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PART I GEOMETRIC TOLERANCING ISSUES |
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1 | (20) |
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Chapter 1 Current and Future Issues in Tolerancing: the GD&T French Research Group (TRG) Contribution |
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3 | (18) |
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3 | (1) |
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1.2 Presentation of the Tolerancing Research Group: objectives and function |
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4 | (1) |
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1.3 Synthesis of the approach and contributions of the group |
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5 | (8) |
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1.3.1 Languages for geometric specification |
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8 | (1) |
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1.3.2 Dimension chains in 3D |
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9 | (1) |
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10 | (1) |
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1.3.4 Manufacturing dimensioning and tolerancing |
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11 | (1) |
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1.3.5 Uncertainties and metrology |
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12 | (1) |
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1.4 Research perspectives |
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13 | (2) |
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1.5 Media examples: "centering" and "connecting rod-crank" |
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15 | (2) |
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17 | (2) |
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19 | (2) |
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PART II GEOMETRIC TOLERANCING LANGUAGES |
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21 | (102) |
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Chapter 2 Language of Tolerancing: GeoSpelling |
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23 | (32) |
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23 | (1) |
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2.2 Concept of the GeoSpelling language |
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24 | (2) |
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26 | (3) |
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26 | (3) |
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29 | (1) |
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29 | (1) |
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29 | (9) |
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2.4.1 Intrinsic characteristic |
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29 | (1) |
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2.4.2 Situation characteristic |
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30 | (3) |
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2.4.3 Situation characteristic between ideal features |
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33 | (3) |
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2.4.4 Situation characteristic between limited and ideal features |
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36 | (1) |
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2.4.5 Situation characteristic between non-ideal and ideal features |
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36 | (1) |
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2.4.6 Situation characteristic between non-ideal features |
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37 | (1) |
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38 | (5) |
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2.5.1 Operations to identify the geometric features |
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39 | (3) |
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2.5.2 Evaluation operation |
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42 | (1) |
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43 | (1) |
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2.7 Specifications on assemblies - quantifiers |
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44 | (1) |
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2.8 Applications to part specification |
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45 | (3) |
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2.9 Applications to product specifications |
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48 | (3) |
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51 | (1) |
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52 | (3) |
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Chapter 3 Product Model for Tolerancing |
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55 | (32) |
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55 | (1) |
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3.2 Objectives and stakes |
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56 | (2) |
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3.2.1 Cover the design cycle of the product |
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56 | (1) |
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3.2.2 Propose an environment of collaborative work |
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57 | (1) |
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3.2.3 Ensure the traceability of geometric specifications |
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57 | (1) |
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3.3 Proposal for a product model |
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58 | (10) |
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58 | (1) |
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3.3.2 General description of the IPPOP product model |
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58 | (1) |
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3.3.3 Basic entities definition of the product model |
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59 | (6) |
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3.3.4 Description of the connection links between basic entities |
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65 | (2) |
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3.3.5 Description of the decomposition and aggregation of basic entities |
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67 | (1) |
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3.3.6 Correspondence between tolerancing data and product model data |
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68 | (1) |
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3.4 Benefits of the IPPOP product model |
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68 | (5) |
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3.4.1 Description of the transfer principle |
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69 | (1) |
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3.4.2 Formalization of the geometric condition transfer activity |
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70 | (3) |
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3.4.3 Traceability of specifications |
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73 | (1) |
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3.5 Application on the centering device |
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73 | (11) |
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3.5.1 Description of the case studied |
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73 | (1) |
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3.5.2 Functional analysis of the centering device |
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74 | (2) |
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3.5.3 Transfer in preliminary design (stage 1) |
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76 | (1) |
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3.5.4 Transfers in embodiment design (stages 2 and 3) |
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77 | (3) |
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3.5.5 Transfer in detailed design (stage 4) |
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80 | (2) |
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3.5.6 Traceability of specifications of axis 3 |
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82 | (2) |
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84 | (1) |
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84 | (3) |
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Chapter 4 Representation of Mechanical Assemblies and Specifications by Graphs |
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87 | (24) |
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87 | (2) |
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4.2 Components and joints |
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89 | (8) |
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4.2.1 Components, surfaces and datum features |
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90 | (1) |
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91 | (1) |
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92 | (3) |
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95 | (2) |
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4.3 The requirements, technical conditions and specifications |
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97 | (3) |
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97 | (2) |
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4.3.2 Technical conditions |
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99 | (1) |
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99 | (1) |
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4.4 Manufacturing set-ups |
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100 | (3) |
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4.5 Displacements between situation features and associated loops |
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103 | (4) |
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4.5.1 Relative displacements |
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103 | (1) |
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104 | (2) |
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4.5.3 Loops with or without a coordinate system on the components |
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106 | (1) |
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107 | (2) |
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4.6.1 The key deviations, surfaces, joints and components |
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107 | (1) |
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4.6.2 The loops and key sub-graphs |
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107 | (2) |
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109 | (1) |
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110 | (1) |
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Chapter 5 Correspondence between Data Handled by the Graphs and Data Product |
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111 | (12) |
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111 | (1) |
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5.2 Correspondence between tolerancing graphs and the product data |
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112 | (6) |
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112 | (2) |
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5.2.2 Graph of the elementary joints |
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114 | (2) |
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5.2.3 Closings of influential loops and traceability of specifications |
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116 | (2) |
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5.3 Correspondence between manufacturing set-ups and the data product |
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118 | (3) |
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5.3.1 Manufacturing graph of body 1 |
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118 | (2) |
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5.3.2 Manufacturing set-up 10 of the body |
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120 | (1) |
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121 | (2) |
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PART III 3D TOLERANCE STACK-UP |
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123 | (84) |
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Chapter 6 Writing the 3D Chain of Dimensions (Tolerance Stack-Up) in Symbolic Expressions |
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125 | (26) |
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125 | (1) |
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6.2 A reminder of the establishment of the unidirectional chain of dimensions by the δ1 method |
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126 | (9) |
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6.2.1 Definition and properties |
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126 | (4) |
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130 | (2) |
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6.2.3 A reminder of the δl method |
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132 | (3) |
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6.3 Establishment in writing of a chain of dimensions in 3D by the method of indeterminates in the case of a rigid body |
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135 | (7) |
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135 | (1) |
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6.3.2 Model of the indeterminates |
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136 | (2) |
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6.3.3 Laws of geometric behavior of a mechanism with gaps and defects |
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138 | (2) |
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140 | (2) |
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6.4 Consideration of the contact between parts in the mechanisms |
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142 | (2) |
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142 | (1) |
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6.4.2 Calculation of the distance between a point and a surface |
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143 | (1) |
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6.4.3 Utilization of the distance function expressed in the symbolic calculation |
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144 | (1) |
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6.5 Mechanisms composed of flexible parts, joints without gap (or imposed contact) and imposed effort |
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144 | (3) |
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144 | (1) |
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6.5.2 Utilization of a coordinate system on the parts |
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144 | (1) |
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6.5.3 Modeling of form defects and deformations |
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145 | (1) |
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6.5.4 Integration of flexibility of the parts |
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146 | (1) |
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6.5.5 The principle of writing an equation(s) for a mechanism composed of a single flexible part |
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146 | (1) |
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147 | (1) |
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148 | (3) |
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Chapter 7 Tolerance Analysis and Synthesis, Method of Domains |
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151 | (32) |
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151 | (1) |
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7.2 Deviation torsor and joint torsor |
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152 | (3) |
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7.2.1 Cartesian frame linked to a surface |
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152 | (1) |
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153 | (1) |
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7.2.3 Relative deviation torsor and absolute deviation torsor |
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154 | (1) |
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7.2.4 Joint torsor, kinematic torsor and clearance torsor |
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155 | (1) |
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155 | (3) |
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7.3.1 Mechanism without clearance or deviation |
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155 | (1) |
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7.3.2 Taking into account the clearances and deviations |
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156 | (2) |
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7.4 Deviation and clearance domains |
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158 | (4) |
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158 | (3) |
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161 | (1) |
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7.5 Representation and properties of the domains |
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162 | (6) |
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7.5.1 Change of Cartesian frame |
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162 | (1) |
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7.5.2 Symmetry with regard to the origin |
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163 | (1) |
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7.5.3 Representation by polytopes |
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164 | (1) |
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7.5.4 Stacking of tolerances and sum of Minkowski |
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165 | (2) |
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7.5.5 Resulting clearance domain |
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167 | (1) |
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7.5.6 Zone corresponding to a domain |
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167 | (1) |
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7.5.7 Cases of axisymmetric systems |
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167 | (1) |
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7.6 Application to the analysis of simple chains |
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168 | (5) |
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7.6.1 Condition of assembly for one loop |
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168 | (1) |
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7.6.2 Application to a chain of dimension taking angular defects into account |
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169 | (2) |
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7.6.3 Application to a connecting rod-crank system |
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171 | (1) |
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7.6.4 Application to the synthesis of tolerances |
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171 | (1) |
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7.6.5 Condition of assembly, virtual state and domain |
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172 | (1) |
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7.7 Case of assemblies with parallel joints |
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173 | (3) |
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7.7.1 Notion of residual clearance domain and inaccuracy domain |
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173 | (1) |
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7.7.2 Condition of assembly for joints in parallel |
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174 | (2) |
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7.8 Taking elastic displacements into account |
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176 | (4) |
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7.8.1 Elastic deviation and joint torsor definition |
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176 | (1) |
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7.8.2 Elastic deviation torsors |
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176 | (1) |
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7.8.3 Elastic joint torsors |
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176 | (1) |
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7.8.4 Use rate and elastic domains |
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177 | (1) |
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7.8.5 Elastic clearance domain |
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177 | (1) |
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7.8.6 Elastic deviation domains |
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178 | (1) |
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7.8.7 Elastic domain duality |
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178 | (1) |
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7.8.8 Application to a simple assembly |
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178 | (1) |
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7.8.9 Assembly without clearances |
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179 | (1) |
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7.8.10 Assembly with clearances in joints |
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179 | (1) |
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180 | (1) |
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180 | (3) |
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Chapter 8 Parametric Specification of Mechanisms |
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183 | (24) |
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183 | (1) |
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8.2 Problem of the parametric specification of complete and consistent dimensioning |
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184 | (4) |
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8.2.1 Model of dimensioning |
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185 | (1) |
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185 | (2) |
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8.2.3 Analysis of the coherence and completeness of dimensioning |
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187 | (1) |
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8.3 Generation of parametric tolerancing by the differential variation of the specification of dimensioning |
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188 | (4) |
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8.3.1 Generation of implictit equations of a parametric tolerancing |
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188 | (1) |
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8.3.2 Case study (continuation) |
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189 | (3) |
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8.3.3 Analysis and resolution of compatibility relations |
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192 | (1) |
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8.4 Problem of the specification transfer |
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192 | (1) |
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8.5 Expression of parametric tolerancing |
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193 | (5) |
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8.5.1 Relation between the variation intervals of specification parameters |
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194 | (2) |
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8.5.2 Interchangeability and "clearance effect" |
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196 | (2) |
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198 | (6) |
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8.6.1 Representation of parts |
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199 | (1) |
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8.6.2 Assembly representation |
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200 | (1) |
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8.6.3 Generation of the equation system associated with the mechanism |
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201 | (1) |
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8.6.4 Generation of compatibility relations |
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201 | (1) |
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8.6.5 "Clerance effect" calculation |
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202 | (2) |
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204 | (1) |
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205 | (2) |
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PART IV METHODS AND TOOLS |
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207 | (68) |
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Chapter 9 CLIC: A Method for Geometrical Specification of Products |
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209 | (32) |
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209 | (1) |
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9.2 Input of a tolerancing problem |
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210 | (2) |
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9.2.1 Definition of nominal model |
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210 | (1) |
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9.2.2 External requirements |
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211 | (1) |
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212 | (5) |
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9.3.1 Setting up of parts |
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212 | (1) |
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213 | (2) |
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9.3.3 Selection of positioning surfaces |
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215 | (1) |
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9.3.4 Virtual part assembly |
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216 | (1) |
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9.4 Tolerancing of positioning surfaces |
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217 | (4) |
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9.4.1 Generation of positioning requirements |
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217 | (1) |
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9.4.2 Generation of positioning tolerancing |
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218 | (3) |
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9.5 Generation of functional requirements |
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221 | (1) |
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9.5.1 Generation of proximity requirements |
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221 | (1) |
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9.6 Specification synthesis |
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222 | (5) |
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222 | (1) |
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222 | (1) |
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9.6.3 Decomposition of complex requirements |
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223 | (2) |
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9.6.4 Tolerancing of the support |
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225 | (2) |
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9.7 Tolerance chain result |
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227 | (7) |
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9.7.1 Analysis lines method |
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227 | (2) |
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229 | (3) |
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232 | (1) |
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9.7.4 Representation in Excel ranges |
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232 | (2) |
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234 | (4) |
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9.8.1 Variation of nominal models |
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234 | (1) |
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9.8.2 Quality optimization |
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234 | (1) |
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9.8.3 Effective method for maximizing tolerances |
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235 | (3) |
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238 | (1) |
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238 | (3) |
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Chapter 10 MECAmaster: a Tool for Assembly Simulation from Early Design, Industrial Approach |
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241 | (34) |
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241 | (1) |
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10.2 General principle, 3D tolerance calculation |
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242 | (3) |
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10.2.1 Kinematic definition of the contact |
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242 | (1) |
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10.2.2 Calculation principle |
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243 | (1) |
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10.2.3 "3D chains of dimension" results |
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244 | (1) |
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10.2.4 Tolerance definition |
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245 | (1) |
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10.3 Application to assembly calculation |
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245 | (18) |
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10.3.1 Preamble: definition of surfaces playing a part in the model |
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246 | (2) |
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248 | (3) |
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10.3.3 Hyperstatism calculation and analysis |
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251 | (2) |
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10.3.4 Possible assembly configurations |
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253 | (2) |
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10.3.5 Quantification of functional conditions, choice of system architecture |
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255 | (8) |
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10.4 From model to parts tolerancing |
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263 | (5) |
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10.4.1 Choice of reference system |
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263 | (1) |
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264 | (1) |
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10.4.3 Identification of specifications: example |
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265 | (2) |
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10.4.4 Identification of numerical values: example |
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267 | (1) |
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10.5 Statistical tolerancing |
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268 | (1) |
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269 | (2) |
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10.6.1 Aeronautic industry: structure |
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269 | (1) |
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10.6.2 Automotive industry: body structure assembly |
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270 | (1) |
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10.6.3 Automotive industry: mechanical assembly---engine group |
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271 | (1) |
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271 | (1) |
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272 | (3) |
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PART V MANUFACTURING TOLERANCING |
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275 | (66) |
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Chapter 11 Geometric Manufacturing Simulation |
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277 | (28) |
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277 | (2) |
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11.2 Modeling of manufacturing set-up |
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279 | (9) |
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11.2.1 Analysis of a set-up |
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279 | (2) |
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11.2.2 Modeling of a set-up |
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281 | (2) |
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283 | (3) |
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11.2.4 Representation of a process plan |
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286 | (2) |
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11.3 Approaches to geometric manufacturing simulation |
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288 | (15) |
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11.3.1 Formal approach to geometric manufacturing simulation |
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288 | (4) |
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11.3.2 Geometric manufacturing simulation with the CAM system |
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292 | (9) |
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11.3.3 Comparison of approaches |
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301 | (2) |
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303 | (1) |
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303 | (2) |
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Chapter 12 3D Analysis and Synthesis of Manufacturing Tolerances |
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305 | (36) |
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305 | (1) |
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12.2 Manufacturing transfer, analysis and synthesis in 1D |
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306 | (8) |
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12.3 3D manufacturing simulation model (MMP) |
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314 | (3) |
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314 | (1) |
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315 | (2) |
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12.4 From the manufacturing process to the MMP |
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317 | (6) |
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12.4.1 Determination of the positioning deviation |
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319 | (4) |
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12.4.2 Determination of machining deviations |
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323 | (1) |
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12.5 3D analysis of the functional tolerances |
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323 | (6) |
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12.5.1 Definition of the virtual gauge and assembly properties |
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323 | (5) |
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12.5.2 Numerical analysis method in the worst case scenario |
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328 | (1) |
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12.6 3D synthesis of manufacturing tolerances |
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329 | (9) |
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12.6.1 Functional tolerance transfer by splitting the inequation Gap GP≥0 |
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330 | (2) |
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12.6.2 Determination of the surfaces concerned |
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332 | (1) |
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12.6.3 Proposition of a group of manufacturing tolerances |
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333 | (2) |
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12.6.4 Verification of the validity of tolerances and values chosen |
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335 | (3) |
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338 | (1) |
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339 | (2) |
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PART VI UNCERTAINTIES AND METROLOGY |
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341 | (34) |
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Chapter 13 Uncertainties in Tolerance Analysis and Specification Checking |
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343 | (32) |
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343 | (1) |
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13.2 Proposal for a statistical model of real surfaces |
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343 | (11) |
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13.2.1 Nominal model and vector modeling |
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343 | (2) |
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13.2.2 Limits and impacts on tolerance analysis and metrology |
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345 | (3) |
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13.2.3 Definition: signature |
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348 | (2) |
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13.2.4 Proposal for a limited model and modeling by random vector |
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350 | (4) |
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13.3 Applications in metrology |
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354 | (13) |
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13.3.1 Independent variables and common components |
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354 | (4) |
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13.3.2 Application on a 2D line |
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358 | (3) |
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13.3.3 Extension to ordinary surfaces |
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361 | (1) |
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13.3.4 2D point/line distance |
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362 | (2) |
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13.3.5 Extension to three fundamental distances |
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364 | (1) |
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13.3.6 Effect of the planning process of measurement |
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364 | (3) |
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13.4 Application to tolerance analysis |
|
|
367 | (6) |
|
13.4.1 Review of the principle of modeling |
|
|
369 | (1) |
|
13.4.2 Effect of the reference surface extent |
|
|
370 | (1) |
|
13.4.3 Effect of surface spacing |
|
|
371 | (1) |
|
13.4.4 Effect of shape defect on reference surfaces |
|
|
371 | (2) |
|
13.4.5 Effect of the choice of a reference system |
|
|
373 | (1) |
|
|
|
373 | (1) |
|
|
|
374 | (1) |
| List of Authors |
|
375 | (2) |
| Index |
|
377 | |
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