Question

What are the upper and lower limits of the shaft represented by $\text{60f8 ?}$

$\text{Use the following data}$

$\text{Diameter 60 lies in the diameter step of 50-80mm}$

$\text{Fundamental tolerance unit}i\text{, (in microns)}$

$i=045D^{1/3}+0.001D$,

$\text{Where D is the representative size in mm;}$

$\text{Tolerance value for}IT8=25i\text{.}$

$\text{Fundamental deviation for}{f}_{\text{shaft}}=-5.5D^{0.41}$

• A. $\text{Lower limit = 59.954 mm}$
  $\text{Upper limit = 60.000 mm}$
• B. $\text{Lower limit = 59.924 mm}$ $\text{Upper limit = 59.970 mm}$
• C. $\text{Lower limit = 59.970 mm}$
  $\text{Upper limit = 60.016 mm}$
• D. $\text{Lower limit = 60.000 mm}$
  $\text{Upper limit = 60.016 mm}$

Answer 1

The correct option is B $\text{Lower limit = 59.924 mm}$ $\text{Upper limit = 59.970 mm}$

$\text{60 mm diameter lies in the diameter step of 50 - 80 mm.}$

$\text{Therefore, geometric mean diameter,}$

$D=\sqrt{D_{min}\times D_{max}}=\sqrt{50\times 80}=63.246mm$

$\text{Fundamental tolerance,}$

$i=(0.45D^{1/3}+0.001D)\mu m$

$=\left[0.45\right(63.245{)}^{1/3}+0.001\left(63.246\right)]$

$=1.859\mu m=0.00186mm$

$IT8=25i=25\times 0.00186=0.04646mm$

$\text{Fundamental deviation for}{}^{\prime }{f}^{\prime }\text{shaft,}$

${ϵ}_d=-5.5D^{0.41}$

$=-5.5[63.246{]}^{0.45}$

$=-0.030115mm$


$\text{Upper limit of shaft = Basic size - Fundamental deviation}$

$=60-0.03012=59.9678mm$

$\approx 59.97mm$

$\text{Lower limit of shaft = Upper limit - Tolerance}$

$=59.97-0.0464=59.9236mm$

$\approx 59.924mm$