Abstract

The effect of bearings on the vibrational behavior of machine tool spindles is investigated. This is done through the development of a calibrated dynamic stiffness matrix (CDSM) method, where the bearings flexibility is represented by mass less linear spring elements with tuneable stiffness. A dedicated MAT LAB code is written to develop and to assemble the element stiffness matrices for the system’s multiple components and to apply the boundary conditions.The developed method is applied to an illustrative example of spindle system.When the spindle bearings are modeled as simply supported boundary conditions, the DSM model results in a fundamental frequency much higher than the system’s nominal value.The simply supported boundary conditions are then replaced by linear spring elements, and the spring constants are adjusted such that the resulting calibrated CDSM model leads to the nominal fundamental frequency of the spindle system.The spindle frequency results are also validated against the experimental data.The proposed method can be effectively applied to predict the vibration characteristics of spindle systems supported by bearings.

Highlights

  • The booming aerospace industry and high levels of competition have forced companies to constantly look for ways to optimize their machining processes

  • It has been established that the service life changes the vibrational behavior of spindle systems, that is, reduced natural frequency over the time, associated with the bearings wear

  • The bearings were included in the model using two different models: rigid, supported, frictionless pins, and flexible linear spring elements

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Summary

Introduction

The booming aerospace industry and high levels of competition have forced companies to constantly look for ways to optimize their machining processes. The proposed model, verified experimentally, allows virtual cutting of a work material with the numerical model of the spindle during the design stage and predicts bearing stiffness, mode shapes, frequency response function (FRF), static and dynamic deflections along the cutter and spindle shaft, and contact forces on the bearings with simulated cutting forces before physically building and testing the spindles. The objective of the present study is to determine the natural frequencies/vibration characteristics of machine tool spindle systems by developing the corresponding dynamic stiffness matrix (DSM) [31, 32] and the proper boundary conditions. These results would be compared to the existing results for a common cutting system to validate/tune the model developed. The proposed formulation can be extended to include torsional degreeof-freedom (DOF) for further modeling purposes

Problem Description and Governing Equations
Dynamic Stiffness Matrix (DSM) Solution
Application of the Theory and Numerical Results
Findings
Discussion and Conclusion
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