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, USA INTRODUCTION Discrete part production by milling is an important manufacturing capability. However, there are many potential obstacles to producing quality parts at low cost in a timely manner. One particular limitation that has received considerable attention in the literature is chatter, or unstable machining; a second is surface location error, or an error in the part dimension caused by dynamic deflections of the tool (and potentially the part/fixture) during stable cutting. In both cases, a primary factor affecting the process performance is the system frequency response function, or FRF. The system FRF, often dominated by the flexibility of the tool-holder-spindle assembly as reflected at the tool’s free end, can be obtained using impact testing, where an instrumented hammer is used to excite the tool at its free end (i.e., the tool point) and the resulting vibration is measured using an appropriate transducer. However, due to the large number of spindle, holder, and tool combinations that may be available in a particular production facility, the required testing time can be significant. Further, the measured response is often strongly dependent on the tool overhang length. Therefore, a model which is able to predict the tool point response based on minimum input data is the preferred alternative. The purpose of this paper is to build on the previous work of Schmitz et al. [1-3], which describes tool point FRF, or receptance, prediction using the Receptance Coupling Substructure Analysis (RCSA) method. In these previous studies, two and three component models of the machine-spindle-holder-tool assembly were defined. In this work, we extend the three component model to include multiple connections between the tool and holder along the interference contact within the (thermal) shrink fit holder. This is shown schematically in Fig. 1, where multiple complex stiffness matrices, K i , describe the connection parameters at each location. In this new model the fully populated K matrix is defined as shown in Eq. 1, which accounts for the displacement imposed by moment and the rotation caused by force through the non-zero off diagonal terms. Finite element models are developed to determine the position-dependent stiffness and equivalent viscous damping values for a thermal shrink fit connection between the tool and holder, which represents the preferred interface for high-speed milling applications. Using these values, the tool point FRF is predicted a priori and compared to measurements. Tool inside holder       ⋅ + ⋅ + ⋅ + ⋅ + = ym m yf f ym ym yf yf c i k c i k c i k c i k K ω ω ω ω θ θ (1) RCSA MODEL The RCSA spindle-holder-tool model is composed of three components. The spindle response is obtained by inserting a standard geometry artifact in the spindle and recording one direct and one cross FRF on the artifact. Using this data, together with a model of the artifact, the spindle receptances may be obtained by decoupling the artifact response from the spindle [3]. As shown in Fig. 1, the holder is separated into two sections: the portion with the tool inserted and the remainder of the Figure 1. Three component RCSA model – the finite stiffness/damping between the tool and holder is represented by multiple K matrices determined from finite element simulation. [K 1 ] [K 2 ] [K 4 ] 4 3 2 1 [K 3 ] [K 5 ] 5