Dynamics of Spindle-Bearing Systems at High Speeds Including Cutting Load Effects

1998 ◽  
Vol 120 (2) ◽  
pp. 387-394 ◽  
Author(s):  
Bert R. Jorgensen ◽  
Yung C. Shin
Keyword(s):  
Natural Frequency ◽  
High Speed ◽  
Dynamic Models ◽  
Complex Geometry ◽  
Beam Theory ◽  
Coupled System ◽  
Influence Coefficient ◽  
High Speeds ◽  
Spindle Bearing ◽  
Influence Coefficient Method

Increased use of high speed machining creates the need to predict spindle-bearing performance at high speeds. Previous spindle-bearing models simplify either spindle or bearing dynamics to the extent of prohibiting a detailed analysis of a spindle with high speed motion. At high speeds, centrifugal loading in the bearing causes stiffness softening, creating a change in natural frequency. Therefore, spindle modeling requires a comprehensive representation of the dynamics of shafts with complex geometry rotating at high speeds and supported by non-linear bearings. This paper presents a coupled system of spindle and bearing dynamic models with numerical solution. Spindle dynamics are modeled using the influence coefficient method of discrete lumped masses, based on Timoshenko beam theory. Both linear and rotational bearing stiffness are included in the spindle model through solution of the angular-contact bearing model. The parameters of cutting loads, tool mass, and rotational speed are analyzed, and all are shown to affect the natural frequency. The computer model is both rapid and robust, and shows excellent agreement with experimental analysis.

Dynamics of Machine Tool Spindle/Bearing Systems Under Thermal Growth

1997 ◽  
Vol 119 (4) ◽  
pp. 875-882 ◽  
Author(s):  
Bert R. Jorgensen ◽  
Yung C. Shin
Keyword(s):  
Thermal Expansion ◽  
Dynamic Response ◽  
Heat Generation ◽  
High Speed ◽  
Transfer Model ◽  
Good Prediction ◽  
High Speeds ◽  
Spindle Bearing ◽  
Thermal Growth ◽  
Bearing Stiffness

Increased use of high-speed machining creates the need to predict spindle/bearing performance at high speeds. Spindle dynamic response is a function of the nonlinear bearing stiffness. At high speeds, thermal expansion can play an important role in bearing stiffness. A complete bearing load-deflection analysis including thermal expansion is derived and is coupled with an analysis of spindle dynamic response. Steady-state temperature distribution is found from heat generation at the contact point and from a quasi three-dimensional heat transfer model. Numerical solutions give a good prediction of thermal growth and heat generation in the bearing. Predicted high-speed spindle frequencies show good agreement with experimentation. The effects of loading condition and bearing material type on bearing stiffness are also shown.

scholarly journals Active Control for Multinode Unbalanced Vibration of Flexible Spindle Rotor System with Active Magnetic Bearing

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaoli Qiao ◽  
Guojun Hu
Keyword(s):  
High Speed ◽  
Control Method ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Active Magnetic Bearing ◽  
Influence Coefficient ◽  
Control Effect ◽  
High Speed Cutting ◽  
Influence Coefficient Method ◽  
Cutting Processes

The unbalanced vibration of the spindle rotor system in high-speed cutting processes not only seriously affects the surface quality of the machined products, but also greatly reduces the service life of the electric spindle. However, since the unbalanced vibration is often distributed on different node positions, the multinode unbalanced vibration greatly exacerbates the difficulty of vibration control. Based on the traditional influence coefficient method for controlling the vibration of a flexible rotor, the optimal influence coefficient control method with weights for multinode unbalanced vibration of flexible electric spindle rotors is proposed. The unbalanced vibration of all nodes on the whole spindle rotor is used as the control objective function to achieve optimal control. The simulation results show that the method has an obvious control effect on multinode unbalanced vibration.

Effect of Uncertainty in the Balancing Weights on the Vibration Response of a High-Speed Rotor

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
Janina Datz ◽  
Mahmoud Karimi ◽  
Steffen Marburg
Keyword(s):  
High Speed ◽  
Probability Distributions ◽  
Probabilistic Method ◽  
Turbine Rotor ◽  
Vibration Response ◽  
Galerkin Projection ◽  
System Response ◽  
Influence Coefficient ◽  
Uncertain Parameters ◽  
Influence Coefficient Method

Abstract This work investigates how uncertainties in the balancing weights are propagating into the vibration response of a high-speed rotor. Balancing data are obtained from a 166-MW gas turbine rotor in a vacuum balancing tunnel. The influence coefficient method is then implemented to characterize the rotor system by a deterministic multi-speed and multi-plane matrix. To model the uncertainties, a non-sampling probabilistic method based on the generalized polynomial chaos expansion (gPCE) is employed. The uncertain parameters including the mass and angular positions of the balancing weights are then expressed by gPCE with deterministic coefficients. Assuming predefined probability distributions of the uncertain parameters, the stochastic Galerkin projection is applied to calculate the coefficients for the input parameters. Furthermore, the vibration amplitudes of the rotor response are represented by appropriate gPCE with unknown deterministic coefficients. These unknown coefficients are determined using the stochastic collocation method by evaluating the gPCE for the system response at a set of collocation points. The effects of individual and combined uncertain parameters from a single and multiple balancing planes on the rotor vibration response are examined. Results are compared with the Monte Carlo simulations, showing excellent agreement.

Further Experiments on Balancing of a High-Speed Flexible Rotor

1974 ◽  
Vol 96 (2) ◽  
pp. 431-440 ◽  
Author(s):  
J. Tonnesen
Keyword(s):  
Computer Program ◽  
Least Squares ◽  
High Speed ◽  
Influence Coefficient ◽  
Flexible Rotor ◽  
Minimum Level ◽  
Absolute Level ◽  
Quality Class ◽  
Influence Coefficient Method ◽  
Coefficient Method

The accuracy of the influence coefficient method is experimentally investigated. The influence of the number of measurement transducers, their location, and type is demonstrated on a flexible rotor where simultaneous balancing is performed in up to five planes and passing through three critical speeds. The correction weights are calculated by means of a computer program, based on a least-squares minimizing procedure. The method itself is shown to be accurate and uses only a minimum of balancing runs to reduce the vibrations to a true minimum level. The overall accuracy in determining the unbalance weights is found to be 4.5 percent. The method’s effectiveness is demonstrated on a rotor with four balancing planes and with unbalance distributed at random in six and seven planes. The absolute level of residual vibrations is found to be in the ISO 0.4 quality class [5].

Analysis of Tilting Effects and Geometric Non-Uniformities in Micro-Hydrostatic Gas Thrust Bearings

2005 ◽  
Author(s):  
C. J. Teo ◽  
Z. S. Spakovszky
Keyword(s):  
High Speed ◽  
Compressible Flows ◽  
Thrust Bearing ◽  
Coupled System ◽  
Orifice Diameter ◽  
Influence Coefficient ◽  
Analysis Tool ◽  
Thrust Bearings ◽  
Tilting Angle ◽  
Concomitant Reduction

The MIT microengine rotors are supported by hydrostatic gas journal and hydrostatic gas thrust bearings. Due to the low length-to-diameter ratio of the devices, the thrust bearings play an important role in providing sufficient tilting stiffness to resist any tilting motion about the spinning axis of the rotor. The performance of the thrust bearings can be influenced by geometric nonuniformities such as thrust bearing clearances and orifice diameters and profiles which arise in the process of microfabrication. To enable stable high speed operation of the micro-devices, it is important to quantify these effects. Furthermore, a thrust bearing analysis tool needs to be developed that is able to explore different thrust bearing arrangements and configurations. In this work, an analytical model is established for analyzing the effects of rotor tilt and geometric non-uniformities in micro-hydrostatic gas thrust bearings for application to microturbomachinery. A previously developed model (Teo and Spakovszky [1]) is generalized and extended for application to thrust bearings with orifices arranged in non-axisymmetric configurations. As a consequence of rotor tilt or geometric non-uniformities, the flow through individual orifices of the thrust bearing becomes non-uniform. The orifice flows are in turn coupled to the hydrostatic pressure field in the thrust bearing pad, and a Green’s function approach is adopted to solve the coupled system. The hydrodynamic thrust bearing forces induced by the pumping action of the rotor rotation are determined by solving the Reynolds equation. The model is able to predict thrust bearing tilting stiffness and variations in the thrust bearing mass flow rates as a function of rotor tilting angle for a variety of orifice arrangements. The model can be applied to analyze the effects of non-uniformities in orifice diameter and the presence of clogged orifices on tilting and the concomitant reduction in tilting stiffness. In addition, the effects of orifice taper are analyzed using an influence-coefficient technique for 1-D compressible flows. Results obtained for various taper ratios are presented and discussed. The model serves as a useful tool for specifying design tolerances during the fabrication of micro-hydrostatic gas thrust bearings and is used in the experiments to estimate the tilting angle of the rotor during operation.

Nonlinear Flutter in Fan Stator Vanes With Time Dependent Fixity

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
R. Srivastava ◽  
J. Panovsky ◽  
R. Kielb ◽  
L. Virgin ◽  
K. Ekici
Keyword(s):  
Natural Frequency ◽  
High Speed ◽  
External Source ◽  
High Amplitude ◽  
Time Dependent ◽  
Turbofan Engines ◽  
Lower Natural Frequency ◽  
High Speeds ◽  
Stator Vane

A new mechanism for fan stator vane failure in turbofan engines at high speed and high loading has been identified and reported in this paper. Highly destructive vane failures have been encountered at Honeywell in a development fan with composite stator vanes. Measured data indicated nonlinear high amplitude vibratory response in fan stator vanes on the stall side of the fan map at high speeds. Analysis showed that under certain steady loading, vane fixity at the hub could change, significantly reducing the vane natural frequency. At this lower natural frequency, the vane was found to be aeroelastically unstable, and calculated response exhibited characteristics similar to those observed during failure. An engine test conducted to validate the role of hub fixity in vane failures showed the failure to be a self-excited phenomenon and not driven by an external source of excitation. It was also shown that failures occur in vanes that are not rigidly fixed, validating the role of hub fixity in vane failures. Test results along with analysis confirm the role of time dependent hub fixity leading to the highly destructive flutter responsible for vane failures.

A Generalized Minmax Influence Coefficient Method for Flexible Rotor Balancing

2005 ◽  
Author(s):  
Costin Untaroiu ◽  
Paul Allaire
Keyword(s):  
High Speed ◽  
Optimization Problem ◽  
Current Method ◽  
Linear Matrix ◽  
Influence Coefficient ◽  
Flexible Rotor ◽  
Influence Coefficient Method ◽  
Rotor Balancing ◽  
Practical Constraints ◽  
Coefficient Method

Rotor balancing is a requirement for the smooth operation of high-speed rotating machinery. In field balancing, minimization of the residual vibrations at important locations/speeds under practical constraints is usually a challenging task. In this paper, the generalized minmax coefficient influence method is formulated as an optimization problem with flexible objective functions and constraints. The optimization problem is cast in a Linear Matrix Inequality (LMI) form and a balancing code is developed to solve it. Two balancing examples are run to verify the efficiency and flexibility of the proposed method. Over the existing methods, current method is more flexible for the various requirements encountered in field balancing and can be solved accurate with current mathematical software.

Dynamic Behavior of All-Ceramic Spindle-Bearing Unit with Preload

2013 ◽  
Vol 365-366 ◽  
pp. 314-317
Author(s):  
Song Hua Li ◽  
Xue Li ◽  
Ming Hao Feng ◽  
Yu Hou Wu ◽  
Xiao Lin Jin
Keyword(s):  
Natural Frequency ◽  
High Speed ◽  
High Hardness ◽  
The Finite Element Method ◽  
Analysis Model ◽  
Engineering Ceramics ◽  
Bearing Unit ◽  
Spindle Bearing ◽  
Low Thermal Expansion ◽  
All Ceramic

Abstract. Because of the extraordinary physical properties of engineering ceramics such as high hardness, low thermal expansion, light weight and abrasion resistant, it accommodates very well with the high-speed and precision requirements of spindle-bearing unit. In order to prove the superior dynamic characteristic of the all-ceramic spindle-bearing unit bacause of the application of engineering ceramics in shaft and bearing of spindle system, the natural frequency and modes of the all-ceramic spindle-bearing unit were analyzed. In this study, spindle-bearing model was built and analyzed by the Finite Element Method(FEM) and Hertz theory, comprehensively considering both of the stiffness of bearing and the effect of preload, which was different from the tranditional spindle analysis model. The research results show that all-ceramic spindle-bearing unit has higher natural frequency and better dynamic characteristics compare of traditional steel spindle-bearing unit.

scholarly journals A New Variance-Covariance Matrix for Improving Positioning Accuracy in High-Speed GPS Receivers

Sensors ◽  
2021 ◽  
Vol 21 (21) ◽  
pp. 7324
Author(s):  
Narjes Rahemi ◽  
Mohammad Reza Mosavi ◽  
Diego Martín
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
High Speed ◽  
Dynamic Models ◽  
Unscented Kalman Filter ◽  
Statistical Characteristics ◽  
Spatial Correlations ◽  
Positioning Accuracy ◽  
High Speeds ◽  
Variance Covariance Matrix

One of the main challenges in using GPS is reducing the positioning accuracy in high-speed conditions. In this contribution, by considering the effect of spatial correlation between observations in estimating the covariances, we propose a model for determining the variance–covariance matrix (VCM) that improves the positioning accuracy without increasing the computational load. In addition, we compare the performance of the extended Kalman filter (EKF) and unscented Kalman filter (UKF) combined with different dynamic models, along with the proposed VCM in GPS positioning at high speeds. To review and test the methods, we used six motion scenarios with different speeds from medium to high and examined the positioning accuracy of the methods and some of their statistical characteristics. The simulation results demonstrate that the EKF algorithm based on the Gauss–Markov model, along with the proposed VCM (based on the sinusoidal function and considering spatial correlations), performs better and provides at least 30% improvement in the positioning, compared to the other methods.

Analysis of the Effect the Modal-Parameter on the Milling Stability

2013 ◽  
Vol 372 ◽  
pp. 459-462
Author(s):  
Ming Chang Tsai ◽  
Te Ching Hsiao ◽  
Shyh Chour Huang
Keyword(s):  
Natural Frequency ◽  
High Precision ◽  
High Speed ◽  
Damping Ratio ◽  
Chatter Stability ◽  
Modal Parameter ◽  
High Speeds ◽  
Stability Lobe ◽  
The Stability ◽  
Chatter Stability Lobes

In the past few years, it has become a tendency to develop machinery of high speeds and high precision. In order to meet the need for high-speed manufacturing of high precision components, the machine tools structure must be very stiff and have high cutting stability levels. Should the process of the firsthand milling be unstable, the effects include cutting tool breakages, decrease in surface accuracy and could even shorten the machine tolls lifespan. Thus, in the manufacturing of milling, chattering often causes problems for the manufacturer. To prevent cases of milling chattering, there is a need to use a chatter stability lobe to predict the chatter stability and to analyze the effect the modal-parameter has on the stability of milling. This research paper uses the Zero-Order Analytical Method (ZOA) to analyze and compare the effects modal-parameter (natural frequency, damping ratio, modal stiffness) has on the stability of the milling system. The results show that level of stiffness and the damping ratio influences the vertical shape of the chatter stability lobes while the natural frequency affects the lateral shape of the lobes.

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