1.1 to calculate heat ?ow within, to and

1.1    
Heat
sources in machine tools

There are internal
and external heat sources that have an impact on machine tool performance.

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1.1.1   
External
heat sources

The significant
external heat source is environmental temperature but there is also an
influence of solar radiation or forced convection. Environmental temperature
fluctuates during day and night but also over the different seasons of the
year.

1.1.2   
Internal
heat sources

Every heat source
connected to machine tool structure directly named as an internal heat source.
Machine elements as bearings, spindle, feed drive as well as additional units
like chillers, coolers etc, as long as come into direct contact, act as an
internal heat source. 20 Heat produce in
these elements result from local power loses due frictional and electrical
effects. The ultimate consequence of this heat is inhomogeneous temperature
field in machine tool structure which is root cause of thermal elastic
deformation, reason for TCP displacement.

1.2    
Sources
of heat generation in HS-55

The major source
of heat generation will be the heat generated by the process, which will be
transferred through the Spindle stock into the machine structure. The
frictional heat generated
through the movement of the Z-axis (horizontal movement of the Spindle stock),
and the heat
generated by the motor will also account for the deformation.

1)         Heat generated by the linear
guides in the cross-directional movement
2)         Linear motors in cross-directional
and 2 motors for movement of table
3)         Frictional heat generated by
the linear guides in the direction of the table movement
4)         Process heat generation

 

1.3    
Fundamental
of Heat transfer

Thermodynamics illustrate
the fundamental behavior of heat and temperature,  encompass the three laws of thermodynamics.
Heat transfer explains the mechanisms of heat exchange and the rate at which
heat ?ows, gives the information about how to calculate heat ?ow within, to and
from objects or the environment. Heat transfer can be classified into three modes conduction, convection and
radiation. 21

 

1.3.1   
Conduction

Conduction is the first mode of heat
transfer. In conduction heat is transferred from hot body to cold body directly
through material by the means of
molecules to molecule interactions. when the body is being heated, particle collide with each other, this phenomenon known
as conduction. Conductors are those material
which let the energy pass through them,
inverse to this insulator do not allow the energy to pass through them. 22

“The
Fourier’s law of heat conduction is a basic law describing a linear conductive
heat flux (heat flow per unit area W/m2) through a material. Heat flows in
the direction opposite to the thermal gradient, thus, from hot to cold. The
rate at which this happens is determined by the temperature difference (K) and
the thermal conductivity (W/(m K)) of the material.” 19

1.3.2   
Convection

Convection is a phenomenon which heat is being transferred
from surface to fluid, fluid could be air of
water. Sometimes other fluids can also be used like oil and alcohol 21. The hotter fluids rise
due to buoyancy effect and smaller
density. This type of heat transfer is called convection.

There are two general types of convective
heat transfer

1.   
Natural: a colder fluid is heavier than heated fluid around it. The change in density results in a fluid flow towards
up. Thermal energy also travels with
fluid, the heat is transferred. 19

2.   
Forced: a fluid can be emigrant
dynamically, e.g., by blowing or pumping, to transfer heat. 19

 

Radiation

Heat can be transferred without the
presence of material. Transfer of heat without the necessity of any material (or medium) is called
radiation. The process is called radiation in which heat is transferred in the
form 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 the
radiation occurs. It also depends on the temperature of the object.

This behavior
is described in the Stefan-Boltzmann Law:

The constant  is this expression is a fundamental physics
constant, Stefan-Boltzmann constant

The
other constant is the emissivity, e. It is a dimensionless number between 0 and
1 that specifies how active the object is in radiating energy. For perfect
radiator value has to be 1. Tests display that objects
absorb radiation from their environments according to the same law, the
Stefan-Boltzmann Law, by which they emit radiation. Thus, if the temperature of
an object is T and its surroundings are at the temperature Ts, the net power
radiated by the object is 22

Measuring the Thermal deformation

Nowadays various methodologies exist to measure the displacement of machine
tool components. Some standards have been
developed to which proved to be a good guideline  as well as some other measuring techniques

 

1.3.3   
Standards

Selecting a best-fit measuring system
depends on errors sources. Temperature change is a gradual due environmental
effect, result in volumetric inaccuracy. Internal heat sources lead to local deformation of machine tool structure and
affect volumetric performance j. may et
al. 11 ISO 230 is key relevant
series on the measuring machine tools. This series deals with different parts
of machine tools. ISO 230-3 Test code machine tools-part 3: Determination of
thermal effects.2007R1  and ISO 10791-10:2007 contains information
about with specific machining centers.

1.3.4   
Environmental
temperature variation error (ETVE)

Environmental temperature variation error
test gives the information about temperature variations effect on machine tool
accuracy. This test can also be conducted for approximation thermally induce
error for other measurements also.

1.3.5   
Thermal
deformation due to spindle

This test is in practice when information
required about spindle distortion due to heat generated in rotating spindle.

1.3.6   
Thermal
deformation by linear motion of axis

Linear motion test of machine components
like feed drives, guides, ball screw and bearings  can be performed for thermal effects. This
test consist of two stages to investigate the elongation of positioning system
and deformation in strcture.

1.4    
Metrology

1.4.1   
Temperature
measurement

Measurement of
temperature has a very important role in machine tool behaviour. Temperature is
the physical property measured by sensing technology.Measurement system
principle can be placed into two categories contact measurement and non-contact
measurement 23.

1.4.2   
Non-contact
Temperature measurement

Infrared
cameras are 24 widely used to measure temperature
distribution on the surface of the machine tool. Body which has temperature non
zero emits IR radiations dpending upon its temprature. This is called
characteristic radiation. This happens because of temperature of of body results
in internal molecules motion. Since the molecule movement represents charge
displacement, electromagnetic radiation (photon particles) is emitted. These
photons travels at the speed of light and behave according to the known optical
principles. They can be deflected,
focused with a lens, or reflected from reflective surfaces

Non-contact temperature measurements show a
high dependency on the emission characteristics and the reflectivity of the analysed surface. The relationship between
emission,
reflection  and transmission  is given by

1.4.3   
Contact
Temperature

Contact
temperature sensors measure their own temperature. One concludes the temperature
of the body to which the sensor is in contact by supposing or knowing that the
two are in thermal equilibrium, that is, there is no heat transfer between
them.

Many possible
measurement error sources exist, when assumptions are made.It is very difficult
measure the temprature of surface specially moving surfce by direct contact. It
is wise to be cautuious when perfoming experiments of taking measuments.

1.4.3.1    
Thermocouples

Thermocouples 20have two different
metal at theirs sensing ends. Voltage is generated when temperature gradient
occurs between hot sensor element and cold reference junction. Variation in
voltage notice as temperature through seebeck effect. The seebeck effect says
that temperature gradient is linearly proportional to voltage and connected through
coefficient of material used in

 

Figure 2–7. Thermocouple construction 20

 

1.4.3.2    
Resistance
temperature detectors

Resistance thermometers are also known as resistance temperature
detectors, or RTDs. They are constructed using
one metal and material property of that material is function of temperature.
The accuracy of resistance thermometers will be high if metal used inside has linear
relation with temperature, such as platinum. By using this linear relationship resistance
of material can be found out and temperature can be measured. 20

1.5    
Computation
of thermo-Mechanical errors of machine tools

There are a lot of different methodologies have been
developed to the model thermo-elastic behaviour of the machine tool in order to
compensate thermal errors. In general, methodologies can be classified into two
categories 25

i)             
Physical models

ii)            
Phenomenological models

1.5.1   
Phenomenological
models:-

Phenomenological model constructs a relationship between
input parameters (e.g. Temperature) and an output value (e.g TCP displacement).
Experiments are carried out at different loads and results with respect to time
are 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   
Physical
model:-

Physical modeling approach simulates thermally induce errors
distinguished, in temperature distribution and distortions, in order to
calculate TCP dislocation and enable real-time compensation. All considerations
are based on physical laws.

FEM models and FDM models approaches are part of physical modeling.

 

1.6    
Reduction
of Thermally induce errors:-

A lot of people have presented different methods to reduce
thermal errors, put into net shell these methods can be classified into three
categories according to thesis
5946,40

i)             
Minimizing  the
temperature fluctuations: for example by cooling or controlled environment
condition as well as minimum heat generation

ii)            
Reducing thermal sensitivity: reducing the sensitivity
of machine tool structural loop to temperature changes

iii)          
Compensation of errors: for example by mean of mathematical
models

1.6.1   
Reducing
the temperature variations:-

Temperature variations can be minimized by reducing the
masses of machine tool structure41,thesis 594, applying cooling to a machine tool, use of oil
shower, through air.

By trying to create even temperature distribution thermal
error can be reduced of machine tool structure. Much lower the temperature
difference will be lower the thermal error present.

The temperature gradient can be reduced by minimizing heat
generated in elements of machine tool. P sekler et al 41 of thesis illustrate thermal error can be reduced by sizing
down the masses of machine tool structure. This usually applies to construct
energy efficient machine tools but also it also helps in reducing the losses
occur in machine tool. With smaller masses less energy is required to move them
result in smaller losses and lower temperature on machine structure.

The most common approach implemented widely in industry is to
apply cooling to machine tool. Some approaches based on try to remove the
excess heat generated in machine tool elements. One of the approaches 40 is
to design special cooling element for the spindle. These cooling tubes try to
make us of Coanda-effect. Working principle of Coanda effect, fluid passage out
from nozzle creating a primary stream. Temperature control of air in a
lithography 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 from
in room temperature.

Various methodologies to reduce thermal errors that does not
directly reduce the temperature gradient on machines but modifies it, is practice
of heating and cooling elements. It can be seen during application of
compensation methods to machine (47,48,49). In order to reduce tool center point
displacement key elements of machine tool either can be heated or cooled. For
special cases feed drives are used to for reduction of angular errors on three
axis machine.

1.6.2   
Reduction
of thermal sensitivity:- 

Other than temperature gradients approach thermal error of
machine tool can also be reduced by minimizing the sensitivity of elements to
temperature changes. Meaning of this machine tool design in this way that large
deformations do not occur. This can be achieved by applying  thermo-symmetrical design to machine tool. In
50, thesis 5946  boundary conditions are applied to headstock
of 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 directional
thermal expansion do not affect that workpiece accuracy. 

1.6.2.1    
Advance
material for compensation of thermal displacement:- (Thermal issues page 782)

Material optimization can be effective in reducing the
thermal errors in machine tool. Alternative materials like carbon fiber
reinforced plastic (CFRP) has negative linear expansion coefficient can be used
to compensate thermal displacement of machine component which have positive
linear expansion coefficient such as aluminum.

Another example thermal distortions due to local temperature
gradients can be reduced by using polymer concrete in machine tool bed. Achieveable
reduction is upto 30%. (thermal
isuue page 783)

 

1.6.2.2    
Active compensation using adaptronic
devices:- (thermal issue 783)

CFRP structure are used for active compensation of angular
displacement of main spindle of housings and heating of unidirectional carbon fibre
reinforced 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 and
Peltier elements.

 

 

1.6.3   
Compensation:-
thermal issue

In general, Thermal displacement can be estimated in two
classes of methods: Direct compensation and indirect compensation. Process
chain of thermal deformation

 

Direct method uses touch probes to compensate error, for that
machine has to be stopped during an operation to take measurements, the big
drawback of direct methodology, ultimately productivity reduce.

On other hand indirect measurement reduce downtime by active
compensation. The indirect approach uses temperature measurement to calculate
TCP displacement with help of mathematical models.  The most common model used for are described
below:-

1.6.3.1    
Method
of thermal error compensation based on linear and nonlinear regression:-

 Regression model  is applied for error compensation, it defines
a relationship between dependent and several independents values. In case of
thermal errors temperature in specific machine tool points are independent
variable and dependent variable are TCP displacement. It is active compensation
method which means without disturbing the machine process errors can be
calculated. The hindrance with indirect compensation is the installation of measuring
system is very costly.

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

1.6.3.2    
Compensation
based on neural networks:- 8
thesis

Using Neural network approach for thermal error compensation
is a common practice. Feedforward networks are used for thermal error
compensation, temperature probes act as input. Neural network approximates the
TCP dislocation relying on the temperature of machine tool. Input and output
layers act as input and output buffer for temperature measurement of machine
and machine thermal errors respectively. Layers in between them are called
hidden layers. The working principle of these to suppress the noise.

Each input is multiplied by the interrelated weight. All of
these weighted inputs are summed up and combined with a threshold to find out
activation level of the neuron.

1.6.3.3    
Physical
models:-

Compare to ANN and RM a lot of others models are in practice.
In 7, thesis 5946  lumped capacitance method is used to
calculate the temperature distribution of the machine tool. To do that thermal
behavior knowledge will be needed because one must know which parts of machine
can be lumped and how to apply proper boundary conditions for lumped bodies. A
series of temperature is used and TCP dislocation is computed by stress-free
theory and rigid body kinematics.

With advancement in computer field and accessibility of
models, e.g FEM models, new reduction procedure can be developed. Denkena et
al, 42 thermal issues 785
applied FEM to calculate thermal deformation of machine tool in steady state
versus load profile. During operation TCP 
displacement are compensated with a linear model comparing temperature
measured on machine tool structure with those computed n steady state. FDEM
approach is endorsed fot real-time compensation of machine tools 141 thermal issues 785.
Unknown boundary condition, simulation-based model, Volumetric TCP
displacement, use of thermal location and components errors as correction
values.

A mixture of FEM and FDM 
used in 76  a transient thermal analysis has been
performed using FDM and TCP displacements has been compensated using FEM.

 R1NEEDS TO CORRECTED

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