Resource Surface Methodology

1. Department Of Mechanical Engineering.
K. J. Somaiya College of Engineering, Vidyavihar,
Mumbai-400077
Academic Year : 2016-2017.
Presented By : - Rahul S. Pawar
FY M. Tech (CAD/CAM) (1605011)
Guided By :- Prof. Dr. R. R. Lekurwale
A Seminar on :-
Wednesday, May 10, 2017 1

2. Contents….
 Introduction
 Literature Review
 Response Model
 Methodology
 Problem Statement
 Results
 Advantages
 Limitations
 Application
 Conclusion
 Learning Outcomes
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3. Introduction….
 In statistics, response surface methodology (RSM) explores the relationships between several explanatory
variables and one or more response variables.
OR
 Response Surface Methodology (RSM) explores the relationships between the primary variables and one or more
output response variables.
 The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response.
 A response surface design is a set of advanced design of experiments (DOE) techniques that help you better
understand and optimize your response. Response surface design methodology is often used to refine models after
you have determined important factors using factorial designs; especially if you suspect curvature in the response
surface.
 Multiple objective functions
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4. Literature Review….
1. Kathleen M. Carley, Natalia Y. Kamneva, Jeff Reminga represents the technical report on “Response Surface
Methodology.” They discussed how to identify and fit the experimental data for an appropriate response surface
model which requires some use of statistical experimental design fundamentals, regression modeling techniques,
and optimization methods.
2. V. Mugendiran, A. Gnanavelbabu, R. Ramadoss represents the paper on “Parameter optimization for surface
roughness and wall thickness on AA5052 Aluminum alloy by incremental forming using response surface
methodology.” They discussed the influence of three input parameters i.e. spindle speed, tool feed, and steps size on
surface roughness and wall thickness as output parameters by RSM.
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5. Response Model….
 Screening Response Model
The screening model that we used for the first order situation involves linear effects and a single cross product
factor, which represents the linear x linear interaction component.
 Steepest Ascent Model
If we ignore cross products which gives an indication of the curvature of the response surface that we are
fitting and just look at the first order model this is called the steepest ascent model:
 Optimization Model
Then, when we think that we are somewhere near the 'top of the hill' we will fit a second order model. This
includes in addition the two second-order quadratic terms.
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6. Methodology….
Most applications of RSM are sequential in nature.
 Phase 0: Screening experiment
 Phase 1: Method of steepest ascent (descent) - Determine if the current settings of the independent variables result
in a value of the response that is near the optimum. If the current settings or levels of the independent variables are
not consistent with optimum performance, then the experimenter must determine a set of adjustments to the process
variables that will move the process toward the optimum.
 Phase 2: Operability region or experimentation region or region of interest - At this point the experimenter
usually wants a model that will accurately approximate the true response function within a relatively small region
around the optimum - true response surface usually exhibits curvature near the optimum, a second-order model (or
perhaps some higher-order polynomial) should be used - this model may be analyzed to determine the optimum
conditions for the process.
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7. Problem Statement….
• To optimize surface roughness and wall thickness through incremental forming on AA5052 Aluminum alloy
at room temperature by controlling the effects of forming parameters.
Table 1 : Factors and levels used in factorial design
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8. Solution….
Table 2 : Study of experimental variables in coded units
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9. Solution(contd)….
Figure 1 : ANOVA for
Response Surface
Quadratic Model
(response: Ra in μm)
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10. Solution(contd)….
Figure 2 : ANOVA for
Response Surface
Quadratic Model
(response: t in mm)
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11. Solution(contd)….
Figure 3 : Residual Plots for Ra and t
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12. Solution(contd)….
Figure 4 : Surface Plots for Ra and t
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13. Solution(contd)….
Figure 5 : Optimization plot for Ra and t
Figure 6 : Ramp function plot for optimized parameters [2]
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14. Results….
 The study also has a higher R^2 value above 0.95
 The Results we got from the Minitab are similar to that of the paper presented.
 When spindle speed, feed and step size were 1931.94 rpm, 654 mm/rev and 0.65 mm a minimum Ra of 2.45151μm
and a maximum t of 0.753 mm can be obtained.
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15. Advantages….
 Linear equations can be solved
 Non-linear equation can be solved
 Data requirement is less
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16. Limitations….
 It is an approximation method
 Large computation is required
 Need of computer for complex problems
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17. Applications….
 Usually applied with factorial design to reduce the cost of experimentation.
 To detect factors that influence a response.
 To find an optimum factor within a experiment.
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18. Conclusion….
 RSM provides a large amount of information with a small amount of experimentation.
 RSM can be used for the approximation of both experimental and numerical responses.
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19. Learning Outcomes….
 We understood how to model the screening response model, steepest ascent model and optimization model.
 We understood how to model the Multiple objective functions.
 We understood the methodology to solve the RSM model.
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20. References….
1. Kathleen M. Carley, Natalia Y. Kamneva, Jeff Reminga ; “Response Surface Methodology”; CMU-ISRI-04-136;
October 2004
2. V. Mugendiran, A. Gnanavelbabu, R. Ramadoss ; “Parameter optimization for surface roughness and wall thickness
on AA5052 Aluminium alloy by incremental forming using response surface methodology”; 12th GLOBAL
CONGRESS ON MANUFACTURING AND MANAGEMENT; 2014
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