Question

Common Data Questions:
A compacting machine shown in the figure below is used to create a desired thrust force by using a rack and pinion arrangement. The input gear is mounted on the motor shaft. The gears have involute teeth of a 2 mm module.

If the drive efficiency is 80%, the torque required on the input shaft to create 1000 N output thrust is

• A. 20 Nm
• B. 25 Nm
• C. 32 Nm
• D. 50 Nm

Answer 1

The correct option is B 25 Nm

$F_I=\text{Force acting along the line of action}$

Given data:
$2F=1000$
$F=500N$
$m=2\text{mm}$

$R=\frac{mT}{2}=\frac{2\times 80}{2}=40\text{mm}$

$=0.040\text{m}$

$\eta =0.80=\frac{T_2\times {\omega }_2}{T_1\times {\omega }_1}$

$=\frac{(500\times 0.040\times 2)}{T_1}\times \frac{20}{80}$
$\therefore [\frac{{\omega }_2}{{\omega }_1}=\frac{T_1}{T_2}]$

$T_1=25$ N-m