Dynamic behavior of direct spring loaded pressure relief valves in gas service: Model development,measurements and instability mechanisms

A synthesis of previous literature is used to derive a model of an in-service direct-spring pressure relief valve. The model couples low-order rigid body mechanics for the valve to one-dimensional gas dynamics within the pipe. Detailed laboratory experiments are also presented for three different commercially available values, for varying mass flow rates and length of inlet pipe. In each case, violent oscillation is found to occur beyond a critical pipe length, which may be triggered either on valve opening or closing. The test results compare favorably to the simulations using the model. In particular, the model reveals that the mechanism of instability is a Hopf bifurcation (flutter instability) involving the fundamental, quarter-wave pipe mode. Furthermore, the concept of the effective area of the valve as a function of valve lift is shown to be useful in explaining sudden jumps observed in the test data. It is argued that these instabilities are not alleviated by the 3% inlet line loss criterion that has recently been proposed as an industry standard.     

The dynamic response of pressure relief valves in vapor or gas service. Part II: Experimental investigation

An experimental testing program designed to evaluate the opening stability characteristics of direct acting pressure relief valves (PRV) in gas/vapor service is described. Three different valve sizes from each of three different manufacturers were tested at two different set pressures to determine their opening characteristics (disk lift vs. time). The valves were tested with several different lengths of inlet piping as well as with and without discharge piping to determine the conditions under which unstable operation (chatter) would occur. Part I of this program described a mathematical model for predicting the dynamic response of PRV's, and the data described in this test program were used to evaluate the accuracy of the model, as described in Part III of this study to follow.     

Robust prediction of chatter stability in milling based on the analytical chatter stability

A major obstacle that limits the productivity in machining operations is the presence of machine tool chatter. Machining is a dynamic process and chatter behavior depends upon a number of different aspects including spindle speeds, material properties, tool geometry, and even the location of tool respect to the rest of machine. Many of the traditional models used to predict chatter stability lobes assume that parameters such as natural frequency, stiffness, and cutting coefficients remain constant. In reality, these parameters vary and they affect the chatter stability. The uncertainty in these parameters can be taken into consideration by employing the robust stability theory into a two degree of freedom milling model. Utilizing the Edge theorem and the Zero Exclusion condition, a robust chatter stability model, based on the analytical chatter stability milling model, is developed. This improves the reliability compared to the projected pseudo single degree of freedom model. The method is verified experimentally for milling operations while considering a changing natural frequency and cutting coefficient.     

Spindle dynamics identification using particle swarm optimization

Optimal parameters to eliminate machining chatter may be identified using analytical stability models which require the dynamics of the tool-holder-spindle-machine assembly. Receptance coupling substructure analysis (RCSA) provides a useful analytical tool to couple measured spindle-machine dynamics with tool-holder models to predict the tool point frequency response function for the assembly. Previous research has demonstrated a procedure to determine all required spindle receptances from a single measurement, where each mode within the measurement bandwidth was modeled as a fixed-free Euler–Bernoulli beam and fit using a manual, iterative procedure. Here, a particle swarm optimization technique is described for fitting the spindle-machine measurement using a fixed-free Euler–Bernoulli beam model for each mode. The performance of the optimization process and RCSA in predicting the tool tip frequency response is evaluated and the results are presented.     

The dynamic response of pressure relief valves in vapor or gas service,part I: Mathematical model

In order to prevent unstable operation, or “chatter”, of a pressure relief the API guidelines recommend limiting the irreversible pressure loss in the inlet line to a pressure relief valve to no more than 3% of the valve set pressure. This criterion is based on steady-state operating conditions and a typical blow-down pressure for the valve of about 7% of the set pressure. However, the stability of the valve is also influenced by other factors such as the dynamic response of the valve disk to the unsteady pressures and forces exerted by the fluid on the disk. A model for the opening lift dynamic response of a pressure relief valve in gas/vapor service is presented here which accounts for all of these effects through a set of five coupled nonlinear algebraic/differential equations. These equations are solved by a numerical method that can be implemented on a spreadsheet to predict the position of the valve disk as a function of time for given valve characteristics, operating conditions, and installation parameters. The model incorporates the influence of the various parameters on the stable/unstable nature of the disk response. An example is presented for a typical valve that illustrates the various modes of stable and unstable dynamic response that can be predicted by the model under various conditions. Two additional papers will be forthcoming: Part II – Experimental Investigation and Part III – Analysis of Data and Comparison with Model Predictions.