NSC Mechanical Technology Fitting and Machining ISO metric V tread: 6.1 A spur gear with 50 teeth ha

6.1 A spur gear with 50 teeth has a module of 3 - NSC Mechanical Technology Fitting and Machining - Question 6 - 2018 - Paper 1

Question 6

6.1 A spur gear with 50 teeth has a module of 3. Calculate the cordal tooth thickness of the gear teeth. 6.2 Calculate the required simple indexing to cut a gear wi... show full transcript

Worked Solution & Example Answer:6.1 A spur gear with 50 teeth has a module of 3 - NSC Mechanical Technology Fitting and Machining - Question 6 - 2018 - Paper 1

Step 1

Calculate the cordal tooth thickness of the gear teeth.

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Answer

To find the cordal tooth thickness ( $t_c$ ), use the formula:$

t_c = rac{T}{2} imes ext{sin} rac{90°}{T} $ Where:

$T$ = Number of teeth.

Plugging in the values:

For $50$ teeth:

egin{align*} ext{Using } T = 50\ \ t_c = rac{50}{2} imes ext{sin} rac{90°}{50} = 4.71 ext{ mm} ext{or} \ t_c = PCD imes ext{sin} rac{90°}{T} \ = rac{150}{50} imes 0.03141 \ = 4.71 ext{ mm} ext{So the cordal tooth thickness is approximately 4.71 mm.} ext{Final Answer: } t_c ext{ = 4.71 mm}

Step 2

Calculate the required simple indexing.

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Answer

To calculate simple indexing for a gear with 13 teeth,

Use the formula for simple indexing:

ext{Simple indexing } = 40 imes rac{N}{ ext{number of turns}}

With N = 40 and the number of teeth = 13:

After determining parameters, set up for 39 hole circle as follows:

= 3 ext{ full turns and 3 holes in a 39 hole circle.}

Step 3

The differential indexing required (Choose 125 teeth.)

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Answer

For differential indexing:

Using the relation:

ext{Indexing } = rac{40}{40} - rac{n}{N} \ N = 127, ext{ thus = } rac{40}{40} - rac{127}{125}

Solving this gives:

Required differential indexing for 125 teeth is $8$ holes on the $25$ hole circle.

Step 4

The change gears required

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Answer

The change gears can be calculated by:

D_r = rac{A_n imes D}{40} \ D_r = 125 - 127 imes rac{40}{125}

Solving, we find:

Change gears required = 64 ratios 100.

Step 5

The direction of rotation of the index plate in relation to the index crank handle.

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Answer

The index plate will turn in the opposite direction to that of the index crank handle.

Step 6

Calculate distance X between the rollers in FIGURE 6.4.

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Answer

To calculate distance $X$ :

Use the geometric relationships:

x = 150 + 2(AB) - 2(CD) - 2r\

Here, with given values and utilizing tan properties:

Obtain $x$ :

= 150 + 2(20.21) - 2(25.98) - 30 = 108.454 ext{ mm}

Step 7

Give TWO reasons why a work piece must be balanced on a centre lathe when a face plate is used.

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Answer

To prevent unnecessary bearing loads.
To avoid excessive vibrations.

6.1 A spur gear with 50 teeth has a module of 3 - NSC Mechanical Technology Fitting and Machining - Question 6 - 2018 - Paper 1

Worked Solution & Example Answer:6.1 A spur gear with 50 teeth has a module of 3 - NSC Mechanical Technology Fitting and Machining - Question 6 - 2018 - Paper 1

Calculate the cordal tooth thickness of the gear teeth.

Calculate the required simple indexing.

The differential indexing required (Choose 125 teeth.)

The change gears required

The direction of rotation of the index plate in relation to the index crank handle.

Calculate distance X between the rollers in FIGURE 6.4.

Give TWO reasons why a work piece must be balanced on a centre lathe when a face plate is used.

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