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Research Papers

New Continuous Dynamic Coupling for Three Component Modeling of Tool–Holder–Spindle Structure of Machine Tools With Modified Effected Tool Damping

[+] Author and Article Information
Mohammad Faraji Ghanati

College of Mechanical Engineering,  Iran University of Science and Technology, Tehran, P.O. Box 18846, Iranmfarajig@iust.ac.ir

Reza Madoliat

College of Mechanical Engineering,  Iran University of Science and Technology, Tehran, P.O. Box 18846, Iranmadoliat@iust.ac.ir

Suppose one component model is obtained from measurement data and is “response model, composed of frequency response functions,” and the other component model is obtained from analytic procedures and is “modal model, composed of natural frequencies and mode shapes.”

J. Manuf. Sci. Eng 134(2), 021015 (Apr 04, 2012) (19 pages) doi:10.1115/1.4006094 History: Received May 09, 2011; Revised January 17, 2012; Published March 30, 2012; Online April 04, 2012

In machine dynamics, the tool point frequency response functions (FRFs) are employed to predict the stable machining conditions. In this paper, a combined analytical– experimental substructuring procedure is proposed to determine the tool point FRFs usable for different holder–tool configurations. Contact interface of holder–spindle and tool–holder is modeled using translational and rotational springs and dampers spread in the length of contact surface. These joint parameters are defined using finite element method. This enables the analyst to introduce the contact stiffness and damping in more detail with taking into consideration the variations of normal pressure in the tool–holder and holder–spindle joints. The dynamic analysis of the holder is done using Timoshenko beam theory by Tchebyshev method. The tool dynamics is modeled based on Euler–Bernoulli beam theory using the method of equivalent diameter. For the purpose of shifting the tool stability lobes to a higher level, tool damping parameter is modified by internal frictional damper and the effect is analyzed by analytical methods and experimental study. After joint parameters are defined continuously by finite element method, a new method for continuous dynamic coupling is presented. The method employs the measured spindle-machine FRFs and analytical models of the tool and holder to predict the tool tip FRFs. In this new method, continuous coupling in two separate domains of response model and modal model is presented. Such structural modeling avoids us to do complex modal tests for a different set of combinations of the holder and tool with specific milling machine. An experimental case study is provided to demonstrate the applicability of the proposed method in dynamic modeling of machine tool.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Holder with taper part

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Figure 2

Tool–holder assembly

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Figure 3

Assumed contact interface parameters between holder and spindle taper

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Figure 4

Finite element model for holder inserted in steel spindle and tool inserted in the holder. The base of the spindle was held fixed and contact between two taper face is defined by ANSYS using different drawbar forces.

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Figure 5

2D model for contact surface of spindle and holder (dimensions in millimeter)

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Figure 6

Half model for contact of spindle and holder

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Figure 7

Contact elements between spindle and holder

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Figure 8

Contact pressure between the holder and spindle (note to node 1 and node 35 along contact length of holder–spindle joint)

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Figure 9

Contact pressure profile between tool and holder (note to node 1 and node 16 along contact length tool–holder joint)

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Figure 10

Simulated contact pressure profile for the spindle–holder interface (10 μm radial interference)

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Figure 11

Contact pressure profile for different radial interference values between the holder and the spindle

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Figure 12

Lateral force divided to three end nodes of the half model

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Figure 13

Stiffness versus force on one middle node in contact length

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Figure 14

Kxf stiffness along contact length of spindle–holder for different force values at the end of contact length

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Figure 15

Kθf stiffness versus force application at the end of contact length

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Figure 16

Kθf stiffness along contact length for different force values at the end of contact length

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Figure 17

Stiffness values for the finite element model of tool–holder interface (note to Fig. 9 for the position of node 1 and node 16)

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Figure 18

Equivalent viscous damping values for applied forces and moments to end point of holder–spindle contact length

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Figure 19

Continuous dynamic coupling of Timoshenko beam to another component

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Figure 20

Expansion of new method to three component coupled structure

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Figure 21

Three-point coupling of holder to spindle according to multipoint coupling method of Schmitz [6-9]

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Figure 22

Boundary conditions of tool [22]

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Figure 23

Tool in holder components and assembly

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Figure 24

Damper parts assembling for tool damper study on chatter

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Figure 25

Relative displacement and resulted friction force along damper contacts

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Figure 26

Section view of the tool with damper inside and friction forces between damper parts

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Figure 27

Spindle–holder layer model as supposed in Ref. [19]

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Figure 28

Comparison of stiffness computed for contact layer of holder–spindle with two methods of finite element and Namazi’s method

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Figure 29

Receptance of point 4 of Fig. 3––comparison of measurement and multipoint coupling of holder to spindle

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Figure 30

Schematic of spindle, impact, and measurement points

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Figure 31

Acceleration components (normal and tangential) of a point in spindle

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Figure 32

Impact test results related to three points (1, 2, and 3 according to Fig. 3 inside taper part of spindle)

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Figure 33

Tool end point frequency response using three component method and measured response model for spindle

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Figure 34

Components of modeling and test structure

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Figure 35

Holder end point (point 4) response

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Figure 36

Comparison of elastic and rigid connection between tool and holder

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Figure 37

Frequency response of nonrotating damped and undamped tool

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Figure 38

Stability lobe diagrams of optimum damped tool and simple tool by experimental FRFs

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Figure 39

Stability determination using sound amplitude spectrum

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Figure 40

Stable depths of cut versus spindle speeds from machining test

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