The susceptibility of spindle motor ball bearings in disk drives to axial shock is considered in this paper. When a hard drive is subjected to an axial shock, the spindle disk pack is excited axially and the ensuing vibrations lead to dynamic forces. Should the maximum force endured by the bearings exceed their rated carrying capacity, permanent bearing damage will take place at the ball/race interface which manifests itself in higher vibration and acoustic levels. To estimate the dynamic bearing force and the shock fragility of a given drive, it is imperative to solve for the vibration of the drive when subjected to shock. This was achieved in the present work by simplifying the dynamics of a hard drive to that of a two degree of freedom mass-spring system. The equivalent mass and stiffness values were obtained by matching the modal frequencies of the 2 DOF model to those of the disk pack. The response of the model to axial shock was next obtained by numerical integration using the Runge-Kutta method. The non-linear bearing stiffness was incorporated using the Hertzian equations in the model. To validate the model, the response of a hard drive to axial shock was measured using an accelerometer mounted on the motor hub. Excellent agreement was obtained between calculated response and experimentally measured motor hub vibration. Having verified the model, the calculated maximum bearing force was used to estimate the drive’s shock threshold. It was found that base casting stiffness and damping play an important role in the dynamic amplification of the bearing force.
{"title":"Shock Fragility of Spindle Motors in Hard Drives","authors":"Hamid Salehizadeh","doi":"10.1115/imece1996-1079","DOIUrl":"https://doi.org/10.1115/imece1996-1079","url":null,"abstract":"\u0000 The susceptibility of spindle motor ball bearings in disk drives to axial shock is considered in this paper. When a hard drive is subjected to an axial shock, the spindle disk pack is excited axially and the ensuing vibrations lead to dynamic forces. Should the maximum force endured by the bearings exceed their rated carrying capacity, permanent bearing damage will take place at the ball/race interface which manifests itself in higher vibration and acoustic levels.\u0000 To estimate the dynamic bearing force and the shock fragility of a given drive, it is imperative to solve for the vibration of the drive when subjected to shock. This was achieved in the present work by simplifying the dynamics of a hard drive to that of a two degree of freedom mass-spring system. The equivalent mass and stiffness values were obtained by matching the modal frequencies of the 2 DOF model to those of the disk pack. The response of the model to axial shock was next obtained by numerical integration using the Runge-Kutta method. The non-linear bearing stiffness was incorporated using the Hertzian equations in the model. To validate the model, the response of a hard drive to axial shock was measured using an accelerometer mounted on the motor hub. Excellent agreement was obtained between calculated response and experimentally measured motor hub vibration. Having verified the model, the calculated maximum bearing force was used to estimate the drive’s shock threshold. It was found that base casting stiffness and damping play an important role in the dynamic amplification of the bearing force.","PeriodicalId":231650,"journal":{"name":"7th International Symposium on Information Storage and Processing Systems","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125061851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is a follow-on to a paper previously presented to ASME on an experimental instrument designed to enable the observation of standing wave modes for flexible media. In that earlier paper qualitative results showing changes in the disk standing waves were obtained using the experimental setup. The current paper presents the same experimental system from the perspective of looking at the system as an optical instrument, and, based on optical ray trace methodology, quantifies the results seen in the previous paper on a more absolute basis. Based on this analysis, the authors also describe design changes from both an instrument setup perspective and the application of other electro-optic sensor technologies which will improve the system’s static and dynamic resolution.
{"title":"Quantification of Standing Wave Patterns in Rotating Flexible Disks Using Optical Reflection Techniques","authors":"Yiping Ma, F. Thomas","doi":"10.1115/imece1996-1068","DOIUrl":"https://doi.org/10.1115/imece1996-1068","url":null,"abstract":"\u0000 This paper is a follow-on to a paper previously presented to ASME on an experimental instrument designed to enable the observation of standing wave modes for flexible media. In that earlier paper qualitative results showing changes in the disk standing waves were obtained using the experimental setup. The current paper presents the same experimental system from the perspective of looking at the system as an optical instrument, and, based on optical ray trace methodology, quantifies the results seen in the previous paper on a more absolute basis. Based on this analysis, the authors also describe design changes from both an instrument setup perspective and the application of other electro-optic sensor technologies which will improve the system’s static and dynamic resolution.","PeriodicalId":231650,"journal":{"name":"7th International Symposium on Information Storage and Processing Systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122658781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The hysteresis properties of a magnetic recording disk drive rotary actuator servo were measured for bearings lubricated with three different types of grease. The three types of grease tested were: 1) mineral oil with a polyurea thickener, 2) polyol ester oil with a polyurea thickener, and 3) perfluorinated polyether (PFPE) oil with a polytetrafluoroethelyne (PTFE) particle thickener. The grease dynamic viscosity and yield stress were measured to characterize the grease flow properties. Actuator bias current was measured on files to quantify changes in the hysteresis and linearity. Head settle times were measured following a random seek pattern. Actuators made with the mineral oil and polyol ester oil polyurea thickened greases had acceptable actuator bias current and head settle times. Actuators made with the PFPE grease exhibited large bias hysteresis, significant non-linearity, and the head settle time was significantly longer than for those actuators made with mineral oil grease. The reasons for the increased hysteresis and settle time observed with the PFPE grease were investigated. It was found that the PTFE grease particles get shredded and deposited in the raceway and they also form large agglomerates that impede the smooth rolling of the bearing.
{"title":"Servo Performance of Actuator Bearing Greases","authors":"W. Prater, G. Stone, Kevin W. Tierney, T. Karis","doi":"10.1115/imece1996-1075","DOIUrl":"https://doi.org/10.1115/imece1996-1075","url":null,"abstract":"\u0000 The hysteresis properties of a magnetic recording disk drive rotary actuator servo were measured for bearings lubricated with three different types of grease. The three types of grease tested were: 1) mineral oil with a polyurea thickener, 2) polyol ester oil with a polyurea thickener, and 3) perfluorinated polyether (PFPE) oil with a polytetrafluoroethelyne (PTFE) particle thickener.\u0000 The grease dynamic viscosity and yield stress were measured to characterize the grease flow properties.\u0000 Actuator bias current was measured on files to quantify changes in the hysteresis and linearity. Head settle times were measured following a random seek pattern.\u0000 Actuators made with the mineral oil and polyol ester oil polyurea thickened greases had acceptable actuator bias current and head settle times. Actuators made with the PFPE grease exhibited large bias hysteresis, significant non-linearity, and the head settle time was significantly longer than for those actuators made with mineral oil grease.\u0000 The reasons for the increased hysteresis and settle time observed with the PFPE grease were investigated. It was found that the PTFE grease particles get shredded and deposited in the raceway and they also form large agglomerates that impede the smooth rolling of the bearing.","PeriodicalId":231650,"journal":{"name":"7th International Symposium on Information Storage and Processing Systems","volume":"287 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121230023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Continuous gyroscopic system eigenvalues and stability are analytically calculable in only a limited set of cases. This paper presents an eigenvalue perturbation analysis to determine approximate eigenvalue loci and stability conclusions in the vicinity of critical speeds and zero speed. The perturbation analysis relies on a formulation of the general continuous gyroscopic system eigenvalue problem in terms of matrix differential operators and vector eigenfunctions. The eigenvalue λ appears only as λ2 in the formulation, and the smoothness of λ2 at the critical speeds and zero speed is the essential feature required for the perturbatton. First order eigenvalue perturbations are determined at the critical speeds and zero speed. The derived eigenvalue perturbations are simple expressions in terms of the original mass, gyroscopic, and stiffness operators and the critical speed/stationary system eigenfunctions. Prediction of whether an eigenvalue passes to or from a region of divergence instability is determined by the sign of the eigenvalue perturbation. Additionally, perturbation of the critical speed/stationary system yields approximations for the eigenvalue loci at speeds away from these. The results provide analytical means for estimating continuous gyroscopic system eigenvalues and stability near critical speeds without numerical computation. The results are limited to systems having one independent eigenfunction associated with each critical speed and each stationary system eigenvalue. The techniques also apply to discrete gyroscopic systems. Examples are presented for an axially-moving, tensioned beam and a rotating rigid body and comparisons with known solutions are given.
{"title":"Stability of Continuous Gyroscopic Systems Using Perturbation Analysis","authors":"R. Parker","doi":"10.1115/imece1996-1071","DOIUrl":"https://doi.org/10.1115/imece1996-1071","url":null,"abstract":"\u0000 Continuous gyroscopic system eigenvalues and stability are analytically calculable in only a limited set of cases. This paper presents an eigenvalue perturbation analysis to determine approximate eigenvalue loci and stability conclusions in the vicinity of critical speeds and zero speed. The perturbation analysis relies on a formulation of the general continuous gyroscopic system eigenvalue problem in terms of matrix differential operators and vector eigenfunctions. The eigenvalue λ appears only as λ2 in the formulation, and the smoothness of λ2 at the critical speeds and zero speed is the essential feature required for the perturbatton. First order eigenvalue perturbations are determined at the critical speeds and zero speed. The derived eigenvalue perturbations are simple expressions in terms of the original mass, gyroscopic, and stiffness operators and the critical speed/stationary system eigenfunctions. Prediction of whether an eigenvalue passes to or from a region of divergence instability is determined by the sign of the eigenvalue perturbation. Additionally, perturbation of the critical speed/stationary system yields approximations for the eigenvalue loci at speeds away from these. The results provide analytical means for estimating continuous gyroscopic system eigenvalues and stability near critical speeds without numerical computation. The results are limited to systems having one independent eigenfunction associated with each critical speed and each stationary system eigenvalue. The techniques also apply to discrete gyroscopic systems. Examples are presented for an axially-moving, tensioned beam and a rotating rigid body and comparisons with known solutions are given.","PeriodicalId":231650,"journal":{"name":"7th International Symposium on Information Storage and Processing Systems","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127664391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is to study forced vibration response of a rotating disk/spindle system consisting of multiple flexible circular disks clamped to a rigid spindle supported by two flexible bearings. In particular, the disk/spindle system is subjected to prescribed translational base excitations as well as externally applied loads. Because of the bearing flexibility, the rigid spindle undergoes infinitesimal rigid-body rotation and translation simultaneously. To model real vibration response that has finite resonance amplitudes, the disks and the bearings are assumed to be viscously damped. Equations of motion are then derived through use of Rayleigh dissipation function and Lagrange’s equation. The equations of motion include three sets of matrix differential equations: one for the rigid-body rocking of the spindle and one-nodal-diameter disk modes, one for the axial translation of the spindle and axisymmetric disk modes, and one for disk modes with two or more nodal diameters. Each matrix differential equation contains either a gyroscopic matrix or a damping matrix or both. The causal Green’s function of each matrix differential equation is determined explicitly in closed form through use of matrix inversion and inverse Laplace transforms. Closed-form forced response of the damped rotating disk/spindle system is then obtained from the causal Green’s function and the generalized forces through convolution integrals. Finally, responses of a disk/spindle system subjected to a concentrated sinusoidal load or an impulsive load are demonstrated numerically as an example.
{"title":"Closed-Form Forced Response of a Damped, Rotating, Multiple Disks/Spindle System","authors":"I. Shen","doi":"10.1115/1.2787313","DOIUrl":"https://doi.org/10.1115/1.2787313","url":null,"abstract":"\u0000 This paper is to study forced vibration response of a rotating disk/spindle system consisting of multiple flexible circular disks clamped to a rigid spindle supported by two flexible bearings. In particular, the disk/spindle system is subjected to prescribed translational base excitations as well as externally applied loads. Because of the bearing flexibility, the rigid spindle undergoes infinitesimal rigid-body rotation and translation simultaneously. To model real vibration response that has finite resonance amplitudes, the disks and the bearings are assumed to be viscously damped. Equations of motion are then derived through use of Rayleigh dissipation function and Lagrange’s equation. The equations of motion include three sets of matrix differential equations: one for the rigid-body rocking of the spindle and one-nodal-diameter disk modes, one for the axial translation of the spindle and axisymmetric disk modes, and one for disk modes with two or more nodal diameters. Each matrix differential equation contains either a gyroscopic matrix or a damping matrix or both. The causal Green’s function of each matrix differential equation is determined explicitly in closed form through use of matrix inversion and inverse Laplace transforms. Closed-form forced response of the damped rotating disk/spindle system is then obtained from the causal Green’s function and the generalized forces through convolution integrals. Finally, responses of a disk/spindle system subjected to a concentrated sinusoidal load or an impulsive load are demonstrated numerically as an example.","PeriodicalId":231650,"journal":{"name":"7th International Symposium on Information Storage and Processing Systems","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132567522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1996-11-17DOI: 10.1142/9789812816610_0012
T. Y. Chuang, D. Lieu, J. McAllister
A parametric study was conducted to determine the effect of motor stator slot widths and rotor permanent magnet pole separation widths on the reluctance torque. This study is based on a finite element analysis of a particular 6-pole/9-slot motor. The analysis can be expanded to other slot/pole combinations. Force and torque calculations were based on an integration of the Maxwell stresses along the center of the airgap. As a general rule, the reluctance torque may be reduced by decreasing the slot width for any given pole separation. For any given slot width, the reluctance torque can be reduced to zero by selection of the proper pole separation. The optimum slot widths are slightly different than those predicted by past analytical formulation. There will be, however, a noticeable effect on the main drive torque and the torque ripple.
{"title":"Optimization of Pole and Slot Widths for Reluctance Torque Reduction in a Brushless DC Spindle Motor","authors":"T. Y. Chuang, D. Lieu, J. McAllister","doi":"10.1142/9789812816610_0012","DOIUrl":"https://doi.org/10.1142/9789812816610_0012","url":null,"abstract":"\u0000 A parametric study was conducted to determine the effect of motor stator slot widths and rotor permanent magnet pole separation widths on the reluctance torque. This study is based on a finite element analysis of a particular 6-pole/9-slot motor. The analysis can be expanded to other slot/pole combinations. Force and torque calculations were based on an integration of the Maxwell stresses along the center of the airgap. As a general rule, the reluctance torque may be reduced by decreasing the slot width for any given pole separation. For any given slot width, the reluctance torque can be reduced to zero by selection of the proper pole separation. The optimum slot widths are slightly different than those predicted by past analytical formulation. There will be, however, a noticeable effect on the main drive torque and the torque ripple.","PeriodicalId":231650,"journal":{"name":"7th International Symposium on Information Storage and Processing Systems","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128905267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1996-11-17DOI: 10.1142/9789812816610_0001
K. Ono, Atsushi Suzuki
This paper presents a theoretical analysis of the friction-induced self-excited vibration of a contact head slider that is one of the head design candidates for future high density recording disk storage. In order to understand the fundamental destabilizing mechanism of the contact slider, the slider-suspension system is modeled as a two-degree-of-freedom (DOF) system. The instability of this system is caused by the asymmetry of the stiffness matrix due to the friction force. The unstable region of this system is examined in terms of the normal and angular natural frequencies, frictional coefficient, slider mass center position and the contact and suspension stiffnesses. The destabilizing mechanism of friction force is made clear by illustrating the mode shape of the complex number. From this model, it is found that the system always becomes stable if the center of mass of the slider is located ahead of the torsional center of slider suspension.
{"title":"Analysis of Friction-Induced Self-Excited Vibration of Contact Recording Head Slider","authors":"K. Ono, Atsushi Suzuki","doi":"10.1142/9789812816610_0001","DOIUrl":"https://doi.org/10.1142/9789812816610_0001","url":null,"abstract":"\u0000 This paper presents a theoretical analysis of the friction-induced self-excited vibration of a contact head slider that is one of the head design candidates for future high density recording disk storage. In order to understand the fundamental destabilizing mechanism of the contact slider, the slider-suspension system is modeled as a two-degree-of-freedom (DOF) system. The instability of this system is caused by the asymmetry of the stiffness matrix due to the friction force. The unstable region of this system is examined in terms of the normal and angular natural frequencies, frictional coefficient, slider mass center position and the contact and suspension stiffnesses. The destabilizing mechanism of friction force is made clear by illustrating the mode shape of the complex number. From this model, it is found that the system always becomes stable if the center of mass of the slider is located ahead of the torsional center of slider suspension.","PeriodicalId":231650,"journal":{"name":"7th International Symposium on Information Storage and Processing Systems","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115535791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
During the dye diffusion thermal printing process a dye-carrying ribbon is brought into contact with a receiver and these two surfaces are compressed between a printhead bead and elastomeric drum, creating the thermal printer nip. Within this highly pressurized contact region both heat and mass transfer takes place. In order to better understand the printing process we have created a finite difference model that simultaneously solves the heat and dye diffusion equation. Using experimental head temperature data we will describe a method for determining a surface boundary condition that can be used in the simulation. This boundary condition will allow us to incorporate different pulse modulation heating schemes in order to predict temperature variations and dye penetration patterns. In the discretization of the diffusion equation we will account for concentration dependence of the diffusivities that is common in many polymer systems. This consideration leads to a nonlinear governing equation for the dye diffusion process.
{"title":"Dye Diffusion Digital Imaging","authors":"John E. LaFleche, R. Benson, Ken Stack, S. Burns","doi":"10.1115/imece1996-1064","DOIUrl":"https://doi.org/10.1115/imece1996-1064","url":null,"abstract":"\u0000 During the dye diffusion thermal printing process a dye-carrying ribbon is brought into contact with a receiver and these two surfaces are compressed between a printhead bead and elastomeric drum, creating the thermal printer nip. Within this highly pressurized contact region both heat and mass transfer takes place. In order to better understand the printing process we have created a finite difference model that simultaneously solves the heat and dye diffusion equation. Using experimental head temperature data we will describe a method for determining a surface boundary condition that can be used in the simulation. This boundary condition will allow us to incorporate different pulse modulation heating schemes in order to predict temperature variations and dye penetration patterns. In the discretization of the diffusion equation we will account for concentration dependence of the diffusivities that is common in many polymer systems. This consideration leads to a nonlinear governing equation for the dye diffusion process.","PeriodicalId":231650,"journal":{"name":"7th International Symposium on Information Storage and Processing Systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130159008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The brushless DC motor is widely used in industry. In this paper, we present a low cost, high accuracy control scheme based on the structure characteristics of a brushless DC motor for speed control. The main features of the control system are as follows: • Optimized motor efficiency • Control of the spindle motor speed by a micro-controller • Accuracy achieved on the operating speed at 3600 rpm is ±0.03%
{"title":"Design of an Accurate Speed Control System for Brushless DC Motor","authors":"Zhang Chen, Joseph T. Ma","doi":"10.1115/imece1996-1078","DOIUrl":"https://doi.org/10.1115/imece1996-1078","url":null,"abstract":"\u0000 The brushless DC motor is widely used in industry. In this paper, we present a low cost, high accuracy control scheme based on the structure characteristics of a brushless DC motor for speed control. The main features of the control system are as follows:\u0000 • Optimized motor efficiency\u0000 • Control of the spindle motor speed by a micro-controller\u0000 • Accuracy achieved on the operating speed at 3600 rpm is ±0.03%","PeriodicalId":231650,"journal":{"name":"7th International Symposium on Information Storage and Processing Systems","volume":"118 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122875682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper uses Lyapunov’s method to examine the stability of a flexible spinning disk that is hydrodynamically coupled to the thin films of air surrounding it. A hydrodynamically coupled Lyapunov functional that defines the stable operational speed range of the disk is presented here for the first time. The stability boundary or, equivalently, the maximum stable speed, defined by this functional is independent of the strength of the coupling and allows significantly higher rotation speeds than allowed in the absence of hydrodynamic coupling. The hydrodynamically coupled critical speed is an order of magnitude higher than the uncoupled critical speed for clamping ratios less than 0.3. Several vibration modes of the disk which travel forwards at one half the rotation speed are stable but not asymptotically stable despite the large hydrodynamic damping present in the system. Unlike many elastohydrodynamic stability problems, calculation of the stability boundary using Lyapunov’s method is linear and tractable. The form of the Lyapunov functional suggests several design features that may be helpful in the design of improved, high speed configurations.
{"title":"The Stability of Flexible Spinning Disks Supported by Incompressible Hydrodynamic Lubrication","authors":"A. A. Renshaw","doi":"10.1115/imece1996-1080","DOIUrl":"https://doi.org/10.1115/imece1996-1080","url":null,"abstract":"This paper uses Lyapunov’s method to examine the stability of a flexible spinning disk that is hydrodynamically coupled to the thin films of air surrounding it. A hydrodynamically coupled Lyapunov functional that defines the stable operational speed range of the disk is presented here for the first time. The stability boundary or, equivalently, the maximum stable speed, defined by this functional is independent of the strength of the coupling and allows significantly higher rotation speeds than allowed in the absence of hydrodynamic coupling. The hydrodynamically coupled critical speed is an order of magnitude higher than the uncoupled critical speed for clamping ratios less than 0.3. Several vibration modes of the disk which travel forwards at one half the rotation speed are stable but not asymptotically stable despite the large hydrodynamic damping present in the system. Unlike many elastohydrodynamic stability problems, calculation of the stability boundary using Lyapunov’s method is linear and tractable. The form of the Lyapunov functional suggests several design features that may be helpful in the design of improved, high speed configurations.","PeriodicalId":231650,"journal":{"name":"7th International Symposium on Information Storage and Processing Systems","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125403970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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