【正文】 Ga 6. Magni?cation and surface roughness Earlier research work [18] carried out on roughness evaluation of surfaces using machine vision involved Table 2 Machining parameters used for milling and the roughness values correlating the spectra of such surfaces to the roughness values and these have been shown to follow power law behavior. Pro?le of such surfaces were shown to be self af?ned which implies that when magni?ed, increasing details of roughness emerge and appear similar to the original pro?le. In this paper an attempt has been made to correlate the grey level average (Ga) values obtained from the images with their respective surface roughness and study the behavior of such a correlation at various degrees of image magni?cation for the three machining operations. Consequently, images of workpieces captured by machine vision were magni?ed by factors 2, 5, 10 and 20 using the magni?cation technique mentioned in Section 3 and improved by Linear Edge Crispening algorithm. The feature of the image under study, Ga, was extracted and a correlation between Gaand surface roughness Rawas established on the basis of data given in Tables 4–6 (for three machining processes). Based on the values of correlation coef?cient so obtained, plots have been drawn between the magni?cation factor and correlation coef?cient from the data and are shown in Fig. 1 for three machining processes. 7. Results and discussion Based on the cubic convolution algorithm, the digital Speed (rpm) 125 250 90 90 Feed (mm/min) 45 Depth of cut (mm) Ga, optical parameter Ra(mm), sty lus parameter images of machined work pieces have been magni?ed for Table 4 Variation of Gawith varying magni?cation factors for ground surfaces Ga(1!)Ga(2!) Ga(5!) Ga(10!) Ga(20!) Ra(mm) 125 180 90 125 63 63 90 125 45 45 45 45 45 1 1 1 1 1 1 232 Table 5 R. Kumar et al. / International Journal of Machine Tools amp。 docC240。 feed C240。 speedC240。 Ga (c) Shaping RaZ 7:182C240。 docC240。 feed C240。 speed K240。 Ga (b) Milling: RaZK0:97 C240。 doc C240。speedK240。 Manufacture 45 (2020) 228–234 Table 3 231 Machining parameters used for grinding and the roughness values Machining parameters used for shaping and the roughness values Speed (rpm) 1801 2204 2593 1809 1501 2020 1800 2202 2593 Depth of cut (doc) (mm) 50 50 50 30 30 30 80 80 80 Ga, optical parameter Ra(mm), stylus parameter Speed (rpm) 12 18 24 18 24 18 18 12 18 24 12 Feed (mm/stroke) Depth of cut (mm) 1 1 1 1 Ga, optical parameter Ra(mm), stylus parameter regression equations have been developed for each of the machining processes based upon the data presented in Tables 1–3. They are as follows: 24 24 1 1 (a) Grinding: RaZ 0:52K240。g 1C g2C/C gn222。j g1K gmjCjg2K gmjC/CjgnKgmj222。 (2) RaZ Xn iZ1 !. jyij n lZKNkZKN The function hnis called the interpolation kernel and it is de?ned differently for different interpolation schemes. It denotes the neighborhood of the point at which brightness is desired. Usually, only a small neighborhood is used, outside which hmis zero. Therefore, the brightness interpolation is, in effect。x K lDx。 kDy222。 Z XN XN gs240。x。 y0222。ZTK1240。x。 y222。 y0Z Ty240。x。 Manufacture 45 (2020) 228–234 229 changes of the incident and re?ected light on the surface. Hisayoshi Sato et al. [6] worked on the estimation of surface roughness using a scanning electron microscope. They showed that the pro?le of a surface could be obtained by processing back scattered electron signals which are in proportion to the surface inclination along the electron beam scanning, which meant that the pro?le of the surface roughness can be derived by integrating the intensity of the back scattered electron signal. Bjuggern et al. [7] developed a total integrated infrared scatterometer to perform the rms roughness measurements of engineering surfaces. Hasegawa et al. [8] employed fractal characteristics of the ARMA model in an approach to model a machined surface pro?les. Carneiro et al. [9] measured the surface roughness using scanning probe microscopy, which includes more than 20 threedimensional roughness parameters to characterize the surface topography. After capturing the images of surfaces using machine vision systems manufactured by various processes including shaping, milling, grinding, etc. Ramamoorthy et al. [10,11] have utilized the grey level intensity histograms, etc. for establishing new optical parameters for roughness evaluation. Ramamoorthy et al. [12] have also used stereometry techniques to get the three dimensional depth pro?les of such surfaces and successfully estimated the surface area and volume of the ponents. Most state of the art digital image magni?cation techniques suffer from the limitation that they do not introduce any new information to the original image. This lack of information, more precisely the absence of high spatial frequency ponents is responsible for the perceptible degradation of magni?ed images, which are re?ected, in blurred edges. Interpolation methods are usually employed in magni?cation of digital images. One of the best interpolation schemes namely cubic convolution developed by Keys [13] approxim