Some standard content:
National Standard of the People's Republic of China
Preferred Numbers and Preferred Number Systems
GB 321-80
Replaces GB 321-6#
This standard is used for the classification of various values. In particular, when determining the number or parameter series of a product, the preferred numbers and preferred number systems must be adopted as far as possible in accordance with the provisions of this standard.
1. Terms and Definitions
1.1 Preferred Number Systems
The preferred number system is a set of approximate geometric number series derived from a theoretical geometric number series with a common ratio of 10, 10, 2/10, 10 or 10, and an integer containing 10 in the required value. Each number series is represented by the symbols R5, R10, R20, R40 and R80, respectively, which are R5 series, R10 series, R20 series, R40 series and R80 series. The series and theoretical common ratio of the priority number system are generally calculated by Rr and 9. (4, = V10), where 1 is 5, 10, 20, 40, and 80, which are the graded numbers of the quality values in the series from 1 to 10, 10 to 100, etc. 1.2 Priority number
The value of each term in the priority number system is the priority number. , The priority number is associated with the theoretical position: that is, the value of the term of the theoretical geometric sequence (, N. The theoretical position is generally an irrational number, which is not convenient for practical application. *Continued N, is an arbitrary integer.
b, the calculation of the priority number: it is the operational value reported to five significant figures of the theoretical value. Compared with the theoretical value, its relative error is less than 1/20000, and it can be used to replace the theoretical value when making accurate calculations of the parameter series. C. The common value of the priority number: that is, the so-called priority number, which is a uniformly specified value after the calculated value is appropriately rounded for practical application. ||tt| |d, the rounded value of the priority number: it is the value obtained by further rounding the commonly used values in the RS, R10, R20 and R40 series, and is only allowed to be used in certain special cases.
1.3 The serial number of the priority number
The N in the sieve formula is called the serial number of the priority number in the R series. It indicates the order of the priority number in the R series, starting from the serial number V of the priority number 1.00 (.00) = 0, forming an arithmetic progression. 2, the class and round number of the series
2,1 Basic series
R5, R10, R20 and R40 are four series in the priority number system, which are called basic series (see Table 1). The maximum relative error of the priority number value in the basic series to the calculated value is +1.26% and -1.01%. The common ratio of each series is: R5: 9. = 10 ~1.60
R10,91. =/10~1.25
R20: 920= 2/10 1.12
R40#940=4/10~1.06
2.2 Supplementary series
R80 series is called supplementary series (see Table 2), its common ratio is 10~1.03, and it can only be considered when the parameter classification is very fine or the priority number in the basic series cannot adapt to the actual situation. National Standard General Release
The First Machinery Industry Ministry of the People's Republic of China proposed
Implementation on July 1, 1981
Drafted by the Standardization Research Institute of the First Machinery Ministry
Basic series (common value)
GB321-80
Basic series
Serial number N
— 27
to 100
Theoretical value
Logarithmic number
Calculated value
1,6788
2,1135
3,5151
Common channel
Constant error
- 0,18
Basic series (common bonds)
GB321--80
to 100
, the theoretical value
! Logarithmic number
, (person" 10 and small" -1 of the optimal number, can be obtained by the decimal extension method described in Article 3, paragraph b of this standard. ③ The relative error with the value of the standard is the calculated value of the three stations × 100%. Let the calculated value
net N is the abbreviation of the serial number W in the R40 series, supplementary series R80
2,3 Derived series and shift series
2.3.1 Derived series
Calculated position
Continued Table 1
With applicable values
Relative error
GB321—80
A derived series is a series derived from the basic series or supplementary series Rr with every p items, expressed as Rr/P. The ratio r/P is the graded number of the item values in each decimal segment such as 1 to 10, 10~~100, etc. The common ratio of the derived series is
Q/=g=(10)=101/
. Derived series with equal ratios have the same common ratio, except that the top value is ambiguous. For example, the common ratio of the derived series R10/3 is 10/==108710=1.2589*~2, which can be derived into three series with different term values, 1.00, 2.00, 4.00, 8.00,,
1.25 ,2.50,5.00,10.0,\
1.60,3,15,6.30,12.5,.
2.3.2 Shift series
Shift series is also a derived series, its common ratio is the same as a basic series, but the value of the term is different from the basic series. For example, the R80/8 series with the value of the term starting from 25.8 is a shift series of the R10 series with the value of the term starting from 25,0. 2.4 Rounding value series
The rounding value series (see Table 3) is a series composed of the normal monthly values of the priority numbers and a part of the rounding values. It is only allowed to be used when the parameter values are subject to special restrictions. The series with smaller rounding value errors is called the first rounding value series, represented by the symbol Rr, and the series with larger errors is called the second rounding value series, represented by the symbol Rr. 2.5 Series code
2.5.1 Basic series and supplementary series codes a. When the series has no limited range, it is represented by R5, R10, R20, R40 and R80. b. When the series has a limited range, the limit value should be indicated. For example: R10 (1.25) - R10 series with 1.25 as the lower limit R20 (.45) - R20 series with 45 as the upper limit R40 (75**300) - R40 series with 75 as the lower limit and 300 as the upper limit. 2.5.2 The code for derived series
a. When the series has no limited range, an item value contained in the series should be indicated. For example, R103 (*80..*) - a derived series containing the item value 80 and extending infinitely at both ends. If the series is increased by 1 and contains the item value 1, it can be abbreviated as Rr/P. For example, R10/3 represents the following series +**, 1, 2, 4, 8, 18, +*+*.
b. When the series has a limited range, the boundary value should be indicated. For example, tR20/4 (112) - a derived series with 112 as the lower limit, R40/5 (*60) - a derived series with 60 as the upper limit, R5/2 (1*10000) - a derived series with 1 as the lower limit and 10000 as the upper limit. 3. The main characteristics of the priority number system
day, the item value of the R5 series j is included in the R10 series, R10 The item values in the series are included in the R20 series, the item values in the R20 series are included in the R40 series, and the item values in the R40 series are included in the R80 series. b. The item values in the R, series can be infinitely extended to both directions according to the decimal method. All priority numbers (or rounded values) greater than 10 and less than 1 can be obtained by multiplying the integer data of 10 (such as 10, 100, 1000, * or 0.1, 0.01, 0.001,) by the priority numbers in Table 1 and Table 2 (or the rounded values in Table 3). This extension method is also applicable to the derived series Rr/P with the ratio / equal to an integer. c. The relative difference of the common values of any two adjacent priority numbers in the same series is approximately unchanged. Among them, the R5 series is about 60%, the R10 series is about 25%, the R20 series is about 12%, the R40 series is about 6%, and the R80 series is about 3%. d, the theoretical common ratio of the R10 series is 10=1.2589, which is very close to 2/2=1.2599. Therefore, the theoretical geometric progression of R10/3, R20/6 or R40/12 is very close to the multiple series with a common ratio of 2. #
The maximum common ratio of the common ratio of the R10 series is %
The combination of the two series (with the combination of the two series) is 1.6
RID R'10
GB321—80
R20R'20
5,37, + 1.66 + 1.66 -5.61
,①The lack of 1~4 in the decline is mostly expressed, rough age (——) basic series,
) first rounded series,
set () second rounded series.
1.83 197 - 4.48 1 + 1.15
+ 2,94
+ 7315
6 h834
② R5, the rounded series in the oxygen series (with brackets) is marked with the effective value 1, and should be used as much as possible. The relative error of each item in the B series is 5 to 40; 10 to 40 + 0.78 - 0.88 5 and 10 - 5.13 ① In special cases, when the cumulative grading does not allow for net adjustment (the item position increases and the item difference decreases), the R40 series allows 1.15 to be calculated as 1.18, 1.20 as the rounded value of 1.25, and the rounded value is 1, 1.05, 1,10, 1,15, 1,20, 1,30 ① The values in the corresponding boxes in the 10th column of the table are the maximum relative errors of the items in the corresponding series. The relative integer of the common ratio between two adjacent terms (the ratio of the common ratio) is the value of the common ratio × 1% of GB327-80. The theoretical product or quotient of any two terms in the same series, or the integer power of any term, is still a priority number value in this series. The common values are similar to each other. For example: the calculated value 7.9433×7.943363.093
the common value 8×8~63
1, the logarithmic values of each priority number in the same series form a standard series: priority number and serial number V, which is a special logarithm with 9 (i.e. 10) as the base estimated by priority number theory. Therefore, the operation of priority numbers can be simplified by converting the operation method of general logarithms into serial number operations. That is:
The serial number of the product of two priority numbers is equal to the sum of the two priority numbers; the serial number of the quotient of two priority numbers is equal to the difference between the two priority numbers. Example 1, 3.15×1.6=5
N (3.15×1.6) =N (3.15) +N (1.6)=20+8=28=(5)
Example 2: 3.13+1.6=2
N(3.15+1.6)=N(3.15)-N(1,6)
=20-8-13=N(2)
4, the principle should be
When formulating the bond number grading plan, the selection of the series depends on the manufacturing, so as to make the comprehensive consideration of technology and economy reasonable. For individual parameterizations that have no clear requirements for parameter series, priority numbers should also be used, and a series with existing rules will be gradually formed with the development of cattle breeding.
4.1 Application of this series
When determining the series scheme of variable parameters (i.e. parameters whose value selection is not restricted by existing standards or supporting products), as long as it can meet the technical and economic requirements, the basic series with larger common values should be selected in the order of R5, R10, R29, and R40. If necessary, the intermediate values can be inserted to form a series with smaller common values. For individual parameter values, the priority numbers should be selected in the above order. 4.2 Application of derived series
When the common value of the basic series can meet the classification requirements, the derived series can be selected. When selecting, the derived series with the common value and the extended value containing the value 1 should be preferred.
The shift series should only be used for the series of variable parameters. 4.3 Application of composite series
When the range of parameter series is very large and it is necessary to use series with different common ratios in different parameter ranges from the perspective of manufacturing and use economy, the most suitable basic series or temperature series can be combined to construct a composite series. Example 1: Use R10 (1040) and R20 (40·100) to form a composite series with two common ratios: 10, 12.5, 16, 20, 25, 31.5, 40, 45, 50, 56, e3, 71, 80, 90, 100 Example 2: Use R5 (...25) → R20/3 (25..35.5), R40/5 (35....63) and R10 (63.-160) to form a composite series with three common ratios: 4, 6.3, 10, 16, 25, 35.5, 47.5, 63, 80, 100, 125, 160 4.4 Calculate the value of
The parameter system is graded according to the priority number and the common ratio is unequal. In some special cases, such as in the case of turbine blades, where exact enlargement is required for similar designs, calculated values may be used in order to obtain a series with equal common ratios. 4.5 Application of rounded values Rounded values and rounded value series may only be used in the following cases, and the first rounded value series R shall be used first. a. Objectively, only integer parameters can be used, for example, the number of teeth of a gear is replaced by 32 instead of 31.5. b. Rounded values are sometimes more appropriate for items that require even numbers, integer multiples, and additive properties if the value is divisible, such as combined dimensions in packaging and component dimensions composed of integer multiples of the module. c. When the precision represented by the effective digits of the priority number has no practical significance and is not convenient for ink measurement, the rounded value series can be used. For example, the exposure time series of the camera adopts the R\10/3 series (1, 1/2, 1/4, 1/8, 1/15, 1/30, 1/60, 1/125... seconds).
d. When the dimension parameter series is limited by the existing supporting products, such as involving a wide range of cooperation and a large amount of existing material foundation, and it is not easy to change, the rounded value series can be used, such as the standard direct control and standard length series. Appendix
1. Main advantages of the priority number system
1,1 Numerical classification system of economic theory
1.2 Basis of unity and simplification
1,3 Wide adaptability
1,4 Simple, easy to remember and easy to use
1.5 Simplified design calculation
2 Calculation of priority numbers
2,1 Calculation by serial number
2.2 Calculation by common logarithm
2.3 List calculation
2.4 Calculation drawing
3. Key points of the application of the priority number system
8.1 Scope of application
3.2 Reasonable selection of parameters using priority numbers
3.3 Reasonable selection of series
9.4 The current standard still prefers the priority number system
4. Application examples
4.1 Application in product parameter series standards4.2 Application in the adjustment and simplification of old products4.3 Application in the classification of quality indicators
4.4 Application in the design of parts series
4.5 Application in the integrated design
4.6 Application in similar design
GB 321--80
Application Guide
G8321-80
Preferred numbers and priority number systems were first proposed by the Frenchman Charles Renard at the end of the 19th century. At that time, the size of the rope used on balloons was arbitrarily determined by the designer, and there were as many as 425 types. In 1877, Renard classified the size according to the geometric progression, simplifying it from 425 to 17 types for the purpose of rationalization. He made such a provision for the geometric progression that every 5 items would increase the item value by 10 times (decimal geometric progression). Let a be the starting term value and be the common ratio, and we can get the relationship α·g\=10a, that is, the common ratio Q=\√1~1.6. The corresponding theoretical series is: a, a/10a(10)\, a(/10), a(/10)10a. The term values are taken to 5 significant figures:
a, 1.5849a, 2.5119a, 3.9311a, 6.3096a10a. Renard used the more practical term value scheme instead of the precise calculation value, and used the integer of 10 as a, thus obtaining the following series: 10, 16.25, 40, 63, 100
This series can be extended in two directions, which is the current R5 series, and further formed the more finely graded R10 and R20.and R40 series. The first standard based on this was formulated in Germany in 1920. In 1935, the International Association for Standardization issued ISA Circular No. 11, recommending "preferred numbers" as international standards. After World War II, the International Organization for Standardization's "Preferred Numbers" Technical Committee (ISO/TC1S) continued its work in this area and published ISO R3 "Preferred Numbers and Preferred Number Systems" in 1953. In order to better apply priority numbers and priority number systems in the work of other ISO technical committees, ISO R17 "Guidelines for the Application of Priority Numbers and Priority Number Systems" was published in 195G, and ISO R497 "Guidelines for the Selection of Preferred Number Systems and Integer Value Series of Priority Numbers" was published in 1966. The above ISO R3, ISO R17 and ISO R497 recommendations were all converted into international standards in 1973: ISO 3-1973, ISO 17-1973 ISO 497-1973.
In 1960, my country promulgated the "Priority Number System" standard (JB109-60). After several years of practice, it was revised into a national standard (GB321-64) in 1964. 1. The main advantages of the priority number system
The priority number is the number that should be used first when grading various quantities (especially product parameters). Its purpose is to limit the "number" (i.e. the size and specification of the product) in actual application to the minimum range, and to create a prerequisite for the priority use of the same number in different combinations, so as to achieve standardization and unification. The priority number system has many advantages. The parameters of various products can select appropriate values from it, so it can also adapt to the various requirements put forward by the housing economic equipment department. 1.1 Numerical grading system based on economic basis
The parameters of the products generally have only a very small numerical range from the smallest to the largest. When grading according to geometric progression, it can meet the needs of all users with fewer varieties and specifications. The economic basis is to reflect the difference in "quality" between different levels. , we must use the concept of "relative relationship" instead of just considering "absolute difference" like the geometric difference series. Taking shaft diameter classification as an example, when 10mm is not suitable, 13mm can be used, then the absolute difference between the two grades is 2mm, and the absolute difference is 20%. But for a 100mm shaft, a 2mm increase to 102mm, the absolute difference is only 2%, which is too small. And for a shaft with a diameter of 1mm, an increase of 2mm to 3mm, the absolute difference is 200%, which is obviously too large. A geometric series is a series with constant relative differences, which will not cause the unreasonable phenomenon of too sparse or too dense scores. The geometric number system is formulated according to the geometric series, therefore, it provides an economical and reasonable numerical grading system. 1.2 Unified and simplified basis
A product (or part) is often produced by different people at the same time in different occasions. The products are designed and manufactured separately, and the parameters of the products often affect the related parameters of a series of products that are matched with them. If there is no commonly followed criterion for selecting data, the dimensional parameters of the same product will inevitably be chaotic, and the varieties and specifications will be too numerous, making it impossible to organize production economically and not conducive to use and maintenance. The priority number system is an internationally unified numerical system that can be used to classify various values so that different places can give priority to the same values. It provides a basis for the unification, simplification and coordination of product parameters in technical and economic work. The parameters and series determined by the priority number system can remain unchanged in the subsequent standardization process (from enterprise standards to departmental standards, national standards, etc.), which is of great significance technically and economically. GB321—80
Tooling and other equipment for self-made and self-used by enterprises The parameters of equipment should also use the preferred number system. In this way, not only can the product specifications be simplified and unified, but also the objects that have not yet been standardized can lay the foundation for standardization from the beginning. In the negotiation of formulating standards and specifying customer parameters, the preferred number system should become the common language between users and manufacturers or between relevant units, so as to reach a consensus on an unbiased basis. 1.3 Wide adaptability
The preferred number system contains a variety of series with different proportions, so it can meet the requirements of dense and sparse classification. Since the values of the sparse series are included in the dense series (R10 contains the value of R5, R20 contains the upper and lower values of R10 and R5, etc.), with the development of production, if necessary, the intermediate values can be added to make the extreme series become the more popular series, while the original item values remain unchanged. When the parameter range is constructed, according to the same factors such as economy and demand, the most suitable series can be selected in sections to form the best series in the form of a composite series.
The R10/8 series of the priority number system is a frequently used number series (1, 2, 4, 8*). The priority numbers 3000, 1500, 760 and 375 in the R40 series are the number of revolutions per minute of the synchronous motor when it is powered by 50Hz AC, and are particularly important in electromechanics. The priority number system also contains some of the most important values in the natural number system (such as 1, 2, 3, 4, 5..), as well as the approximate values of some important band numbers in engineering technology, for example = 3.1415-**~3,15,
T=0.735*~0.80,
#2 = 9,8696-~10,
2 - 1, 414--~1,4,
2 - 6,2331- ~6,3,
, = 0.098 2-
10 -3.1623.*-23,15,
3 2 -1.2599**α1.25,
g = 9.3066.~10m/scc*,1\=25,1225mn. In addition, due to the important characteristic of "the expression of the priority function is still the priority number", the application scope of the priority number is further expanded. For example, the diameter of a circle can be expressed as a priority number, and the element can also be replaced by the priority number 3, 15. The approximate values of the circumference and the product of a circle are also priority numbers. This is also applicable to the calculation of the speed of a circle, the cutting speed, the product and volume of a circle, the product and volume of a sphere, etc. www.bzxz.net
1.4 Simple, easy to remember, easy to use
The priority function system is a geometric sequence, which contains 10 integers (such as 1, 10, 100, 0.1, 0, 01, .). As long as you remember the value in one decimal segment, the values in other decimal segments can be obtained by moving the center point. Generally, you only need to remember the 20 values in R20. The method of memory is to use the multiplication of the R20/6 series. Remember 1.12 (the common ratio of R20), and it is easy to arrange other numbers:
1,2,4,8,1.6(16), 3.15,6.3,1.25 (12.5), 2.5, 5,1(10).1,12,2.24,4.50,9.00,1,8(18),3,55,7.10,1.40(14),2,80,5.60,1.12(11.2) The above values, except for the numbers with horizontal lines at the bottom, are slightly rounded, and the rest are all accurate multiple relationships. Just put them in ascending and descending order to get the R20 series, take the values of alternate items to get the R10 series, and take the values of R10 items to get the R5 series. 1.5 Simplify design calculations
The priority number system is a geometric progression, so the product and quotient of any priority numbers are still priority numbers, and the logarithm (or serial number) of the priority number is an arithmetic progression. These characteristics can greatly simplify design calculations. 2. Calculation of priority numbers
2.1 Calculation with serial numbers
Substitute the serial number N of the priority number to show the theoretical value of (V10)N=q\ for the order of priority numbers in the RI series. For example, in the Chi 5 series, the relationship between the serial number of the priority number and the priority number is as follows: Serial number Ns
Theoretical value of priority number
g=(10s
Common value of priority number
GB 321—80
0.39811 0,630981.0000,1.58492.5119:3.98116,30960.10
15,849
From the extended meaning of logarithm, we know that the serial number N is the logarithm value of the theoretical value of the priority number with the common ratio 9 as the base. Therefore, the operation of the priority number can be converted into its serial number operation and simplified. Its operation rules are exactly the same as those of general logarithm calculation. The R40 series includes the item values of all basic series. , the priority number N in the R40 series (see GB321-80 Table 1, NM is the abbreviation of N..) can replace N and N1N to meet general calculation requirements. When calculating the priority number of the supplementary series R80, the sequence N should be used.
The sequence number N used in the following calculations refers to the sequence number in the R40 series. N=0～40 applies to the priority number n in the 1～10-1 selection segment, and the priority number of other decimal segments×10*(x is an integer 1, 2, 3,..), its serial number is; N(×10+*)=N(n)±xN(10)=N(n)±40x, that is, every time the priority number n increases by 10 times, its serial number increases by 40, and every time it decreases by 10 times, its serial number decreases by 40. Example 1: N(2.5) =16,N(250) =N(2.5) +2×40=16 -80 = 96N(0.025) =N(2,5)-2×40=16-80= -64Example 2,250=63000
N (250*) 2V(250) = 2× 9G = 192 = 32+4× 40 = N (6.3) + N(10*) = N (G,3 × 104)Example 3
Y 0.025 - 0.4
N(0.0251*+) =
1-N(0.025) = -1-)
-X(-64)=-16=24-40=N(0.4)
1×16-5-
Example 4; 2,5 =2.51* is not enough for the priority number in the basic series, the doctor is N(2,G1>\)- -3
is not enough for an integer. From this, we can see that the Kth root of the priority number is not necessarily the priority number. Only when the product of its sign and the fractional exponent N (n) is equal to the number of signs, the square root value is still the priority number in the basic series. R
2.2 Calculation with common logarithms
It is also convenient to calculate the priority number with common logarithms. The common logarithm mantissa of the theoretical value of the priority number in the R40 series is listed in the 8th column of Table 1 of GB321-80, and it has the following relationship with the serial number N! Ign -Ig10N/40-
Reverse 1: Find the common logarithm of the perfect number
1g4500 - 3,650
1g0.00045 - 4.650
The common logarithm of the perfect number 0.650 is 4.5. Example 2.3.15x1.6=5
1g3.15+1gl6=0.500-0.2000.700=1g5.00 Example a450=430+is not a perfect number. The year is
1g450=2.650,
11g450 yuan
X2.650=0.883
This position is not a perfect number. [0.883 is between 0.875 and 0.900, and the value of 450 is between 7.50 and 8.00. GB321-80
Example 4z, calculate the circumferential speed V_ndn
(m/min)
IgV=Ign+Igd+Ign-1g1000
=0.500+2.300+2.900-3,000=2,700V=500m/min
2.3 List calculation
The product or quotient of two variables (parameters) graded by the priority number system can be calculated by list calculation method to save a lot of calculation work and avoid calculation errors. When calculating, just calculate any two adjacent items to obtain the common ratio of the series. The common ratio of the series can also be directly obtained from the functional formula between the variables, and the value of any item can be calculated to exclude the remaining values. The values of each item in the basic series Rr are multiplied by themselves to the power of p, and the resulting values constitute the derived series Rr/P. For example, if the diameter d is the R10 series, the period area -4- is the derived series R10/2, and the torsion section number gd* of the shaft is the original series R10/3. Understanding these 4
relationships is very important for list calculation. Example: Find the series of the area A of the rectangular cross-section conductor. Suppose the cross-section thickness a uses the R20 series, and the width 6 uses the R40 series. Just calculate the three underlined data in Table 1 by the formula A=α·b, and you can directly exclude all the data in the table according to their common ratio (the horizontal number system is R20 or R40/2, and the level number system is R40). If we analyze the series of A directly from the function A=a·b, we can consider three cases: ①a takes a constant value, 6 changes according to the R40 series, then A is also the R40 series (see Table 1 vertical row); ②6 takes a constant chain, a changes according to the R20 series, then A is the R20 or R40/2 series (see Table 1 horizontal row); ②a changes according to the R20 series, 6 changes according to the R40 series, then the common ratio of the A series is: 10/ ×10+/40=108/*/=g40/8
Therefore, A is the derived series of R40/3 (see the main oblique series in the table. According to the combination of a and value, there can be 1.60, 1.90, 2.24, or 1.80, 2,12, 2,50, .. or 1.70, 2,00, 2.36... etc. series》Aa.b(mm*)
2.4 Calculation diagram
degree aR20
In engineering technology, in order to simplify calculations, functions with multiplication, division, exponentiation and square root relationships are often made into calculation diagrams. The logarithmic scale usually used in the calculation diagram has unequal scale intervals, which is troublesome to draw. If the priority number is used as the scale value of the logarithmic coordinate, the equally spaced scale lines can be obtained, which is very easy to draw. The comparison between the two is shown in Figure 1.The torsional section carrying number gd* of the shaft is the original series R10/3. Understanding these 4
relationships is very important for table calculations. Example: Find the series of the conductor area A of a rectangular cross section. Assume that the section thickness a adopts the R20 series and the width 6 adopts the R40 series. Only the three underlined data in Table 1 can be calculated by the formula A=α·b, and all the data in the table can be directly arranged according to their common ratio (the horizontal number system is R20 or R40/2, and the level number system is R40). If the series of A is directly analyzed by the function formula A=a·b, three situations can be considered: ①a takes a constant value, 6 changes according to the R40 series, then A is also the R40 series (see Table 1 vertical row): ②6 takes a constant chain, a changes according to the R20 series, then A is the R20 or R40/2 series (see Table 1 horizontal row), ②a changes according to the R20 column, 6 changes according to the R40 column, then the common ratio of the A series is: 10/ ×10+/40=108/*/=g40/8
Therefore, A is the derived series of R40/3 (see the main oblique series in the table. According to the combination of a and value, there can be 1.60, 1.90, 2.24, or 1.80, 2,12, 2,50, .. or 1.70, 2,00, 2.36... etc. series》Aa.b(mm*)
2.4 Calculation diagram
degree aR20
In engineering technology, in order to simplify calculations, functions with multiplication, division, exponentiation and square root relationships are often made into calculation diagrams. The logarithmic scale usually used in the calculation diagram has unequal scale intervals, which is troublesome to draw. If the priority number is used as the scale value of the logarithmic coordinate, the equally spaced scale lines can be obtained, which is very easy to draw. The comparison between the two is shown in Figure 1.The torsional section carrying number gd* of the shaft is the original series R10/3. Understanding these 4
relationships is very important for table calculations. Example: Find the series of the conductor area A of a rectangular cross section. Assume that the section thickness a adopts the R20 series and the width 6 adopts the R40 series. Only the three underlined data in Table 1 can be calculated by the formula A=α·b, and all the data in the table can be directly arranged according to their common ratio (the horizontal number system is R20 or R40/2, and the level number system is R40). If the series of A is directly analyzed by the function formula A=a·b, three situations can be considered: ①a takes a constant value, 6 changes according to the R40 series, then A is also the R40 series (see Table 1 vertical row): ②6 takes a constant chain, a changes according to the R20 series, then A is the R20 or R40/2 series (see Table 1 horizontal row), ②a changes according to the R20 column, 6 changes according to the R40 column, then the common ratio of the A series is: 10/ ×10+/40=108/*/=g40/8
Therefore, A is the derived series of R40/3 (see the main oblique series in the table. According to the combination of a and value, there can be 1.60, 1.90, 2.24, or 1.80, 2,12, 2,50, .. or 1.70, 2,00, 2.36... etc. series》Aa.b(mm*)
2.4 Calculation diagram
degree aR20
In engineering technology, in order to simplify calculations, functions with multiplication, division, exponentiation and square root relationships are often made into calculation diagrams. The logarithmic scale usually used in the calculation diagram has unequal scale intervals, which is troublesome to draw. If the priority number is used as the scale value of the logarithmic coordinate, the equally spaced scale lines can be obtained, which is very easy to draw. The comparison between the two is shown in Figure 1.
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