Brad A. Miller

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. @DOI: 10.1115/1.1308015#

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. @DOI: 10.1115/1.1510876#

Numerical Techniques for Computing Rotordynamic Properties of Mechanical Gas Face Seals

The gas film stiffness and damping properties for a spiral grooved mechanical face seal in a flexibly mounted stator configuration are computed using the step jump method and a novel direct numerical frequency response method. The seal model has three degrees of freedom, including axial displacement of the stator and two stator tilts about mutually perpendicular diametral axes. Results from both methods agree well with previously published results computed using the perturbation method, but the two new methods have the advantage of employing computer programs used in the direct numerical simulation of motion. Based on the linearized analysis, the two angular modes are proven to be coupled together and decoupled from the axial mode. Anomalies in the gas film properties tend to occur at large compressibility numbers. The step jump method requires less computing time than the direct frequency response method but at a sacrifice in accuracy at high excitation frequencies.

Nonlinear Modeling of Mechanical Gas Face Seal Systems Using Proper Orthogonal Decomposition

An approach based on proper orthogonal decomposition and Galerkin projection is presented for developing low-order nonlinear models of the gas film pressure within mechanical gas face seals. A technique is developed for determining an optimal set of global basis functions for the pressure field using data measured experimentally or obtained numerically from simulations of the seal motion. The reduced-order gas film models are shown to be computationally efficient compared to full-order models developed using the conventional semidiscretization methods. An example of a coned mechanical gas face seal in a flexibly mounted stator configuration is presented. Axial and tilt modes of stator motion are modeled, and simulation studies are conducted using different initial conditions and force inputs. The reduced-order models are shown to be applicable to seals operating within a wide range of compressibility numbers, and results are provided that demonstrate the global reduced-order model is capable of predicting the nonlinear gas film forces even with large deviations from the equilibrium clearance.

Clearance Regulation of Mechanical Gas Face Seals: Part II—Analysis and Control

This article presents the analysis and control of noncontacting mechanical gas face seals based on the state space model developed in Part I. Methods to analyze the controllability and observability of axial and tilt modes are described. The controllability analysis determines to what extent the dynamic response of the seal system modes can be shaped in a closed-loop feedback system, and the observability analysis determines if the seal system modes can be reconstructed from specific state measurements of the axial clearance and stator tilts. The error state-space method is employed to design a tracking controller to regulate the seal at a prescribed axial clearance. The control law is a function of all axial states; therefore, reduced order linear observers are designed to observe the unmeasured axial and tilt seal states. The axial clearance and tilt state estimates are used to reconstruct the gas film axial force and moments, which cannot be directly measured, for design and analysis. The analysis and control techniques are applied to the illustrative example presented in Part I. The results demonstrate that the gas film forces and moments can be estimated well and the seal system can be satisfactorily regulated with a sufficiently damped response that is within the bandwidth of todays electropneumatic actuators.

Clearance Regulation of Mechanical Gas Face Seals: Part I—Modeling

A new state space model is presented for coned face flexibly mounted stator (FMS) mechanical gas face seals. The model employs an analytical representation of the linearized gas film stiffness and damping properties. States are defined for the generalized gas film force modes and the mechanical dynamic modes. The state space formulation is convenient for determining stability limits and also allows for efficient time domain simulation as compared to simulations where convolution integrals must be computed or full numerical simulations employing the Reynolds equation must be utilized. The modeling techniques are applied to a noncontacting mechanical gas face seal, the stability limit is found, and simulation results are compared to a full numerical simulation utilizing the Reynolds equation. The simulation results validate the developed model. The state space model is utilized in Part II to perform controllability and observability analyses and to design reduced order observers to estimate states that cannot be measured and robust tracking controllers to regulate the seal clearance to maintain system stability.

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 technigue 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.

Real-Time Force and Moment Estimation for Mechanical Gas Face Seal Systems Using Reduced-Order Kalman Filters

A method using reduced-order Kalman filters is developed to estimate the thin gas film axial force and moments in real-time for mechanical gas face seal systems in a flexibly mounted stator configuration. First-order Gauss-Markov stochastic models, combined with the stator motion equations, form the basis for the reduced-order Kalman filter estimators. Two schemes are presented to estimate axial force and moments based on stator motion measurements. In one scheme, the force and moments are directly estimated and, in another scheme, a set of proper orthogonal decomposition (POD) weighting functions are estimated, from which the gas film force and moments are computed. Both estimators are shown to approximate the gas film axial force and moments successfully for different forcing functions over a wide range of compressibility numbers.