PRECISION MACHINING TECHNOLOGY PACKAGE
3rd Edition
ISBN: 9780357262788
Author: Hoffman
Publisher: CENGAGE L
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Chapter 2.1, Problem 11RQ
What does GHS stand for?
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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 2 Solutions
PRECISION MACHINING TECHNOLOGY PACKAGE
Ch. 2.1 - Briefly describe what you believe are the two most...Ch. 2.1 - Briefly describe what you believe are the two most...Ch. 2.1 - What should be done in the case of a personal...Ch. 2.1 - What does OSHA stand for and what is OSHA's...Ch. 2.1 - List three specific clothing items that should not...Ch. 2.1 - If someone working around machinery has long hair,...Ch. 2.1 - Never operate machinery without proper ______ in...Ch. 2.1 - What is PPE?Ch. 2.1 - What is the most common and important piece of PPE...Ch. 2.1 - What does HCS stand for?
Ch. 2.1 - What does GHS stand for?Ch. 2.1 - What is a pictogram?Ch. 2.1 - What does NFPA stand for?Ch. 2.1 - What does HMIS stand for?Ch. 2.1 - Prob. 15RQCh. 2.1 - Prob. 16RQCh. 2.1 - Class A fire extinguishers use ______ as a media...Ch. 2.1 - What class of fire extinguisher should be used on...Ch. 2.1 - What class of fire extinguisher should be used on...Ch. 2.1 - What is the purpose of lockout and tagout...Ch. 2.2 - What is the inch equivalent of 1 millimeter?Ch. 2.2 - What is the inch equivalent of 32.5 mm to the...Ch. 2.2 - Use the decimal equivalent chart on page 69 to...Ch. 2.2 - Use the decimal equivalent chart on page 69 to...Ch. 2.2 - Use the decimal equivalent chart on page 69 to...Ch. 2.2 - What does parallel mean?Ch. 2.2 - What does perpendicular mean?Ch. 2.2 - What is the radius of a 3.65-inch-diameter circle?Ch. 2.2 - What is the circumference of the circle in the...Ch. 2.2 - What are the Cartesian coordinates of the four...Ch. 2.2 - Label the hypotenuse, adjacent side, and opposite...Ch. 2.3 - Define semi-precision measurement.Ch. 2.3 - What is comparison measurement?Ch. 2.3 - List three rules to follow when or storing...Ch. 2.3 - List the parts of the combination set.Ch. 2.3 - Describe four uses of the combination set.Ch. 2.3 - What semi-precision tool is used to take angular...Ch. 2.3 - What type of square has a blade that can be tilted...Ch. 2.3 - Identify the following tools.Ch. 2.4 - List three key points in caring for precision...Ch. 2.4 - What type of fixed gage can be used to check hole...Ch. 2.4 - What type of fixed gage can be used to check a...Ch. 2.4 - How is the go member of a go/no-go ring gage set...Ch. 2.4 - What type of fixed gage can be used to check...Ch. 2.4 - A _____________ can provide a reference plane for...Ch. 2.4 - What two other tools could be used with the answer...Ch. 2.4 - ___________ is the process of attaching gage...Ch. 2.4 - What is the smallest graduation on an English...Ch. 2.4 - What is the smallest graduation on a metric...Ch. 2.4 - A micrometer uses an accurate __________ to...Ch. 2.4 - What is the smallest graduation on an inch...Ch. 2.4 - What is the smallest graduation on a metric...Ch. 2.4 - What is calibration and why is it important?Ch. 2.4 - What is a transfer-type measuring tool?Ch. 2.4 - What are the two basic types of indicator...Ch. 2.4 - Briefly describe the main difference between the...Ch. 2.4 - A sine tool uses the trigonometric function of...Ch. 2.4 - List the two most common methods for measuring...Ch. 2.4 - What are one advantage and one disadvantage of...Ch. 2.4 - A(n) ________ displays a magnified image of a part...Ch. 2.4 - What other tool can be useful for measuring very...Ch. 2.4 - What does CMM stand for?Ch. 2.5 - What are the four basic parts of a process plan?Ch. 2.5 - Briefly define quality control and explain its...Ch. 2.5 - Briefly explain the purpose of a sampling plan.Ch. 2.5 - What is the purpose of an inspection plan?Ch. 2.5 - What is the important factor to consider when...Ch. 2.5 - What does SPC stand for?Ch. 2.5 - What does an X-bar chart track?Ch. 2.5 - What does an R-chart track?Ch. 2.5 - If an X-bar chart graph is between LCL and the...Ch. 2.5 - If an X-bar chart graph falls below the LCL or...Ch. 2.6 - What is the difference between ferrous and...Ch. 2.6 - Briefly describe an alloy.Ch. 2.6 - Name three alloying elements added to steel.Ch. 2.6 - What is cast iron?Ch. 2.6 - What element is in stainless steel that makes it...Ch. 2.6 - Small particles of________ alloys are flammable.Ch. 2.6 - What are the two major benefits of titanium?Ch. 2.6 - What does AISI stand for?Ch. 2.6 - What does SAE stand for?Ch. 2.6 - What is (are) the major alloying element(s) in...Ch. 2.6 - What is (are) the major alloying element(s) in...Ch. 2.6 - What does IADS stand for?Ch. 2.6 - What is the overall purity of 1030 aluminum?Ch. 2.6 - What is (are) the major alloying element(s) of...Ch. 2.6 - What does UNS stand for?Ch. 2.7 - Briefly define the term heat treatment.Ch. 2.7 - Direct hardening can be performed on steel...Ch. 2.7 - ________ is the rapid cooling of metal during heat...Ch. 2.7 - What type of hardening operation that leaves the...Ch. 2.7 - In what two ways can the process described in the...Ch. 2.7 - What method is used to harden low-carbon steels?Ch. 2.7 - List two methods of performing the operation...Ch. 2.7 - After hardening, steel is very hard and brittle....Ch. 2.7 - Briefly define annealing.Ch. 2.7 - Prob. 10RQCh. 2.7 - A dual-chamber furnace allows the user...Ch. 2.7 - In addition to standard PPE, what specific PPE and...Ch. 2.7 - What hardness testing scale uses many different...Ch. 2.7 - What is a Brale penetrator and what hardness scale...Ch. 2.8 - Why is a routine maintenance plan important?Ch. 2.8 - What is a lubricant?Ch. 2.8 - List three methods of applying lubricants to...Ch. 2.8 - List two components of machine tools that should...Ch. 2.8 - Briefly describe a gib.Ch. 2.8 - What are the purposes of cutting fluids?Ch. 2.8 - What are the two major types of cutting fluids?Ch. 2.8 - Prob. 8RQCh. 2.8 - What two ingredients are often used as additives...Ch. 2.8 - Oils that can be combined with water are...Ch. 2.8 - What is the major benefit of cutting fluids that...Ch. 2.8 - What is the difference between synthetic and...Ch. 2.8 - A______ can be used to measure cutting fluid...Ch. 2.8 - List three methods of applying cutting fluids.Ch. 2.8 - Always review the________ before using any...Ch. 2.8 - What type of cutting fluids should never be used...
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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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