Do you know why roughness is 0.8, 1.6, 3.2, 6.3, 12.5?
Let's take it slow

 

During machining process of parts, due to influence of plastic deformation of metal surface, vibration of machine tool and tool marks left by tool on the surface during cutting, various surfaces of parts, no matter how smooth they are processed, even observed under a microscope, can see uneven peaks and valleys, as shown in figure.

 

Microscopic geometrical shape feature composed of peaks and valleys with small spacing on machined surface is called surface roughness. Generally speaking, surface roughness formed by different processing methods is also different.

1) Surface roughness affects wear resistance of parts. The rougher surface, the smaller effective contact area between mating surfaces, the greater pressure, and the faster wear.
2) Surface roughness affects stability of mating properties. For clearance fit, the rougher surface is, the easier it is to wear, so that clearance gradually increases during working process; for interference fit, due to flattening of microscopic peaks during assembly, actual effective interference is reduced and connection strength is reduced.
3) Surface roughness affects fatigue strength of parts. There are large troughs on the surface of rough parts, which are sensitive to stress concentration like sharp corner notches and cracks, thus affecting fatigue strength of parts.
4) Surface roughness affects corrosion resistance of parts. Rough surface is easy for corrosive gas or liquid to penetrate into inner metal layer through microscopic valleys on the surface, causing surface corrosion.
5) Surface roughness affects sealing of parts. Rough surfaces do not fit tightly, gas or liquid leaks through gaps between contact surfaces.
6) Surface roughness affects contact stiffness of parts. Contact stiffness is ability of joint surface of a part to resist contact deformation under action of external force. Stiffness of machine is largely determined by contact stiffness between various parts.
7) Affect measurement accuracy of parts. Surface roughness of measured surface of part and measuring surface of measuring tool will directly affect accuracy of measurement, especially in precise measurement.
In addition, surface roughness will have varying degrees of influence on coating, thermal conductivity and contact resistance of parts, reflectivity and radiation properties, resistance to liquid and gas flow, and current flow on conductor surface.

 

Surface finish is another term for surface roughness. Surface finish is proposed according to human visual point of view, while surface roughness is proposed according to actual microscopic geometry of surface. Because of conformity with international standards (ISO), China adopted surface roughness after 1980s and abolished surface finish. After promulgation of national standards for surface roughness GB3505-83 and GB1031-83, surface finish is no longer used.
There is a corresponding comparison table for surface finish and surface roughness (see figure below). Roughness has a calculation formula for measurement, while smoothness can only be compared with a sample gauge. Therefore, roughness is more scientific and rigorous than smoothness.

Everything comes from great priority number system!
French engineer Reynolds saw that wire ropes on hot air balloon had a variety of specifications, so he thought of a way to multiply 10 to fifth power to get a number 1.6, and then multiply them to get 5 priority numbers as follows:
1.0  1.6  2.5  4.5  6.3
This is a proportional sequence, the latter number is 1.6 times the former number, then there are only 5 kinds of wire ropes below 10, and only 5 kinds of wire ropes from 10 to 100, namely 10, 16, 25, 40, 63.
However, this method of division is too sparse, so Mr. Lei made persistent efforts to open 10 to power of 10 to obtain R10 priority number system as follows:
1.0  1.25  1.6  2.0  2.5  3.15  4.0  5.0  6.3  8.0
Common ratio is 1.25, so there are only 10 kinds of wire ropes within 10, only 10 kinds of wire ropes between 10 and 100, which is more reasonable. At this time, someone must have said that numbers in front of this sequence seem to be not very different, such as 1.0 and 1.25.
Reasonable or unreasonable, let's make an analogy. For example, natural numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 seem to be very smooth. We use this sequence to pay wages. Zhang San is given 1,000, and Li Si is given 2,000. Both of them are convinced. Sudden inflation, 8,000 to Zhang San and 9,000 to Li Si. In the past, Li Si's salary was twice that of Zhang San, but now it is 1.12 times. Do you think Li Si can be willing? He is supervisor, and it is almost same as sending him 16,000. Zhang San will not complain that supervisor has 8,000 more than him.
There are two ways of comparing this natural thing, that is, "relative" and "absolute"! Priority number system is relative.
Some people say that his product specifications are 10 tons, 20 tons, 30 tons, and 40 tons. It seems unreasonable now, right? If you take twice, it should be 10 tons, 20 tons, 40 tons, 80 tons, or keep head and tail, it should also be 10 tons, 16 tons, 25 tons, 40 tons, and ratio is 1.6 is reasonable.
This is "standardization". I often see people talking about "standardization" on forum. In fact, they are talking about "standard parts". Work they do is to sort out standard parts of the whole machine, which is called standardization. In fact, this is not case. For real standardization, you need to serialize all parameters of your product according to priority number system, and then serialize functional parameters and dimensions of all components with priority number system.
Natural numbers are infinite, but in the eyes of mechanical designers, there are only 10 numbers in the world, and it is R10 priority number. Moreover, multiplying, dividing, exponentiating, and rooting these 10 numbers, result is still within these 10 numbers, how amazing! When you are designing, when you don't know what size to choose, just choose from these 10 numbers, how convenient you say!
1.0 N0  1.12 N2  1.25 N4  1.4 N6  1.6 N8  1.8 N10  2.0 N12  2.24 N14  2.5 N16  2.8 N18 3.15 N20  3.55 N22  4.0 N24  4.5 N26  5.0 N28  5.6 N30  6.3 N32  7.1 N34  8.0 N36  9.0 N38
Two priority numbers, such as 4 and 2, whose serial numbers are N24 and N12 respectively, multiply them, add their serial numbers, result is equal to N36, which is 8; divide, and subtract serial numbers, which is equal to N12, which is 2; For cube of 2, multiply its serial number N12 by 3 to get N36, which is 8; for square root of 4, divide its serial number N24 by 2 to get N12, which is 2, which is fourth power of 2? N12*4=N48, there is none here, what should I do?
Above list, without a number, is 10. Its serial number is N40. If serial number is greater than 40, only look at part greater than 40. For example, N48 looks at N8, which is 1.6, and then multiplied by 10 to get 16. If serial number is N88, look at N8 to get 1.6, then multiply it by 100 to get 160, because serial number of 100 is N80, serial number of 1000 is N120, and so on for mechanical design, it is enough to use these 20 numbers for a lifetime.
But sometimes it is necessary to use R40 number system. If there are 40 numbers, it is more complete. If it is not enough, there is also R80 system. I have memorized R40 number system by heart, and I don't need a calculator for general calculations. In simple terms, to calculate torsional resistance of 45 steel with a diameter of 40, its torsional coefficient is 0.5*π*R^3, torsional stress is selected as half of yield point 360, which is 180MPa, pi is selected as 3.15, left and right hands pinch decimal point, and add or subtract serial number mentally. Come out in a while. Did someone say you don't add a safety factor? Come on, should I take 1.25, or 1.5, or 2? Ha ha.
Golden ratio is 0.618, which is 1.618, and there is also 1.6 here.
Square root sequence is square root of 1, square of 2, and square of 3. It is easy to find, right? (Serial number of 3 is N19)
What is square of pi? equals 10. You think it's convenient when pressure bar is stable, right?
Torsion coefficient of round rod is about 0.1*D^3. Now you can calculate torsion coefficient by mouth, right?
Why did big screw jump directly from M36 to M40?
Why does gear ratio have a 6.3 or 7.1?
Why does channel steel have a 12.6 gauge that is rarely seen in the market?
Why did outsourcing factory call and say that there is no 140 square tube, but there are 120 and 160? Because R5 number system takes precedence over R20 number system.
Why do parameters of standard parts have a first sequence and a second sequence? Generally, the first sequence is R5 sequence.
Why does Inventor's screw hole list have M11.2? Now you know it's not a gibberish number, right?
There are also steel plate thickness, section steel model, gear module, all standard parts, functional parameters on all industrial product samples, dimensional parameters, standard tolerance tables, etc., etc. Their sources are slowly becoming clear in our hearts at this moment. . It can be said that we have understood half of mechanical design manual, as well as those industrial products that have not yet been made.
Then, when we design a product, we can design a series at the same time, instead of so-called "standardization" after design; further, if product is destined to be serialized, then we can even analyze actual working conditions. Design products without knowing much, because priority number system has all models included.
Application of priority number system, listed above, can be described as a drop in the ocean, and endless applications are waiting for us to develop ourselves.