5.1 A spur gear with 118 teeth must be cut on a universal milling machine. Calculate the indexing required to cut this gear with the help of a Cincinnati dividing head. 5.2 Use simple line sketches to explain the difference between up-cut milling and down-cut milling on a milling machine. Indicate the work-piece feed and cutter rotation. 5.3 A tapered gib-head key must be made to fit a 102 mm diameter shaft. Calculate the following key dimensions: 5.3.1 The width of the key: 5.3.2 The thickness of the key: 5.3.3 The length of the key: 5.3.4 The thickness of the key at the smaller end: 5.4 A spur gear has 60 teeth and a module of 3. Calculate the following in respect of the spur gear: 5.4.1 Addendum: 5.4.2 Dedendum: 5.4.3 Clearance: 5.4.4 Pitch circle diameter: 5.4.5 Outside diameter: 5.4.6 Cutting depth: 5.4.7 Circular pitch:

NSC Mechanical Technology Automotive Basic calculations: 5.1 A spur gear with 118 teeth m

5.1 A spur gear with 118 teeth must be cut on a universal milling machine - NSC Mechanical Technology Automotive - Question 5 - 2017 - Paper 1

Question 5

5.1 A spur gear with 118 teeth must be cut on a universal milling machine. Calculate the indexing required to cut this gear with the help of a Cincinnati dividing he... show full transcript

Worked Solution & Example Answer:5.1 A spur gear with 118 teeth must be cut on a universal milling machine - NSC Mechanical Technology Automotive - Question 5 - 2017 - Paper 1

Step 1

5.1 A spur gear with 118 teeth must be cut on a universal milling machine. Calculate the indexing required to cut this gear with the help of a Cincinnati dividing head.

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Answer

To calculate the indexing required, use the formula:

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

where:

Total holes in the dividing head = 59
Number of teeth on the spur gear = 118

From the calculation:

Let n = 2 (the minimum required for the indexing)
Then,

$Indexing = \frac{40}{2} = 20$

This indicates that 20 divisions are needed to complete the cut.

Step 2

5.2 Use simple line sketches to explain the difference between up-cut milling and down-cut milling on a milling machine. Indicate the work-piece feed and cutter rotation.

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Answer

Up-Cut Milling

In up-cut milling, the cutter rotates against the feed direction. The cutting begins at the bottom of the workpiece and increases in thickness as the cutter rises. This can be visualized with the cutter on the left and the feed moving towards it.

Down-Cut Milling

In down-cut milling, the cutter rotates in the same direction as the feed. The cutting action starts at the top of the workpiece and decreases in thickness as it goes down. This can be illustrated with the cutter situated above the workpiece feeding downwards.

Sketches

Up-Cut Milling: Cutter rotates counterclockwise
Down-Cut Milling: Cutter rotates clockwise

Workpiece Feed & Cutter Rotation:

Up-Cut: Workpiece moves towards the cutter, against rotation
Down-Cut: Workpiece combines movement with cutter rotation

Step 3

5.3.1 The width of the key:

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Answer

The width of the key can be calculated using the formula:

$Width = \frac{D}{4}$

where D is the diameter of the shaft. Thus:

$Width = \frac{102}{4} = 25.5\text{ mm}$

Step 4

5.3.2 The thickness of the key:

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The thickness of the key is calculated as:

$Thickness = \frac{D}{6}$

Hence:

$Thickness = \frac{102}{6} = 17\text{ mm}$

Step 5

5.3.3 The length of the key:

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Answer

The length of the key can be calculated using:

$Length = D \times 1.5$

Therefore:

$Length = 102 \times 1.5 = 153\text{ mm}$

Step 6

5.3.4 The thickness of the key at the smaller end:

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Answer

The formula for the thickness at the smaller end is:

$t = T - \frac{L}{100}$

Substituting the relevant values:

T = 17 mm (thickness at larger end)
L = 153 mm

Thus:

$t = 17 - \frac{153}{100} = 15.47\text{ mm}$

Step 7

5.4.1 Addendum:

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Answer

The addendum can be defined as:

$Addendum = m = 3\text{ mm}$

Step 8

5.4.2 Dedendum:

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The dedendum is calculated using:

$Dedendum = 1.157m = 1.157 \times 3 = 3.47\text{ mm}$

Step 9

5.4.3 Clearance:

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The clearance is defined as:

$Clearance = 0.157m = 0.157 \times 3 = 0.47\text{ mm}$

Step 10

5.4.4 Pitch circle diameter:

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The pitch circle diameter (PCD) can be calculated as:

$PCD = \text{Number of Teeth} \times m = 60 \times 3 = 180\text{ mm}$

Step 11

5.4.5 Outside diameter:

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The outside diameter (OD) is defined as:

$OD = PCD + 2m = 180 + 2 \times 3 = 186\text{ mm}$

Step 12

5.4.6 Cutting depth:

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The cutting depth is calculated as:

$Cutting Depth = 2.157m = 2.157 \times 3 = 6.47\text{ mm}$

Step 13

5.4.7 Circular pitch:

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The circular pitch (CP) can be derived using:

$Circular\ Pitch = \frac{\pi \times D}{N} = 3 \times \pi \approx 9.43\text{ mm}$

5.1 A spur gear with 118 teeth must be cut on a universal milling machine - NSC Mechanical Technology Automotive - Question 5 - 2017 - Paper 1

Worked Solution & Example Answer:5.1 A spur gear with 118 teeth must be cut on a universal milling machine - NSC Mechanical Technology Automotive - Question 5 - 2017 - Paper 1

5.1 A spur gear with 118 teeth must be cut on a universal milling machine. Calculate the indexing required to cut this gear with the help of a Cincinnati dividing head.

5.2 Use simple line sketches to explain the difference between up-cut milling and down-cut milling on a milling machine. Indicate the work-piece feed and cutter rotation.

Up-Cut Milling

Down-Cut Milling

Sketches

5.3.1 The width of the key:

5.3.2 The thickness of the key:

5.3.3 The length of the key:

5.3.4 The thickness of the key at the smaller end:

5.4.1 Addendum:

5.4.2 Dedendum:

5.4.3 Clearance:

5.4.4 Pitch circle diameter:

5.4.5 Outside diameter:

5.4.6 Cutting depth:

5.4.7 Circular pitch:

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