Variability in digital integrated circuits makes timing verification an extremely challenging task. In this paper, a canonical first-order delay model that takes into account both correlated and independent randomness is proposed. A novel linear-time block-based statistical timing algorithm is employed to propagate timing quantities like arrival times and required arrival times through the timing graph in this canonical form. At the end of the statistical timing, the sensitivity of all timing quantities to each of the sources of variation is available. Excessive sensitivities can then be targeted by manual or automatic optimization methods to improve the robustness of the design. This paper also reports the first incremental statistical timer in the literature, which is suitable for use in the inner loop of physical synthesis or other optimization programs. The third novel contribution of this paper is the computation of local and global criticality probabilities. For a very small cost in computer time, the probability of each edge or node of the timing graph being critical is computed. Numerical results are presented on industrial application-specified integrated circuit (ASIC) chips with over two million logic gates, and statistical timing results are compared to exhaustive corner analysis on a chip design whose hardware showed early mode timing violations.

This research effort is focused on improving the efficiency of CNC machining by automatic computer selection of feedrate for 3-axis sculptured surface machining. A feedrate process planner for complex sculptured end milling cuts is developed from mechanistic and geometric end milling models. The selection program uses tool deflection, surface finish, tool failure and machine power to set constraints on the cutting force and the feed-per-tooth for rough, semi-finish, and finish passes. A NC part program is processed one tool move at a time by the planner. For each tool move a geometric model calculates the cut geometry, and an inverse mechanistic model uses this information along with the constraint force to calculate a desired feedrate. The feedrate is written into the part program resulting in a file that contains a feedrate for each tool move. Experimental results for a sculptured surface show the accuracy of the algorithms in maintaining a desired force.

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The purpose of this research is to determine feasibility and develop software tools for automatically generating adaptive feedrates for use in five-axis CNC end milling. The complicated part geometries often involved with five-axis milling, combined with the rotational degrees of freedom of the machines, make it difficult to manually estimate acceptable feedrates without being overly conservative. Our approach for automatic feedrate generation is to use a computer simulation of the milling process. This software estimates the feeds required to maintain a desired peak cutting force on a per-tool-move basis, and consists of three distinct portions: a discrete mechanistic model, a discrete geometric model, and a model of the specific CNC machine on which the part is to be cut. The mechanistic model estimates cutting forces as a function of cut geometry, cutter-tostock relative velocity, and material constants. Used in an inverse manner, the mechanistic model may be used to estimate the feedrates necessary to maintain a constant peak cutting force. This force value may be selected to prevent cutter breakage, maintain a desired part tolerance, or to meet some other criteria (e.g. machine constraints). The results of this research have shown that it is possible to automatically generate adaptive feeds that maintain a desired force level using these combined models. INTRODUCTIONThe focus of this research is adaptive feedrate selection for five-axis contour milling of complex surfaces. The use of adaptive feedrates can reduce the machining time necessary to cut a given part, improve part tolerance, and improve the overall process reliability, as the feeds continually adjust with the changing cutting conditions. The complex surface geometries involved in contour milling, combined with the often unpredictable kinematics and controller behavior of five-axis mills, make it difficult to manually estimate acceptable feedrate values. The complexity of the problem offers little hope for efficient manual optimization. In the interest of protecting the machine and the part, manually estimated feeds are often overly conservative, based on perceived worst-case conditions which may occur very infrequently during the milling process.Through computer simulation of the milling process it is possible to generate adaptive feeds which vary on a per tool-move basis with the changing cutting conditions, and are near optimal based on a desired force constraint. This can greatly reduce the machining time, reduce the chance for cutter breakage, and produce more predictable results. Additionally it simplifies and expedites the feed selection process.The approach for force-based feedrate selection presented in this paper does not rely on a single model. Instead an integrated approach is used, combining three separate discrete models. These models represent the three primary contributors to the force-feedrate relation, and are referred to in this research as the mechanistic model, the geometric model, and the machine model.

This research effort is focused on improving the efficiency of CNC machining by automatic computer selection of feedrate for 3-axis sculptured surface machining. A feedrate process planner for complex sculptured end milling cuts is described and the geometric model of ball end milling is developed in detail. For each tool move, the geometric model calculates the cut geometry, and a mechanistic model is used along with a maximum allowable cutting force to determine a desired feedrate. The results are written into the part program resulting in a file with optimized feedrates. Experimental tests on a sculptured surface demonstrate the robustness and efficiency of the algorithms in maintaining a desired force.