Fixture unit stiffness is defined as the force required for a unit deformation of the fixture unit in normal and tangential directions at the contact position with the workpiece. For example, Figure 1.3 shows the definition of the fixture unit stiffness Ky, in the norma taken into account because of the expense of computation. Figure 1.4 A Basic Assembly Unit of T-Slot-Based Modular Fixture Figure 1.5 Sketch of Fixture Deformations Figure 1.7 Integrated Fixture Design System as to gain insight into the nature of the interaction between fixture components. drilling processes. Figure 2.1 shows the fixture-workpiece model that was used in FEA. Figure 2.1 Fixture-Workpiece Model Table 2.1 Literature Survey of Fixture-workpiece Model Table 2.2 Literature Survey of Fixture Stiffness Table 2.3 Literature Surveys of Contact Parameters 2.3 Summary of Current Research As a result, the current state-of-the art technologies suffer some major limitations that can Figure 3.1 Contact Model of Two Fixture Components friction. Figure3.2 Physical Model of the Contact Conditions Figure 3.3 Sketch of Contact Force on the Contact Surface equations in the three contact conditions (note that {n, t, t} is the local coordinate Figure 3.4 (a) Flow Chart of the Analysis Procedure 1.75x10’ Ib/in, and the tangential contact stiffness, kt = 1.75x10’ Ib/in. Figure 3.5 Contact Problem between Two Beams Subjected to End Loads show the significant effects of contact stiffness on the deformation of the contact beams. Figure 3.7 Comparison of the Deflection of a Contact Beam (at the Position Y=0 in. and Z=10 in.) Having Variable Contact Stiffness with the Corresponding Single Continuous Beam the right beam becomes larger. The results from the FEA validate the contact model and shown in Figure 3.8. Figure 3.8 The FEA Model of a Typical Fixture Unit components (a 500x500x100 mm fixture base and a 100x100x300 mm support), as Table 3.1 Deflection of the Fixture Unit for Different Load Combinations fixtures. Figure 3.9 Typical Deflection Curve of Fixture Units from FEA problems, such as the wear of fixture components, particularly when using modular Figure 3.10 Deflection Curves under Different Fastening Forces from FEA Figure 3.11 Deflection Curves from Previous Experiments (Zhu, 1993) The frictional force acting on the contact surface follows the Coulomb law of friction. Figure 4.3 Levels of Independent Variables Table 4.1 Material Prosperity of Specimens Table 4.1. The contact surface was generated in a turning operation. The experimental setup is comprised of multimeters (HP3478A), the power supply loads. The proximities are calibrated. normal direction. A torque wrench with a capacity of 250 in-Ib is used to measure normal Figure 4.5 Experimental Setup preload bolt and the indenter are used to apply uniform distribution of normal loads in a locks, two riser plates, and the base plate were chosen as a fixed reference frame. The Table 4.2 Applied torque, the resulted normal loads and surface pressure (Surface finish Ra = 3.08; Radius =0.5in) (Surface Finish Ra = 3.08; Radius =0.5in) Figure 4.9 Structure Stiffness and Contact Stiffness versus Normal Loads Figure 4.11 Effects of the Contact Area on the Contact Stiffness Figure 4.12 Roughness Profile Measurement surface finish leads to higher contact stiffness. Figure 4.15 One-Dimensional Model for Normal contact Stiffness position x is shown in Figure 4.16. The longitudinal strain at x is given by With use of a bar in Figure 4.15, a small element of length dx (the limiting case of 5x) at The longitudinal stress at the cross-section at x is o=Ee and, hence, the longitudinal force Table 4.4 Relationship between B and A; When B is Changed from 0.1 to 10 from the comparison of experimental results and theoretical results. Then the results of dynamic tests, as shown in Figure 4.22. is obtained and used in the calculation of natural frequencies, and then compared with the Values Based on Static Test experimental condition, i.e., the same experimental device and preloads, contact stiffness with the previous static measurement results of contact stiffness. Under the same stiffness of these contact surfaces depends on their statistical topographical parameters. given by Eq. 4.24. Figure 4.25 Model of the Fixture Components in Contact specimen. The response was obtained at point M, at the other side of the specimen. Figure 4.27 shows the relationships between tangential contact stiffness and natural Figure 4.27 Tangential Stiffness vs. the First Two Natural Frequencies preloads. The contact stiffness can be determined based on the relationships shown it and numerical results. 1. Preload bolt 2. Upper plate 3. Riser Plate 4. Proximity 5. Base plate 6. Support 7. Specimen 8 Indenter agreement. Figure 4.30 Natural Frequencies of First Two Modes versus Preloads Figure 4.31 Tangential Contact Stiffness under Different Preloads Figure A.2 Mean Values of All Relative Data vs. Normal Loads Table A.3 All Relative Data vs. Normal Loads Table A.6 Displacements (Mean Value) vs. Surface Pressure Figure A.3 Displacements (Mean Value) vs. Surface Pressure Table B.3 All Relative Data vs. Normal Loads Table B.4 Surface Pressure Caused by Normal Loads Table C.4 Surface Pressure Caused by Normal Loads Table C.3 All Relative Data vs. Normal Loads Figure C.2 Mean Values of All Relative Data vs. Normal Loads Table D.2 Relative Measured Data (Unit: Volt) Figure D.1 All Relative Data vs. Normal Loads Table D.3 All Relative Data vs. Normal Loads Figure D.2 Mean Values of All Relative Data vs. Normal Loads
