Method of complex glass relief surfaces mechanical grinding

. Presented research is devoted to solving the problem of treatment complex glass relief surfaces by mechanical vibration grinding. The dependences of the obtained grinding results on the type of relief surface, grain size and vibration parameters are investigated. Results: Mathematical dependences of the change in the light transmission of the ground glass on the type of the ground glass surface pattern, grain size and vibration parameters are obtained.


Introduction
Mechanical grinding of glass, known since ancient times, is widespread today. Used in both technical and artistic glassmaking, mechanical grinding of glass is reduced to the influence of a grinding tool sturdiness exceeding the hardness of the processed material on a hardness of the working surface -glass.
Operation principles of currently used grinding glass surfaces tools are reduced to a conventional rotational or translational effect of the working surface on the material being treated. At the same time, the abrasive of various fractions and hardness can form a single unit with the working tool, or it can be delivered separately to the processing zone in the form of a suspension.
The main limitation in mechanical grinding of glass is the surface shape to be ground. The variety of forms used in glassmaking requires an individual approach to the grinding tool, as well as to the principles of mechanical action on glass. The most common are flat and spherical glass surfaces, and grinding tools with spherical or radial working surfaces are usually made on an individual basis, depending on the required grinding task. For example, when processing glass lenses.
The most difficult and unresolved problem of glass mechanical grinding is the grinding of embossed and asymmetrical surfaces. The main issues that arise in this case: -the processing surface uniqueness; -the problem of uniform surface exposure due to the complexity of the pattern; -horizontal movement restrictions of the grinding tool due to the surface pattern. The aim of the study is to determine the dependence of the change in the light transmission of glass on the complexity of the ground pattern, grain size and parameters of mechanical impact on the treated relief asymmetrical surface.
The object of the study is a sheet glass with relief surface obtained by the method of molling [1].

Methods and materials
The study was carried out on glass samples with relief asymmetrical surface 6 mm thick and pattern height from 0.0 to 3.0 mm. The relief surface was obtained by vacuum molling by the device described in [1]. Technological parameters of molling: temperature 810 o C, depression in the form of 0.5 bar. The original glass complies with GOST 111-2014 [2].
Measurements of light transmission before and after treatment by vibration grinding using a tool with an abrasive surface were carried out using the IS-2 device [3].

Results
Because of the impossibility of objective control of the light transmission of relief glasses, related to the requirement of a sensors tight fit to the glass surface [3], modeling of a relief asymmetrical glass surface was carried out.
The concept of "the average angle of the relief surface" (αave), defined from equation (1), was introduced.
where Sр is the projection area of the relief surface, Sr is the surface area of the pattern. During the experiment, the actual area of relief surface of the sample shown in Figure 1 was determined by scanning the sample surface, followed by calculating the area of the triangulated surface in the 3D Max program. The results of computer modeling showed that the area of the relief surface is 1.22 times larger in relation to its projection. Therefore, the average angle of the relief embossed shown in Figure 1 is: To visually represent the average angle of the relief surface, the computer model of the actual relief surface was transformed and ordered, as shown in Figure 2. Based on the proposed assumption, conditioned by computer modelling and transformation of the relief surface, the calculation of the average angle of the relief surface can be carried out for the pattern, the projection of which is a circle or a regular polygon.
Next, a grinding tool with an abrasive surface and grinding rig were made, simulating the position of a flat glass at an angle equal to the average angle of the relief surface.
For the manufacture of grinding tools, polyurethane resin with a hardness of 30-35 A Shore was chosen as a binder, and electrocorundum powder of the 43A-45A brand with fractions of 10-40 μm, 40-80 μm, 80-120 μm, 120-160 μm was chosen as abrasive filler. The binder: filler ratio is 3: 1. Four grinding tools with an appropriate abrasive surface were manufactured. As a result of sedimentation of abrasive particles in an uncured suspension, their distribution over the thickness of the grinding tool occurred, as shown in Figure 3.  For fixing flat glass (2), Fig.4, a turntable (1) was made with fixing the angle of deviation (6) equal to the average angle of the pattern, the applied force (4) to the grinding tool (3) is directed at an angle to the glass plane being ground.
The treatment of flat glass took place on an inclined table, as shown in Figure 4, with the application of a vibration processing force at an angle equal to the average value for the relief surface. Mechanical processing of glass was carried out using a manufactured grinding tool with measurement of the degree of light transmission changes. Table 1 shows the technological parameters of glass processing. The abrasive grain of the tool, μm 120-160 80-120 40-80 10-40 The initial light transmission of the glass before the start of processing was 60%. The angle of inclination of the table corresponded to the average angle of the relief surface of the sample α = 39 o .
The results of the study of the influence of machining parameters on light transmission are shown in Table. 2 and in Fig. 5.  Table 2. Change in light transmission of glass (τv) before and after mechanical treatment. Next, the change in the light transmission (τv) of the glass sample was determined depending on the change in the average angle of the relief surface from 0 o to 60 o , to determine the mathematical dependence of the change in the light transmission degree on the parameters of grinding pattern asymmetrical glass surfaces with different average angles of reliefs. Figure 6 shows the dependences of the light transmission change (τv) of glass treated with a grinding tool with different fractions of abrasive material depending on the change in the average angle of the relief surface. The initial glass light transmission before the processing start was 60%. The grinding parameters are shown in Table 1.

Fraction
During the tests, the dependences of the light transmission coefficient (τv) on the average angle of the relief surface (αave) and the average size of the grain fraction of the abrasive powder (N) were obtained, described by the following formula (3): where (τv) -is the light transmission coefficient after processing the embossed glass surface with a grinding tool with an abrasive surface; A and B are dimensionless coefficients determined by formulas (4) and (5) τvо -is the light transmission coefficient before processing the embossed glass surface; αave -the average angle of the relief surface where N -is the average grain size of the abrasive powder fraction used for processing the glass surface, μm.

Discussion
The relevance of the study was caused by the need for mechanical grinding of glass surfaces with complex asymmetrical pattern.
The concept of the "average angle of the relief surface" was introduced and justified, as the arccos of the ratio of the projection area of the relief surface to its total surface area. This dependence can be applied to projections that have a round shape or the shape of a regular polygon.
For preliminary determination of the required degree of light transmission, a method is proposed to simulate a relief surface using an inclined table mounted at an angle corresponding to the average angle of the relief surface.
It is shown that the use of vibration grinding allows to achieve certain results, but to achieve a greater degree of light transmission, it is necessary to use an abrasive with a lower degree of hardness.
The mathematical dependence of the light transmission measurement on the average angle of the glass surface pattern and the abrasive fraction is derived. The studies were carried out using an electrocorundum abrasive of the 43A-45A brand. To deduce the mathematical dependence of abrasives of other hardness, additional research is required.

Conclusion
Mechanical grinding has been and still remains an important method of glass surfaces treatment, the main limiting factor of which is the relief of the glass surface.
The processing method of asymmetrical relief glass surfaces proposed in this research paper makes it possible to automate this process to a large extent.
For a more detailed study of the process of mechanical grinding of asymmetrical relief glass surfaces, additional research is required.