Pieter is a machinist and is tasked to cut a spur gear with a module of 1,5 and 200 teeth - NSC Mechanical Technology Fitting and Machining - Question 6 - 2021 - Paper 1

The dedendum can be calculated using the formula:

$Dedendum = 1.157 \times m$

Plugging in the value of $m$: $Dedendum = 1.157 \times 1.5 = 1.7355 \ mm \ (or \ 1.74 \ mm)$

The outside diameter (OD) can be calculated with the formula:

$OD = PCD + 2 \times m$

Inserting the previously calculated PCD: $OD = 300 + 2 \times 1.5 = 303 \ mm$

The working depth (WD) can be determined using:

$WD = 2 \times m$

Thus, $WD = 2 \times 1.5 = 3 \ mm$

To calculate the maximum width distance of the dovetail (W), we use:

$W = 210 + 2 \times (DE)$

Firstly, we must find DE: Using the tangent function:

$tan(\theta) = \frac{DE}{AD}$

Assuming $\theta = 30^\circ$, we have: $DE = tan(30^\circ) \times 45 = 25.98 \ mm$

Then, substituting back into W's formula: $W = 210 + 2 \times (25.98) = 261.96 \ mm$

To find the measurement between the precision rollers (m), we can use:

$m = W - 2(AC) - 2(R)$

With $R = 17 \ mm$ and previously calculated $W = 261.96 \ mm$: First, we find AC: Using the tangent function again:

$tan(60^\circ) = \frac{BC}{AC}$ This allows finding: $AC = \frac{BC}{tan(60^\circ)} = \frac{17}{\sqrt{3}} = 29.44 \ mm$

Substituting back: $m = 261.96 - 2(29.44) - 2(17) = 169.08 \ mm$

To determine the indexing, we use:

$Indexing = \frac{40}{N}$

Where $N = 137$ (the number of teeth): $Indexing = \frac{40}{137} \Rightarrow 0.292 \ units$

To calculate the change gears.

Use the formula:

$D_r = \frac{(A - n) \times 40}{N}$

Where:

• $A = 140$ (divisions)
• $n = 137$ (teeth) $\Rightarrow D_r = \frac{(140 - 137) \times 40}{140} = 3$\nThus, possible values for change gears can be: \nMultiple connections with division ratios 12 and 14 can also support the correct ratio.