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Tool-holder Connection Modeling for Frequency Response Prediction in Milling |
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Equipment, Machines & Instruments: Analysis & Modeling |
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Tool-holder connection modeling for frequency response prediction in milling
Kevin B. Powell, Dongki Won, Tony L. Schmitz, G. Scott Duncan, W. Gregory Sawyer, John C. Ziegert
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611
Keywords: Receptance coupling; high-speed machining; finite element; shrink fit
A finite element model is used to determine the stiffness and damping behavior at the interface between the tool and thermal shrink fit holder. The continuous contact stiffness/damping profile between the holder and portion of the tool inside the holder is approximated by defining coordinates along the contact length interface and assigning position-dependent stiffness and equivalent viscous damping values between the tool and holder. These values are incorporated into the third generation Receptance Coupling Substructure Analysis (RCSA) method, which is used to predict the tool point frequency response for milling applications [1]. Once the holder and inserted tool section are connected using the finite element analysis-based stiffness and damping values [2], this subassembly is then rigidly coupled to the (measured) spindle-holder base and (modeled) tool.
Finite element models for selected tool-holder assemblies were constructed using ANSYS. The boundary conditions were set as fixed-free and only the extended holder and tool were modeled (the flange and holder taper were considered part of the spindle-holder base, which was not included in this portion of the analysis). The coordinate directions for the model were: x – horizontal, y – vertical, z – along the tool axis. Material properties include elastic modulus, mass density, Poisson’s ratio and coefficient of friction. The position-dependent stiffness values were determined using the following steps. At the end of the two time intervals (pressure growth due to the shrink fit interference followed by force or moment application in the y direction), the y direction displacements of the tool at nodes along the tool top centerline were recorded. The y displacements, as a function of z location, imposed by the force/couple were then computed by differencing the two results. By applying a range of forces and couples, translational stiffness values were calculated directly from the slope of the load-displacement curves for each node under consideration. For the rotational stiffness values, the rotation was first calculated by central finite difference from the displacement data, and then the stiffness values were obtained from the load-rotation curve slope values.
It was assumed that damping in the shrink fit connection occurred due to relative micro-slip between the tool and holder along the tool axis during the force/couple application. This Coulomb-type damping was converted to position-dependent equivalent viscous damping values by first computing the frictional (damping) force for each element, next calculating the viscous damping value for each element, and finally summing the damping values for the elements located around the tool circumference for the selected z location. The friction force was calculated from the product of the element area, element contact pressure, and the assumed coefficient of friction.
The addition of stiffness and damping will build on previous work in which a rigid connection was assumed [1]. Experimental validation is provided for the new approach.
1. Schmitz, T., and Duncan, G.S., 2005, Three-Component Receptance Coupling Substructure Analysis for Tool Point Dynamics Prediction, Journal of Manufacturing Science and Engineering, 127/4: 781-790.
2. Schmitz, T. and Duncan, G.S., 2006, Receptance Coupling for Dynamics Prediction of Assemblies with Coincident Neutral Axes, Journal of Sound and Vibration, 289/4-5: 1045-1065.
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