Thermal.

----W H I T E P A P E R

COSMOS

Thermal Analysis

SolidWorks Corporation

C O N T E N T S

Introduction 1-2

Using design validationfor thermal analysis 3

Heat transferfundamentals 4-10

Desired capabilities ofthermal designvalidation software 11

A sample of designproblems which canbe solved withCOSMOSWorksthermal 12-16

COSMOS T H E R M A L A N A LY S I S no. 1

To reduce product development cost and time, traditional prototyping andtesting has largely been replaced in the last decade by a simulation-drivendesign process. Such a process, which reduces the need for expensive andtime-consuming physical prototypes, allows engineers to successfully predictproduct performance with easy-to-modify computer models (figure 1).

Design verification tools are considered invaluable in studying such structuralproblems as deflections, deformations, stresses or natural frequencies.However, the structural performance of new products is only one of manychallenges facing design engineers. Other common problems are thermallyrelated, including overheating, the lack of dimensional stability, excessivethermal stresses and other challenges related to heat flow and the thermalcharacteristics of their products.

Thermal problems are very common in electronics products. The design ofcooling fans and heat sinks must balance the need for small size withadequate heat removal. At the same time, tight component packaging muststill ensure sufficient air flow so that printed circuit boards do not deform orcrack under excessive thermal stress (figure 2).

Thermal challenges also abound in traditional machine design. Obviousexamples of products that must be analyzed for temperature, heat dissipationand thermal stresses are engines, hydraulic cylinders, electric motors orpumps - in short, any machine that uses energy to perform some kind ofuseful work.

I N T R O D U C T I O N

Motion simulation providescomplete, quantitativeinformation about thekinematics - including position,velocity, and acceleration, andthe dynamics - including jointreactions, inertial forces, andpower requirements, of all thecomponents of a movingmechanism.

Figure 1Traditional versussimulation-drivenproduct designprocesses

Figure 2Electronic packagingrequires careful analysis ofhow heat produced byelectronic components isremoved to the environment.


Perhaps less obvious candidates for thermal analysis are material-processing machines where mechanical energy turns into heat affecting notonly the machined piece but also the machine itself. This situation isimportant not only in precision machining equipment, where thermalexpansion may affect the dimensional stability of the cutting tool, but also inhigh power machines such as shredders, where components may suffer fromexcessive temperature and thermal stresses (figure 3).

As a third example, most medical devices should be analyzed for thermalperformance. Drug-delivery systems must assure proper temperature of theadministered substance while surgical devices must not subject the tissue tothe point of excessive thermal shock. Similarly, body implants must notdisrupt heat flow inside the body, while dental implants must also withstandsevere external mechanical and thermal loads (figure 4).

Finally, all electrical appliances such as stoves, refrigerators, mixers, ironsand coffee- makers - in short, anything that runs on electricity - should beanalyzed for thermal performance to avoid potentially dangerous overheating.This applies not only to consumer products that run off AC power, but also tobattery-operated devices such as remote-controlled toys and cordless powertools (figure 5).

I N T R O D U C T I O N

Figure 3Potential overheating of anindustrial shredder is an importantconsideration in the design of itstransmission and bearings.

The motion simulation programuses material properties fromthe CAD parts to define inertialproperties of the mechanismcomponents, and translates CADassembly mating conditions intokinematic joints.

Figure 4Dental implants must not affectthermal conditions of thesurrounding tissue and must alsowithstand thermal stresses.

Figure 5Adequate cooling of a highcapacity battery on a cordlesstool requires understanding thethermal conditions of this tool.

Using design validation for thermal analysisAll of the above thermal design problems and many more can be simulatedwith design validation software. Most design engineers are already familiarwith this approach for structural analysis, so expanding its scope to thermalanalysis requires very little additional training. Structural and thermalsimulations are based on exactly the same concepts, follow the same well-defined steps, and share multiple analogies (figure 6).

Furthermore, thermal analyses are performed on CAD models the same wayas structural analyses so, once a CAD model has been created, a thermalverification can be completed with very little extra effort.

Thermal analyses can be executed to find temperature distribution,temperature gradient and heat flowing in the model, as well as the heatexchanged between the model and its environment.

Thermal effects such as temperatures are easy to simulate, but may be quitedifficult to measure, especially inside parts or assemblies, or if temperaturesare changing rapidly. This often means that software-based design validationmay indeed be the only method available to engineers interested in thedetailed thermal conditions of their products.


U S I N G D E S I G N V A L I D A T I O N F O R T H E R M A L A N A L Y S I S

Figure 6Analogies betweenstructural and thermaldesign validation

Motion simulation conductsinterference checks in real time,and provides the exact spatialand time positions of allmechanism components as wellas the exact interferingvolumes.

Figure 7Typical resultsprovided by thermaldesign validation


H E A T T R A N S F E R F U N D A M E N T A L S

Heat transfer fundamentalsConduction and convectionThere are three mechanisms responsible for heat transfer: conduction,convection and radiation. Conduction describes heat flowing inside a body, withthe latter most often modeled as a CAD part or assembly. Conduction andradiation both involve heat exchange between the solid body and theenvironment.

An example of heat transfer by conduction is heat flow across a wall. Theamount of transferred heat is proportional to the temperature differencebetween the hot side THOT and the cold side TCOLD of the wall, to the area Aof the wall, and to the reciprocal of the wall thickness L. The proportionalityfactor K, called thermal conductivity, is a well-known material property (figure 9).

In addition to mechanismanalysis, product developers canalso use motion simulation formechanism synthesis byconverting trajectories of motioninto CAD geometry.

Figure 8Main characteristicsof three heattransfer mechanisms

Figure 9Heat is conducted through thewall from the higher to thelower temperature.



Thermal conductivity K varies widely for different materials; this factor is whatdifferentiates between heat conductors and insulators (figure 10).

The mechanism of heat exchange between an external face of a solid bodyand the surrounding fluid such as air, steam, water or oil is called convection.The amount of heat moved by convection is proportional to the temperaturedifference between the solid body face TS and the surrounding fluid TF, and tothe area A of the face exchanging (dissipating or gaining) heat. Theproportionality factor h is called the convection coefficient, also known as afilm coefficient. Heat exchange between the surface of a solid body and itssurrounding fluid requires movement of the fluid (figure 11).

Figure 11Heat dissipated byconvection always requiresmovement of the fluidsurrounding the body.

Designers can also usetrajectories of motion to verifythe motion of an industrialrobot.

Figure 10Conduction coefficientsfor different materials

To understand how motionsimulation and FEA worktogether in mechanismsimulation, it helps tounderstand the fundamentalassumptions on which eachtool is based.



The convection coefficient strongly depends on the medium (e.g., air, steam,water, oil) and the type of convection: natural or forced. Natural convectioncan only take place in the presence of gravity because fluid movement isdependent on the difference between the specific gravity of cold and hotfluids. Forced convection is not dependent on gravity (figures 12, 13).

To see how conduction and convection work together, consider a heat-sinkassembly (figure 14).

A microchip generates heat throughout its entire volume. Heat moves withinthe microchip by conduction then is transferred to an aluminum radiatorwhere it also travels by conduction. As heat travels from the porcelainmicrochip to the aluminum radiator, it must overcome a thermal resistancelayer formed by imperfections at the porcelain-aluminum interface. Finally,heat is dissipated by convection from the outside faces of the radiator to thesurrounding air.

Figure 13Heat convectioncoefficients fordifferent media andfor different typesof convection.

Figure 14A ceramic microchip generatingheat is embedded in analuminum radiator. The radiatoris cooled by the surrounding air.

Figure 12Natural convection isinduced by adifference in hot andcold fluid density. Inforced convection,fluid movement isforced, for example,by a cooling fan.

Adding a cooling fan or immersing the radiator in water does not change themechanism of heat transfer. Heat is still removed from the radiator faces byconvection. The only difference between air and water acting as coolants andbetween natural and forced convections is a different value of convectioncoefficient.

The temperature field in the heat-sink assembly is shown in figure 15. Themovement of heat from the radiator face to the ambient air can be picturedby plotting heat-flux vectors (figure 15, right). Heat flux vectors "coming out"of the radiator faces visualize heat removed to the surrounding fluid. Novectors cross the bottom face because in the model the bottom faces of theradiator and microchip are insulated.

Note that modeling the heat flowing in the heat-sink assembly requiresaccounting for a resistance to heat flow at the interface between the ceramicmicrochip and the aluminum radiator. In some design verification programs,the thermal resistance layer must be modeled explicitly; in others, likeCOSMOSWorks, it can be entered in a simplified way as a thermal resistancecoefficient.



The difference between astructure and a mechanism maynot be obvious at first sight.

Figure 15Temperature distribution and heatflux in the heat-sink assembly.



Conduction, convection and radiationSo far this discussion of heat transfer in the heat-sink assemblyconsiders only two heat-flow mechanisms: conduction (responsible formoving heat inside the solid bodies: microchip and radiator) andconvection (which dissipates heat from the external faces of theradiator to the ambient air). Heat transfer by radiation can be ignoredbecause at the operating temperature of heat-sink radiation, heattransfer is very low. The next example highlights a heat transferproblem where radiation can't be ignored.

Radiation can move heat between two bodies of different temperaturesor it can radiate heat into space. It does not depend on whether or notthe bodies are immersed in a fluid or are surrounded by a vacuum(figure 16).

The amount of heat exchanged by radiation between the faces of twosolid bodies with temperatures T1 and T2 is proportional to thedifference of the fourth power of absolute temperatures to the area Aof the faces participating in the heat transfer, and to the emissivity ? ofthe radiating surface. Emissivity is defined as the ratio of the emissivepower of the surface to the emissive power of a blackbody at the sametemperature. Materials are assigned an emissivity value between 0 and1.0. A blackbody, therefore, has an emissivity of 1.0 and a perfectreflector has an emissivity of 0. Because heat transfer by radiation isproportional to the fourth power of the absolute temperature, itbecomes very significant at higher temperatures.

"Coupled" simulation offers theadvantage of defining FEA loadsautomatically, eliminatingguesswork and possible errorscommon to manual setup.

Figure 16Heat is exchanged byradiation between any twobodies of differenttemperatures. Heat canalso be radiated by asingle body out to space.



Consider a spotlight providing illumination in a large vacuum chamber.Assume that the vacuum chamber is so large that any heat reflectedfrom the chamber walls back to the spotlight can be ignored. The light-bulb and reflector are exposed to a vacuum, while the back side of thealuminum housing is surrounded by air (figure 17).

The heat generated by the light-bulb is partially radiated out to space,while the rest is received by the parabolic face (reflector) of the housing.Only a very small portion of heat enters the housing by conduction wherethe light-bulb is attached to the housing. The radiated heat received bythe housing is again split into two portions: the first is radiated out, andthe second is moved inside the housing volume from the vacuum side tothe air side. Once it reaches the face exposed to air, it is dissipated byconvection.

As analysis results indicate, the temperature of the aluminum housing ispractically uniform because heat is conducted easily in aluminum due toits high conductivity (figure 18).

Note that since radiation heat-transfer becomes effective only at hightemperatures, the light-bulb must run very hot to dissipate all the heat itproduces.

Analysts most often look for thehighest reactions because theanalysis under the maximum loadsshows the maximum stressesexperienced.

Figure 18Temperature distributionin a spotlight

Figure 17In the spot-light model, the reflector and light-bulb are exposed toa vacuum and the back side of the housing is exposed to air.

Transient thermal analysisThe analyses of both the heat sink and the spotlight dealt with heattransfer in a steady state, based on the assumption that enough time haspassed for heat flow to stabilize. Analysis of a steady-state heat transferis independent of the time it took for the heat flow to reach that steadystate, which in practice may take seconds, hours or days.

An analysis of heat flow changing with time is called transient thermalanalysis, as for example, the analysis of a coffee pot kept hot by a heatingplate. The temperature of the heating plate is controlled by a thermostatreading the temperature of the coffee. The thermostat turns the poweron if the temperature of the coffee drops below a minimum temperature,and turns it off when the temperature exceeds a maximum, preset value.Temperature oscillations over a specified period of time are shown infigure 19.

Thermal stressesHeat flowing through a solid body will cause a change in temperatures inthis body. Consequently the body will expand or shrink. Stresses causedby this expansion or shrinkage are called thermal stresses.

Thermal stresses occur in a mug when hot coffee is poured into it. Athermal analysis of such stresses requires identifying the temperaturedistribution; on the inside faces of the mug, the temperature is that ofthe hot coffee, while on the outside faces user-defined convectioncoefficients control heat loss to the surrounding air. Since cooling is arelatively slow process, a steady-state thermal analysis is applied tocalculate the resultant temperature distribution in the coffee mug. Thetemperature distribution is non-uniform, causing thermal stresses thatcan easily be calculated in COSMOSWorks by running a static analysisusing the temperature results from the thermal analysis (figure 20)



Both motion simulation and FEAuse a CAD assembly model as apre-requisite for analysis.

COSMOSFloWorks can alsodetermine whether the performanceof the oven will be more efficient ifthe designer adds air flowdeflectors.

Figure 19The connecting rod ispresented to FEA as astructure so that stressescan be calculated.

Figure 20Non-uniform temperature field,found by steady-state thermalanalysis (left), induces thermalstresses which are calculated in astructural static analysis (right).

Desired capabilities of thermal design validation softwareConsidering the typical problems briefly introduced here, thermalanalysis design validation software used in a product-design processmust be able to model:

Heat flow by conduction Heat flow by convection Heat flow by radiation The effect of a thermal resistance layer Time-dependent thermal effects such as heating or cooling (transient

thermal analyses) Temperature-dependent material properties, heat power, convection

coefficients and other boundary conditions

There are also other requirements that a validation program used as adesign tool should satisfy that are not only specific to thermal analysisbut apply as well to structural or electromagnetic analyses. Since newproducts are universally designed on CAD, the efficient use of any type ofvalidation software as a design tool also places the followingrequirements on CAD software:

The CAD system should be: A feature-based, parametric, fully associative solid-modeler Able to create all geometry, both manufacturing specific and analysis

specific Able to move between design and analysis representations of the

model while keeping geometries linked

The above requirements call for an advanced simulation system whichcombines ease of use with high computational power, such as theCOSMOSWorks design validation program integrated with SolidWorksCAD (a leading 3D parametric, feature-based CAD system).

State-of-the-art integration between COSMOSWorks and SolidWorksallows users to run thermal and structural analyses using the samefamiliar SolidWorks interface, thus minimizing the need to learnanalysis-specific tasks and menus (figure 21)


DES IRED CAPAB IL IT I ES OF THERMAL DES IGN VAL IDAT ION SOFTWARE

The SolidWorks CAD programtogether with COSMOSWorks (FEA)and COSMOSMotion (motionsimulation) as add-ins representsthe state-of-the-art in integratedsimulation tools.

Figure 21Analysis such as thermalanalysis of a circuit board isconducted using the familiarSolidWorks interface,minimizing the need forusers' training.


A SAMPLE OF DESIGN PROBLEMS WHICH CAN BE SOLVED WITH COSMOSWORKS THERMAL

A sample of design problems which can be solved withCOSMOSWorks thermalThe following sections present some examples of design problems solvedusing the thermal and structural analysis capabilities of COSMOSWorks.

Sizing the cooling fins of a heat sinkA microchip radiator must be designed to provide enough cooling to keepthe microchip below 400K. The microchip sits on a base plate. Becauseof the thermal resistance layer separating the plate from the rest of theassembly, the base plate provides only negligible cooling.

Running a thermal analysis on the initial design with a cooling-fin heightof 20mm shows a temperature of 461K (figure 22 top). Changing thecooling fins to 40mm high increases the cooling, but not enough to meetthe specification; the microchip temperature is now 419K (figure 22). Athird iteration with 60mm high fins proves successful, as the microchiptemperature is now 400K, an acceptable value (figure 22).

Convection coefficients, which are an important consideration in this study,can be found in engineering textbooks or can be calculated using web-based calculators. Alternatively, a study of fluid flow around the radiatormay be conducted using COSMOSFloWorks to determine these values.

Designing a heating elementA heating element consists of an aluminum plate with an embeddedheating coil. The m-shaped coil design shown in figure 23 is preferred forits low cost. However, thermal analysis proves that it generates a non-uniform temperature on the outside of the plate as shown in figure 23.

Simulation of the motion, dynamics,and stresses of this complexmechanism reduced empiricaltesting requirements to a singleprototype.

Figure 23A simple design of a heatingelement embedded in analuminum plate.

Figure 22Heat sink with threedesign configurations.

A re-designed heating plate features the heating element forming a spiralas shown in figure 24. Repeating the thermal analyses on the modifieddesign demonstrates that the distribution of temperature is now almostuniform (figure 24).

Finding thermal stresses in a spotlight housingA spotlight (figure 17) is rigidly supported along the circumference as shownin figure 25. The housing develops thermal stresses because it can not freelyexpand while its temperature increases.

Finding thermal stresses requires a combination of thermal and structuralanalyses, where temperature results (figure 25) are exported to a staticanalysis in order to calculate thermal stresses. Design validation is neededto examine whether the thermal stresses exceed the yield strength of thealuminum housing. The stress plot in figure 25 shows in red those areas ofthe housing where stress does indeed exceed the yield strength. Thesestress results prove that the housing as designed will yield.

Note that thermal stresses develop not because the temperature of thehousing is non-uniform but because the restraint prevents the housing fromexpanding freely. Also, note that these stresses develop in the absence ofany structural loads.



Through the use of SolidWorks andCOSMOSMotion, it realized anestimated $45,000 in cost savings,and reduced testing time to just 10%of its former build-and-test process.

Figure 24A re-designed heating plate isshown with uniform distribution oftemperatures.

Figure 25A spotlight is supported asshown in the top picture. Themiddle picture presentssteady-state temperaturedistribution, and the bottomone shows in red wherestresses exceed the yieldstrength.



The presence of rigid bodymotion(s) classifies the object asa mechanism.

Finding thermal stresses in a flexible pipeSuppose that a corrugated pipe, while free to deform, is subjected todifferent temperatures at its two ends. This results in the temperature fieldshown in figure 26. The question of interest is whether it will develop anythermal stresses due to these differences.

Using the temperature results in a static analysis, the software calculatesthe pure effect of non-uniform temperature in the absence of anystructural loads or supports. Figure 26 shows in red where the stressexceeds the pipe material's yield strength.

If desired, a structural load (figure 27) may be applied to the pipe tocalculate the combined effect of thermal and structural stresses (figure 27)

Figure 27A corrugated aluminum pipesubjected to a tensile load(top) as well as thermalstresses, develops combinedstructural and thermalstresses (bottom).

Figure 26Due to a non-uniformtemperature field, the pipedevelops thermal stressesexceeding the yield strength ofthe pipe material.



Modes of vibration require analysiswith FEA rather than with MotionSimulation.

Overheating protection of an electronic circuit boardThe preferred temperature of an electronic circuit board shown in figure 28is 700C and should not exceed 1200C. To prevent it from overheating, acontroller cuts off the power when the temperature of the microchipexceeds 1200C. It turns the power back on when the temperature dropsbelow 700C. However, because of thermal inertia, the temperature of themicrochip may still exceed 1200C.

Investigating the range of temperature fluctuations involves conducting athermal transient analysis with the heat power controlled by a thermostatfeature. This is similar to the coffee pot example in figure 19. Havingdefined the material properties, convection coefficients, initial temperatureand heat power, the analysis is run for a period of 300 seconds.Fluctuations in microchip temperature are shown in figure 29.

The results of the transient thermal analysis clearly indicate that thecontroller power cut-off temperature must be lowered below 1200C tocompensate for the thermal inertia of the system. The desired settingscould be easily found in the next two to three iterations.

Figure 28An electronic circuitboard is protected fromoverheating by acontroller.

Figure 29Temperature of themicrochip fluctuates aspower is cycled on and off.Because of thermal inertia,the value exceeds themaximum allowed 1200C.



Modes of vibration require analysiswith FEA rather than with MotionSimulation.

Deformation analysis of a composite bearing-housingA composite bearing-housing is subjected to an elevated temperature dueto friction in the bearings. It is also subjected to bearing reaction loads.The challenge is to find the deformation of the bores where the bearingssit (figure 30, top), to make sure that the bearings will not loosen theretaining press fit. This requires a combination of steady-state thermal andstatic analyses.

The first step is to find the temperature across the bearing housing (figure30 bottom).

Based on these results, a static analysis is performed to calculate thedeformation caused by the combined effect of thermal deformations andstructural load. Figure 31 shows the radial displacement components ofboth bores.

If necessary, both thermal and structural analyses can account for anychange in material properties (such as thermal conductivity or themodulus of elasticity) which the composite material may experience withthe rise of temperature.

Figure 31Radial displacementcomponents ofdeformation of thebearing housing edges.

Figure 30Bearing housing (top) issubjected to non-uniform temperaturefield due to heatgenerated in thebearings (bottom)

For additional information about COSMOS products, check out the COSMOS website http://www.cosmosm.com.

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