Rotor Runout Research Articles

State Observers and Run-Out Reduction for Magnetically Levitated Motor Systems

Magnetically levitated motor systems create opportunities for new applications of electromechanical power conversion where high-speed and contact-free operation are required. These systems require position sensors and control algorithms for stable levitation which often require filters to reduce feedback noise. Noisy position feedback creates challenges for high-bandwidth estimation of velocity and disturbance force; however, these unmeasured states can be helpful for high-performance control algorithms. This common problem in drives for electric motors has been solved using the Luenberger-style motion state observer. This article investigates the applicability of the observer to digitally-controlled magnetically levitated systems. First, the observer's embedded plant model is derived for discrete-time implementation. Then, it is shown that the most advantageous use-case of the observer is different for magnetically levitated systems versus rotary motor systems. Unlike motor systems, the zero-lag filtering property of observers is minimally useful, while the ability to estimate and reject disturbances yields significant performance improvements for applications that care about run-out. Comprehensive experimental results are provided on a prototype bearingless motor which validate the observer's performance versus frequency and its ability to estimate disturbance forces for use in reducing the rotor run-out. Experimental results achieve over 10× run-out reduction at low-medium speeds while also reducing control current by 50%.

Analysis of total rotor runout components with multi-probe roundness measurement method

Several standards for vibration testing of rotating machinery define limits for relative shaft displacement during rotation. With requirements for relative shaft displacement, limits are given for combined electrical and mechanical runout, which is the eddy probe reading error and the error caused by geometry of the measured shaft. Some standards allow for compensation of the mechanical and electrical runout by vectorially subtracting them from the eddy current probe values.This paper presents a measurement procedure applying multi-probe error separation to accurately determine the roundness profile and center point motion of electric motor shafts. The roundness error and center point movement obtained from multi-probe measurement with tactile displacement probes are compared with eddy current sensor displacement measurements to separate the total displacement measured with an eddy current probe into three components: center point motion, roundness error and electrical runout. Additionally, a transform for the measured eccentric component is presented to obtain an estimate for permanent rotor bow regardless of the rotor support arrangement during measurement.The relevant industrial vibration testing standards were reviewed. Several issues were found in the measurement methods required by the standards. The requirements of the standards and the used terminology are assessed critically and improvement proposals are presented.

On the Accuracy of Hemolysis Models in Couette-Type Blood Shearing Devices.

Hemolysis is one of the most challenging issues faced by blood contacting devices. Empirical hemolysis models often relate hemolysis to shear stress and exposure time. These models were generally derived from the experimental results of Couette-type blood shearing devices, with assumption of uniform exposure time and shear stress. This assumption is not strictly valid since neither exposure time nor shear stress is uniform. Hence, this study evaluated the influence of the nonuniform exposure time and rotor eccentricity or run-out on the accuracy of power-law hemolysis models, using both theoretical and CFD analysis. This work first provided a systematic analysis of the flow regime in a typical Couette shearing device, and showed the axial flow component can be regarded as fully developed laminar plane Poiseuille flow. It was found that the influence of nonuniform exposure time is within 4% for several widely used power-law models, which were validated by steady CFD simulations. A theoretical relationship was then built between the rotor run-out and hemolysis. We noticed that the influence of rotor run-out on hemolysis is within 5% for a moderate rotor run-out ratio of 0.2. Next, transient CFD simulations were performed to investigate the influence of rotor run-out on hemolysis with run-out ratios of 0.1 and 0.2. The results showed negligible effects for a moderate run-out ratio of 0.1. However, a run-out ratio of 0.2 led to a significant increase of hemolysis, resulting from back flows induced by the run-out of the rotor. These findings will be of great importance for the improvement of the hemolysis estimation and blood compatibility design.

Application of Second-Order Sliding-Mode Concepts to Active Magnetic Bearings

Rotor mass imbalance is a common problem to rotating machines due to the unavoidable imperfections in manufacturing. These imbalance forces can be viewed as harmonic disturbances which lead to a periodic rotor runout during rotation. Furthermore, the runout length increases with the rotational speed squared. Moreover, for variable rotational speed applications, these harmonic disturbances are also time-varying. Active magnetic bearings (AMB) provide a means of actively attenuating these disturbances. Although various imbalance compensation schemes have been proposed in the literature to handle this problem, they are often more suitable for constant rotational speed applications where disturbances can be handled at a predetermined rotational speed. This study proposes the application of second-order sliding-mode control (2-SMC) to regulate AMB systems throughout a wide operating speed range. The proposed controllers are composed of two components. The first component is a linear controller for the sake of stabilizing the inherently unstable system, while the second component is a 2-SMC to handle the model uncertainties of the system as well as the exogenous harmonic disturbances. Simulation and experimental results are provided to demonstrate the effectiveness and superiority of the proposed techniques compared to the conventional linear controller.

Analysis and Suppression of the Suspended Rotor Displacement Fluctuation Influence for Motor System

Suspended rotor displacement fluctuation would result in unbalanced magnetic pull and inaccurate speed measurement, which degrades the suspended rotor stability and motor performance. In order to reduce the blight, some research studies have been conducted. First, the influence on the motor magnetic field has been analyzed between motors with iron-cored and coreless stator structures. It is found that with the coreless stator, the air-gap magnetic flux density variation can be neglected. Second, the law of the speed fluctuation caused by the rotor runout has been studied. In addition, two methods, which are based on the use of notch filter and speed correction, have been proposed for suppressing the fluctuation. Third, the performances of the closed-loop systems with the proposed speed fluctuation suppression methods have been analyzed. Finally, experimental results are presented to demonstrate the correctness of the analysis and the validity of the proposed methods.

Analyses of both steady behavior and dynamic tracking of non-contacting spiral-grooved gas face seals

The analyses for steady and unsteady sealing behaviors of spiral-grooved gas face seals are presented by finite element method. The element with nine nodes and four quadratic cures is used. And for avoiding the film thickness discontinuity over the grooves, two of them coincide with the circular arcs and the others approximate to the spiral lines. In steady-state analysis, the steady-state Reynolds equation is used, and different element meshes are utilized for different sealed pressures. The load capacity and the lubricant leakage on gas face seals are shown for different compressibility numbers and sealed pressures. Thus the optimal sealed pressure and the gas amount needed in actual applications can be determined according to the numerical results. For the dynamic tracking of the stator, the direct-dynamic analysis is used, and the explicit form of the unsteady compressible Reynolds equation is found by weighting the film thickness in each element. The initial pressure profile and the initial closing force are determined at the given sealed pressure. The dislocations due to the external shock disturbances are considered, including the rotor runout only, the stator misalignment only, and the mixed dislocations. The possibility of face contact, the detectable central clearance between stator and rotor, and the leakage under unsteady operation are concerned.

Adaptive Control of Mechanical Gas Face Seals With Rotor Runout and Static Stator Misalignment

This paper presents a control methodology that utilizes a robust model reference adaptive control technique to regulate the dynamic behavior of a coned mechanical gas face seal system in a flexibly mounted stator configuration. Individual adaptive controllers are designed for the three stator rigid body degrees of freedom based on the linear portions of their respective equations of motion. The force and moments generated within the gas film are estimated using Kalman filter-based estimators and directly cancelled in the control algorithm using offset control signals. The estimation errors are considered as bounded disturbances to the seal system and are taken into account by the robust adaptive controllers. Simulation results show that the controllers effectively stabilize the stator motion and control the stator tilts to synchronously track the rotor runout with near-zero relative misalignment magnitude and phase shift, thus, minimizing gas leakage.

An Evaluation Method for Spindle Motor Runout Measurement

In order to study the vibration characterization of a spindle motor, the rotor runout must be measured accurately. In this paper, a method based on measurement uncertainty is presented to evaluate different measurement systems and measurement confidence. The principle optic interferometer (iRVM) system is introduced in this paper, which is based on optical interference technology. The results of the iRVM are compared with another two methods that make use of capacitance probe and laser Doppler velocimetry.

Semi-Analytical Dynamic Analysis of Spiral-Grooved Mechanical Gas Face Seals

A novel semi-analytical formulation is presented for the linearized dynamic analysis of spiral-grooved mechanical gas face seals. The linearized rotordynamic properties of the gas film are numerically computed and then represented analytically by a constitutive model consisting of a cosine modified Prony series. The cosine modification enables the Prony series to characterize the gas film properties of face seals in applications with large compressibility numbers. The gas film correspondence principle is then employed to couple the constitutive model to the dynamics of the mechanical face seal. Closed-form solutions are presented for the transient natural response to initial velocity conditions, the steady-state response to rotor runout and initial stator misalignment, the transmissibility ratios, and the stability threshold. Results from the closed-form solutions are all within a few percent of the results from a full nonlinear numerical simulation.

Numerical Modeling of Dynamic Sealing Behaviors of Spiral Groove Gas Face Seals

A numerical model is developed for the dynamic analysis of gas lubricated spiral groove face seals. Effects of the rotor runout, misalignment, face contact, as well as the stiffness and damping of the secondary seal are considered. Seal axial and angular motions and key parameters such as torque, power loss, and flow rate are obtained by a global time integration scheme, which traces the time history of the dynamic sealing behaviors. The analysis of gas film lubrication, face contact, and the seal dynamics is cast as an inverse problem and the solution is obtained iteratively at each time step. Dynamic tracking motion and key sealing characteristics of a representative spiral groove gas seal undergoing transient operations are presented.

A Parametric Analysis of the Transient Forced Response of Noncontacting Coned-Face Gas Seals

A properly designed mechanical face seal must satisfy two requirements: (1) the seal must be stable, and (2) the seal forced response must be such that the stator tracks the misaligned rotor with the smallest clearance possible, with the smallest relative tilt, and with the largest minimum film thickness. The stability issue was investigated in a previous paper. Here a numerical solution is presented for the transient response of a noncontacting gas lubricated face seal that is subjected to stator and rotor forcing misalignments. The seal dynamic response is obtained in axial and angular modes of motion in a coupled analysis where the Reynolds equation and the equations of motion are solved simultaneously. The steady-state response is first identified for a reference case. Subsequently a parametric study is performed to gauge the influence of the various seal effects, such as speeds, inner to outer radii ratios, face coning heights, pressure drops, support stiffness and damping, and forcing misalignments. The transient responses to static stator misalignment and rotor runout are given, showing that properly designed coned face seals can operate in a stable mode with the stator tracking dynamically a misaligned rotor.

Numerical Formulation for the Dynamic Analysis of Spiral-Grooved Gas Face Seals

A numerical formulation is presented for the dynamic analysis of spiral-grooved gas lubricated mechanical face seals with a flexibly mounted stator. Axial and angular modes of motion are considered. Both finite volume and finite element methods are employed for the spatial discretization of the unsteady, compressible form of the Reynolds equation. Self-adapting unwinding schemes are employed in both methods, making them suitable for situations when the compressibility number is high. Both the lubrication analysis and the kinetic analysis are arranged into a single state space form, which makes coupling the two analyses straightforward. The resulting set of equations is solved using a linear multistep ordinary differential equation solver. Examples of the transient response to static stator misalignment and rotor runout are given. Although a properly designed spiral grooved face seal provides good dynamic performance, it is shown that unacceptably large face separation can occur when large angle spiral grooves are employed together with a sealing dam.

A Study on Run-out Characteristics of Externally Pressurized Gas Journal Bearing. 2nd Report. Rotor Run-out Characteristics.

The run-out characteristics of a rotor supported by an externally pressurized gas journal bearing are analyzed theoretically with special attention to the relation with the machining errors of the bearing system. Both the static and dynamic run-out characteristics are discussed. The form deviation of the rotor cross section (i. e., out-of-roundness) is attributed to the critical factor which may govern the run-out characteristics of the rotor. The effects of size deviation of the supply holes are also investigated. The obtained results may offer a fundamental concept of the precision design of the externally pressurized gas bearing with respect to the rotating accuracy of the rotor.

A Study on the Running Accuracy of an Externally Pressurized Gas Thrust Bearing. Rotor Run-Out Characteristics.

To establish a fundamental concept for the precision design of a gas bearing, the static and dynamic run-out characteristics of a rotor supported by an externally pressurized gas-lubricated thrust-collar bearing are investigated in this paper. The concept is based on the theoretical results developed in the previous papers on load capacity fluctuation, which is caused by machining errors such as the out-of-perpendicularity of the rotor-end surface and the size deviation of supply holes of the bearing, as well as on the fundamental bearing characteristics such as stiffness and damping coefticient. The "averaging effect" for the rotor run-out characteristics is evaluated quantitatively. The experimental results for the amplitude of the rotor vibration coincide well with the theoretical results, which may confirm the validity of the theoretical model used in this study.

Nonlinear Dynamic Analysis of Noncontacting Coned-Face Mechanical Seals

The complete nonlinear equations of motion of a flexibly mounted stator in a noncontacting coned-face mechanical seal are solved numerically. The solution utilizes a transient dynamic analysis and takes into account rotor axial runout and assembly tolerances in the form of initial stator misalignment. Cavitation of the fluid film is also accounted for. A parametric investigation is performed and the effect of various design parameters and operation conditions on the seal dynamics is presented and discussed. A critical shaft speed is found above which the seal becomes dynamically unstable. A critical rotor runout is found which, if exceeded, will cause seal failure due to local face rubbing contact. A comparison is made between the numerical results and those of a simpler analytical solution. It is found that the analytical solution is valid for most practical applications of mechanical seals. Presented at the 40th Annual Meeting in Las Vegas, Nevada May 6–9, 1985

Stability Threshold and Steady-State Response of Noncontacting Coned-Face Seals

The dynamic behavior of a noncontacting coned-face seal is analyzed. Stiffness and damping properties of the fluid film and flexible support including elastomeric secondary seal are fully accounted for. Stability threshold and steady-state response in the presence of rotor axial runout and assembly misalignment are investigated. An expression is provided for the critical speed above which the seal becomes dynamically unstable. For stable operation, the relative misalignment between the mating faces is given as a function of rotor runout, assembly misalignment, design parameters, and operation conditions. An expression is provided for the critical rotor runout above which the seal will fail due to face contact. Although the analysis is based on small perturbation assumption, it is shown to be valid in many practical cases.

Experimental Observation of the Dynamic Behavior of Noncontacting Coned-Face Mechanical Seals

The dynamic behavior of a coned-face noncontacting seal is experimentally observed by means of three proximity probes monitoring the motion of the flexibly mounted stator. The various tilts of the stator are analyzed and the relative misalignment between stator and rotor is found. The effects of both the rotor runout and the flexible support on the relative misalignment are discussed. The tests demonstrate both stable and transition to unstable modes of seal operation. Reasons for failure and other phenomenon during stable seal operation are explained.

A Computational Technique for Optimizing Correction Weights and Axial Location of Balance Planes of Rotating Shafts

An iterative procedure is presented for the balancing of a flexible rotor. In addition to determining optimal correction weights, the number and axial positions of the balance planes are optimized. A linear programming solution is employed using a linearized approximation of the axial variation of the influence coefficients. First the correction weights are found and then the axial locations of the balance planes are adjusted. These computations are repeated until the optimal values that lead to minimum rotor runout are determined. Numerical results are discussed.

A Linear Programming Approach for Balancing Flexible Rotors

The feasibility of a new flexible rotor balancing method is demonstrated. Discrete “effective” unbalance components which produce the same observed response as the actual rotor unbalance are identified, and subsequently removed, using linear programming. In addition to satisfying rotor runout observations, the unbalance may be identified such that it is potentially harmful to response at a speed above the level at which the shaft can safely run without balancing. The potentially harmful response corresponds to the linear programming objective function, while the observations become constraints. In addition, further constraints can be included to assure that the size of the calculated balance weights are within practical limits. The versatility of the new approach is demonstrated with example problems using a rotor model for which the response is obtained with a computer code.