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French engineer Reynaud, seeing the wide variety of specifications for steel cables used in hot air balloons, came up with a solution. He calculated 10 to the power of 5, obtaining the value 1.6; by multiplying this value repeatedly, he arrived at five priority values: 1.0, 1.6, 2.5, 4.0, and 6.3. This is a geometric sequence, with each subsequent value being 1.6 times the previous one. As a result, there are only 5 types of steel cables below 10, and also 5 types for cables ranging from 10 to 100 – namely 10, 16, 25, 40, and 63. However, this classification was too sparse, so Mr. Lei made further efforts by raising 10 to the power of 10, resulting in the following R10 priority scale: 1.0, 1.25, 1.6, 2.0, 2.5, 3.15, 4.0, 5.0, 6.3, 8.0. With a common ratio of 1.25, there are only 10 types of steel cables within the range of 10, and also 10 types in the range from 10 to 100, which is more reasonable. At this point, someone might say that in this sequence, the preceding numbers seem to differ by not much – for example, 1.0 and 1.25; there’s almost no difference at all. I usually round such values off, but the gap between 6.3 and 8.0 is quite large. Is this reasonable? Whether it’s reasonable or not, let’s use an example. For example, the natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 seem quite logical; we can use this sequence to pay salaries – giving Zhang San 1000 and Li Si 2000, with both of them being satisfied with that arrangement. Suddenly, due to inflation, Zhang San is given 8,000 and Li Si is given 9,000. Previously, Li Si’s salary was twice that of Zhang San, but now it is 1.12 times. Do you think Li Si would be willing? He is the supervisor after all; 16,000 should be a fair amount to give him. Zhang San won’t complain that the supervisor gets 8,000 more than him. For things in nature, there are two ways of making comparisons: “relative” and “absolute”! Priority systems are relative. Some people say his product specifications include 10 tons, 20 tons, 30 tons, and 40 tons – but that doesn’t seem reasonable now, does it? If you double it, it should be 10 tons, 20 tons, 40 tons, 80 tons; or if you keep the starting and ending values, it should still be 10 tons, 16 tons, 25 tons, 40 tons. A ratio of 1.6 is the reasonable one. This is what is meant by “standardization.” On forums, it’s common to hear people talk about “standardization,” but what they actually mean are standard components. What is done is merely to organize the standard components of a complete device, and that is called standardization – but in reality it’s not that simple. For true standardization, you need to arrange all the parameters of your product in a sequence based on a priority system, and likewise, you must sequence the functional parameters and dimensions of all components using that same priority system. Natural numbers are infinite, but in the eyes of mechanical designers, there are only 10 numbers in the world, and they are the R10 priority numbers. Moreover, when these 10 numbers are multiplied, divided, raised to powers, or taken to roots, the results remain among these 10 numbers itself – what a wonder! When designing and not knowing what size to choose, you can simply pick from these 10 numbers – how convenient that is! 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. For two priority levels, such as 4 and 2, their corresponding values are N24 and N12 respectively; by multiplying these values and adding their indices together, the result is N36, which is 8 ； Divide, subtract the sequence numbers, and the result is N12; that is, 2 ； The cube of 2; multiplying its sequence number N12 by 3 gives N36, which is 8 ； The square root of 4 is 2. If we divide its index, N24, by 2, we get N12, which is also 2. So, what about finding the fourth power of 2? N12*4=N48, it’s not here, what should I do? In the list above, the number that isn’t listed is 10; its sequence number is N40. For any sequence number greater than 40, only the part greater than 40 is considered. For example, for N48, we take N8, which is 1.6, and then multiply it by 10 to get 16. If the sequence number is N88, then for N8 the value is 1.6; multiplying that by 100 gives 160. This is because the sequence number for 100 is N80, and for 1000 it is N120, and so on. Simply put, to calculate the torsional strength of 45 steel with a diameter of 40, use the formula torsion coefficient = 0.5*π*R^3. The torsional stress is taken as half of the yield strength, which is 360 MPa; thus it’s 180 MPa. Use π equal to 3.15, adjust the decimal point accordingly, and perform mental arithmetic to get the result quickly. Did someone say you don’t use a safety factor? Tell me, should it be 1.25, 1.5, or 2? Hehe. The golden ratio is 0.618, or 1.618; here too we have 1.6. The square root sequence is sqrt(1), sqrt(2), sqrt(3) – it’s easy to calculate, right? (Sequence number 3 is N19) What is the value of pi squared? It equals 10. It’s convenient when you calculate the stability of the compression bar, right? The torsional coefficient of a circular rod is approximately 0.1*D^3; now you can calculate the torsional coefficient mentally, right? Why does the large screw go straight from M36 to M40? Why is the gear transmission ratio 6.3 or 7.1? Why is there a 12.6 grade for channel steel, which is rarely seen in the market? Why did the subcontractor call to say that the 140 mm square tubes are not available, while the 120 mm and 160 mm ones are? Because the R5 number system has priority over the R20 number system. Why are there a first series and a second series of parameters for standard parts? Generally, the first sequence is the R5 sequence. Why is there an M11.2 in Inventor’s screw hole list? Now you know it’s not a made-up number, right? There’s also the thickness of steel plates, the types of steel profiles, the gear module, all the functional parameters and dimensional parameters listed on the specifications for standard components and industrial products, as well as the standard tolerance tables, and so on. The origins of these things are gradually becoming clear to us 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 created. So, when designing products, we can create a whole series at once, rather than carrying out so-called “standardization” after the design is complete” ； Furthermore, if a product is destined to be serialized, we can even design it without having a thorough understanding of the actual operating conditions, as the priority system already includes all models. The applications of priority number systems – as listed above – are just a drop in the ocean; countless more applications await us to discover. Memorize the priority number system; it’s a one-time task that will solve the problem forever.