1.1    Heatsources in machine toolsThere are internaland external heat sources that have an impact on machine tool performance.1.1.1   Externalheat sourcesThe significantexternal heat source is environmental temperature but there is also aninfluence of solar radiation or forced convection.

Environmental temperaturefluctuates during day and night but also over the different seasons of theyear.1.1.2   Internalheat sourcesEvery heat sourceconnected to machine tool structure directly named as an internal heat source.Machine elements as bearings, spindle, feed drive as well as additional unitslike chillers, coolers etc, as long as come into direct contact, act as aninternal heat source.

 20 Heat produce inthese elements result from local power loses due frictional and electricaleffects. The ultimate consequence of this heat is inhomogeneous temperaturefield in machine tool structure which is root cause of thermal elasticdeformation, reason for TCP displacement.1.2    Sourcesof heat generation in HS-55The major sourceof heat generation will be the heat generated by the process, which will betransferred through the Spindle stock into the machine structure. Thefrictional heat generatedthrough the movement of the Z-axis (horizontal movement of the Spindle stock),and the heatgenerated by the motor will also account for the deformation.1)         Heat generated by the linearguides in the cross-directional movement 2)         Linear motors in cross-directionaland 2 motors for movement of table3)         Frictional heat generated bythe linear guides in the direction of the table movement4)         Process heat generation  1.3    Fundamentalof Heat transferThermodynamics illustratethe fundamental behavior of heat and temperature,  encompass the three laws of thermodynamics.

Heat transfer explains the mechanisms of heat exchange and the rate at whichheat ?ows, gives the information about how to calculate heat ?ow within, to andfrom objects or the environment. Heat transfer can be classified into three modes conduction, convection andradiation. 21 1.3.1   ConductionConduction is the first mode of heattransfer. In conduction heat is transferred from hot body to cold body directlythrough material by the means ofmolecules to molecule interactions.

when the body is being heated, particle collide with each other, this phenomenon knownas conduction. Conductors are those materialwhich let the energy pass through them,inverse to this insulator do not allow the energy to pass through them. 22 “TheFourier’s law of heat conduction is a basic law describing a linear conductiveheat flux (heat flow per unit area W/m2) through a material. Heat flows inthe direction opposite to the thermal gradient, thus, from hot to cold.

Therate at which this happens is determined by the temperature difference (K) andthe thermal conductivity (W/(m K)) of the material.” 191.3.2   ConvectionConvection is a phenomenon which heat is being transferredfrom surface to fluid, fluid could be air ofwater. Sometimes other fluids can also be used like oil and alcohol 21. The hotter fluids risedue to buoyancy effect and smallerdensity. This type of heat transfer is called convection. There are two general types of convectiveheat transfer1.

   Natural: a colder fluid is heavier than heated fluid around it. The change in density results in a fluid flow towardsup. Thermal energy also travels withfluid, the heat is transferred. 192.   Forced: a fluid can be emigrantdynamically, e.g., by blowing or pumping, to transfer heat.

 19 RadiationHeat can be transferred without thepresence of material. Transfer of heat without the necessity of any material (or medium) is calledradiation. The process is called radiation in which heat is transferred in theform of electromagnetic radiation. The energy released per time by an object that is,the radiated power, P-is proportional to the surface area, A, over which theradiation occurs. It also depends on the temperature of the object. This behavioris described in the Stefan-Boltzmann Law: The constant  is this expression is a fundamental physicsconstant, Stefan-Boltzmann constant Theother constant is the emissivity, e.

It is a dimensionless number between 0 and1 that specifies how active the object is in radiating energy. For perfectradiator value has to be 1. Tests display that objectsabsorb radiation from their environments according to the same law, theStefan-Boltzmann Law, by which they emit radiation.

Thus, if the temperature ofan object is T and its surroundings are at the temperature Ts, the net powerradiated by the object is 22Measuring the Thermal deformationNowadays various methodologies exist to measure the displacement of machinetool components. Some standards have beendeveloped to which proved to be a good guideline  as well as some other measuring techniques  1.3.3   StandardsSelecting a best-fit measuring systemdepends on errors sources. Temperature change is a gradual due environmentaleffect, result in volumetric inaccuracy.

Internal heat sources lead to local deformation of machine tool structure andaffect volumetric performance j. may etal. 11 ISO 230 is key relevantseries on the measuring machine tools. This series deals with different partsof machine tools. ISO 230-3 Test code machine tools-part 3: Determination ofthermal effects.2007R1  and ISO 10791-10:2007 contains informationabout with specific machining centers.1.

3.4   Environmentaltemperature variation error (ETVE)Environmental temperature variation errortest gives the information about temperature variations effect on machine toolaccuracy. This test can also be conducted for approximation thermally induceerror for other measurements also.1.

3.5   Thermaldeformation due to spindleThis test is in practice when informationrequired about spindle distortion due to heat generated in rotating spindle. 1.3.6   Thermaldeformation by linear motion of axisLinear motion test of machine componentslike feed drives, guides, ball screw and bearings  can be performed for thermal effects. Thistest consist of two stages to investigate the elongation of positioning systemand deformation in strcture.

1.4    Metrology1.4.1   TemperaturemeasurementMeasurement oftemperature has a very important role in machine tool behaviour.

Temperature isthe physical property measured by sensing technology.Measurement systemprinciple can be placed into two categories contact measurement and non-contactmeasurement 23.1.4.2   Non-contactTemperature measurementInfraredcameras are 24 widely used to measure temperaturedistribution on the surface of the machine tool. Body which has temperature nonzero emits IR radiations dpending upon its temprature. This is calledcharacteristic radiation.

This happens because of temperature of of body resultsin internal molecules motion. Since the molecule movement represents chargedisplacement, electromagnetic radiation (photon particles) is emitted. Thesephotons travels at the speed of light and behave according to the known opticalprinciples.

They can be deflected,focused with a lens, or reflected from reflective surfacesNon-contact temperature measurements show ahigh dependency on the emission characteristics and the reflectivity of the analysed surface. The relationship betweenemission,reflection  and transmission  is given by 1.4.

3   ContactTemperatureContacttemperature sensors measure their own temperature. One concludes the temperatureof the body to which the sensor is in contact by supposing or knowing that thetwo are in thermal equilibrium, that is, there is no heat transfer betweenthem.Many possiblemeasurement error sources exist, when assumptions are made.It is very difficultmeasure the temprature of surface specially moving surfce by direct contact. Itis wise to be cautuious when perfoming experiments of taking measuments.1.4.

3.1    ThermocouplesThermocouples 20have two differentmetal at theirs sensing ends. Voltage is generated when temperature gradientoccurs between hot sensor element and cold reference junction. Variation involtage notice as temperature through seebeck effect.

The seebeck effect saysthat temperature gradient is linearly proportional to voltage and connected throughcoefficient of material used in  Figure 2–7. Thermocouple construction 20 1.4.3.

2    Resistancetemperature detectorsResistance thermometers are also known as resistance temperaturedetectors, or RTDs. They are constructed usingone metal and material property of that material is function of temperature.The accuracy of resistance thermometers will be high if metal used inside has linearrelation with temperature, such as platinum. By using this linear relationship resistanceof material can be found out and temperature can be measured. 201.

5    Computationof thermo-Mechanical errors of machine toolsThere are a lot of different methodologies have beendeveloped to the model thermo-elastic behaviour of the machine tool in order tocompensate thermal errors. In general, methodologies can be classified into twocategories 25i)             Physical modelsii)            Phenomenological models1.5.1   Phenomenologicalmodels:-Phenomenological model constructs a relationship betweeninput parameters (e.g. Temperature) and an output value (e.g TCP displacement).Experiments are carried out at different loads and results with respect to timeare observed by regression model (RM).

Other methods like neural networks (NN)and Fuzzy logic (FL) for compensation also listed in phenomenological models.1.5.2   Physicalmodel:-Physical modeling approach simulates thermally induce errorsdistinguished, in temperature distribution and distortions, in order tocalculate TCP dislocation and enable real-time compensation. All considerationsare based on physical laws.FEM models and FDM models approaches are part of physical modeling. 1.6    Reductionof Thermally induce errors:-A lot of people have presented different methods to reducethermal errors, put into net shell these methods can be classified into threecategories according to thesis5946,40i)             Minimizing  thetemperature fluctuations: for example by cooling or controlled environmentcondition as well as minimum heat generationii)            Reducing thermal sensitivity: reducing the sensitivityof machine tool structural loop to temperature changesiii)          Compensation of errors: for example by mean of mathematicalmodels1.

6.1   Reducingthe temperature variations:-Temperature variations can be minimized by reducing themasses of machine tool structure41,thesis 594, applying cooling to a machine tool, use of oilshower, through air.By trying to create even temperature distribution thermalerror can be reduced of machine tool structure. Much lower the temperaturedifference will be lower the thermal error present.

The temperature gradient can be reduced by minimizing heatgenerated in elements of machine tool. P sekler et al 41 of thesis illustrate thermal error can be reduced by sizingdown the masses of machine tool structure. This usually applies to constructenergy efficient machine tools but also it also helps in reducing the lossesoccur in machine tool. With smaller masses less energy is required to move themresult in smaller losses and lower temperature on machine structure.The most common approach implemented widely in industry is toapply cooling to machine tool. Some approaches based on try to remove theexcess heat generated in machine tool elements. One of the approaches 40 isto design special cooling element for the spindle.

These cooling tubes try tomake us of Coanda-effect. Working principle of Coanda effect, fluid passage outfrom nozzle creating a primary stream. Temperature control of air in alithography application is shown in 42. Compensation using oil shower is used in 43 and 44.Another advantage of using oil shower is that insulation from fluctuations fromin room temperature.

Various methodologies to reduce thermal errors that does notdirectly reduce the temperature gradient on machines but modifies it, is practiceof heating and cooling elements. It can be seen during application ofcompensation methods to machine (47,48,49). In order to reduce tool center pointdisplacement key elements of machine tool either can be heated or cooled.

Forspecial cases feed drives are used to for reduction of angular errors on threeaxis machine.1.6.2   Reductionof thermal sensitivity:-  Other than temperature gradients approach thermal error ofmachine tool can also be reduced by minimizing the sensitivity of elements totemperature changes. Meaning of this machine tool design in this way that largedeformations do not occur.

This can be achieved by applying  thermo-symmetrical design to machine tool. In50, thesis 5946  boundary conditions are applied to headstockof lathe in such a way that center of axis does not move during the thermal expansion.Thermal deformation on machine tools 51 present a methodology according to that non-sensitive machine  can be design in such way that specific directionalthermal expansion do not affect that workpiece accuracy.  1.6.2.1    Advancematerial for compensation of thermal displacement:- (Thermal issues page 782)Material optimization can be effective in reducing thethermal errors in machine tool.

Alternative materials like carbon fiberreinforced plastic (CFRP) has negative linear expansion coefficient can be usedto compensate thermal displacement of machine component which have positivelinear expansion coefficient such as aluminum.Another example thermal distortions due to local temperaturegradients can be reduced by using polymer concrete in machine tool bed. Achieveablereduction is upto 30%. (thermalisuue page 783)  1.

6.2.2    Active compensation using adaptronicdevices:- (thermal issue 783)CFRP structure are used for active compensation of angulardisplacement of main spindle of housings and heating of unidirectional carbon fibrereinforced laminate.In an adaptronic system, negative thermal expansion of CFRP-structure compensate the thermal displacement. Thermal sensors, controllers,and CFRP actuators make possible controlled heating of  CFRP laminate by heating filaments andPeltier elements.

  1.6.3   Compensation:- thermal issue In general, Thermal displacement can be estimated in twoclasses of methods: Direct compensation and indirect compensation. Processchain of thermal deformation Direct method uses touch probes to compensate error, for thatmachine has to be stopped during an operation to take measurements, the bigdrawback of direct methodology, ultimately productivity reduce. On other hand indirect measurement reduce downtime by activecompensation. The indirect approach uses temperature measurement to calculateTCP displacement with help of mathematical models.  The most common model used for are describedbelow:-1.6.

3.1    Methodof thermal error compensation based on linear and nonlinear regression:- Regression model  is applied for error compensation, it definesa relationship between dependent and several independents values. In case ofthermal errors temperature in specific machine tool points are independentvariable and dependent variable are TCP displacement. It is active compensationmethod which means without disturbing the machine process errors can becalculated. The hindrance with indirect compensation is the installation of measuringsystem is very costly.

The drawback of RA is selecting positions for temperaturesensors if too many positions are taken it will increase the cost if few thanthe accuracy of the solution will be compromised.1.6.3.

2    Compensationbased on neural networks:- 8thesisUsing Neural network approach for thermal error compensationis a common practice. Feedforward networks are used for thermal errorcompensation, temperature probes act as input. Neural network approximates theTCP dislocation relying on the temperature of machine tool. Input and outputlayers act as input and output buffer for temperature measurement of machineand machine thermal errors respectively.

Layers in between them are calledhidden layers. The working principle of these to suppress the noise. Each input is multiplied by the interrelated weight.

All ofthese weighted inputs are summed up and combined with a threshold to find outactivation level of the neuron.1.6.

3.3    Physicalmodels:-Compare to ANN and RM a lot of others models are in practice.In 7, thesis 5946  lumped capacitance method is used tocalculate the temperature distribution of the machine tool. To do that thermalbehavior knowledge will be needed because one must know which parts of machinecan be lumped and how to apply proper boundary conditions for lumped bodies. Aseries of temperature is used and TCP dislocation is computed by stress-freetheory and rigid body kinematics.With advancement in computer field and accessibility ofmodels, e.g FEM models, new reduction procedure can be developed.

Denkena etal, 42 thermal issues 785applied FEM to calculate thermal deformation of machine tool in steady stateversus load profile. During operation TCP displacement are compensated with a linear model comparing temperaturemeasured on machine tool structure with those computed n steady state. FDEMapproach is endorsed fot real-time compensation of machine tools 141 thermal issues 785.Unknown boundary condition, simulation-based model, Volumetric TCPdisplacement, use of thermal location and components errors as correctionvalues. A mixture of FEM and FDM used in 76  a transient thermal analysis has beenperformed using FDM and TCP displacements has been compensated using FEM.

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