A new analytical method of chatter stability prediction in milling is presented. A general formulation for the dynamic milling system is developed by modeling the cutter and workpiece as multi-degree-of-freedom structures. The dynamic interaction between the milling cutter and workpiece is modeled considering the varying dynamics in the axial direction. The dynamic milling forces are governed by a system of periodic differential equations with delay whose stability analysis leads to an analytical relation for chatter stability limit in milling. The model can be used to determine the chatter free axial and radial depth of cuts without resorting to time domain simulations.

Analytical Prediction of Chatter Stability in Milling-part I : General Formulation

Improving Productivity and Part Quality in Milling of Titanium Based Impellers by Chatter Suppression and Force Control

An optimized positioning procedure for flank milling ruled surfaces with cylindrical cutter is described in the paper. The tool axis trajectory surface is a ruled surface, which is generated by moving the tool axis. The proposition that the envelope surface of cylindrical cutter is the offset surface of tool axis trajectory surface is proved using kinematics approach. It is a complement of Bedi's [Bedi S, Mann S, Menzel C. Flank milling with flat end cutter. Comput Aided Des 2003; 35:293-300] analysis about the envelope surface of cylindrical cutter. Subsequently, we get another proposition that the deviation at extremum point between the designed surface and the envelope surface of cylindrical cutter is equal to that between the offset surface of designed surface and the tool axis trajectory surface. Based on this proposition, we propose three points offset (TPO) strategy to approximate the offset surface. In order to reduce errors further, a simple least square approximation scheme is established to make the tool axis trajectory surface fit the offset surface of designed surface as much as possible. By solving the linear system of equations, the tool axis trajectory surface is deformed. Simultaneously, the corresponding envelope surface is deformed to approximate the designed surface better. Two examples are given to verify the effectiveness of the developed 5-axis flank milling technique.

Improved positioning of cylindrical cutter for flank milling ruled surfaces

A probabilistic methodology to quantify the impact of geometric variability on compressor aerodynamic performance is presented. High-fidelity probabilistic models of geometric variability are derived using a Principal-Component-Analysis (PCA) of blade surface measurements. This probabilistic blade geometry model is then combined with a compressible, viscous blade-passage analysis to estimate the impact on the passage loss and turning using a Monte Carlo simulation. Finally, a mean-line multi-stage compressor model, with probabilistic loss and turning models from the blade-passage analysis, is developed to quantify the impact of the blade variability on overall compressor efficiency and pressure ratio. The methodology is applied to a flank-milled Integrally-Bladed Rotor (IBR). Results demonstrate that overall compressor efficiency can be reduced by approximately 1% due to blade-passage effects arising from representative manufacturing variability.Copyright © 2003 by ASME

Impact of Geometric Variability on Axial Compressor Performance

A new method for 5-axis flank computer numerically controlled (CNC) machining is proposed. A set of tappered ball-end-mill tools (aka conical milling tools) is given as the input and the flank milling paths within user-defined tolerance are returned. Thespace of lines that admit tangential motion of an associated truncated cone along a general, doubly curved, free-form surface is explored. These lines serve as discrete positions of conical axes in 3D space. Spline surface fitting is used to generate a ruled surface that represents a single continuous sweep of a rigid conical milling tool. An optimization-based approach is then applied to globally minimize the error between the design surface and the conical envelope. The milling simulations are validated with physical experiments on two benchmark industrial datasets, reducing significantly the execution times while preserving or even reducing the milling error when compared to the state-of-the-art industrial software.

Highly accurate 5-axis flank CNC machining with conical tools

It is generally conceived that a blade surface is flank millable if it can be closely approximated by a ruled surface ; otherwise the slow machining process of point milling has to be employed. However, we have now demonstrated that the ruled surface criterion for flank milling is neither necessary nor sufficient. Furthermore, many complex arbitrary surfaces typical of our blades in fans, axial compressors, and centrifugal impellers in aviation gas turbines are actually closely flank millable and can be rendered exactly flank millable with one or more passes per surface often without sacrificing, indeed usually with gain, in performance.

Arbitrary Surface Flank Milling of Fan, Compressor, and Impeller Blades

It is generally conceived that a blade surface is flank millable if it can be closely approximated by a ruled surface; otherwise the slow machining process of point milling has to be employed. However, we have now demonstrated that the ruled surface criterion for flank milling is neither necessary nor sufficient Furthermore, many complex arbitrary surfaces typical of our blades in fans, axial compressors, and centrifugal impellers in aviation gas turbines are actually closely flank millable and can be rendered exactly flank millable with one or more passes per surface often without sacrificing, indeed sometimes with gain, in performance.Copyright © 1994 by ASME

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C. Y. Wu

Papers

Arbitrary Surface Flank Milling of Fan, Compressor, and Impeller Blades

Arbitrary Surface Flank Milling of Fan, Compressor, and Impeller Blades