Optimization of Nano-Topography Distribution by Compensation Grinding

Optical surfaces are required to have high form accuracy and smoothness. The form accuracy must be below 50 nm. Form accuracy is currently on the order of several tens of nanometers or less; however, further improvement is required. To improve form accuracy, compensation grinding is performed based on form measurement results. However, when the form error is small, a small periodical waviness occurs on the ground surface, which is known as nano-topography. This waviness cannot be compensated for using conventional compensation methods because the nano-topography distributions are not reproducible. A previous study showed that grinding conditions affect the spatial frequency of nano-topography. Therefore, in this study, optimum grinding conditions are estimated from the view point of nano-topography distributions, and the grinding conditions are compensated to optimize these distributions.

Optimization of flexible fixture layout to improve form quality using parametric finite element model and mixed discrete-integer genetic algorithm

Dimensional and form accuracy of the workpiece can be improved by effective fixture layout design which shows minimum deformation of the workpiece during machining. Flexible fixtures are inevitable in industries owing to high product variety and shortened production time. Hence, an integrated approach is presented to select the optimum position of locating and clamping elements in a flexible fixture that provide good form accuracy. In this approach, a Parametric Finite Element Model (PFEM) is developed using the information about the workpiece, fixture plan and machining condition. PFEM is used to predict the elastic deformation of the workpiece for the fixture layouts generated using a discrete Genetic Algorithm (GA) with mixed integer-discrete variables. The objective is to minimize the maximum deformation of the workpiece by optimizing fixture layouts. The stability of the workpiece and fixture system is ensured by implementing non-negative reaction force constraints in GA. The proposed approach is applied for a prismatic workpiece to carry out pocket milling operation. The significance of this work is to express the flexibility and computational effectiveness of PFEM to accommodate variation in the workpiece, machining condition and fixture plan while designing flexible fixtures. Further, it highlights a significant reduction in search space due to the use of discrete GA and stability constraint as it takes less objective function calculations. An experimental analysis is performed to study the effectiveness of the proposed approach. Therefore, the proposed approach provides a viable solution to the optimization problem in flexible fixtures.

Diamond Fly Cutting Applied to Improve Curved Surface Machining by In-Process Measurement and Control on an Ordinary Milling Machine

To improve the accuracy of the machined surface produced by an ordinary milling machine, a system called workpiece-referred form accuracy control (WORFAC) was developed and confirmed in diamond turning. However, non-rotational symmetric surface structures, such as V-grooves, pyramid structures, F-theta lenses, and other free form surface cannot be machined by diamond turning. We proposed to improve the form accuracy of a machined surface produced by an ordinary milling machine by diamond fly cutting using controlled cutting with reference surface (CCRS), an in-process measurement and control method. Fly cutting is usually used to manufacture ultra-precision microstructures with nanometric surface roughness and submicrometric form accuracy, without the need for subsequent polishing. Nevertheless, a high level of accuracy has only recently been achieved on ultra-precision milling machines. In this study, we verified the effectiveness of fly cutting with CCRS on an ordinary milling machine. CCRS improves machined surface accuracy by controlling the relative displacement between the tool and workpiece. Diamond fly cutting using CCRS was demonstrated to reduce the table motion error on an ordinary milling machine. The experiments of curved surface machining by uncontrolled machining and control machining were conducted, and the effectiveness of improving the circular are machining accuracy of the general-purpose milling machine was confirmed.

Improvement of the Form Accuracy Ground by a Slender Wheel in Internal Grinding

In the case of internal grinding of a deep hole, the inner surface of the hole was ground by a slender grinding wheel that has a high aspect ratio. A slender grinding wheel is bent by the normal grinding force during the grinding process. Therefore, the form accuracy of the ground workpiece is decreased especially when the aspect ratio of a wheel is high. In our previous study, it was confirmed that the biggest factor that generated the form error of the workpiece was the elastic deformation owning to the normal grinding force. To reduce the form error of the ground workpiece, it is effective to expand the spark-out duration. However, the expansion of the spark-out duration leads to the low productivity. In this study, the form of the grinding wheel was modified by a diamond dresser to improve the form accuracy of the workpiece without expanding the spark-out duration. The modified form of a wheel was determined to compensate the form error of the workpiece generated by the elastic deformation of the grinding wheel. Thorough several grinding experiment, it was confirmed that the form accuracy of the ground workpiece was successfully improved by modifying the form of a slender grinding wheel without expanding the spark-out duration.

Measurement and Compensation of Tool Contour Error Using White Light Interferometry for Ultra-Precision Diamond Turning of Freeform Surfaces

In ultra-precision diamond turning of freeform optics, it is necessary to obtain submicron-level form accuracy with high efficiency. In this study, we proposed a new method for the quick measurement and compensation of tool contour errors to improve the form accuracy of the workpiece. In this method, the nanometer-scale contour error of a diamond tool is quickly and precisely measured using a white light interferometer and then compensated for, before machining. Results showed that the contour of a diamond tool was measured with an error less than 0.05 μm peak-to-valley (P-V) and the feasibility of error compensation was verified through cutting experiments to create a paraboloid mirror and a microlens array. The form error decreased to 0.2 μm P-V regardless of the contour error of the diamond tools when cutting the paraboloid mirror, and that of the microlens array was reduced to 0.15 μm P-V during a single machining step.

Modeling and Simulation of Vibrations of Non-Homogeneous Annular Plate of Quadratic Thickness Resting on Elastic Foundation

Mathematical modeling is presented to analyze natural frequencies of vibrations of an isotropic annular plate of quadratic varying thickness resting on Winkler type elastic foundation where numerical simulation is carried out using quintic spline technique for three different combinations of edge conditions. Effect of elastic foundation, together with nonhomogeneity variation, on the natural frequencies of vibration is illustrated for variety of thickness variation for the first three modes. To compare parametric effect on a specific plate, transverse displacements are presented in normalized form. Accuracy of the results and validity of numerical method is demonstrated by comparing the existing results in the literature.