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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.
Design
Design decisions were made based on how the torsion test will be performed. The device is designed to hold rods with diameters ranging from 2mm to 5mm. The rod must have a 90 degree bend at both ends pointing in the same direction. The length of the bent parts can range from 2 cm to 5 cm. The part of the rod which undergoes torsion has a length of 20 cm. The device performs the torsion test by firmly holding the rod in place at one end while holding and twisting the other end using a pulley attached to a weight. The parts of the device are made entirely of acrylic in order to be cheap and easy to manufacture.
Specimen used for the torsion test
Solidworks model of the device
Base Design
The base of the device needed to be stable and allow the end of the rod to be firmly held in place while also allowing the length of the rod to rotate freely. The end of the rod is securely held in place by the top plate (orange), base plate (grey), and the two plates in between them (blue). In order for the clamping mechanism to be capable of holding rods of varying diameters, slots were made in the base plate and top plate so that the space in which the end of the rod fits is adjustable.
There are also two long pieces (blue) that run parallel to the length of the rod. These pieces act as rails to ensure that the rod only undergoes torsion and not deflection. These pieces do not firmly clamp the rod however, as this would introduce friction and not allow the rod to freely rotate.
The base plate is supported by four rectangular pieces that link to the base plate and with each other to form a solid platform. These support pieces have tabs that fit into the base plate. The tabs contain slots in them so that a small piece or pin can be inserted into them to prevent the tabs from coming out of the slots in the base.
Exploded view of base in Solidworks
Pulley Design
The pulley is made up of three acrylic discs that are bolted together. The acrylic disc in the middle (blue) has a smaller diameter than the outer discs (orange and purple), creating a space for string to be wound up. The middle disc has a slot that can fit rods with diameters as large as 5mm. The rear disc has a hole near the edge so that string can be tied to it. The first disc (orange) also has protractor markings etched into it. This allows students to determine the amount of angular deflection more easily.
Protractor markings on the front disc
One of the challenges for this design was to come up with a way for the pulley to be able to securely hold rods of varying diameters. The solution for this is an L-shaped piece (pink) with slots in it. The slots in the middle disc and front disc (orange and blue) have a width of 5mm. In order to firmly hold smaller specimens, the L-shaped piece has diagonally positioned slots which allow it to push the rod into the top corner of the slots in the front disc and middle disc. This allows smaller diameter rods to stay as close to the center of the discs as possible. Also, the corner of the slots in the front and middle discs is offset from the center of the discs by 2mm in the x and y directions. The reason for this is to ensure that the center of the disc is as close as possible to the center axis of the rod. This allows the pulley to spin as concentrically as possible.
Assembly of the pulley in Solidworks. It consists of the front (orange), middle (blue), and rear (purple) disc
Rear view of middle disc showing how the center of the disc (orange dot) matches up with the center of the rod (blue circle) when the rod is held against the corner of the slot
Manufacturing and Assembling
Lasercutting
Since this device is made of acrylic pieces, the manufacturing process of the device consisted mostly of lasercutting. All of the pieces were made from lasercutting 4.5 mm thickness sheets of acrylic. The lasercutter reads a dwg file of the piece and cuts along the lines of the drawing. When cutting parts that need to mate together, it is important to consider how lasercutting affects the measurements of the piece. The laser is able to cut pieces by melting the material along the specified lines, which causes a certain thickness of the material to be lost. This means that holes made by the lasercutter will be slightly larger than what was specified in the drawing, and extrusions will be slightly smaller. If a hole is dimensioned to have an exact fit with a screw (the diameter of the hole is equal to the OD of the screw), the fit will be noticeably loose.The protractor design was also etched into the front disc using the lasercutter. (more on lasercutting can be found here)
Assembly
The acrylic pieces are joined together using 1/4"-20 grade 5 steel hex head screws and nuts. When assembling the device, the order in which the pieces are put together and fastened can affect how difficult it is to assemble. If the base is placed on to the support pieces before all of the bolts are put in, it will be very difficult to tighten the nuts. For the most ease of assembly, it is best to fasten the pieces that rest on the base plate first. When fastening the pieces that are adjustable, it is best to place the rod in the device and then position the pieces based on the rod's diameter before fastening them in place. The discs which make up the pulley can also be fastened using barrel nuts. This will allow more ease of assembly.
Picture of the device
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.
Performing the Torsion Test
After the device has been assembled and the rod has been fixed in place, the device will need to be clamped to the table so that it does not flip over during the torsion test. This can be done by using a C-clamp to grip the baseplate and the underside of the table. Before winding up the string to the pulley, the string must be tied using the hole at the edge of the rear disc. The string must be wound in a counter-clockwise direction when facing the rear disc. A counter-clockwise rotation will ensure that the force on thedevice
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Next Steps
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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