Optimization of cutting force of turning of AISI 1018 mild carbon steel using RSM

With passage of time technologically advanced machines have been developed. But the problem of the tool wear and cutting force for a particular machining process remains to be improved. So, to avoid or to cope-up with this problem it is necessary to find the best combination of machining parameters for obtaining optimum cutting force. In this work the optimization of cutting force for a given combination is done in a useful and easy way. Three factors are selected that affect the optimizing parameters in case of turning. These factors are optimized to get the optimum cutting force. This is achieved by employing response surface methodology and signal to noise ratio calculation. One factor is varied by keeping the other two constant at same range. Through the response surface methodology 2D and 3D graphs are obtained and optimization is achieved. The S/N ratio is done to find out which factor has the most influence on the output that is cutting force.

technologically advanced machines have been developed. But the problem of the tool wear and cutting force for a particular machining process remains to be improved. So, to up with this problem it is necessary f machining parameters for obtaining optimum cutting force. In this work the optimization of cutting force for a given combination is done in a useful and easy way. Three factors are selected that affect the optimizing parameters in case factors are optimized to get the optimum cutting force. This is achieved by employing response surface methodology and signal to noise ratio calculation. One factor is varied by keeping the other two constant at same range. Through the hodology 2D and 3D graphs are obtained and optimization is achieved. The S/N ratio is done to find out which factor has the most influence Cutting Force; Depth of cut; Spindle tio; ANNOVA Turning is the most effective method for forming any work piece, because through turning we can easily remove unwanted material. It is used to remove rust, improve shape near to tolerance limit, improve surface finish, and many more. Turning encloses different metals for machining such as alloy steel, carbon steel, cast iron, stainless steel, aluminum, copper, magnesium, zinc. Machining process involves some parameters which affects machining. These are spindle speed, depth of cut, feed etc. these param are called independent factors whereas some dependent factors are cutting force, surface finish, tool wear, tool life etc. which are needed to be minimized or maximized depending on the type of factors. Here cutting force is optimized with respect to the independent factors within a given range.
In this research work the optimization of cutting force is done theoretically using response surface methodology. The S/N ratio calculation is done for finding out the most effective parameters for cutting force.

II. DESIGN & ANALYSIS
This method is designed by taking a given range of independent parameters from a HMT 22 lathe. The parameters are spindle speed, depth of cut, and feed.
Here, three levels are taken for each parameter and Design of Experiments (DOE) is applied on it. This is a structured method which is used to identify various relationships between input and output. One of the DOE methods is RSM. The three levels obtained are fed into factorial combination in which we obtain 27 combinations of the parameters. Here optimization is done using AISI 1018 mild carbon steel. ifferent metals for machining such as alloy steel, carbon steel, cast iron, stainless steel, aluminum, copper, magnesium, zinc. Machining process involves some parameters which affects machining. These are spindle speed, depth of cut, feed etc. these parameters are called independent factors whereas some dependent factors are cutting force, surface finish, tool wear, tool life etc. which are needed to be minimized or maximized depending on the type of factors. Here cutting force is optimized with respect to the independent factors within a given range.
In this research work the optimization of cutting force is done theoretically using response surface methodology. The S/N ratio calculation is done for finding out the most effective parameters for cutting

DESIGN & ANALYSIS
This method is designed by taking a given range of independent parameters from a HMT 22 lathe. The parameters are spindle speed, depth of cut, and feed. Here, three levels are taken for each parameter and (DOE) is applied on it. This is a structured method which is used to identify various relationships between input and output. One of the DOE methods is RSM. The three levels obtained are fed into factorial combination in which we obtain 27 the parameters. Here optimization is done using AISI 1018 mild carbon steel.
Where, x 1 … x n are the independent input parameters and ε is the random error. Y is the output or response variable which has to be optimized.
In a turning operation with three input variables, the response function can be written as - Where, x 1 = log d, x 2 = log f, and x 3 = log N. Y = log F C and ε is the random error.
RSM is mostly applied through multiple regression models. For example, the first order or linear multiple regression model can be used - For better approximation, interaction terms can be included - The second order or quadratic regression model includes the square terms in addition to the terms above -Y = β 0 +β 1 x 1 + β 2 x 2 + β 3 x 3 + β 11 x 1 2 + β 22 x 2 2 + β 33 x 3 2 + β 12 x 1 x 2 + β 13 x 1 x 3 + β 23 x 2 x 3 + ε --- (5) In this case equation 5 is used to have the response surfaces in the design expert software.
(B) SUMMARY OF TURNING PARAMETERS AND FORMULAS N= rotational speed of the work piece in rpm f=feed in mm/rev or in/rev V C =cutting speed of work piece in m/min or ft/min =π D N/1000 or ω R [Since, ω = 2ΠN/60] D= diameter of work piece in mm ω = angular velocity rev/sec or rad/sec R = radius of the job d = depth of cut in mm or in MRR = Material removal rate in mm 3 /sec or in 3 /min = V C *f*d P=Power in hp or in lb/min or joule/sec or watt = E*MRR E=specific energy consumption T=Torque in lb-in or N-m =P/2ΠN F C =Cutting force in N or lb =T/R

N (D) SIGNAL-TO-NOISE RATIO(S/N)
The S/N ratio calculation is done for finding out the most effective parameters for cutting force.
Calculating S/N ratio for smaller is better for cutting force, the equation is, S/N (Y i ) = -10 log (∑ (X i 2 )/n) Where Y i = S/N ration for respective result X i = Cutting force for each combination = 1 to 27 n = No. of results for each combination for combination no. i Here rank 1, 2, 3 indicates that depth of cut is the most influencing factor for cutting force followed by feed and spindle speed. The analysis of variance (ANOVA) was used to study the significance and effect of the cutting parameters on the response variables i.e. cutting force. From Table 6, we can see that the P-Value for the model is 0.0001 which is lesser than the significance value of 0.05. Hence, the model is significant. Feed and depth of cut is found to be the most influential parameters affecting the cutting force with low P-value among all three parameters.   The graphs interpret that cutting force increases with increasing depth of cut and varies approx linearly with feed. It is also clear from the S/N ratio calculation that the main parameter which effect cutting force is depth of cut.

(F) OPTIMIZATION
The desirability function is used as a decision support tool which is to identify the process parameters that are resulting in the near-optimum settings for process responses. The optimization is done in design expert software version 11.

IV. CONCLUSION
From the above research work it can be concluded that the cutting force in case of turning can be improved when operated under optimum combination of the influencing parameters. Here the optimum combinations of the parameters for best cutting force are given above. Regression equation obtained here by software can be used to find one parameter when the other two are known so as to get the best cutting force within the range and is also used to obtain graphs. ANNOVA is also done to check the accuracy by R 2 value. From the S/N ratio the importance of one factor with respect to others can be obtained.