Manufacturing Engineering & Technology
7th Edition
ISBN: 9780133128741
Author: Serope Kalpakjian, Steven Schmid
Publisher: Prentice Hall
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Chapter 17, Problem 1RQ
Describe briefly the production steps involved in making powder metallurgy parts.
Expert Solution & Answer
To determine
Describe briefly the production steps involved in making powder metallurgy parts.
Explanation of Solution
There are several sequential steps in making powder metallurgy parts. It involves powder production, followed by blending and compaction. After that sintering is carried out and finally the finishing operations.
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Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.
Chapter 17 Solutions
Manufacturing Engineering & Technology
Ch. 17 - Describe briefly the production steps involved in...Ch. 17 - Name the various methods of powder production and...Ch. 17 - Explain why metal powders may be blended.Ch. 17 - Describe the methods used in metal powder...Ch. 17 - What is isostatic pressing? How is it different...Ch. 17 - What hazards are involved in PM processing?...Ch. 17 - Describe what occurs to metal powders during...Ch. 17 - Prob. 8RQCh. 17 - Why might secondary and finishing operations be...Ch. 17 - Prob. 10RQ
Ch. 17 - Prob. 11RQCh. 17 - Prob. 12RQCh. 17 - Prob. 13RQCh. 17 - What is screening of metal powders? Why is it...Ch. 17 - Why are protective atmospheres necessary in...Ch. 17 - Why is there density variation in the compacting...Ch. 17 - What is the magnitude of the stresses and forces...Ch. 17 - List the similarities and differences of forging...Ch. 17 - Give some reasons that powder-injection molding is...Ch. 17 - How does the equipment used for powder compaction...Ch. 17 - Explain why the mechanical and physical properties...Ch. 17 - What are the effects of the different shapes and...Ch. 17 - Describe the relative advantages and limitations...Ch. 17 - How different, if any, are the requirements for...Ch. 17 - The powder metallurgy process can be competitive...Ch. 17 - What are the reasons for the shapes of the shown...Ch. 17 - Should green compacts be brought up to the...Ch. 17 - Because they undergo special processing, metal...Ch. 17 - In Fig. 17.12, it can be seen that the pressure is...Ch. 17 - Why do the compacting pressure and the sintering...Ch. 17 - What will be stronger: a blend of stainless steel...Ch. 17 - Name the various methods of powder production and...Ch. 17 - Estimate the maximum tonnage required to compact a...Ch. 17 - Refer to Fig. 17.11a. What should be the volume of...Ch. 17 - Determine the shape factors for (a) a cylinder...Ch. 17 - Estimate the number of particles in a 500-g sample...Ch. 17 - Prob. 37QTPCh. 17 - A coarse copper powder is compacted in a...Ch. 17 - A gear is to be manufactured from iron powders. It...Ch. 17 - What volume of powder is needed to make the gear...Ch. 17 - The axisymmetric part shown in Fig. P17.41 is to...Ch. 17 - Prepare an illustration similar to Fig. 13.1,...Ch. 17 - Prob. 44SDPCh. 17 - Compare the design considerations for PM products...Ch. 17 - Prob. 46SDPCh. 17 - Prob. 47SDPCh. 17 - Using the Internet, locate suppliers of metal...Ch. 17 - Explain why powder metal parts are commonly used...Ch. 17 - Prob. 50SDPCh. 17 - Describe how the information given in Fig. 17.15...Ch. 17 - It was stated that, in the process shown in Fig....Ch. 17 - Prob. 53SDPCh. 17 - The axisymmetric parts shown in Fig. P17.54 are to...Ch. 17 - Assume you are working in technical sales. What...
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- Problem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forward
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