Thabo is a machinist and is tasked to cut a spur gear with a pitch-circle diameter of 136 mm and a module of 4 - NSC Mechanical Technology Fitting and Machining - Question 6 - 2021 - Paper 1

The dedendum (d) can be calculated using the formula:

$d = m + 1.157$

Substituting in the given values:

• m = 4

$d = 4 + 1.157 = 5.157 ext{ mm}$

Therefore, the dedendum is approximately 5.16 mm.

The outside diameter (OD) is given by the formula:

$OD = m(T + 2)$

Substituting our values:

• m = 4
• T = 34

$OD = 4(34 + 2) = 4(36) = 144 ext{ mm}$

Thus, the outside diameter is 144 mm.

The circular pitch (CP) is calculated with the formula:

$CP = m \pi$

By substituting in the values:

• m = 4

$CP = 4 \pi \approx 12.57 ext{ mm}$

So, the circular pitch is approximately 12.57 mm.

To find the minimum width (w) of the dovetail, use the formula:

$w = 190 - 2(DE)$

First, we need to calculate DE using geometrical relationships:

$\tan(60^ ext{°}) = \frac{AD}{ED}$

Given:

• AD = 38 mm
• Thus, DE can be found as:

$DE = AD \tan(30^ ext{°})$

Calculating DE:

$DE = 38 \tan(30^ ext{°}) \approx 21.94 ext{ mm}$

Substituting DE back into the width equation:

$w = 190 - 2(21.94) = 190 - 43.88 ext{ mm} = 146.12 ext{ mm}$

Therefore, the minimum width of the dovetail is 146.12 mm.

To calculate the distance over the precision rollers (M), we use the formula:

$M = w + 2(AC) + 2(R)$

Using previously calculated values:

• w = 146.12 mm
• AC = 25.98 mm (calculated from the triangle relationships)
• R = 15 mm

Substituting these values into the formula:

$M = 146.12 + 2(25.98) + 2(15) = 146.12 + 51.96 + 30 = 228.08 ext{ mm}$

Thus, the distance over the precision rollers is approximately 228.08 mm.

To calculate the indexing needed, the formula used is:

$\text{Indexing} = \frac{D_{BR}}{(A - n)}$

Where:

• D_{BR} = 40
• A = 40
• n = 0 (as specified)

Thus:

$\text{Indexing} = \frac{40}{(40 - 0)} = 1$

So, the indexing needed is essentially 1.

For the calculation of the change gears needed:

Given:

• D_{G} = 40
• D_{BR} = 163 (the teeth count for spur gear)

Using:

$D_{G} = D_{BR} \cdot \frac{(D_{G})}{(A)},$

By substituting the values, we derive:

$D_{G} = (163 - 40) \cdot \frac{40}{160}$

Calculating this will yield the specific change gears needed.