1、选择最佳工具几何形状和切削条件Selection of optimum tool geometry and cutting conditionsusing a surface roughness prediction model for end millingAbstract Influence of tool geometry on the quality of surface produced is well known and hence any attempt to assess the performance of end milling should include the too
2、l geometry. In the present work, experimental studies have been conducted to see the effect of tool geometry (radial rake angle and nose radius) and cutting conditions (cutting speed and feed rate) on the machining performance during end milling of medium carbon steel. The first and second order mat
3、hematical models, in terms of machining parameters, were developed for surface roughness prediction using response surface methodology (RSM) on the basis of experimental results. The model selected for optimization has been validated with the Chi square test. The significance of these parameters on
4、surface roughness has been established with analysis of variance. An attempt has also been made to optimize the surface roughness prediction model using genetic algorithms (GA). The GA program gives minimum values of surface roughness and their respective optimal conditions.1 IntroductionEnd milling
5、 is one of the most commonly used metal removal operations in industry because of its ability to remove material faster giving reasonably good surface quality. It is used in a variety of manufacturing industries including aerospace and automotive sectors, where quality is an important factor in the
6、production of slots, pockets, precision moulds and dies. Greater attention is given to dimensional accuracy and surface roughness of products by the industry these days. Moreover, surface finish influences mechanical properties such as fatigue behaviour, wear, corrosion, lubrication and electrical c
7、onductivity. Thus, measuring and characterizing surface finish can be considered for predicting machining performance. Surface finish resulting from turning operations has traditionally received considerable research attention, where as that of machining processes using multipoint cutters, requires
8、attention by researchers. As these processes involve large number of parameters, it would be difficult to correlate surface finish with other parameters just by conducting experiments. Modelling helps to understand this kind of process better. Though some amount of work has been carried out to devel
9、op surface finish prediction models in the past, the effect of tool geometry has received little attention. However, the radial rake angle has a major affect on the power consumption apart from tangential and radial forces. It also influences chip curling and modifies chip flow direction. In additio
10、n to this, researchers 1 have also observed that the nose radius plays a significant role in affecting the surface finish. Therefore the development of a good model should involve the radial rake angle and nose radius along with other relevant factors.Establishment of efficient machining parameters
11、has been a problem that has confronted manufacturing industries for nearly a century, and is still the subject of many studies. Obtaining optimum machining parameters is of great concern in manufacturing industries, where the economy of machining operation plays a key role in the competitive market.
12、 In material removal processes, an improper selection of cutting conditions cause surfaces with high roughness and dimensional errors, and it is even possible that dynamic phenomena due to auto excited vibrations may set in 2. In view of the significant role that the milling operation plays in today
13、s manufacturing world, there is a need to optimize the machining parameters for this operation. So, an effort has been made in this paper to see the influence of tool geometry (radial rake angle and nose radius) and cutting conditions (cutting speed and feed rate) on the surface finish produced duri
14、ng end milling of medium carbon steel. The experimental results of this work will be used to relate cutting speed, feed rate, radial rake angle and nose radius with the machining response i.e. surface roughness by modelling. The mathematical models thus developed are further utilized to find the opt
15、imum process parameters using genetic algorithms.2 ReviewProcess modelling and optimization are two important issues in manufacturing. The manufacturing processes are characterized by a multiplicity of dynamically interacting process variables. Surface finish has been an important factor of machinin
16、g in predicting performance of any machining operation. In order to develop and optimize a surface roughness model, it is essential to understand the current status of work in this area. Davis et al. 3 have investigated the cutting performance of five end mills having various helix angles. Cutting t
17、ests were performed on aluminium alloy L 65 for three milling processes (face, slot and side), in which cutting force, surface roughness and concavity of a machined plane surface were measured. The central composite design was used to decide on the number of experiments to be conducted. The cutting
18、performance of the end mills was assessed using variance analysis. The affects of spindle speed, depth of cut and feed rate on the cutting force and surface roughness were studied. The investigation showed that end mills with left hand helix angles are generally less cost effective than those with r
19、ight hand helix angles. There is no significant difference between up milling and down milling with regard tothe cutting force, although the difference between them regarding the surface roughness was large. Bayoumi et al. 4 have studied the affect of the tool rotation angle, feed rate and cutting s
20、peed on the mechanistic process parameters (pressure, friction parameter) for end milling operation with three commercially available workpiece materials, 11 L 17 free machining steel, 62- 35-3 free machining brass and 2024 aluminium using a single fluted HSS milling cutter. It has been found that p
21、ressure and friction act on the chip tool interface decrease with the increase of feed rate and with the decrease of the flow angle, while the cutting speed has a negligible effect on some of the material dependent parameters. Process parameters are summarized into empirical equations as functions o
22、f feed rate and tool rotation angle for each work material. However, researchers have not taken into account the effects of cutting conditions and tool geometry simultaneously; besides these studies have not considered the optimization of the cutting process.As end milling is a process which involve
23、s a large number f parameters, combined influence of the significant parameters an only be obtained by modelling. Mansour and Abdallaet al. 5 have developed a surface roughness model for the end milling of EN32M (a semi-free cutting carbon case hardening steel with improved merchantability). The mat
24、hematical model has been developed in terms of cutting speed, feed rate and axial depth of cut. The affect of these parameters on the surface roughness has been carried out using response surface methodology (RSM). A first order equation covering the speed range of 3035 m/min and a second order equa
25、tion covering the speed range of 2438 m/min were developed under dry machining conditions. Alauddin et al. 6 developed a surface roughness model using RSM for the end milling of 190 BHN steel. First and second order models were constructed along with contour graphs for the selection of the proper co
26、mbination of cutting speed and feed to increase the metal removal rate without sacrificing surface quality. Hasmi et al. 7 also used the RSM model for assessing the influence of the workpiece material on the surface roughness of the machined surfaces. The model was developed for milling operation by
27、 conducting experiments on steel specimens. The expression shows, the relationship between the surface roughness and the various parameters; namely, the cutting speed, feed and depth of cut. The above models have not considered the affect of tool geometry on surface roughness.Since the turn of the c
28、entury quite a large number of attempts have been made to find optimum values of machining parameters. Uses of many methods have been reported in the literature to solve optimization problems for machining parameters. Jain and Jain 8 have used neural networks for modeling and optimizing the machinin
29、g conditions. The results have been validated by comparing the optimized machining conditions obtained using genetic algorithms. Suresh et al. 9 have developed a surface roughness prediction model for turning mild steel using a response surface methodology to produce the factor affects of the indivi
30、dual process parameters. They have also optimized the turning process using the surface roughness prediction model as the objective function. Considering the above, an attempt has been made in this work to develop a surface roughness model with tool geometry and cutting conditions on the basis of ex
31、perimental results and then optimize it for the selection of these parameters within the given constraints in the end milling operation.3 MethodologyIn this work, mathematical models have been developed using experimental results with the help of response surface methodology. The purpose of developi
32、ng mathematical models relating the machining responses and their factors is to facilitate the optimization of the machining process. This mathematical model has been used as an objective function and the optimization was carried out with the help of genetic algorithms.3.1 Mathematical formulationRe
33、sponse surface methodology (RSM) is a combination of mathematical and statistical techniques useful for modelling and analyzing the problems in which several independent variables influence a dependent variable or response. The mathematical models commonly used are represented by:where Y is the machining response, is the response function
