Question

A hole shaft pair has been designated as 64 mm $H_8{f}_7$. The diameter steps are is 50 mm and 80 mm. For shaft designation f, upper deviation is assumed as $-5.5D^{0.41}$

$\begin{array}{cc}\text{For}& \text{Tolerance}\\ H_8& 25i\\ f_7& 16i\end{array}$

The limit sizes of the shaft are

• A. $64\begin{array}{c}+0.47\\ +0.000\end{array}$
  
• B. $64\begin{array}{c}+0.47\\ -0.060\end{array}$
  
• C. $64\begin{array}{c}-0.030\\ -0.060\end{array}$
  
• D. $64\begin{array}{c}+0.47\\ +0.030\end{array}$
  

Answer 1

The correct option is C $64\begin{array}{c}-0.030\\ -0.060\end{array}$


64 mm diameter lies in the diameter step of 50-80 mm. Therefore,

Geometric mean diameter,

$D=\sqrt{D_{min}\times D_{max}}$

$=\sqrt{50\times 80}$

= 63.246 mm

Fundamental tolerance unit(i)

$=(045D^{\frac{1}{3}}+0.001D)\mu m$

$=\left[0.45\right(63.246{)}^{\frac{1}{3}}+0.001\left(63.246\right)]$

$=1.859\mu m$

= 0.00186 mm

$25i=25\times 0.00186=0.04646mm$
Fundamental deviation of 'f' shaft

$=-5.5D^{0.41}$

$=-5.5[63.246{]}^{0.41}$

= -0.30115 mm

$16i=16\times 0.00186=0.029$

$\text{Shaft size is}64\begin{array}{c}-0.030\\ -0.060\end{array}$

$\text{Hole size is}64\begin{array}{c}+0.046\\ 0.000\end{array}$

Allowance = 64.000 -63.970

$=0.030mm=30\mu m$