To calculate the power that can be transmitted through a splined connection, we first need to determine the contact area between the splines. Then, using the allowable pressure and the rotational speed, we can find the power transmission capability.
Step 1: Calculate the contact area
The total contact area \( A \) between the splines can be calculated using the formula:
\[ A = n \times L \times h \]
where:
- \( n \) = number of splines = 10
- \( L \) = length of splines = 70 mm = 0.070 m
- \( h \) = height of each spline = 5 mm = 0.005 m
Substituting the values:
\[ A = 10 \times 0.070 , \text{m} \times 0.005 , \text{m} = 0.0035 , \text{m}^2 \]
Step 2: Calculate the allowable force
The allowable force \( F \) on the splines can be calculated using the formula:
\[ F = P \times A \]
where:
- \( P \) = allowable pressure = 6 MPa = \( 6 \times 10^6 , \text{Pa} \)
Substituting the values:
\[ F = 6 \times 10^6 , \text{Pa} \times 0.0035 , \text{m}^2 = 21,000 , \text{N} \]
Step 3: Calculate the power
The power \( P \) transmitted can be calculated using the formula:
\[ P = \frac{F \times \text{RPM} \times \pi \times D}{60} \]
where:
- \( F \) = force in Newtons = 21,000 N
- \( D \) = diameter of the shaft = 60 mm = 0.060 m
- \( \text{RPM} \) = rotational speed = 2,750 r/min
Substituting the values:
\[ P = \frac{21,000 , \text{N} \times 2,750 , \text{rev/min} \times \pi \times 0.060 , \text{m}}{60} \]
Calculating it step-by-step:
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Calculate \( \pi \times D \): \[ \pi \times 0.060 = 0.1884 , \text{m} \]
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Calculate the entire expression: \[ P = \frac{21,000 \times 2,750 \times 0.1884}{60} \]
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Calculate the numerator: \[ = 21,000 \times 2,750 \times 0.1884 = 108,267,000 \]
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Then divide by 60: \[ P = \frac{108,267,000}{60} = 1,804,450 , \text{W} \approx 1,804.45 , \text{kW} \]
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Finally convert to kW: \[ P \approx 1,804.45 , \text{W} \approx 1.80 , \text{kW} \]
Conclusion
The power that can be transmitted at 2,750 r/min is approximately 1.80 kW.