Precision Machining Technology
3rd Edition
ISBN: 9781337795302
Author: Peter, Hoffman.
Publisher: Cengage Learning,
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Chapter 5.5, Problem 7RQ
What is the limitation of the tool bit taper turning method?
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Note : Exam is open notes &tables / Answer all questions.
Q.1. The press shown for Figure.1 has a rated load
of 22 kN. The twin screws have double start Acme
threads, a diameter of 50 mm, and a pitch of 6 mm.
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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.
Chapter 5 Solutions
Precision Machining Technology
Ch. 5.1 - List the four main parts of the engine lathe.Ch. 5.1 - What are the two main purposes of the lathe...Ch. 5.1 - What part of the lathe is used to set the feed...Ch. 5.1 - Prob. 4RQCh. 5.1 - Prob. 5RQCh. 5.1 - What is the purpose of the leads crew of a lathe?Ch. 5.1 - What two functions can the lathe tailstock...Ch. 5.1 - The standard taper in most lathe tailstocks is the...Ch. 5.1 - Define the swing and the bed length of a lathe.Ch. 5.2 - What is the special name for the type of jaw-type...
Ch. 5.2 - The most common variation of the above chuck has...Ch. 5.2 - Name two material shapes that can be properly held...Ch. 5.2 - List two advantages of using a self-centering...Ch. 5.2 - Name two material shapes that can be properly held...Ch. 5.2 - List three benefits of holding a workpiece between...Ch. 5.2 - List three potential advantages of using an...Ch. 5.2 - List three characteristics of a workpiece that...Ch. 5.2 - What type of mandrel would be ideal for gripping a...Ch. 5.2 - Name the type of tailstock center that raid be...Ch. 5.2 - What two auxiliary devices can be used to...Ch. 5.2 - Explain the differences between the two auxiliary...Ch. 5.2 - Name the device that is used to transmit the...Ch. 5.2 - Which two tool posts are the most efficient if...Ch. 5.2 - What is the major advantage of using...Ch. 5.2 - What direction is a right-hand turning tool...Ch. 5.2 - What is an inscribed circle related to carbide...Ch. 5.2 - Would a 0.010 or 0.031 tool nose radius be...Ch. 5.2 - Which device may be used for either toolholding or...Ch. 5.3 - If a 0.050" depth of cut is taken on the diameter...Ch. 5.3 - A lathe cross slide uses a diameter-reading...Ch. 5.3 - In what units are feed rates measured for lathe...Ch. 5.3 - Are deeper cuts used for roughing or finishing...Ch. 5.3 - Calculate spindle RPM and machining time for...Ch. 5.3 - List three safety precautions related to clothing...Ch. 5.3 - What two materials are most commonly used for...Ch. 5.3 - What feature of a lathe cutting tool has a direct...Ch. 5.3 - Is a left-hand or right-hand tool normally used...Ch. 5.3 - What part of the lathe is used to feed the tool...Ch. 5.3 - When facing, why should the tool not be fed past...Ch. 5.3 - Should a left-hand or right-hand tool be used when...Ch. 5.3 - When and how should chips he removed from the work...Ch. 5.3 - What are two reasons for center drilling on the...Ch. 5.3 - When drilling and reaming on the lathe, how are...Ch. 5.3 - How can hole depth be controlled during drilling...Ch. 5.3 - What are two reasons boring may be selected to...Ch. 5.3 - Why must extra care be taken when performing...Ch. 5.3 - How can a tap be aligned when threading a hole on...Ch. 5.3 - Briefly define form cutting.Ch. 5.3 - How do grooving and cutoff speeds compare to...Ch. 5.3 - How can tool binding be overcome when cutting deep...Ch. 5.3 - List the two basic knurl patterns.Ch. 5.3 - How is knurling different from other lathe...Ch. 5.3 - List and briefly describe the two different types...Ch. 5.4 - The distance of actual contact of two mating...Ch. 5.4 - What feature of mating threads determines the...Ch. 5.4 - How many classes of fit are there in the Unified...Ch. 5.4 - Determine the major diameter limits for the...Ch. 5.4 - Determine the minor diameter limits for the...Ch. 5.4 - Determine the pitch diameter limits for the...Ch. 5.4 - Determine the approximate compound-rest in-feed...Ch. 5.4 - What is the name for the rotating device that...Ch. 5.4 - When threading, what is the reason for feeding the...Ch. 5.4 - Prob. 10RQCh. 5.4 - Why should the depth of cut be reduced for each...Ch. 5.4 - What dimension of the thread is measured by using...Ch. 5.4 - What measuring tool is used to visually inspect...Ch. 5.4 - List two applications of Acme threads.Ch. 5.4 - What type of thread is machined on a tapered...Ch. 5.5 - Briefly define a taper.Ch. 5.5 - What is the difference between an included angle...Ch. 5.5 - What does TPI stand for in relation to tapers?Ch. 5.5 - What are the TPI and TPF of a part with end...Ch. 5.5 - What are the corresponding centerline and included...Ch. 5.5 - What is the corresponding centerline angle of a...Ch. 5.5 - What is the limitation of the tool bit taper...Ch. 5.5 - What must be known to use the compound-rest taper...Ch. 5.5 - What taper turning methods allow use of the lathes...Ch. 5.5 - What two steps can be taken to eliminate backlash...Ch. 5.5 - The TPI specified on a print is 0.030". If...Ch. 5.5 - If TPF is 0.42", how much movement should register...Ch. 5.5 - What is the benefit of using the offset tailstock...Ch. 5.5 - What are two ways to reduce uneven pressure on...Ch. 5.5 - Calculate tailstock setover for a 13.5" part with...
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- 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.arrow_forwardProblem 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_forward
- Problem 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_forwardI 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_forward
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