Question

The speed range ratio of a machine tool is (where the symbols used have their usual meanings)

• A. $\frac{D_{max}\times V_{min}}{D_{min}\times V_{max}}$
• B. $\frac{D_{max}\times V_{max}}{D_{min}\times V_{min}}$
• C. $\frac{D_{min}\times V_{max}}{D_{max}\times V_{min}}$
• D. none

Answer 1

The correct option is B $\frac{D_{max}\times V_{max}}{D_{min}\times V_{min}}$

The extreme spindle speeds of a machine tool main gearbox, $n_{max}$ can be determined by
$n_{max}=\frac{1000V_{max}}{\pi D_{min}},n_{min}=\frac{1000V_{min}}{\pi D_{max}}$
The speed range $R_n$ becomes,
$R_n=\frac{n_{max}}{n_{min}}=\frac{V_{max}.D_{max}}{V_{min}.D_{min}}$