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Why are the roughness values 0.8, 1.6, 3.2, 6.3, and 12.5?

Do you know why the roughness is 0.8, 1.6, 3.2, 6.3, 12.5?

Do you know why the cylinder diameter of the oil cylinder is 63, 80, 100, 125?

Do you know why the cylinder pressure is 6.3, 16, 25, 31.5?

Do you know why the thread specifications are 6, 8, 10, 12, 14, 16?

Do you know how the countless tables in the mechanical design manual and the parameter tables on all product samples were obtained?

Everything comes from the great priority number system.

French engineer Renault saw that there were various specifications of steel wire ropes on the hot air balloon, so he came up with a solution. He divided 10 by 5 to obtain a number 1.6, and then multiplied it repeatedly to obtain the following 5 priority numbers:

1.0

1.6

2.5

4.0

6.3

This is an arithmetic sequence, where the last digit is 1.6 times the first digit. Therefore, there are only 5 types of steel wire ropes below 10, and only 5 types of steel wire ropes between 10 and 100, namely 10, 16, 25, 40, and 63.

However, this method of division is too sparse, so Mr. Lei continued to work hard and divided 10 by 10 to the power of 10, resulting in the following priority number system for R10:

1.0

1.25

1.6

2.0

2.5

3.15

4.0

5.0

6.3

8.0

The nominal ratio is 1.25, so there are only 10 types of steel wire ropes within 10, and only 10 types between 10 and 100, which is quite reasonable. At this point, someone must have said that the numbers in front of this sequence don't seem to differ much, such as 1.0 and 1.25, which are almost identical. Usually, I round them up, but the interval between 6.3 and 8.0 is too large. Is this reasonable?

Reasonable or unreasonable, let's make an analogy. For example, natural numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 look very smooth. We use this sequence to pay salaries, giving Zhang San 1000 and Li Si 2000. Both of them are convinced. Sudden inflation, give Zhang San 8000 and Li Si 9000. Previously, Li Si's salary was twice that of Zhang San, but now it has become 1.12 times. Do you think Li Si would be willing? He is the supervisor, sending him 16000 is more than enough. Zhang San wouldn't complain that the supervisor is 8000 more than him.

There are two ways to compare things in nature, which are "relative" and "absolute"! The priority number system is relative.

Someone said that his product specifications are 10 tons, 20 tons, 30 tons, and 40 tons. Now it seems unreasonable, right? If you take twice the amount, it should be 10 tons, 20 tons, 40 tons, 80 tons, or to maintain the balance, it should also be 10 tons, 16 tons, 25 tons, 40 tons, with a nominal ratio of 1.6.

This is "standardization". It is common to see people on forums say "standardization", but in reality they are referring to "standard parts". The work they do is just to organize the standard parts of the entire machine, which is called standardization, but in reality it is not like that. True standardization requires serializing all parameters of your product according to a priority number system, and then serializing the functional parameters and dimensions of all components using a priority number system.

Natural numbers are infinite, but in the eyes of mechanical designers, there are only 10 numbers in the world, which is the R10 priority number. And, when these 10 numbers are multiplied, divided, multiplied, and square root, the result is still within these 10 numbers. How wonderful! When you are designing and don't know what size to choose, choosing from these 10 numbers is so convenient!

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, with sequence numbers N24 and N12 respectively, multiply them and add their sequence numbers together. The result is N36, which is 8;

Dividing and subtracting the sequence numbers equals N12, which is 2;

The cube of 2, multiply its number N12 by 3 to obtain N36, which is 8;

What is the square root of 2 if we divide the number N24 by 2 to obtain N12? N12*4=N48， There's nothing here, what should we do? The above list does not include a number, which is 10. Its index is N40. For any index greater than 40, only look at the part greater than 40. For example, if N48, look at N8, which is 1.6, and multiply it by 10 to get 16. If the serial number is N88, N8 gives 1.6, and then multiplying by 100 gives 160, because the serial number of 100 is N80, the serial number of 1000 is N120, and so on.

To do mechanical design, using these 20 numbers for a lifetime is enough. But sometimes the R40 series is needed, with 40 numbers, it is even more complete. If it is not enough, there is also the R80 series. I have memorized the R40 number system backwards and can handle general calculations without the need for a calculator.

In brief, calculate the torsional capacity of 40 diameter 45 steel, the torsional coefficient is 0.5 * π * R ^ 3, the torsional stress is 180 MPa, half of the yield point 360, and the circumference is 3.15. Hold the decimal point in both hands, add or subtract the serial number in your mind, and you will be out soon. Did someone say you didn't add a safety factor? Tell me, should we take 1.25, 1.5, or 2? ha-ha.

The golden ratio is 0.618, also known as 1.618, and here there is also 1.6. The square root sequence, which is root 1, root 2, and root 3, is easy to find, right? (The serial number of 3 is N19)

What is the square of π equal to? Equivalent to 10. Is it convenient for you to calculate when the pressure bar is stable? The torsion coefficient of a circular rod is about 0.1 * D ^ 3. Can you now calculate the torsion coefficient orally?

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

Why is the gear ratio 6.3 or 7.1?

Why is there a rare 12.6 grade in the market for channel steel?

Why did the outsourcing factory call and say that they don't have 140 square tubes, but they have 120 and 160?

Because the R5 number system takes 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 is there an M11.2 screw hole list in Inventor? Now you know it's not a fabricated number, right?

There are also steel plate thickness, steel type, gear module, functional parameters, dimensional parameters, standard tolerance tables, and so on on on all standard parts and industrial product samples. Their sources are gradually becoming clear in our minds at this moment. It can be said that we have already understood half of the mechanical design manual, as well as those industrial products that have not yet been made.

So, when designing products, we can simultaneously create a series of designs, rather than going through the so-called "standardization" after the design is completed; Furthermore, if the product is destined to be serialized, we can even design it without a good understanding of the actual working conditions, as the priority number system already includes all models.

The applications of priority number systems, as listed above, are like a drop in the ocean, with endless applications waiting for us to develop on our own. Recite the priority number system, this is a permanent task.