ComputerAided_Design_Engineering_amp_Manufactur.pdf

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expression, M, D indicate CMM coordinate and CAD coordinate, respectively, and they are M T 1 Mx My � Mz 1 D � � (4.17) where the T 1 matrix of 4 � 4 is considered for the rotation/translation movement between the two coordinate systems. For the rotation movement between the two coordinate systems, the reduced transformation matrix, RT 1 of 3 � 3, is considered. The components are RT 1 ax ay az O�x bx by bz O�y cx cy cz O�z 0 0 0 1 � ax ay az bx by bz cx cy cy (4.18) Once the relationship between the two coordinate systems based on the rough phase alignment has been set up, the CNC code for the inspection can be obtained by multiplication of the T 1 matrix and the CAD coordinate data of measurement points. That is M � T1( D � rN) (4.19) where D is the CAD coordinate, r is the probe radius of the CMM, and N is the unit vector at the target points defined by Equation 4.3. D � rN is used for considering the outward offset points from the measurement target points. The approaching direction of CMM, DM, is also calculated from multiplication of the RT 1 matrix and the normal vector components on the measurement target points. Thus DM � RT1N (4.20) Therefore the rough phase of alignment is performed and the CNC code is generated in a widely accepted machine code format such as DMIS (Dimensional Measuring Interface Specification), 13 and downloaded into CMM. The initial measurement procedure is followed on the curved parts. Fine Alignment Procedure Based on the Iterative Least Squares Technique Although the rough phase alignment is performed using the six points probing around the reference block, the CMM often fails to measure the parts of thin geometry such as edges because of residual misalignment error due to the form error of the reference block, etc. The residual misalignment error can be calculated and compensated for by introducing a second transformation matrix, T 2, based on initial measurement data for the curved surfaces. When the measured data MM of the curved surfaces are converted to the CAD coordinate system, they can be compared with the nominal CAD data, resulting possibly in a slight deviation between them. Thus, the second transformation matrix, T 2, can be introduced to link the Dx Dy D z 1
deviation between the nominal CAD data and the converted measurement data. The measured data �1 can be converted to the nominal CAD coordinate system, by multiplying T1 to the measured data, MM. Thus, the relationship can be formed as, (4.21) The T2 matrix of 4�4 can be determined by the least squares technique, minimizing the sum of �1 squares of distance between the converted measurement data ( T1 MM) and the nominal CAD data (D � rN). The sum, E, is E � S|T1 (4.22) The variational principle can be applied to solve the components of T 2 matrix. A convenient method for the evaluation of T 2 matrix is to use the pseudo-inverse technique for computational efficiency. Therefore, T 2 matrix can be calculated as follows T 2 � (4.23) where MM is the CMM measurement data for the surface, and ( )T indicates the transposed matrix. The calculated T 2 matrix is now used to generate the updated CNC codes downloaded into the CMM, and the second measurement data, MM(2), are obtained. When the generated measurement path still fails to measure the thin section of parts, further iterative procedures can be introduced. Based on the second measurement data MM(2), the second iterative T2(2) matrix can be evaluated in that case. Prior to going to further iterations, ERR, the sum of squares of distance can be used as a criterion. That is, where ERR � sum of squares of distance �1 T1 MM � T2 D�rN �1 MM T2 D�rN 1 T1 ( ) � ( )| 2 for all measurement points � MM( D � rN )T[ ( D�rN) ( D�rN)T] � 1 � � |T 1 ERR £ TOL �1 ( k) MM � ( k) T2 D � rN ( )| (4.24) (4.25) and is the kth iterative measurement data, and is the kth iterative T2 matrix. When the criterion is not met, further iterations can be performed, and finer alignment procedures can be followed. Figure 4.5 shows the flowchart for a typical alignment system using the rough- and fine-phase alignments. The illustrated alignment technique can be applied to practical manufacturing of turbine blades, for ex<strong>amp</strong>le. A turbine blade is modeled into four features such as two chord-length-based cubic spline curves and two very small edge circles of around 0.15 mm radius. After locating on a CMM, the turbine blade is probed around the reference block by the six points based on the rough alignment procedure. The transformation matrix T1 of the rough phase alignment is calculated, and initial measurement procedures are performed on the pressure/suction surfaces. Based on the measurement data, the T2 transformation matrix is calculated using the least squares technique. The sum of squares of distance are calculated as a criterion for further iterative measurement procedures. Figure 4.6 shows a typical distance deviation between the nominal CAD data points and the measured points. It is noteworthy that, in this figure, the sum of squares of distance is greatly reduced at the first iteration, and further iterations are not needed. Figure 4.7 shows a typical measurement path before and after the fine phase alignment; the measurement path is slightly changed so as to measure the thin edges after the fine alignment procedure. 12 MM k ( ) T2 ( k) 2
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COMPUTER-AIDED DESIGN, ENGINEERING,
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Library of Congress Cataloging-in-P
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Editor Cornelius T. Leondes, B.S.,
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Chapter 1 Chapter 2 Chapter 3 Chapt
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the implementation of the IPD syste
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In our IPD system implementations,
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2. Specification of analysis-specif
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FIGURE 1.2 base or the design insta
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FIGURE 1.4 System architecture of t
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of a beam is considered for FEA. Th
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FIGURE 1.7 through the control expe
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2. machining facility (e.g., gang m
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from the FBDS. The user also specif
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Depending on the type of feature to
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TABLE 1.6 Tolerance synthesis is de
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FIGURE 1.12 Display of the NC tool
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component geometric entities and va
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FIGURE 1.14 The system architecture
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TABLE 1.10 User Input for the Toler
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TABLE 1.11 Tolerance Specifications
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7. Z. Young and I. R. Groose. A rul
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FIGURE 2.1 Tool paths generated for
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FIGURE 2.2 sented by instances of f
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TABLE 2.1 A CAD-Generated Hole Conf
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FIGURE 2.6 mounted on the rotary ta
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FIGURE 2.8 fixture for the machinin
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FIGURE 2.10 or best-fit, or the cur
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FIGURE 2.11 Linear approximation of
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FIGURE 2.13 Circular approximation
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FIGURE 2.14(b) Circular approximati
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FIGURE 2.16 Types of biarcs. FIGURE
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FIGURE 2.18 Approximation of scanne
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FIGURE 2.20 A touch trigger probe c
Page 67 and 68: TABLE 2.4 Substitute Elements in CM
Page 69 and 70: FIGURE 2.21 CMM planning requiremen
Page 71 and 72: Product Model Representation for Co
Page 73 and 74: © 2001 by CRC Press LLC TABLE 2.5
Page 75 and 76: TABLE 2.7 Partial Listing of Dimens
Page 77 and 78: 24. Makinouchi, S., Okamoto, M., an
Page 79 and 80: Bijan Shirinzadeh Monash University
Page 81 and 82: FIGURE 3.1 Trends in flexible manuf
Page 83 and 84: FIGURE 3.3 and constrain different
Page 85 and 86: Other Fixturing Techniques There ar
Page 87 and 88: FIGURE 3.6 contact point. The geome
Page 89 and 90: FIGURE 3.8 The vertical support fix
Page 91 and 92: and moments about the contact point
Page 93 and 94: een identified, the normals are use
Page 95 and 96: one of choosing the variables: such
Page 97 and 98: Fixture Module Location An importan
Page 99 and 100: FIGURE 3.15 Illustration of functio
Page 101 and 102: FIGURE 3.18 Minimum separation test
Page 103 and 104: direction) the face, respectively.
Page 105 and 106: FIGURE 3.21 Software structure for
Page 107 and 108: 3.8 Conclusion A reconfigurable fix
Page 109 and 110: Heui Jae Pahk Seoul National Univer
Page 111 and 112: FIGURE 4.1(b) Conceptual framework
Page 113 and 114: 4.3 Measurement Points Sampling and
Page 115 and 116: Surface S2 Measurement Path FIGURE
Page 117: FIGURE 4.4 Rough phase alignment ba
Page 121 and 122: FIGURE 4.6(a) Sum of squares distan
Page 123 and 124: FIGURE 4.7(c) Trailing edge. (c) th
Page 125 and 126: FIGURE 4.8(a) Profile tolerance of
Page 127 and 128: The calculated minimum form error i
Page 129 and 130: FIGURE 4.11(a) A typical mold havin
Page 131 and 132: FIGURE 4.11(d) Inspection results f
Page 133 and 134: FIGURE 4.12(c) Maximum deviation (p
Page 135 and 136: 5.1 Introduction Developments in th
Page 137 and 138: process plan for a part (Figure 5.3
Page 139 and 140: FIGURE 5.5 leading to the developme
Page 141 and 142: the previously stored process plan
Page 143 and 144: FIGURE 5.7 Techniques of defining a
Page 145 and 146: Feature Recognition and Extraction
Page 147 and 148: in relation to another feature (e.g
Page 149 and 150: FIGURE 5.9 Framework for building a
Page 151 and 152: FIGURE 5.10 Process plan content.
Page 153 and 154: FIGURE 5.12 Schematic sketch of the
Page 155 and 156: Several techniques of defining a fe
Page 157 and 158: TABLE 5.1 Data Structure for Repres
Page 159 and 160: FIGURE 5.16 Classification of the t
Page 161 and 162: system to ensure that the part bein
Page 163 and 164: FIGURE 5.19 Graphical model of the
Page 165 and 166: TABLE 5.4 Data Structure for Repres
Page 167 and 168: FIGURE 5.20 Mapping between machini
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algorithms. (Some details of the pr
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FIGURE 5.24 An example rotational p
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FIGURE 5.26 Down_face-turn-up_face
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FIGURE 5.27 Procedure for machine t
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FIGURE 5.28 Determining the number
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DL is needed to be set only if the
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FIGURE 5.31 Operation sequencing co
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Cutting Tool Selection Selection of
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1. A tool is searched for in the da
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FIGURE 5.32 Inputs to optimization
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When these values are substituted,
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Usually, maximum and minimum speed
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FIGURE 5.33 Solution methodology.
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TABLE 5.6 Process Plan Internal Rep
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In a strict theoretical perspective
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18. Domazet, D. S. and Lu, S. C. Y,
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63. Prasad, A. V. S. R. K., Rao, P.
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CAD systems. The sample consists of
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learn to master the new system. An
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Although researchers appear to agre
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Link and Zmud28 found that organic
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Informal Training Informal CAD trai
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informal training programs, felt th
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6. C. A. Beatty, Tall Tales and Rea
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A.Y.C. Nee National University of S
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FIGURE 7.1 Planning, design, and ma
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A metal stamping can have the follo
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FIGURE 7.3 Strips used to notch out
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A Skeletal Approach for the Recogni
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These findings can be used to devel
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Semi-Direct Piloting In cases where
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a larger value, the die operations
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FIGURE 7.9 Symbolic relationship be
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FIGURE 7.11 The shape of the envelo
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TABLE 7.1 Schema for the Generation
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strong reasons to support a move to
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FIGURE 7.16 3-D CAD model of a part
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References Cheok, B.T. et al. (1994
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include the once forbidden generati
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A temporal matrix (T-Matrix) is pro
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FIGURE 8.1 A basic process. (From R
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FIGURE 8.4(a) Generate a new IG usi
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Note if the pair of nodes are both
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TABLE 8.1 Summary of the Rules Cond
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The correctness of these rules is e
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needs to show that after each full
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ule is violated, a warning should b
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Π1 Π3 Π4 FIGURE 8.8(a) After add
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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A ik � ‘U’ and is in a cycle
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FIGURE 8.12(a) Add [p2 t7 p7 t8 p4]
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FIGURE 8.12(c) Add a token to p8 vi
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FIGURE 8.12(e) Add [p8 t9 p14 t10 p
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FIGURE 8.13 An example of rule TT.0
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FIGURE 8.14 A GPN model of a machin
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FIGURE 8.15(b) The first exclusive
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FIGURE 8.15(d) The last exclusive T
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FIGURE 8.15(f) After entering the a
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FIGURE 8.15(h) Completion of Compon
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FIGURE 8.15(j) Two PP-generations:
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FIGURE 8.15(l) The last exclusive T
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t1 t5 p1 p5 t6 (a) t2 t3 t4 2 2 p2
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FIGURE 8.17 An example of partial f
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Theorem 10: If pi → pk in a synth
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Note that control transitions are o
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t j than the lower at , it indicate
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• Programming logic and VLSI arra
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7. Chao, D. Y. and D. T. Wang, Appl
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53. Villaroel, J. L., J. Martinez,
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q u : the numerator of the least ra
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geometric modeling, engineering ana
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In dimension driven or parametric d
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FIGURE 9.3 configuration of bodies
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FIGURE 9.6 FIGURE 9.7 Geometric Int
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FIGURE 9.8 Intersection of degrees
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will introduce a way to propagate p
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Completeness of Dimensions Complete
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FIGURE 9.12 3-D constraints. © 200
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The distance constraint from pt �
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therefore: Now merge the lists and
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Quantity analysis methods have the
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y a revolute joint. By selecting al
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