The torque diagram of a shaft is analogues to the shear force and bending moment diagram of a beam. It is an important engineering diagram from the pulley shaft design point of view. The steps required to draw it will be discussed with the help of the following example:
- Finding The Internal Torque Of A Free Spinning Shaft Is Known
- Finding The Internal Torque Of A Free Spinning Shaft Is Measured
- When a shaft is subjected to a torque or twisting a shearing stress is produced in the shaft. The shear stress varies from zero in the axis to a maximum at the outside surface of the shaft. The shear stress in a solid circular shaft in a given position can be expressed as: τ = T r / J (1) where. Τ = shear stress (Pa, lbf/ft2 (psf)).
- In this problem we want to determine the internal resisting torque in each segment of the displayed shaft and we also want to draw an internal torque diagram.
Problem: The below picture is showing a machine shop set up, where three machines namely: milling, drilling and lathe are drawing torques from the main shaft at the points B, C and D respectively. The main shaft is rotating by taking torque from the motor. The bearings E and F are assumed to be frictionless so not taking any torques from the torque, theoretically
The details of the input and output torques are shown below:
Milling M/C – 20 N-m
Known variables: Weight (lbs), Linear Velocity (ft/min), Speed of Driving Motor (RPM), Change in Speed (RPM), and Time to Accelerate Total System (sec) In addition to the torque required to drive the load at a steady speed, torque is required to accelerate the load. Accelerating Torque for Linear Motion. Input Weight, w (lbs).
Drilling M/C – 30 N-m
Lathe M/C – 40 N-m
Solution:
Step-1:Draw FBD of the entire shaft: The FBD of the entire shaft will look like below:
Please observe that the direction of the torque for the motor is opposite than the three machines. This is because the above FBD is showing the reaction torques and the direction of the reaction torques for the machines are opposite to that of the motor for obvious reason. The fact will be re-emphasised from the Step-2 below.
Step-2: Calculate the input torque required from the motor: From the equation for equilibrium, we know that total torque must be equal to zero. So, we can write:
Σ T = 0
Or, TA+20+30+40=0
Or, TA= – 90 N-m
Step-3: Calculate the torque @ section AB: Take a section anywhere between the point A and B and consider the portion of the shaft on the left of the section for equilibrium. The equilibrium equation becomes:
TA + TA-B=0
or, TA-B = – TA=90 N-m
Where,
TA-B – The torque at the section anywhere between A and B
Step-4: Calculate the torque @ section BC: Take a section anywhere between the point B and C and consider the portion of the shaft on the left of the section for equilibrium. The equilibrium equation becomes:
TA + TB+TB-C=0
or, TB-C = – TA-TB=70 N-m
Where,
TB-C – The torque at the section anywhere between B and C
Step-5: Calculate the torque @ section CD: Take a section anywhere between the point C and D and consider the portion of the shaft on the left of the section for equilibrium. The equilibrium equation becomes:
TA + TB+TC+TC-D=0
or, TC-D = – TA-TB-TC=40 N-m
Where,
Finding The Internal Torque Of A Free Spinning Shaft Is Known
TC-D – The torque at the section anywhere between C and D
Step-6: Draw the torque diagram: Plot the length of the shaft in X-axis and the torque values (calculated in step-3,4,5) at the different sections in Y-axis. Like below:
The torque values obtained from the torque diagram is used as input for the pulley shaft design.
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Finding The Internal Torque Of A Free Spinning Shaft Is Measured
Hi, I am Shibashis, a blogger by passion and an engineer by profession. I have written most of the articles for mechGuru.com. For more than a decades i am closely associated with the engineering design/manufacturing simulation technologies. I am a self taught code hobbyist, presently in love with Python (Open CV / ML / Data Science /AWS -3000+ lines, 400+ hrs. )