Page:Practical Treatise on Milling and Milling Machines.djvu/62

56 on hand, for if H contains a factor not found in the gears, x cannot usually be obtained, unless the factor is canceled by the difference between HV and Nn, or unless N contains the factor.

When HV is greater than Nn and gearing is simple, use 1 idler.

When HV is greater than Nn and gearing is compound, use no idlers.

When HV is less than Nn and gearing is simple, use 2 idlers.

When HV is less than Nn and gearing is compound, use 1 idler.

Select "n" so that the ratio of gearing will not exceed 6:1 on account of the excessive stress upon the gears.

A few examples are given herewith to illustrate the application of the above formulae:

Example 1:
 * N = 59. Required H, n and x.
 * Assume H=33, n = 22.
 * Then $$x=\frac{\left(33\times40\right)-\left(59\times22\right)}{33}=\tfrac{22}{33}=\tfrac{2}{3}$$.

We now select gears giving this ratio, as 32 and 48, the 32 being the gear on spindle and the 48 the gear on worm. HV is greater than Nn, and the gearing is simple, requiring 1 idler.

Example 2:
 * N = 319. Required H, n and x.
 * Assume H= 29, n = 4.
 * Then $$x=\frac{\left(319\times4\right)-\left(29\times40\right)}{29}=\tfrac{116}{29}=\tfrac{4}{1}$$.

When the ratio is not obtainable with simple gearing, try compound gearing.

$4⁄1$ can be expressed as follows:

$$\frac{3\times4}{1\times3}$$ or $$\frac{72\times64}{24\times48}$$ for which there are available gears.

HV is less than Nn and the gearing is compound, requiring 1 idler.

Head Geared for 271 Divisions

Fig. 9 shows the spiral head geared, simple gearing, for 271 divisions. Referring to the table on page 216, the gears called for are: C, 56 teeth, and E, 72 teeth, with