The example considered here is the simulation of a machining process [9] using the integrated approach of the Taguchi method and the finite element method. During the metal removing process, a large amount of heat is generated and some of the heat generated is dissipated to the surrounding and the remaining heat flows into the workpiece. The heat which flows into the workpiece results in thermal distortion of the workpiece. In order to machine the workpiece to a close tolerance, it is essential that the heat flow into the workpiece should be minimized. With this objective in mind, the following experiments are conducted to study the influence of various factors that minimizes the heat flow into the workpiece.
While the above experiment could have been done using
a real experiment, there are many practical difficulties of machining
at high speed and other constraints. With the computer simulated
experiment, the design of experiments has become much easier.
6.2 Input Data
The various factors that affect the heat flow into
the workpiece are as follows. The schematic diagram of the metal
removing operation is shown in Figure 6.1.
Figure 6.1 Design variables that affect the heat
flow into the workpiece
6.3 The finite element model
The finite element model of the above machining process
consists of 2-D thermal solid elements (Stiff 55 of ANSYS Software).
This element type is used for conducting the steady state thermal
analysis with conduction capability. In addition to this the
heat generation within the body and convection along the edges
can be simulated. From the heat flux calculations, it is possible
to find out the total heat flow into the workpiece. The partial
listing of ANSYS parametric input file for the above model, called
metcut.log, has been given in the
Appendix B. The meshed model
of the machining process is shown in Figure 6.2. Every time the
experiment is conducted, the geometry automatically gets changed
depending on the level settings of the design variables.
6.4 Conducting the experiments
The following are the steps involved in the experimental
design of machining process.
6.4.1 Reading the input file
The first step is reading the ANSYS parametric file.
The listing of the input file is given in Appendix B. Once the
ANSYS file is read, the program retrieves the complete set of
design variables from the ANSYS file. These variables are stored
in the blackboard database. The typical blackboard database information
stored for the above case is shown in Figure 6.3.
Figure 6.3 Object oriented black board database
6.4.2 Selection of the independent variables
There are totally 85 assigned variables which are
defined in the input file. Though only 13 design variables are
identified for the above problem, the remaining variables are
meant for node and element generation and other purposes. Hence
one shall not choose the modeling variables as a design variable.
Figure 6.4 Selection of independent design variables
From the set of possible design variables, the following
seven variables are considered for experimental study: 1) Depth
of cut 2) Width of cut 3) Shear angle 4) Rake angle 5) Cutting
Force 6) Tangential force and 7) Ambient temperature. For each
design variable selected, the user inputs 3 different level
values. This allows nonlinear effects of the design variables
on the response to be represented. If all the level values of
a particular design variable are same, then the variable is not
considered for the design of experiment.
6.4.3 Selection of the Objective function
The objective function is the post-processing item
of ANSYS software. In case the objective function is not directly
expressible by a single equation, a set of ANSYS command may
be necessary to obtain the objective function value. For the present
case, the heat flow into the workpiece calculated separately and
is stored in a separate file. The file, post.ans has been used
for this purpose which is listed in
Appendix C.
6.4.4 Conducting the Taguchi Experiment
Once the design variables are selected, the program
automatically selects the L18 orthogonal array. The L18 orthogonal
array is meant for conducting the experiments with maximum of
7 independent design variables, each having 3 levels.
After the selection of the orthogonal array, the
ANSYS input file is modified with different level combinations
of design variables. For each experiment, a new ANSYS parametric
file is created. Since the geometry of the problem is changed
in each experiment, ANSYS program calculates the stiffness matrix
for every experiment and solves the problem. At the end of each
experiment, the process parameter values are appended to a file.
This is used for post processing process.
6.5 Post processing
Once the experiments are over, the program calculates
the mean value of each level of all the variables, the sum of
squares, the percent contribution and the near optimum level of
each design variable. Based on the near optimum level of each
variable, a new experiment is conducted with each design variable
set to the near optimum level value. The program also calculates
the F-value for each design variable. The summary of experimental
results are shown in Table 6.1. The detailed output listing is
given in Appendix D.
