In this paper we outline a general method that can be used to model spindle assembly, which consists of spindle shaft, angular contact ball bearings and housing. The spindle shaft and housing are modeled as Timoshenko's beam by including the centrifugal force and gyroscopic effects. The bearing is modeled as a standard nonlinear finite element based on Jones' bearing model that includes the centrifugal force and gyroscopic effects from the rolling elements of bearings. By applying cutting forces to the spindle for a given preload, the stiffness of the bearings, contact forces on bearing balls, natural frequencies, time history response, and frequency response functions of the spindle assembly can be evaluated. In the paper we provide details of the mathematical model supported by experimental results obtained from an instrumented test spindle.

A General Method for the Modeling of Spindle-Bearing Systems

Vibration suppression of rotating machinery is an important engineering problem. In this paper, a review of the research work performed in real-time active balanc- ing and active vibration control for rotating machinery, as well as the research work on dynamic modeling and analy- sis techniques of rotor systems, is presented. The basic methodology and a brief assessment of major difficulties and future research needs are also provided.

/pdf/active-balancing-and-vibration-control-of-rotating-machinery-3edr2htqn3.pdf

Active Balancing and Vibration Control of Rotating Machinery: A Survey

Mechanical model development of rolling bearing-rotor systems: A review

This paper presents a general, integrated model of the spindle bearing and machine tool system, consisting of a rotating shaft, tool holder, angular contact ball bearings, housing, and the machine tool mounting. The model allows virtual cutting of a work material with the numerical model of the spindle during the design stage. The proposed model predicts bearing stiffness, mode shapes, frequency response function (FRF), static and dynamic deflections along the cutter and spindle shaft, as well as contact forces on the bearings with simulated cutting forces before physically building and testing the spindles. The proposed models are verified experimentally by conducting comprehensive tests on an instrumented-industrial spindle. The study shows that the accuracy of predicting the performance of the spindles require integrated modeling of all spindle elements and mounting on the machine tool. The operating conditions of the spindle, such as bearing preload, spindle speeds, cutting conditions and work material properties affect the frequency and amplitude of vibrations during machining.

Modeling of spindle-bearing and machine tool systems for virtual simulation of milling operations

Linear models and synchronous response are generally adequate to describe and analyze rotors supported by hydrodynamic bearings. Hence, stiffness and damping coefficients can provide a good model for a wide range of situations. However, in some cases, this approach does not suffice to describe the dynamic behavior of the rotor-bearing system. Moreover, unstable motion occurs due to precessional orbits in the rotor-bearing system. This instability is called “oil whirl” or “oil whip”. The oil whirl phenomenon occurs when the journal bearings are lightly loaded and the shaft is whirling at a frequency close to one-half of rotor angular speed. When the angular speed of the rotor reaches approximately twice the natural frequency (first critical speed), the oil whip phenomenon occurs and remains even if the rotor angular speed increases. Its frequency and vibration mode correspond to the first critical speed. The main purpose of this paper is to validate a complete nonlinear solution to simulate the fluid-induced instability during run-up and run-down. A flexible rotor with a central disk under unbalanced excitation is modeled. A nonlinear hydrodynamic model is considered for short bearing and laminar flow. The effects of unbalance, journal-bearing parameters and rotor arrangement (vertical or horizontal) on the instability threshold are verified. The model simulations are compared with measurements at a real vertical power plant and a horizontal test rig.

R. L. Ruhl

Papers

A Finite Element Model for Distributed Parameter Turborotor Systems