At work, we are all too familiar with surface roughness! However, do you know why the common surface roughness is 0.8, 1.6, 3.2, 6.3, and 12.5? Did this question confuse you? Let’s take it slow…

## 01 The concept of surface roughness

During the machining process of the parts, due to the plastic deformation of the metal surface during cutting, the vibration of the machine tool, and the knife marks left by the tool on the surface, the various surfaces of the parts, no matter how smooth the processing, are observed under a microscope. You can see the unevenness of the peaks and valleys, and its microscopic surface can be represented by the figure below.

The micro-geometric shape features composed of peaks and valleys with small spacing on the processed surface are called surface roughness. Generally speaking, the surface roughness formed by different processing methods is also different.

## 02 Is surface roughness the same as a surface finish?

Surface finish is another term for surface roughness. The surface finish is proposed according to the human visual point of view, while the surface roughness is proposed according to the actual microscopic geometry of the surface. Because it is in line with the international standard (ISO), China adopted surface roughness after the 1980s and abolished surface finish. After the promulgation of national standards for surface roughness GB3505-83 and GB1031-83, surface finish is no longer used.

Surface roughness has a calculation formula for measurement, while smoothness can only be compared with a sample gauge. Therefore, surface roughness is more scientific and rigorous than smoothness.

Renault, a French engineer, saw that the wire ropes on the hot air balloon had a variety of specifications, so he thought of a way to raise 10 to the 5th power to get a number 1.6, and then multiply them together to get 5 priority numbers as follows:

1.0

1.6

2.5

4.0

6.3

This is a geometric sequence, the last number is 1.6 times the first number, then there are only 5 types of steel wire ropes below 10, and there are only 5 types of steel wire ropes from 10 to 100, namely 10, 16, 25, 40, 63.

However, this division method is too sparse, so Mr. Lei made persistent efforts to raise 10 to the 10th power and obtained the 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

The common ratio is 1.25, so there are only 10 types of wire ropes within 10, and only 10 types of wire ropes from 10 to 100, which is more reasonable. At this time, some people must say that the numbers in front of this series seem to have little difference, such as 1.0 and 1.25. There is no difference. I usually round up, but the interval between 6.3 and 8.0 is large. Is this reasonable?

Reasonable or unreasonable, let’s make an analogy. For example, the natural numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 seem to be very smooth. We use this sequence to pay wages. We give Zhang San 1000 and Li Si 2000. Both of them are convinced. Sudden inflation, 8000 to Zhang San and 9000 to Li Si. In the past, Li Si’s salary was twice that of Zhang San’s, but now it has become 1.12 times. Do you think Li Si can be willing? He is the supervisor, and it’s about the same to send him 16,000. Zhang San will not complain that the supervisor has 8,000 more than him.

There are two ways to compare this natural thing, namely “relative” and “absolute”! The priority number system is relative.

Some people say that his product specifications are 10 tons, 20 tons, 30 tons, and 40 tons. Now it seems unreasonable, right? If you take double, it should be 10 tons, 20 tons, 40 tons, 80 tons, or keep the head and tail, it should also be 10 tons, 16 tons, 25 tons, 40 tons, the common ratio is 1.6 to be reasonable.

This is “standardization”. I often see people say “standardization” on forums, but they mean “standard parts”. The work they do is just sorting out the standard parts of the whole machine, which is called standardization. It is not like this. . For true standardization, you need to serialize all the parameters of your product according to the priority number system, and then serialize the functional parameters and dimensions of all parts and components with the 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 the priority number R10. Moreover, these 10 numbers are multiplied, divided, squared, and square rooted, and the result is still in these 10 numbers, how amazing! When you are designing and 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 and add their serial numbers, and the result is equal to N36, which is 8; when dividing, the serial numbers are subtracted, which is equal to N12, which is 2 For the cube of 2, multiply its serial number N12 by 3 to get N36, which is 8; for the root of 4, divide its serial number N24 by 2 to get N12, which is 2. What if you want to find the fourth power of 2? N12*4=N48, not here, what should I do? In the above list, if there is no number written, it is 10, and its serial number is N40. If the serial number is greater than 40, only look at the part greater than 40. For example, for N48, look at N8, which is 1.6, and then multiply it by 10 to get 16. . If the serial number is N88, look at N8 to get 1.6, and then multiply it by 100 to get 160, because the serial number of 100 is N80, and the serial number of 1000 is N120, and so on for the mechanical design. It is enough to use these 20 numbers for a lifetime. But sometimes the R40 number system is needed. If there are 40 numbers, it will be perfect. If it is not enough, there is also the R80 series. I have memorized the R40 number system backward, and I don’t need a calculator for general calculations. Simply speaking, to calculate the torsional capacity of 45 steel with a diameter of 40, the torsion coefficient is 0.5*π*R^3, the torsional stress is selected to be half of the yield point 360, which is 180MPa, and the pi is selected to be 3.15. Come out in a while. Did someone say you don’t add a safety factor? Tell me, is it 1.25, 1.5, or 2?

The golden section is 0.618, which is 1.618, and there is also 1.6 here.

The square root number sequence is the root number 1, the root number 2, and the root number 3. It is easy to find out, right? (The serial number of 3 is N19)

What is the square of pi equal to? equals 10. Is it convenient when the pressure bar is stable?

The torsion coefficient of a round rod is about 0.1*D^3, now you can calculate the torsion coefficient by mouth, right?

Why did the big screw jump directly from M36 to M40?

Why is the transmission ratio of the gears 6.3 or 7.1?

Why does the channel steel have a size of 12.6, which is rarely seen in the market?

Why did the outsourcing factory call and say that there is no 140 square tube, but there are 120 and 160? Because the R5 number system has priority over the R20 number system.

Why do the parameters of standard parts have a first sequence and a second sequence? Generally speaking, the first sequence is the R5 sequence.

Why does Inventor’s screw hole list have M11.2? Now you know it’s not a made-up number, right?

There are also steel plate thickness, section steel type, gear modulus, all standard parts, functional parameters, dimensional parameters, standard tolerance tables on all industrial product samples, and so on. Their sources are slowly becoming clear in our hearts at this moment. . It can be said that we have understood half of the 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 carrying out the so-called “standardization” after the design is completed; further, if the product is destined to be serialized, then we can even compare the actual working conditions Design the product without knowing it well because the priority number system has included all models.

The applications of the priority number system, listed above, can be described as a drop in the ocean, and endless applications are waiting for us to develop ourselves.