International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 01, January 2019, pp. 1272-1282, Article ID: IJMET_10_01_129
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=1
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
Scopus Indexed
OPTIMIZATION COMPARISON OF
ROUNDNESS ERROR IN WIRE- EDM
MACHINING BY VARIABLE METHODS
S. AJAYA KUMAR
Asst. Prof. Dept of Mech Sri Venkateshawara Engineering College, Suryapet
DR.A.PRABHU KUMAR
Professor Department of Mechanical Engineering, JNTUH, Hyderabad, Telangana, India
DR.B.BALU NAIK
Professor and Principal, JNTUH College of Engineering, Sultanpur, Telangana, India
ABSTRACT
Roundness error can be evaluated perfectly for the by product life after
manufacturing, leading the major criteria in assembly errors and vibration control
mechanisms. Components with round profiles must have to go for a quality check,
different optimal techniques like Least Squares Circle (LSC), Minimum Circumscribed
Circle (MCC), Maximum Inscribed Circle (MIC) and Minimum Zone Circles (MZC)
are available internationally to validate the error variations in roundness. This paper
focuses on roundness evaluation using nonlinear optimization techniques, for the
manufactured components in Wire- EDM. The Computer Aided Inspection (CAI)
procedures have gained a prominent role in the field of inspection and evaluation of
the manufactured parts. In the recent years, the Coordinate Measuring Machines
(CMMs) have gained popularity in automated inspection for both online and offline
inspection of manufactured components. Present comparison of practical components
inspection by CMM with optimal methods.
Keywords Roundness error, Wire- EDM, Optimization techniques
Cite this Article: S. Ajaya Kumar, Dr. A. Prabhu Kumar And Dr. B. Balu Naik,
Optimization Comparison of Roundness Error in Wire- Edm Machining by Variable
Methods, International Journal of Mechanical Engineering and Technology, 10(01),
2019, pp. 1272-1282.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=1
1. INTRODUCTION
Circular feature is one of the most basic geometric elements of mechanical parts [1]. In
manufacturing environments, variations on circular features may occur due to imperfect
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S. Ajaya Kumar, Dr. A. Prabhu Kumar And Dr. B. Balu Naik
rotation, erratic cutting action. An inscribed circle is then drawn inside the profile based on
the center of the minimum circumscribed circle. The out of roundness value is the difference
between the radii of the inscribed and circumscribed circle. The roundness error can be
evaluated through solving nonlinear unconstrained optimization problems. As long as the
mathematical objective function has to build correctly, the results can be obtained without the
preparation of the solution processes; therefore, the solution process is very simple.
2. BACKGROUND OF THE WORK
The tolerance of out-of-roundness is the annular space between two concentric circles. A
work piece is within the tolerance if these two circles enclose its profile. Numerical
assessment of out-of-roundness is done by measuring the peak-to-valley deviation of the
actual profile from a reference circle fitted to that profile. Four reference circles are
internationally accepted for roundness measurements [2]. Roundness error of the work-piece
and radial error of the spindle are measured simultaneously by using 4 probes mounted with
certain angle arrangement. This method gives high accuracy for all harmonics, which is
difficult for three point method. Evaluation of roundness error is formulated as a nondifferentiable unconstrained optimization problem and hard to handle. The maximum
inscribed circle and the minimum circumscribed circle are all easily solved by iterative
comparisons. Based on the minimum zone circle, the maximum inscribed circle and the
minimum circumscribed circle can be easily determined [3]. Machining is one of the most
important and widely used manufacturing processes. Due to complexity and uncertainty of the
machining processes, soft computing techniques are being preferred to physics based models
for predicting the performance of the machining processes and optimizing them.
3. OPTIMIZATION COMPARISON WITH CMM
The Taguchi method has been widely used in engineering analysis and is a powerful tool to
design a high quality system. Moreover, the Taguchi method employs a special design of
orthogonal array to investigate the effects of the entire machining parameters through the
small number of experiments. The present CMM results with least square method and
nonlinear probing methods have observed in the experimental output components of wire
EDM.
3.1. Minimum Zone circle (MZC)
The MZC method uses the minimum zone circle as the reference circle to evaluate the
roundness.
In a PSO algorithm, each candidate solution, called a particle, is treated as a position in
the n-dimensional solution space. ‘‘Particle swarm’’ is represented by X = (X1, X2-, . .
.,Xm)T where m is the swarm size and the ith particle is represented as Xi = (xi1, xi2, . . .,xin).
Each particle has a velocity Vi = (vi1, vi2, . . .,vin) which decides the flying distance and
direction, and also has its fitness value which is determined by the target optimization
function F with the positions of the particles as input values. In the PSO algorithm used in this
paper, the position and velocity of each particle are adjusted each iteration, expressed by
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Optimization Comparison of Roundness Error in Wire- Edm Machining by Variable
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Are the learning factors used to adjust the flying distances of the particles from the
individual optimal value and from the global optimal value, respectively; r1, r2 are two
random numbers in the range of x is the inertia weight
3.2. MZC-based roundness error evaluation with the PSO algorithm
Point (xj, yj) on the profile of a circular section to the centre radii of two concentric circles is
given as
Then the roundness error eMZC is represented by
Figure 1 Roundness error variation of EN24  10mm to PSO-CMM
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Figure 2 Roundness error variation of EN24  12mm to PSO-CMM
Figure 3 Roundness error variation of EN24  14mm to PSO-CMM
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Optimization Comparison of Roundness Error in Wire- Edm Machining by Variable
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Figure 4 Roundness error variation of EN24  profile 1 to PSO-CMM
Figure 5 Roundness error variation of EN24  profile 2 to PSO-CMM
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S. Ajaya Kumar, Dr. A. Prabhu Kumar And Dr. B. Balu Naik
Figure 6 Roundness error variation of
H13 at dia 10mm to PSO-CMM
Figure 7 Roundness error variation of
H13 at dia 12mm to PSO-CMM
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Optimization Comparison of Roundness Error in Wire- Edm Machining by Variable
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Figure 8 Roundness error variation of
Figure 9 Roundness error variation of
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H13 at dia 14mm to PSO-CMM
H13 at profile 1 to PSO-CMM
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S. Ajaya Kumar, Dr. A. Prabhu Kumar And Dr. B. Balu Naik
Figure 10 Roundness error variation of H13 at profile 2 to PSO-CMM
Figure 11 Roundness error variation of SS316 at 10mm Dia to PSO-CMM
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Optimization Comparison of Roundness Error in Wire- Edm Machining by Variable
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Figure 12 Roundness error variation of SS316 at 12mm Dia to PSO-CMM
Figure 13 Roundness error variation of SS316 at 14mm Dia to PSO-CMM
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S. Ajaya Kumar, Dr. A. Prabhu Kumar And Dr. B. Balu Naik
Figure 14 Roundness error variation of SS316 at profile 1 to PSO-CMM
Figure 15 Roundness error variation of SS316 at profile 2 to PSO-CMM
4. DISCUSSION
When the sample size is larger, the two roundness errors both increase with an increase in the
sample size with a decreasing increment, which can be concluded from the fact that when the
sample size is no smaller than 50, a larger sample size is corresponding to a larger roundness
error. The variation trend of the difference between the PSO–CMM based roundness errors
with the sample size is similar to that of the two roundness errors with the sample size. The
roundness error defined in the manuscript is to give estimate on outliers, which has a higher
probability as sample size increases.
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5. CONCLUSION
The standard PSO algorithm was introduced and theory analysis about the impact of value
selection of diameter with the algorithm’s performance was carried on so as to provide a basis
for giving these parameters better values in roundness error. While comparing the values of
roundness error it is noticed that the for all the materials taken EN24, H13, SS316 the PSO
approach gives least error rate than experimental approach (CMM) which is suggested to be
the better one.
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