Development of a simplified procedure for rocket engine thrust chamber life prediction with creep

An analytical method for predicting engine thrust chamber life is developed. The method accounts for high pressure differentials and time-dependent creep effects both of which are significant in limiting the useful life of the shuttle main engine thrust chamber. The hot-gas-wall ligaments connecting adjacent cooling channels ribs and separating the coolant flow from the combustion gas are subjected to a high pressure induced primary stress superimposed on an alternating cyclic thermal strain field. The pressure load combined with strain-controlled cycling produces creep ratcheting and consequent bulging and thinning of these ligaments. This mechanism of creep-enhanced ratcheting is analyzed for determining the hot-gas-wall deformation and accumulated strain. Results are confirmed by inelastic finite element analysis. Fatigue and creep rupture damage as well as plastic tensile instability are evaluated as potential failure modes. It is demonstrated for the NARloy Z cases analyzed that when pressure differentials across the ligament are high, creep rupture damage is often the primary failure mode for the cycle times considered

Development of a simplified procedure for thrust chamber life prediction

An analytical design procedure for predicting thrust chamber life considering cyclically induced thinning and bulging of the hot gas wall is developed. The hot gas wall, composed of ligaments connecting adjacent cooling channel ribs and separating the coolant flow from the combustion gas, is subjected to pressure loading and severe thermal cycling. Thermal transients during start up and shut down cause plastic straining through the ligaments. The primary bending stress superimposed on the alternate in-plane cyclic straining causes incremental bulging of the ligaments during each firing cycle. This basic mechanism of plastic ratcheting is analyzed and a method developed for determining ligament deformation and strain. The method uses a yield surface for combined bending and membrane loading to determine the incremental permanent deflection and pregressive thinning near the center of the ligaments which cause the geometry of the ligaments to change as the incremental strains accumulate. Fatigue and tensile instability are affected by these local geometry changes. Both are analyzed and a failure criterion developed

The dynamic stability and nonlinear resonance of a flexible connecting rod: Continuous parameter model

The transverse vibrations of a flexible connecting rod in an otherwise rigid slider-crank mechanism are considered. An analytical approach using the method of multiple scales is adopted and particular emphasis is placed on nonlinear effects which arise from finite deformations. Several nonlinear resonances and instabilities are investigated, and the influences of important system parameters on these resonances are examined in detail.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43330/1/11071_2004_Article_BF00162233.pd

On a Numerical Method for Solution of the Mathieu-Hill Type Equations

This paper presents a computer-programmable numerical method for the solution of a class of linear, second order differential equations with periodic coefficients of the Mathieu-Hill type. The method is applicable only when the initial conditions are prescribed and the solution is not requiried to be periodic. The solution is facilitated by representing the coefficient functions as a sum of step functions over corresponding sub-intervals of the fundamental interval. During each sub-interval, the solution form is assumed to be that of the differential equations with constant coefficients. Constraint equations are derived from imposing the conditions of compatibility of response at the end nodes of the intermediate sub-intervals. This set of simultaneous linear equations is expressed in matrix form. The matrix of coefficients may be represented as a triangular one. This form greatly simplifies the solution process for simultaneous equations. The method is illustrated by its application to some specific problems

Hierarchy of Equations of Motion of Planar Mechanism with Elastic Link

The governing equations of motion are derived for a planar slider-crank linkage with rigid crank and elastic connecting rod, taking into account its distributed mass and elasticity. The system unknowns, namely, the axial displacement, the transverse displacement and the cross-sectional angular displacement of the elastic link, appear in the nonlinear equations of motion. The equations include the effects of shear deformation and rotatory inertia, and are also applicable for large displacements. As simplifications are systematically introduced, these equations are shown to degenerate into some well known equation forms

Effect of Internal Material Damping on the Dynamics of a Slider-Crank Mechanism

A study of the effect of internal material damping on the dynamic response behavior of a slider-crank mechanism is presented in this paper. In developing the governing equations of motion, an assumption of a linear viscoelastic model for the connecting rod is made. A perturbation approach is utilized for reducing these coupled axial and transverse nonlinear equations to a nonhomogeneous damped Mathieu equation, describing the transverse vibration of the connecting rod. Both steady-state and transient solutions are determined and compared to those obtained from the use of an undamped connecting rod. It is demonstrated that the viscoelastic material damping can have significant influence, both favorable and adverse, in attempting to attenuate the steady-state and transient response of the connecting rod. The response is computed for several combinations of the excitation parameter and the frequency ratio. The stability of the transverse vibration of the connecting rod is also investigated in this paper

Member Initial Curvature Effects on the Elastic Slider-Crank Mechanism Response

Parametric vibration of initially curved columns loaded by axial-periodic loads has received considerable attention, concluding that regions of instability exist and that excitation frequencies less than the natural frequency of the principal resonance may occur. Recent publications have cautioned against the use of curved members in machines designed for precise operation, suggesting a detrimental coupling of the longitudinal and transverse deformations. In this work, the dynamic behavior of a slider-crank mechanism with an initially curved connecting rod is investigated. Governing equations of motion are developed using the Euler-Bernoulli beam theory. Both steady-state and transient solutions are determined, and compared with those obtained for the mechanism possessing a geometrically perfect (straight) connecting rod. A very small initial curvature is shown to cause a significantly greater steady-state response. The magnification in its transient response is shown to be even greater than that due to a straight connecting rod. Additionally, an excitation frequency less than the natural frequency is also shown to occur