W The motor thermal resistance is determined by subtracting the test thermal resistance from the measured total. The motor thermal resistance is calculated by: R T R TH R S Thus: R T 0.62 C/W C/W 0.56 C/W The application discussed above with a motor running at maximum temperature dissipated just over 66 Watts. In a 70 C ambient, the system thermal resistance limit is R S T P 125 C 70 C 66Watts 0.83 C/W The thermal budgeting process calculates the maximum heat sink thermal resistance R as follows: HM R HM R S R Which for this example the thermal resistance of the heat sink is: T R HM 0.83 C/W 0.56 C/W.27 C/W In the next sections the selection of a heat sink to achieve proper cooling will be discussed. Heat Sink Application (Practice and Nasty Realities) The keys to proper motor cooling are the system specification and the component thermal resistances. The total system thermal resistance is composed of a motor thermal resistance element and a heat dissipation thermal resistance element in series. The total of these series resistances must be low enough to allow the needed amount of heat to flow without overheating any element in the series path. The October 1, 2007 Page 9 of Linear Motor-Heat Sink

10 following diagram illustrates a simplified thermal model with discrete thermal elements illustrating a Linear motor coil and attached heat sink. Airflow through the heat sink in the diagram below would be in the direction of the paper. The parallel circuit paths for heat spreading are not shown: Figure 3: Heat flow from the Linear motor to a convection-cooled heat sink The power to be dissipated must be determined for your application. Remember to follow the thermal limits shown in the motor specification. For moving coil systems the motion calculation should include an estimate of the heat sink mass. The system thermal resistance limit is calculated (using equation 5) by dividing the allowable heat rise by the power that is to be dissipated. The motor thermal resistance can be determined by dividing the 105 C temperature rise by the continuous power rating shown in the data sheet. The maximum limit for heat sink thermal resistance is calculated by subtracting the motor thermal resistance from the system thermal resistance. A search for an appropriate heat sink is the next step. Many on-line resources are available to aid in this search. See If an appropriate heat sink cannot be found, perhaps a shorter version of a larger motor can be specified to allow proper cooling to take place. The larger motor and new heat sink mass must be re-checked as above. It may be necessary to repeat the above steps to fully resolve heat sink sizing where the mass of the heat sink is a significant portion of the moving mass. A larger motor may need to be selected to produce the required force while maintaining an acceptable operating temperature. At higher ambient temperatures, such as that October 1, 2007 Page 10 of Linear Motor-Heat Sink

11 used in the above calculation must derate the Linear motor force constant to account for reduced magnet track flux. Once a heat sink has been chosen, it should be reviewed against the motion profile for preferred mounting orientation, as this can affect the efficiency of the heat transfer from heat sink to the air. With slow moving applications, the heat sink can be mounted with the fins arranged transverse to the motor, allowing additional cooling through use of the heat sink fin web to spread heat through the heat sink. Faster moving applications should have the heat sink fin direction parallel with the direction of travel to make best use of induced airflow. Most on-line resources can predict performance for a heat sink at or about the same width as the motor. Wider heat sinks must be used with care to account for the additional thermal resistance caused by the longer thermal path. A high thermal conductivity heat spreading plate may need to be added to the system to maintain desired performance levels. The next few example calculations shown below, use data from the AAVID web site for illustration only. AAVID part number is 4.8 wide, 1.77 high, 10 long, weighs 2.85 pounds and has a.45 C /W thermal resistance. Good practice dictates that at least a design margin be used when specifying, as the manufacturer of the heat sink is specifying his best configuration for a given type with assumes evenly distributed heat load and usually a preferred orientation. Heat sink performance increases as the square root of the heat sink length. The air is warmed as it travels down the heat sink fins resulting in a smaller temperature difference as the heat sink is increased in length. A heat sink extrusion that is cut to 5 long and properly cools a motor will, when applied in a 10 length to a motor, only provide 1.4 times the cooling. Heat sink manufacturers specify the heat sink as if the device to be cooled covered the entire base. The specified heat sink thermal resistance will be higher when applied to a Linear motor, as the heat sink can be much wider than the motor. See the heat spreading discussion below. The system designer must avoid the temptation to use the calculations for one vendor s heat sink to size a different vendor s heat sink, or worse to use a published surface area to evaluate the effectiveness of a homemade heat sink or mounting plate. Even small changes in web thickness; fin geometry, material alloy or surface finish will make large changes in the effectiveness of heat transfer to the air. When initially considering a heat sink, a rough approximation of the heat sink block volume to thermal resistance is 500 to 800 cm 3 C/W. As an example we will try to estimate the thermal resistance of the heat sink published above. The volume based thermal resistance, R T is calculated for the AAVID heat sink described above: R T V / Vc Where: October 1, 2007 Page 11 of Linear Motor-Heat Sink

12 V Heat sink volume in cm 3 Airex Corporation Vc Volume to thermal resistance reference constant of 650 cm3 C/W The above heat sink is about 1350 cubic centimeters (cm 3 ) in volume. The thermal resistance is calculated as shown: Rt 650 cm 3 C/W / 1350 cm C/W This value is very close to the published.45 C/W thermal resistance. Altitude can affect convection cooling performance. The system designer must derate heat sink performance for increasing altitude. A typical efficiency scaling value for altitude is 75% at 12,000 feet. It is also important to note the location of the Linear motor heat sink relative to nearby sources of heat as well as heat sensitive devices such as encoders and interferometers. Heat sources adjacent to the Linear motor can interfere with heat removal. The correct motor mounting practices must be employed to achieve the calculated cooling capacity. The motor bracket must be securely attached to a mounting surface that is at least the full length of the motor coils. The mounting surface must be flat and must have a fine surface finish. High quality thermal grease must be used at every transition surface and the mounting screws should be evenly tightened. The motor coil should be mounted as centered as possible in the track to avoid transfer of heat to magnets due to accidental contact, as magnets will demagnetized when heated above their maximum operating temperature. A transition or heat spreading plate (sometimes made from copper) can be used to allow the heat to spread from the relatively narrow motor bracket to a wider heat sink. This approach must be used with care as it increases both the mass and the path length that heat must travel through to be dissipated. Low thermal resistance material must be used in the construction of the spreading plate. The following table lists the thermal conductivities (inverse of the thermal resistance) for several materials. The practices recommended for motor cooling must be carefully followed to gain benefit from the spreading plate. Remember: flat surfaces, smooth surface finish, thermal grease, evenly and fully and evenly tighten all fasteners. The following table lists the thermal conductivities (inverse of the thermal resistance) for several materials: October 1, 2007 Page 12 of Linear Motor-Heat Sink

13 Material Thermal Conductivity (W/ / C) Copper 9.6 Aluminum 5.52 Epoxy The thermal resistance of a spreading plate can be determined with the following simplified formula: Thermal Monitoring θ 1 A 2l ln 2 k ( A B ) B 2l Where: + + B A θ Thermal Resistance for the plate in C/W k Thermal conductivity of the material A, B The width and length of the plate l The thickness of the plate It is very important to maintain the motor temperature at or below the maximum safe operating temperature. There are many ways to verify this: First, the ambient temperature coil resistance and increase in resistance with motor under power can be used to calculate the average operating temperature. Advanced controls and some amplifiers can monitor the voltage and current to allow operation up to a set point, which when exceeded causes a correction back to the safe operating point. The thermistor is a resistive device that produces a continuous resistance proportional to the motor temperature. A resistance measurement of the thermistor is often done while the system is being set-up and tuned. Some control systems can monitor the thermistor through the use of an ADC. Two thermistor types are available; 1) a NTC type that has a room temperature resistance of typically 10 k- Ohms, decreasing non-linearly to about 300 Ohms for a hot motor; 2) a PTC type that has a room temperature resistance of 100 Ohms, Linearly increasing resistance with temperature. See the following graphs (figures 4 and 5) for PTC and NTC temperature to resistance conversion reference: October 1, 2007 Page 13 of Linear Motor-Heat Sink

14 160 Positive Tc Thermistor 150 Resistance, ohms Temperature, *C 14 Negative Tc Thermistor 12 Resistance, Kohms Temperature, *C Figure 4 and Figure 5 Thermistor temperatures to resistance conversion graphs A thermostat is often located in the motor bracket (replaces the thermistor) for thermal protection. The switch activates when the bracket temperature reaches a October 1, 2007 Page 14 of Linear Motor-Heat Sink

15 critical limit. Thermostat switches are specified as Close on rise or Open on rise. The typical Linear motor thermostat Activates at 105 C and deactivates at 100 C. The thermostat is an on/off device and can only indicate when the system is already in trouble. Thermostats must be used with care, as they can give short false indications when subject to acceleration and vibration. A thermostat must not be used to carry much current as the device self heats when handling large currents. Linear Motor Application Examples A motor coil is installed in a 20 C ambient temperature environment. It is moving at 1 mm/s. The application requires a force of 14.4 pounds, which requires a current of 3.6 Amps. The motor can run at the maximum temperature. Specify a suitable heat sink: 1. Find the resistance of the coil. R 3.79Ohms ( (125 C 20 C) 5. 36Ohms 2. Find the power to be dissipated by the system and the system thermal resistance limit. 2 P 3.6Amps 5.36Ohms 69. 5Watts R S T P 125 C 20 C 69.5Watts 1.51 C/W 3. Find the maximum heat sink resistance by subtracting the motor thermal resistance from the system thermal resistance. R HM 1.51 C/W 1.24 C/W.27 C/W The search for a suitable heat sink located an AAVID Part number Heat spreading for this wide heat sink is an issue but the thick heat sink base plate could allow for sufficient cooling. The thick base could also act as a structural member for the motion system components. At the slow speed used in this example, the heat sink weight will have little impact on the motion. An output from the AAVID web site product search engine can be seen in Figure 6: October 1, 2007 Page 15 of Linear Motor-Heat Sink

16 Figure 6. AAVID Heat sink selection A motor coil is installed in a 20 C ambient temperature environment. It is moving at 1 m/s. The application requires a force of 14.4 pounds, which requires a current of 3.6 Amps. The motor can run at the maximum temperature. Specify a suitable heat sink: 4. Find the resistance of the coil. R 3.79Ohms ( (125 C 20 C) 5. 36Ohms 5. Find the power to be dissipated by the system and the system thermal resistance limit. 2 P 3.6Amps 5.36Ohms 69. 5Watts R S T P 125 C 20 C 69.5Watts 1.51 C/W 6. Find the maximum heat sink resistance by subtracting the motor thermal resistance from the system thermal resistance. R HM 1.51 C/W 1.24 C/W.27 C/W October 1, 2007 Page 16 of Linear Motor-Heat Sink

17 The search for a suitable heat sink located an AAVID Part number Heat spreading for this wide heat sink is an issue but the thick heat sink base plate could allow for sufficient cooling. The thick base could also act as a structural member for the motion system components. At the slow speed used in this example, the heat sink weight will have little impact on the motion. The following is an application example where a Linear motor is used at a 75-Watt power level where the maximum heat rise of the coil must not exceed 55 Degrees C. The machine maximum ambient temperature is 40 Degree C. The motor achieves a velocity of 2 meters per second for a 50% duty cycle. 1. The differential between the ambient and the motor is [ degrees C]. The resulting temperature is below the motor maximum operating temperature of 125 degrees C. 2. The system thermal resistance is [55 degrees C / 75 Watts.733 Degrees C/Watt] 3. Subtracting the motor specified thermal resistance of Degrees C/Watt (for the motor) from the system thermal resistance of.733 Degrees C/Watt, the maximum heat sink thermal resistance is.422 Degrees C/Watt. 4. A search for a suitable heat sink on the AAVID web site yields 4 pages of heat sink shapes. Many of these are heavy or very large. P/N is 7.2 wide, by 2.83 tall. This unit weighs 6.08 pounds. 5. The movement of the coil allows some forced cooling to take place. A search for small heat sinks with a thermal resistance slightly higher than.4 Degrees C/Watt located part # (4.8 wide, 1.77 tall, 10 long, 24 fins, weighs 2.85 pounds). This unit has a thermal resistance of about 0.25 Degrees C/Watt with an average airflow of 1 meter per second (based on the 50% duty motion). If the heat-sink mass is an issue this is clearly an interesting option. October 1, 2007 Page 17 of Linear Motor-Heat Sink