Table of Contents
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Introduction to Torsion
Torsion refers to the twisting of an object as a result of an applied torque. The torque creates shear stress within the material causing it to twist. Torsion is involved in a vast number of engineering appications [1]. Because of this, it is essential for engineers to have a solid understanding of torsion and shear stress. For students, having a firm grasp of these concepts can be challenging due to their theoretical nature. Therefore, to help students understand this fundamental engineering concept, an interactive and visual approach can be enriching and beneficial.
Shear Stress and Shear Strain
Similar to the stress and strain used to describe tensile testing, shear stress and shear strain describe how much angular deflection a specimen undergoes when placed under a certain amount of shear stress. Shear strain is the amount of angular deflection of an object under a torque. Shear stress in a cylindrical rod is determined by the applied torque, radius, and length of the rod. To understand the torsional properties of a rod, a shear stress-strain curve can be graphed by observing the data from a torsion test. The first portion of this graph represents the elastic portion of the test. This elastic part is characterized by its linear slope, and any deflection occurring within this range of strain values will return to zero after the stress is removed. The slope of this elastic portion represents the shear modulus of the material [1]. The torsion testing device addressed in this case study currently only tests the elastic portion of the shear stress-strain curve.
Shear Stress-Strain Curve [1]
Equation for shear stress(τ):
τ = Tr/J
T is the applied torque
r is the radius if the shaft
J is the polar moment of inertia
Equation for shear strain(Υ) in a circular shaft:
Υ = rθ/L
r is the radius of the shaft
θ is the angle of deflection
L is the length of the shaft
Equation for shear modulus(G):
G = τ/Υ
It can also be written as:
G = TL/Jθ
Applications of Torsion
Torsion is a common occurrence that happens in a wide range of engineering applications. For example, in most powertrains, power is transferred from a motor using a shaft. This shaft has a large amount of torque that acts along its center axis. When the shaft is transfering torque, shear stress acts on the shaft which can subsequently cause shear strain. Therefore, the torsional properties of the shaft are very important to its performance. Overall, torsion is a part of any mechanical system that involves a torque acting parallel to the length of a beam or shaft.
Project Description
This torsion testing device was designed and built for the purpose of providing students with an interactive method to perform a torsion test on a metal rod. By using this device to perform a torsion test, students can actively participate in the test and witness changes in the specimen first-hand as it undergoes torsion. This allows them to gain a more solid understanding of material properties.
This device can be used by students to obtain data needed to complete a materials lab or for other in-class activities. The device is designed to allow groups of students to perform a torsion test on a small diameter rod using weights and collect their own data. So far, the device has been designed and tested to perform a torsion test for the elastic portion of the shear stress-strain curve.
Theoretical Results
In order to calculate how much angular deflection will occur in a specimen when a torque is applied, an equation is needed that relates the torque to the angular deflection based on the properties of the specimen. This can be done by rearranging the equation for the shear modulus.
G = TL/Jθ
θ = TL/JG [2]
G - shear modulus, T - applied torque, L - length of rod, J - polar moment of inertia, θ - angle of deflection
Based on the above equation which relates the torque applied on the rod to the amount of angular deflection, the shear modulus of different metals can be calculated. To determine the torsional properties of different metal specimens, all geometrical values must be the same for each metal. This ensures that any change in performance is due to the properties of the material. In this scenario, the radius and length of each rod will remain consistent, and only the shear modulus will change depending on the type of metal. By performing these calculations and graphing the result, the effect of changing the shear modulus becomes apparent. Also, it should be noted that these calculations only depict the elastic portion of the torsion test.
The calculations were done to analyze the theoretical values for this specific torsion testing machine. Therefore, the values needed are shown below:
- Diameter of rod: 3mm
- Length of rod under torsion: 20cm
- Length of moment arm acting on the rod by the mass: 6cm
This graph displays how much a rod made of a certain metal should deflect when tested with the torsion testing device.
References
[1] D. Collins, “Shafts in torsion: Mechanical properties of materials,” Linear Motion Tips, 06-Aug-2021. [Online]. Available: https://www.linearmotiontips.com/mechanical-properties-of-materials-shafts-in-torsion/. [Accessed: 18-Nov-2021].
[2] M. van Biezen, “Physics - Mechanics: Torsion (5 of 14) Torsion of the Thin Rod,” Youtube, 01-Feb-2017. [Online]. Available: https://www.youtube.com/watch?v=1xRe5lecQhg. [Accessed: 18-Nov-2021].
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User Last Update Areeb Mohammed 1021 days ago