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Q1:MEFG413 GOALS Week 1 Lab -Modeling Options Due Wednesday of Week 2 at Midnight (10 points) • Refresh your modeling skills • Become familiar with the operation of different CAD software packages • Create a simple part that can be used for future CAM activities • Get some technical writing practice INSTRUCTIONS • Open the attached part in the modeling software of your choice. OSU currently has NX and Solidworks. Several are available on the web (free for students or trial) including Fusion 360 and OnShape. 3D Paint is always an option. Re-create/reverse engineer the model o Obtain the dimension using the software's measure tool • • Re-create the part in two different software packages (three total) • Research some of the important aspects of the software (e.g. cost, delivery method (local installation vs web app), ...) Summer 2023 ASSIGNMENT • Create a short report using the What I Did, Why I Did It, What I Learned format • Include comparisons of at least some of the following features o Cost o Delivery method (online (app) or local) o Direct vs parametric modeling o Integrated CAM or other tools/features o Support network o Usability Include screenshots as appropriate to support your findings DELIVERABLES Keep in mind that the model doesn't have to be perfect. The assignment is to compare softwares-you just need enough information go make an informed decision Upload a copy of your report to the Gradescope assignmentSee Answer
Q2:● Create CAD drawings (NOT part files, but drawing files) of the following components. o 4 gears to size (isometric views) in one drawing file o 6 bearings to size (isometric views) in one drawing file o 4 keys to size (orthographic views with dimensions) in one drawing file o Input shaft (front view with dimensions) in one drawing file O Intermediate shaft (front view with dimensions) in one drawing file Output shaft (front view with dimensions) in one drawing file o Assembly of all parts (orthographic and isometric views) in one drawing file o Exploded view of assembly with bill of materials in one drawing file • All drawing files must in PDF format Submit a single PDF file combining all drawings.See Answer
Q3:● Create CAD drawings (NOT part files, but drawing files) of the following components. 4 gears to size (isometric views) in one drawing file 6 bearings to size (isometric views) in one drawing file 4 keys to size (orthographic views with dimensions) in one drawing file o Input shaft (front view with dimensions) in one drawing file O Intermediate shaft (front view with dimensions) in one drawing file O O Output shaft (front view with dimensions) in one drawing file o Assembly of all parts (orthographic and isometric views) in one drawing file Exploded view of assembly with bill of materials in one drawing file • All drawing files must in PDF format Submit a single PDF file combining all drawings.See Answer
Q4:I would like to know the step by step method of how the general solutions in the pictures were obtained. The generalized mode mass, the displacement solution, velocity solution, internal forces solution. For the fixed-free impacted rod/n CHAPTER 3 MATHEMATICAL MODEL 3.1. Introduction The study of stress wave propagation in elastic bodies has a long history. The elastic rod can undergo longitudinal, lateral, and torsional vibration. The longitudinal propagation of stress waves in rods has been investigated extensively over the last two centuries. Axial impact on an elastic body result in a disturbance that initially propagates away from the impact site at a specific speed. This disturbance is a pulse or wave of particle displacement (and consequent stress). Wave propagation relates to propagating a coherent pulse of stress and particle displacement through a medium at a characteristic speed. Typical manifestations of this phenomenon are the transmission of sound through air, water waves across the sea's surface, and seismic tremors through the earth, i.e., waves exist in gases, liquids, and solids. Sources of excitation may be either concentrated or distributed spatially and brief or continuous functions of time. The unifying characteristic of waves is propagating a disturbance through a medium. Properties of the medium that result in waves and determine the propagation speeds are the density p and moduli of deformability, e.g., young's modulus E, shear modulus G, bulk modulus K, etc. 3.2. Longitudinal impact of a rigid mass against an elastic rod Considering a stationary homogenous elastic rod with mass m, young modulus E, density p, variable cross-sectional area A(x), and length L. The rod struck on the right end x = L at time t = 0 by a moving rigid mass Mp of mass ratio y = mrod / Mp and initial velocity vo, see Figure 3.1. mrod, P, E Mp L "↑ 12 Tr(x) L k (b) (a) Figure 3.1: Longitudinal impact of a mass on a rod of variable cross-section; (a) impact model and (b) Shape and variables of the rod. Y. CS CamScanner 3.2.1. Assumptions for the derivation of the equation of motions We consider the following assumptions in the derivation of the wave equation of motion Plane, parallel cross sections remain plane and parallel during deformation so that the local contact region's deformation and transverse waves of the rod and vibrations of the striking mass are neglected. ● ● Frictionless contact surface The rod material is homogeneous so that E and p do not vary with x. Uniform distribution of stress across the cross section. Rod material behaves elastically (Hooke's Law). No body forces These assumptions allow the displacement to be specified as a function of one space coordinate indicating location along the rod's length. However, lateral deformation can be found in any cross-section. 3.2.2. The governing differential equation The resulting motion after impact is assumed to be one-dimensional with longitudinal displacement u(x, t), as shown in Figure 3.2. The equation of motion can be obtained from the force equilibrium equation for an element dx of the rod in x-direction [10], [15][17] as follows HIT მთ A- ax L +0 dx JA ax JA A+ dx ax Figure 3.2: An element from a variable cross-section rod. JA 1 -0A + (a +=dx) (A + x) = 0 {A+ (4 + 2dx)} dx -σA dx (A dxdx- əx at² ot = PA 13 aa dx a²u at² x (3.1) (3.2) CS CamScanner Then: Or where A(x), o (x, t), u(x, t) are the cross-sectional area, the stress across the cross section, and the longitudinal displacement, respectively. Now assume that the rod material behaves elastically, and the simple Hooke's law applies, where E is the Young's modulus and e(x, t) is the axial strain, defined by: where Co = 1 a Адх u(0, t) = 0 du(0, t) Əx du(0, t) AE əx ·(σA) = P₁ ɛ(x, t) = = = 0 By assuming that the rod material is homogeneous so that E and p do not vary with x, the equation of motion becomes: = ku(0, t) o(x, t) = E E a A dx du(x, t) əx ди (ADU) a²u at² du(x, t) əx 0x2 ²u 1 dA du + ax² Adx ax 0x2 = P = √E/p. For the rod with constant cross-section area dA/dx = 0 ²u c? 0t² ²u at² 1 0²u c²t² 1 0²u 14 (3.3) Eq. 3.8 is the wave equation of the longitudinal displacement u at the position x at time t, and . Co denotes the longitudinal wave propagation velocity of the infinitesimal elastic pulse in the rod. (when the rod at x = 0 is fixed- no displacement) (when the rod at x = 0 is free - no stress) (when the rod at x = 0 is attached with a spring) (3.4) 3.2.3. The boundary conditions The rod could have fixed, free, or elastic (spring with stiffness k attached) boundary conditions at x = 0 as follows: (3.5) - (3.6) (3.7) (3.8) (3.9) CS CamScanner At x = L, the rigid mass will remain in contact with the rod for period of contact time t, an Lis: the contact force is compressive, then the boundary condition at x = BA du(L, t) əx EA = - Mp Ju(L, t) əx After that time, the rigid mass is no longer in contact with the rod, and the rod perform free vibration without the mass at the tip. Hence: du(x,0) at = 0 a²u(L, t) at² = 0 =-vo for 3.2.4. The initial conditions According to St. Venant's contact theory, at the instant of the impact, the velocity of th struck end of the rod becomes immediately equals to the velocity of the rigid mass vo. u(x,0) = 0 for 0≤x≤L du(x, 0) at at for 0<t≤tc x = L t> tc 0≤x <L u(x, t) = f(x - ct) + g(x+c₂t) u(x, t) = p(x)q(t) (3.10) 15 (3.11) 3.2.5. Analytical solutions The solution of Eq. 3.8 can be obtained using either the wave solution approach or th mode of separation of variable. The wave solution of Eq. 3.8 can be expressed, as (3.12) Although this solution (Eq. 3.13) is useful in the study of certain impact and way propagation problems involving impulses of very short duration, it is not very useful in th study of vibration problems. The method of separation of variables followed by the eigenvalu and modal analysis is more useful in the study of vibrations. (3.13) To develop the solution using the method of separation of variables, the solution of Eq 3.8 is written as (3.14) where p(x) and q (t) are the mode shape and frequency functions, respectively, substitute Eq 3.14 into Eq. 3.8 leads to CS CamScanner cd²1d²q dx² q dt² 1 के Since the left-hand side of Eq. 3.15 depends only on x and the right-hand side depends only on t, their common value must be a constant, which can be shown to be a negative number. denoted as-w². Thus, Eq. 3.15 can be written as two separate equations: d²p(x) w² dx² d²q (t) dt² + cz $(x) = 0 +w²q(t) = 0 The solution of Eqns. 3.16 and 3.17 can be represented as W W (x) = A₁ sin-x+ A₂cos-x Co Co q(t) = B₁ sin wt + B₂ cos wt W u(x, t) = $(x)q(t) = (A₁ sin x + A₂cosx) (B₂ sin wt + B₂cos wt) Co Co (3.15) 16 (3.16) (3.17) (3.18) where w denotes the frequency of vibration, the function (x) represents the normal mode, the constants A₁ and A₂ can be evaluated from the boundary conditions, the function q(t) indicates harmonic motion, and the constants B₁ and B₂ can be determined from the initial conditions of the bar. The complete solution of Eq. 3.8 becomes (3.19) (3.20) CS CamScannerSee Answer
Q5:Q1 [Total 4 marks] For the plane-stress condition given below: Ox = 400 MPa Oy = 500 MPa Txy = - 30 MPa Construct a Mohr's circle of stress, find: (a) the principal stresses and the orientation of the principal axes relative to the x,y axes [1 mark]; (b) determine the stresses on an element, rotated in the x-y plane 60° counter- clockwise from its original position [1 mark]; Show these stresses on a sketch of an element oriented at this angle [1 mark]; (c) Also, using the matrix transformation law to compare the solutions with Mohr's circle [1 mark].See Answer
Q6:Q2 [Total 5 marks] The state of stress at a point of an elastic solid is given in the x-y- z coordinates by: oxx [0]= 0,₂x 6 s σyy 0x 0₂ 6 = oy 6 = = 90 180 0 180 240 0 0 MPa 0 120 (a) Using the matrix transformation law, determine the state of stress at the same point for an element rotated about the x-axis 60° clockwise from its original position [1 mark]; (b) Calculate the stress invariants and write the characteristic equation for the original state of stress [1 mark]; (c) Calculate the deviatoric invariants for the original state of stress [1 mark]; (d) Calculate the principal stresses and the absolute maximum shear stress at the point [1 mark]; (e) What are the stress invariants and the characteristic equation for the transformed state of stress [1 mark].See Answer
Q7:Q3 [Total 2 marks] The 3-dimensional state of strain at a material point in x, y, z coordinates is given by: Ex 0 0 0 xy yy [ε]=&yx Ey Eyz = 0 = 0 -1 -3 *104 Ey Ezz 0 -3 5 Ex E (a) Calculate the characteristic equation and determine the principal strains for the three-dimensional state of strain [1 mark]; (b) Calculate the volumetric strain and the deviatoric strain invariants [1 mark].See Answer
Q8:Q4 [Total 4 marks] The 3-dimensional state of strain at a material point in x, y, z coordinates is given by: [ε ] = Exy E yx yy Eyz Ezy = -120 0-150 00 0 -150 0 240 *10-6 (a) Calculate the volumetric strain and the deviatoric strain invariants [1 mark] (b) Calculate the mean stress and the deviatoric stress tensor [1 mark] (c) Write the characteristic equation of strain [1 mark] (d) Write the characteristic equation of stress [1 mark] The material is linear elastic (E=210GPa, v=0.3).See Answer
Q9:Q5 [Total 2 marks] It was found experimentally that a certain material does not change in volume when subjected to an elastic state of stress. Calculate Poisson's ratio for this material?See Answer
Q10:Q6 [3 marks] An aluminium rod shown in (a) has a circular cross section and is subjected to an axial load of 10 kN. If a portion of the stress-strain diagram is shown in (b), determine the approximate elongation of the rod when the load is applied. Take Eal = 70 GPa. σ (MPa) 56.6.60 50 Jy = 40 30 20 10 O 0.02 (b) 0.04 0.0450 0.06 10 kN 600 mm 20 mm (a) 15 mm 400 mm 10 kNSee Answer
Q11:Prepare a short report for the company which covers both electrical resistance strain gauging and digital image correlation for use in experimental stress analysis. The report should briefly introduce experimental stress analysis and its relevance, introduce strain gauges and digital image correlation methods and give relevant background to each. You should then cover the fundamental concepts and mode of operation (how it works!) associated with each technique and give guidance for obtaining accurate measurements. Finally, critically compare the methods, give suitable applications for each technique in aircraft engineering and offer conclusions and recommendations to the aerospace company using the information you have gathered as evidence.See Answer
Q12:Every group is assigned a group of settings from Ultimaker Cura. You will need to discuss the meaning of each parameter and its effect on the printed part. Provide examples to validate your explanation for major parameters. (use Expert settings)See Answer

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