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# Torsion Measurement Lab Report Engineering Assignment (Essay Sample)

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Torsion Measurement Lab Report
Introduction
The application of a given torque on the shaft whether stationary or in rotational motion generate shear stress as the shaft twists. The presence of bending or stretching force components makes the sample material to fail. The experiment focuses on establishing the shear modulus of elasticity for the materials used (aluminum, brass, and steel) and determines the relationship that exists between different metal components include the torque, clumping span and angle of twist. The completion of experiment relies on the timely monitoring of the performance of different components. The clamping of specimens and application of boundary condition, as opposed to the twist at the end, generate relevant data for the efficient force analysis. Systematic loading of the system and data collected in the experiment generated significant information that helped the students to establish the influence of strain on the torsion of the material. The investigation focuses on the angular displacement of the rod due to applied force that generates failure component in the material used (Love 47).
Verification of Coulomb's torsion theory compares the force exerted between two points, as well as the product of forces acting on the material from two different directions. According to Coulomb's torsion theory, the force and the product of force between these materials are inversely proportional to the square of the separation distance. The torsion concept generated by Coulombs considered the torsion fiber and balance that adopted science-based instruments in the study. The study relied on the radiation pressure and gravitational tension balance. The concept provides a basic reference point for torsion determination in mechanics and engineering material analysis. The principal of torsion developed by Coulomb’s generated significant progress in the application of different materials, for instance, counterbalancing the gauge door depends on the proper understanding of the torsion concept (Kurier 12). The design of pop-up doors, digital cameras, and compact disc players indicates the critical application of the system. The tension bar suspension originated from coulomb’s theory that facilitates smooth operation of the vehicle as the vehicle system is able to facilitate shock absorption between the road and the car tires. The existence of balance spring facilitates smooth operation of clocks as the modulus of rigidity represents the ratio of shear stress to strain developed within the elastic limit of a material supported by the formula;
G = q/f
Where; G-modulus of rigidity, q – shear stress of the material within the elastic limits, f- shear strain of the material at the same condition
Yield stress is the maximum elastic condition the material poses upon which a load increment beyond this limit initiates component failure. The parameter of yield stress facilitates determination of safety levels of engineering materials. The principle of torque yield-related rotational is equivalent to the displacement at a specified velocity, and this concept is relevant to the establishment of the overall performance of the system (Love 48). Torque represents force applied at a specified distance from the axis of rotation of the material that conforms to the formula;
Torque (() = r*F*SinОё
Where; r- represents rod length, F- applied weight, Оё- displacement angle due to applied rod.
Fig Force performance (Kurrer 14)
Force and equivalent mass requirements coincide to torque that defines angular rates of momentum or force applied to cause rotation of an object relative to mass that represents the energy required to initiate change projected in the system due to torsion.
Theory
The torsion performance tests conducted on the three selected materials generated significant shearing stresses during twisting. The material with increased rigidity and highly resistant to twist tends to have a higher modulus of rigidity. In most cases, the value of the modulus of rigidity of a specific material is the same. The data generated from experiment depended on the existing material samples tested that poses similar geometric characteristic, yet differ in type. The tests involved brass, aluminum, and steel. The determination of modulus of elasticity will comply with the basic concept and formulae established by Coulomb and Newton. Loading of the materials will progress steadily without reaching plastic deformation for safer evaluation of the torque required to accomplish the twist in the system. The application of axial loading facilitated the establishment of the modulus of elasticity as present in the graphical representation of stress versus strain graphs. The establishment of twist angle for the samples provided a relevant indicator of the torsion performance (Kurrer 15). The Vanier and torque scales provided relevant conversion factors that helped the students to attain the twist and torque values related to shear and strain elements in the experiment. The experimental analysis involves a wide range of torque wrenches and other torsion measuring device used in the system during data collection. The establishment of initial torsion depends on the torque performance. Establishment of the experimental elements depends on the principle formulae;
Shear modulus (G) = shear stress (() / shear strain (()
The formula is effective as long as the forces applied to the test samples operate within the elastic boundaries of the material. The exaggerated polar moments often determines the magnitude of the twist or torsion that a material may withstand. For example;
Polar moment of inertia (J) =ПЂD4/32
Fig Torsion (Love, 54)
Torque = twist force* torque arm's length while the angle or twist (Оё) =Tl/ GJ
Shear stress for circular bars (() = td/2J
The elastic deformation is a condition where a material retains its original shape once the stressing load is out. Ceramics and crystalline materials have a small elastic interval with linear elasticity. Consequently, the plastic deformation is an irreversible state attained by a material where the material may not gain its original conditions, regardless of the initiatives (Love 58).
Fig Stress vs. Strain curve (Love, 60)
Materials
The accomplishment of an experimental investigation on torque will rely on the use of angle and torque measuring device, a tension measuring device, three torsion samples; brass, aluminum, and steel, Vanier Calipers.

Fig Torsion test device (Kurrer 17).
Experimental procedure
Assemble the apparatus and mount the shaft/ rods onto the test device’s chuck by loosening the screw and sliding the specimen, tighten the screw and sliding arm. Note the star of the fixed length, measure the diameter of the rod. Measure the separation of the force application point and center of the rod. Take the measurement of the distance between Vanier measuring point and the center of the rod. Set the Vanier reading to zero marks at no load. Apply the loads gradually and record the Vanier readings. Increase the load at an interval of 20Nm and record the deflection readings. Carry out the process for each sample and record the observed readings (Love 72).
Table: torsion test data (Kurrer 20)
Weights(gm)Torque (Nm)Brass twist angle (degrees)Aluminum twist angle (degrees)Steel twist angle (degrees)0.00.0000.000.00.0200.2613.24.31.3400.5236.3
8.5
2.8
60
0.784
9.4
12.6
4.3
80
1.045
12.5
16.2
5.7
100
1.306
15.8
20.7
7.2
120
1.571
18.7
24.6
8.7
The theoretical shear modulus vs. experimental;
G = [(TD)/2J]/ [rОё)/l]
Experimental values of G
Brass = (12.5-9.4)/ (1.045-0.784) =3.1/ 0.261 = 11.88
Aluminum = (12.6-8.5) / (0.784 -0.523) = 4.1/0.261 =15.71
Steel= (5.7-4.3)/ (1.045-0.784) = 1.4/0.261 =5.36
Theoretical values of G
Brass =44GPa
Aluminum = 26GPa
Steel = 80GPa
Graph: Sample twist angle vs. Torque

Table: Sample diameter (Kurrer 21)
ElementTrial 1(mm)Trial 2 (mm)Trial 3(mm)Average (mm)Brass0.1250.1250.1250.125Aluminum0.1240.1240.1250.1243Steel0.1240.1240.1250.1243Average diameter = (Trial1+Trial2 +Trial3) /3
Data Analysis
J =ПЂD4/32 (m4) (Love, 76)
J for brass = 22* 0.1244/ (32*7) =0.00537/224 = 0.000024m4
J for aluminum =22*0.12434 / (32*7) = 0.00525/ 224 =0.000023m4
J for steel =22*0.12434 / (32*7) = 0.00525/ 224 =0.000023m4
Graph: Brass twist angle vs. deflection Error

Graph: Aluminum twist angle vs. deflection Error

Graph: Steel twist angle vs. deflection Error

Discussion
The experiment provides significant analysis relative to the performance of materials on the basis of their center of mass and strength over fixed points. The evidence of distortion with varying limits of error presents the prominent determinant in material selection based on their yield strength and level of rigidity that in turn affect the product performance once subjected to different loads and loading pattern. The level of deflection depends on the extent of the malleability of the material, for instance, the three samples portray that brass is highly malleable making it deflect the furthest followed by aluminum and then steel that indicates the least deflection under a similar loading. The rods of the same diameter and length expressing different deflection angles indicate the disparity in the internal characteristic of the specimen. Comparing the experimental and theoretical values indicate a significant level of error that generates the disparity in force measurements. The three graphs developed from the data collected ...
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