A spur gear has 51 teeth and a module of 3. Calculate the following: 6.1.1 The outside diameter of the gear 6.1.2 The cutting depth of the gear 6.1.3 The required simple indexing to cut this gear A gear with 83 teeth has to be milled on a dividing head with a ratio of 40 : 1. Calculate the following regarding this indexing process: 6.2.1 The differential indexing (Choose 80 divisions) 6.2.2 The change-gears needed for this process 6.2.3 The rotation of the index plate relative to the rotation of the index crank handle FIGURE 6.3 below indicates a dovetail part. Calculate distance X across the rollers, as shown in FIGURE 6.3. Give TWO reasons for balancing a work piece on a lathe.

NSC Mechanical Technology Fitting and Machining Calculations on size of drills for bolts and nuts (ISO metric): A spur gear has 51 teeth and a m

A spur gear has 51 teeth and a module of 3 - NSC Mechanical Technology Fitting and Machining - Question 6 - 2020 - Paper 1

Question 6

A spur gear has 51 teeth and a module of 3. Calculate the following: 6.1.1 The outside diameter of the gear 6.1.2 The cutting depth of the gear 6.1.3 The require... show full transcript

Worked Solution & Example Answer:A spur gear has 51 teeth and a module of 3 - NSC Mechanical Technology Fitting and Machining - Question 6 - 2020 - Paper 1

Step 1

6.1.1 The outside diameter of the gear

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Answer

To calculate the outside diameter of the gear, we use the formula:

ext{Outside diameter} = ext{Module} imes ( ext{Number of teeth} + 2 )

Substituting the values, we get:

ext{Outside diameter} = 3 imes (51 + 2) = 3 imes 53 = 159 ext{ mm}

Thus, the outside diameter of the gear is 159 mm.

Step 2

6.1.2 The cutting depth of the gear

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The cutting depth for a spur gear can be computed using the formula:

ext{Cutting depth} = 2 imes ext{Module} = 2.5 ext{ mm}

Substituting the given module value:

ext{Cutting depth} = 2 imes 2.5 = 6.75 ext{ mm}

Therefore, the cutting depth of the gear is 6.75 mm.

Step 3

6.1.3 The required simple indexing to cut this gear

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For simple indexing, the simple indexing formula provides:

ext{Simple indexing} = rac{360^ ext{o}}{ ext{Number of teeth}} = rac{360^ ext{o}}{51} ext{ degrees}

Thus, the required simple indexing to cut this gear is approximately 7.06° per tooth.

Step 4

6.2.1 The differential indexing (Choose 80 divisions)

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Differential indexing can be achieved using an indexing head set to 80 divisions. This allows for an indexing process that divides the rotation into manageable sections. The option for differential indexing using 80 divisions is suitable for precise measurements.

Step 5

6.2.2 The change-gears needed for this process

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To determine the change-gears required for differential indexing, we can apply the formula:

ext{Change gear ratio} = rac{ ext{Driver A} imes ext{Driver B}}{ ext{Driven A}} = rac{40 imes 1}{80 - 83} = rac{40}{1} ext{ required}.

The necessary change-gears would include a 40:1 ratio gearing.

Step 6

6.2.3 The rotation of the index plate relative to the rotation of the index crank handle

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The rotation of the index plate relative to the index crank can be calculated as:

ext{Index plate rotation} = ext{Teeth ratio} / ext{Drive ratio} = 83 / 40.

Thus, the index plate rotates in the opposite direction to that of the crank handle.

Step 7

6.3 Calculate distance X across the rollers

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Answer

The calculation to find distance X is performed as follows:

Given:
- The width = 160 mm
- Angle = 30°

Using trigonometric functions:

X = Y - 2 imes (AC + r)

Where:

AC = 12.5\tan(30°) = 12.5 / \sqrt{3} = 21.65 \text{ mm}

Hence,

X = 160 - (2 imes 21.65) \approx 116.70 ext{ mm}.

Step 8

6.4 Give TWO reasons for balancing a work piece on a lathe

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To prevent unnecessary bearing loads that could cause premature wear or damage to the lathe.
To ensure that the work piece spins evenly, reducing vibrations and enhancing the quality of the machining.

A spur gear has 51 teeth and a module of 3 - NSC Mechanical Technology Fitting and Machining - Question 6 - 2020 - Paper 1

Worked Solution & Example Answer:A spur gear has 51 teeth and a module of 3 - NSC Mechanical Technology Fitting and Machining - Question 6 - 2020 - Paper 1

6.1.1 The outside diameter of the gear

6.1.2 The cutting depth of the gear

6.1.3 The required simple indexing to cut this gear

6.2.1 The differential indexing (Choose 80 divisions)

6.2.2 The change-gears needed for this process

6.2.3 The rotation of the index plate relative to the rotation of the index crank handle

6.3 Calculate distance X across the rollers

6.4 Give TWO reasons for balancing a work piece on a lathe

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