Water sandpaper plays a great role in the production of models, such as eliminating water gates from parts, polishing cutouts from parts cut from runners, and sometimes using fine sandpaper to polish away the gloss of paint, remove the oxidation layer of metal parts, and restore the original metallic luster. When oil is applied to sandpaper, it can also create a soft gloss on wooden models.
Water sandpaper has the following advantages:
(1) It increases grinding efficiency by 30%-50%.
(2) It has a long service life and produces less heat when grinding.
(3) It has high strength and tear resistance.
(4) It has good anti-clogging effect.
(5) It avoids sandpaper fading and affecting the surface quality of the workpiece.
(1) Waterproof sandpaper is mainly used for grinding and polishing automobile, furniture, leather, household appliances, and mechanical parts. It has the characteristics of grinding with water, high surface smoothness of the workpiece, and no dust pollution during operation.
(2) Coated sandpaper is suitable for grinding soft materials such as wood, paint, and soft metals. It has the advantages of no shedding and not easy to clog during use.
(3) Wood sandpaper is used for grinding various woods, non-metallic fillers, and glass. It can also be used for manicuring finger and toenails.
The seemingly ordinary sandpaper actually involves statistical problems in making the surface of an object smooth. We consider dividing the surface of the object into many small pieces. Each time the sandpaper rubs against the object, each small piece of the object's surface may be partially ground by each sand grain, denoted as 1, or may not be ground, denoted as 0. Assuming the probability of being ground or not being ground is equal, after two sand grains rub against the object, there are four possibilities for each small piece of the object's surface: (0,0), (0,1), (1,0), and (1,1), which means it is ground by 0, 1, or 2 small parts. Their probabilities are 1/4, 1/2, and 1/4, respectively. After three sand grains rub against the object, there are eight possibilities: (0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0), and (1,1,1), which means it is ground by 0, 1, 2, or 3 small parts. Their probabilities are 1/8, 3/8, 3/8, and 1/8, respectively.
Generally, after sand grains rub against the object, there are 2^n possibilities for each small piece of the object's surface to be ground or not, and each possibility is the same. Since each sand grain rubs against the object to grind on average half a small part of each small piece of the object's surface, after n sand grains rub against the object, each small piece of the object's surface is ground on average by n/2 small parts. From the perspective of possibility, it can be calculated that the probability of a small piece of the object's surface being ground by about n/2 small parts is the highest. Because a piece of sandpaper has many sand grains on it, every time a sand grain rubs against the object's surface, each small piece of the object's surface has already undergone many rounds of grinding by many sand grains. After multiple rounds of grinding, the value of n is very large, and the difference between each small part actually ground is negligible. Therefore, coarse water sandpaper can make the object's surface smooth.