There temperature variations:- Temperature variations can be minimized

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



Phenomenological models:-

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.



Physical model:-

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

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


Reduction of Thermally induce

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

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

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

of errors: for example by mean of mathematical models

Reducing the 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.

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

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

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.

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. 

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

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

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)


compensation using adaptronic devices:- (thermal issue 783)

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

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.



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:-

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

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


of weighted inputs and threshold

signal received by artifical neurons


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.

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

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