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A machined surface study was performed according to the surface roughness post-process polishing operation on the aspheric mold core using a diamond turning machine. Machined surface features in the bokeh image must be removed with a subsequent surface polishing process after the aspheric glass molding pressing, as surface defects are caused by the mechanical resolution of ultraprecision diamond turning machines. Therefore, in this paper, we analyze the interrelationship between surface roughness, interference frequencies, and error-approximation aspherical error values to propose a baseline measure for machined surface removal. From the results of profilometer measurements, the form error accuracy before polishing is 1.3 $\mu$m, and after polishing is 0.2 $\mu$m. As a result of the LUPHOS, the root mean square (RMS) average of interference frequencies before polishing is 20 nm, and after polishing is 3 nm. The machining marks are removed from the bokeh image only when the RMS roughness is maintained at 5 nm or less.

This paper focused on the illumination model of machined surface based on micro-image. According to micro-image forming condition, the theory that the image brightness is related to the microfacet topography and surface reflection characteristics is presented. The distribution rule of micro-topography and reflection characteristics of sample surface is analyzed according to the measured data. An illumination mode of machined surface is established based on the analysis result, and the model parameters are obtained by using the simulated annealing algorithm. Verification results show that this proposed model can improve the simulation accuracy significantly and describe the lighting effect of machined surface. The research will provide a new idea and method for the 3D reconstruction.

Analysis of the machined surface is one of the major issues in machining operations. On the other hand, investigating about the variations of cutting forces in machining operation has great importance. Since variations of cutting forces affect the surface quality of machined workpiece, therefore, analysis of the correlation between cutting forces and surface roughness of machined workpiece is very important. In this paper, we employ fractal analysis in order to investigate about the complex structure of cutting forces and relate them to the surface quality of machined workpiece. The experiments have been conducted in different conditions that were selected based on cutting depths, type of cutting tool (serrated versus. square end mills) and machining conditions (wet and dry machining). The result of analysis showed that among all comparisons, we could only see the correlation between complex structure of cutting force and the surface roughness of machined workpiece in case of using serrated end mill in wet machining condition. The employed methodology in this research can be widely applied to other types of machining operations to analyze the effect of variations of different parameters on variability of cutting forces and surface roughness of machined workpiece and then investigate about their correlation.

Obtaining the optimum surface finish is one of the key factors in machining operations. For this purpose, engineers apply a set of machining parameters to obtain the desired surface quality. On the other hand, tool faces wear during machining operation that itself affects the surface quality of machined surface. Therefore, tool wear and surface finish of machined workpiece should be related to each other. In this research, we employ fractal analysis in order to investigate the correlation between variations of complex structure of machined surface and tool wear in turning operation. In fact, we changed the machining parameters between different experiments and investigated how the machined surface is correlated with the tool wear. Based on the obtained results, we can see the correlation between the complexity of machined surface and tool wear by increasing the depth of cut, spindle speed and feed rate in different experiments. The method of analysis employed in this research can be widely applied to other machining operations in order to find the correlation between the surface quality of machined surface and tool wear.

Investigating about the machined surface is an important issue in every machining operation. One of the factors that affect the quality of machined surface is the vibration of machine that is caused by different parameters such as the spindle speed. Therefore, the analysis of the relation between the machine vibration and surface quality of machined surface is very important. In this research, we analyze the relation between the machined surface and machine vibration from the complexity point of view. For this purpose, we employ fractal analysis. We investigate the variations of fractal structure of vibration signal collected from lathe machine versus the variations of fractal structure of the machined surface, for different depths of cut, feed rates and spindle speeds. Based on the obtained results, the variations of fractal structures of machined surface and vibration signal show a similar trend with the variations of depth of cut and feed rate, where by the increment of depth of cut and feed rate, vibration signal and machined surface get more complex. However, the obtained results in the case of variation of spindle speed do not show a consistent trend between variations of fractal structures of vibration signal and machined workpiece. The obtained method in this research can be applied to other machining operations in order to analyze the relation between the complexities of machine vibration and machined surface.

Surface finish is one of the most important issues that is discussed in machining of materials. In fact, reaching the required surface finish is the key scale in analysis of the quality of machined workpiece. Chip formation is an important factor that highly affects the surface finish of machined workpiece. In this research, we analyze the relationship between surface finish and chip formation by fractal analysis of their surfaces. Since both patterns have complex structures, we calculate their fractal dimension in case of different experiments in which machining parameters change. The result of analysis indicates that the variations of fractal dimension of machined surface show a reverse pattern compared to the fractal dimension of chip surface in case of variations of depth of cut and feed rate. However, in case of variations of spindle speed, the variations of fractal dimension of machined surface show a similar pattern with the fractal dimension of chip surface. Therefore, it can be said that the complexity of machined surface is linked to the complexity of chip surface. The method of analysis used in this research can be further applied to other manufacturing operations.

Surface finish of machined workpiece is one of the factors to evaluate the performance of machining operations. There are different factors such as machining parameters that affect the surface finish of machined workpiece. Tool wear is an unwanted machining issue that highly affects the surface finish of machined workpiece. In a similar way, different parameters (e.g. cutting speed, feed rate and depth of cut) also affect tool wear. In this research, we investigated how the complex structure of machined workpiece is related to the complex structure of tool wear. For this purpose, we benefited from the fractal analysis. The experiments were conducted based on the variations of machining parameters (depth of cut, feed rate and spindle speed), and accordingly the fractal dimension of machined surface was analyzed versus the fractal dimension of tool wear. Based on the obtained results, the complexity of machined surface is related to the complexity of tool wear. Fractal analysis could be applied to other machining operations to analyze the complex structures of machined surface and tool and potentially make a relationship between them.

Fractal dimension ($D$) is a widely used quantity to represent the irregularity of surfaces or profiles, e.g. it is often applied together with surface roughness to evaluate the quality of machined surfaces objectively and precisely. There are some conventional algorithms to calculate $D$ values through the morphological images of measured surfaces. However, the accuracies or efficiencies of these algorithms sometimes might be insufficient to satisfy the requirement of high-precision machining technology. In this paper, an artificial neural network (ANN) model is proposed to evaluate the $D$ value based on a single morphological image. First, the artificial fractal surfaces with preset ideal $D$ values are generated via Weierstrass–Mandelbrot (W–M) function. Then these surfaces are divided into a training dataset and a test dataset, which are used to train the ANN model and compare the model against the conventional algorithms (including box counting, power spectral density, autocorrelation function, structural function, and roughness scaling extraction with flatten order of 1), respectively. The accuracy and efficiency of $D$ calculation by using the trained ANN model are much superior. The mean relative error of ANN model is just 0.25%, while those of conventional algorithms are in the range of 2.22–9.33%. The average time cost for $D$ calculation of ANN model is 1.87ms, while those of conventional algorithms are in the range of 46ms–8s. Based on the advantages verified above, the trained ANN model is utilized to calculate the $D$ values of machined surfaces and investigate the influences of different cutting parameters. It is found that the $D$ values of machined surfaces could be influenced significantly by the feed rate, while the cutting speed and depth are relatively irrelevant.