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The metric dimensioning of new designs often uses the concept of preferred numbers This includes size ranges such as weight, volume, horse power, electrical resistance or other physical properties that
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may determine the size of a product Generally, the sizes within a range increase at an approximately constant rate For instance, the size ranges of electric motors are as follows: hp hp motor increase 50% 5 hp 7 hp motor increase 50% Therefore, a 5 hp motor would be unnecessary The manufacture of large quantities of each size in a limited size range will enable motors to be supplied at a lower price than if a wider choice is given It serves as a guide for engineers to minimize unnecessary size variations in the final design by selecting the nearest size in a pre selected (preferred) series making it economical for both the producer and the user A similar reasoning is applied to the dimensional aspects of many products such as the diameter of bolts, twist drills, milling cutters, the thickness of steel sheets and the speed range in machine tools, including spindle speed and feeds The rational series of standard sizes will tend to follow a geometric series: a, ar, ar2, ar3, arn where r is the constant rate of increase and a is the initial basic size However, there are a few exceptions due to conventional developments Many of the standard sizes such as BS Whitworth threads are arrived at empirically It does not follow the geometric rate of increase In order to avoid unnecessary duplication and to obtain the maximum advantages of standardization, the size of new products should follow a suitable series of preferred numbers The preferred number is a series that is based on the ideas of the French engineer Col Charles Renard in 1877 and are designated as R5, R10, R20, R40 and so on These series are internationally accepted, and the R3 series is recommended by the ISO According to the concept of preferred numbers of R5, every fifth step of a geometric series is the 10th multiple of the value a ar5 = 10a
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5 a5r = 10
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= , = 5 10 , = 5 10 , = 5 10 , = 5 10 , 10= , a, 1585a, 2512a, 398a, 631a, 10a, a is a power of 10, positive, zero or negative 010, 016, 025, 040, 063, 100, 10, 16, 25, 40, 63, 100, 10, 16, 25, 40, 63, 100, 100, 160, 250, 400, 630, 1000, A summary of all the available series is shown in Table 56 In addition, there are also derived series The examples are shown next The R10/3 and R20/3 series are more common than the rest
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3 2 = 126 10, 10(126), 10(126)2, 10(126)3, 10(126)4, 10(126)5, 10(126)6, 10(126)7, 10(126)8, 10(126)9, 10(126)10,
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Table 56
Series R5 R10 R20 R40 R80
Preferred numbers
Ratio
5 10 20 40 80
Percentage of increase 58 26 12 6 3
10 = 158 10 = 126 10 = 112 10 = 106 10 = 103
100, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1000, R10/3 series: r = 2 10, 20, 40, 80, 160, 05, 1, 2, 4, 8, 16, 32, 63, 125, 250, 500, 1000, 2000, 0012, 0025, 005, 01, 02, 04, 08, 16, 32, 63, 125, 25, 50, R20/3 series: r = 14 10, 14, 20, 28, 40, 56, Example: Preferred Numbers It is required to standardize parallel keyways ranging from 2 mm to 28 mm The first seven sizes are to follow the R10 series and the remainder to follow the R20 series Suitable ranges of key widths are to be developed For the R10 series, geometric ratio, r = 1001 = 1259 Calculated values: 2, 252, 317, 399, 502, 633, 796, and 1002 Rounded values: 2, 3, 4, 5, 6, 8, and 10 For the R20 series, geometric ratio, r = 10005 = 1122 Calculated values: 10, 1122*, 1259, 1412, 1584, 1778, 1995, 2238, 2512, 2818 Rounded values: 10, 12, 14, 16, 18, 20, 22, 25, and 28 *It would be illogical to include an 11 mm size because the last step in the R10 series gives a 2 mm interval The results can be summarized in three arithmetic series as follows: 2 6 mm in 1 mm steps 6 22 mm in 2 mm steps 22 28 mm in 3 mm steps
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