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Transmission shaft is subjected to a fluctuating torque that varies from - 120 n·m to 500 n-m. let the stress concentration factor 1.5 and factor of safety be 2. determine the required diameter of shaft. shaft material is c45 steel.?
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Transmission shaft is subjected to a fluctuating torque that varies fr...
Solution:
Given parameters:
- Fluctuating torque = -120 N·m to 500 N·m
- Stress concentration factor = 1.5
- Factor of safety = 2
- Shaft material = C45 steel
Determine the required diameter of the shaft.
Step 1: Calculate the mean torque
- Mean torque, Tm = (500 N·m - 120 N·m)/2
- Tm = 190 N·m
Step 2: Calculate the alternating torque
- Alternating torque, Ta = (500 N·m - (-120 N·m))/2
- Ta = 310 N·m
Step 3: Calculate the maximum torque
- Maximum torque, Tmax = Tm + (Ta/2)
- Tmax = 345 N·m
Step 4: Determine the bending moment
- Bending moment, M = (Tmax * 1000)/2
- M = 172.5 N·m
Step 5: Determine the required diameter of the shaft
- Using the bending moment equation, M = (pi/32) * (sigma_b * d^3), where sigma_b is the bending stress and d is the diameter of the shaft.
- Rearranging the equation, d = (32 * M)/(pi * sigma_b)
- For C45 steel, the endurance limit for bending stress is 150 MPa.
- The maximum bending stress, sigma_b = (32 * M)/(pi * d^3)
- Substituting the values, sigma_b = (32 * 172.5)/(pi * d^3)
- sigma_b = 9.1 MPa
- The required diameter of the shaft, d = (32 * M)/(pi * sigma_b)
- d = (32 * 172.5)/(pi * 9.1)
- d = 46.8 mm
Step 6: Check for the factor of safety
- The factor of safety, FS = (yield strength of material)/(maximum bending stress)
- For C45 steel, the yield strength is 450 MPa.
- FS = 450/9.1
- FS = 49.5
- Since the calculated factor of safety is greater than the given factor of safety, the shaft is safe.
Therefore, the required diameter of the shaft is 46.8 mm.
Given parameters:
- Fluctuating torque = -120 N·m to 500 N·m
- Stress concentration factor = 1.5
- Factor of safety = 2
- Shaft material = C45 steel
Determine the required diameter of the shaft.
Step 1: Calculate the mean torque
- Mean torque, Tm = (500 N·m - 120 N·m)/2
- Tm = 190 N·m
Step 2: Calculate the alternating torque
- Alternating torque, Ta = (500 N·m - (-120 N·m))/2
- Ta = 310 N·m
Step 3: Calculate the maximum torque
- Maximum torque, Tmax = Tm + (Ta/2)
- Tmax = 345 N·m
Step 4: Determine the bending moment
- Bending moment, M = (Tmax * 1000)/2
- M = 172.5 N·m
Step 5: Determine the required diameter of the shaft
- Using the bending moment equation, M = (pi/32) * (sigma_b * d^3), where sigma_b is the bending stress and d is the diameter of the shaft.
- Rearranging the equation, d = (32 * M)/(pi * sigma_b)
- For C45 steel, the endurance limit for bending stress is 150 MPa.
- The maximum bending stress, sigma_b = (32 * M)/(pi * d^3)
- Substituting the values, sigma_b = (32 * 172.5)/(pi * d^3)
- sigma_b = 9.1 MPa
- The required diameter of the shaft, d = (32 * M)/(pi * sigma_b)
- d = (32 * 172.5)/(pi * 9.1)
- d = 46.8 mm
Step 6: Check for the factor of safety
- The factor of safety, FS = (yield strength of material)/(maximum bending stress)
- For C45 steel, the yield strength is 450 MPa.
- FS = 450/9.1
- FS = 49.5
- Since the calculated factor of safety is greater than the given factor of safety, the shaft is safe.
Therefore, the required diameter of the shaft is 46.8 mm.
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Transmission shaft is subjected to a fluctuating torque that varies from - 120 n·m to 500 n-m. let the stress concentration factor 1.5 and factor of safety be 2. determine the required diameter of shaft. shaft material is c45 steel.?
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Transmission shaft is subjected to a fluctuating torque that varies from - 120 n·m to 500 n-m. let the stress concentration factor 1.5 and factor of safety be 2. determine the required diameter of shaft. shaft material is c45 steel.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Transmission shaft is subjected to a fluctuating torque that varies from - 120 n·m to 500 n-m. let the stress concentration factor 1.5 and factor of safety be 2. determine the required diameter of shaft. shaft material is c45 steel.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Transmission shaft is subjected to a fluctuating torque that varies from - 120 n·m to 500 n-m. let the stress concentration factor 1.5 and factor of safety be 2. determine the required diameter of shaft. shaft material is c45 steel.?.
Transmission shaft is subjected to a fluctuating torque that varies from - 120 n·m to 500 n-m. let the stress concentration factor 1.5 and factor of safety be 2. determine the required diameter of shaft. shaft material is c45 steel.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Transmission shaft is subjected to a fluctuating torque that varies from - 120 n·m to 500 n-m. let the stress concentration factor 1.5 and factor of safety be 2. determine the required diameter of shaft. shaft material is c45 steel.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Transmission shaft is subjected to a fluctuating torque that varies from - 120 n·m to 500 n-m. let the stress concentration factor 1.5 and factor of safety be 2. determine the required diameter of shaft. shaft material is c45 steel.?.
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