Spindle head of a machine tool presently in production has travel of 700 mm. Usi
ID: 3230702 • Letter: S
Question
Spindle head of a machine tool presently in production has travel of 700 mm. Using standardized preferred numbers from R5 series calculate travel of spindle head for 4 new machines currently under development, all of which are based on the existing one. Two of the new machines will be smaller versions of the existing one and the other two will be bigger versions. Remember to round off final results of your calculations, but by no more than plusminus 2% of the calculated value (relative error of reported result should be no bigger than plusminus 2% of the calculated value) R5: 10, 16, 25, 40, 63, 100 (ISO R5 Standardized Series of Preferred Numbers)Explanation / Answer
Two of the new machines will be smaller versions of existing machine (of length 700 mm) and remaining two will be bigger versions.
Renard series are a system of preferred numbers dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps. This set of preferred numbers was proposed in the 1870s by French army engineer Colonel Charles Renard. Renard's system of preferred numbers divides the interval from 1 to 10 into 5, 10, 20, or 40 steps. The factor between two consecutive numbers in a Renard series is approximately constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (approximately 1.58, 1.26, 1.12, and 1.06, respectively), which leads to a geometric sequence.
Hence, the Reynard R5 series, or the preferred number series goes like this:
10, 16, 25, 40,63,100, 160, 250, 400, 630, 1000, 1600, 2500
Therefore, the length of the 2 spindle heads having lesser dimension should be: 400 mm and 630 mm, since these two lengths are closest to the existing spindle length of 700 mm.
And, the length of the 2 spindle heads having higher dimension should be: 1000 mm and 1600 mm, since these two lengths are closest to the existing spindle length of 700 mm.
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