Solid Rocket Motor Grain Research Articles

Finite element method for viscoelastic medium with damage and the application to structural analysis of solid rocket motor grain

This paper studies the damage-viscoelastic behavior of composite solid propellants of solid rocket motors (SRM). Based on viscoelastic theories and strain equivalent hypothesis in damage mechanics, a three-dimensional (3-D) nonlinear viscoelastic constitutive model incorporating with damage is developed. The resulting viscoelastic constitutive equations are numerically discretized by integration algorithm, and a stress-updating method is presented by solving nonlinear equations according to the Newton-Raphson method. A material subroutine of stress-updating is made up and embedded into commercial code of Abaqus. The material subroutine is validated through typical examples. Our results indicate that the finite element results are in good agreement with the analytical ones and have high accuracy, and the suggested method and designed subroutine are efficient and can be further applied to damage-coupling structural analysis of practical SRM grain.

An integrated framework for solid rocket motor grain design optimization

Traditional grain designs, which identify the best combination of geometrical parameters to improve the grain performance and meet the flight-mission requirements, are often performed manually. In this article, an integrated framework is presented to perform the design optimization of solid rocket motor propellant grains. In the proposed framework, the level set method is adapted to solid propellant burnback analysis and this technique does not have any restriction on the grain configuration and is capable of handling grains of multi-stage and various burning forms. Along with the level set method, a dedicated algorithm is developed using application programming interfaces of commercial computer-aided design software to transform the initial grain shape into a special data file that can be fed to the level set codes to activate the burnback analysis. Moreover, a hybrid optimization method incorporating genetic algorithm and sequential quadratic programming is exploited to improve the grain design efficiency. Finally, two case studies have been performed to verify the feasibility and general-purpose characteristics of the proposed grain design optimization environment. The results obtained show that the proposed design framework facilitates the grain optimization process and various grain design requirements can be met. The design cycle has been remarkably reduced because of the introduction of hybrid optimization method.

Aerospace design optimization using a compound repulsive particle swarm

This study shows the benefits of using a compound repulsive particle swarm optimizer (RPSO) for use in aerospace design applications. A new hybrid optimizer has been developed for this study involving a separate particle swarm imbedded within the standard RPSO. The engineering design problems for this study include the development of a desired solid rocket motor grain, a solid motor sounding rocket, and a single stage solid propellant missile system. The methods are used independently to match a prescribed set of parameters defining the propellant characteristics and/or the missile’s geometry. The design study was conducted using both the standard RPSO and the newly developed compound RPSO. The algorithms are compared based on their speed and effectiveness in solving the design problem, with the figure of merit being a factor based on a set of desired performance goals.

Robust performance optimization of dual thrust rocket motor

PurposeDuring any design phase, the associated process variations and uncertainties can cause the design to deviate from its expected performance. The purpose of this paper is to propose a robust design optimization (RDO) strategy for the 3D grain design of a dual thrust solid rocket motor (DTRM) under uncertainties in design parameters.Design/methodology/approachThe methodology consists of design of 3D complex grain geometry and hybrid optimization approach through genetic algorithm, globally and simulated annealing, locally considering the uncertainties in design parameters. The robustness of optimized data is measured for a worst case parameter deviation using sensitivity analysis through stochastic Monte Carlo simulation considering variance of design parameters mean.FindingsThe important achievement that can be associated with this methodology is its ability also to evaluate and optimize the propulsion system performance in a complex scenario of intricate 3D geometry under uncertainty. The study shows the objective function to maximize the average thrust in dual levels could be achieved by the proposed optimization technique while satisfying constraints conditions. Also, this technique proved to be a great help in reducing the design space for optimization and increasing the computational quality.Originality/valueThis is the first paper to address the dual thrust solid rocket motor grain design under uncertainties using robust design and hybrid optimization approach.

Analysis on the Structural Reliability of Solid Rocket Motor Grains

Based on Integral Stochastic Finite Element Method (ISFEM), the structural reliability of solid propellant grain was analyzed. Viscoelastic finite element method was determined and ISFEM is utilized to improve calculation efficiency. The thermally accelerated aging experiments at 40°C，50°C，60°C and 70°C were carried out, and the mechanical property parameters were investigated. Considering the randomness of Poisson’s ratio and relaxation modulus, structural reliability and its variation tendency solid rocket motor grain under the ignition pressurization case were investigated in combination with failure criterion. The results show that the reliability of SRM grain descends not evidence before twelve years, but quickly descends after 12 years.

Stability Analysis of Cracks in the Stress-Release Boot of Solid Rocket Motor Grain with J-Integral

The stress-release boot is always used in the fore and rear of SRM grain to relief stress-strain concentration under thermal loading. Since the debonded crack in the stress-release boot may be propagation unstable when the internal pressure entered the debonded crack cavity, the SRM with debonded cracks is very dangerous when it is lunched. So the stability analysis of the debonded cracks is very important to evaluate the defect grain structure integrity. In order to investigate the stability of debonded cracks in the stress-release boot of SRM grain during ignition pressurization, three-dimension (3-D) viscoelastic finite element models of the SRM grain with debonded cracks are established. The 3-D singular crack elements at the tips of cracks are developed to simulate the stress-release boot debonded crack propagation. And all the singular crack elements are included in the 3-D J-integral loop surface to improve the calculation precision. Along with the debonded crack propagation, the 3-D J-integrals of the debonded crack tips are respectively calculated to prejudge its expanding trend. The results show that the most dangerous situation will occur in the fore stress-release boot debonded cracks during the rocket being launched.

Multidisciplinary Design and Optimization of Multistage Ground-launched Boost Phase Interceptor Using Hybrid Search Algorithm

This article proposes a multidisciplinary design and optimization (MDO) strategy for the conceptual design of a multistage ground-based interceptor (GBI) using hybrid optimization algorithm, which associates genetic algorithm (GA) as a global optimizer with sequential quadratic programming (SQP) as a local optimizer. The interceptor is comprised of a three-stage solid propulsion system for an exoatmospheric boost phase intercept (BPI). The interceptor's duty is to deliver a kinetic kill vehicle (KKV) to the optimal position in space to accomplish the mission of intercept. The modules for propulsion, aerodynamics, mass properties and flight dynamics are integrated to produce a high fidelity model of the entire vehicle. The propulsion module comprises of solid rocket motor (SRM) grain design, nozzle geometry design and performance prediction analysis. Internal ballistics and performance prediction parameters are calculated by using lumped parameter method. The design objective is to minimize the gross lift off mass (GLOM) of the interceptor under the mission constraints and performance objectives. The proposed design and optimization methodology provide designers with an efficient and powerful approach in computation during designing interceptor systems.

Multiscale Modeling of Solid Rocket Motors: Computational Aerodynamic Methods for Stable Quasi-Steady Burning

We consider the problem of efficiently computing the stable burnback of a solid rocket motor when the motor is in the quasi-steady burning regime of operation. When the motor is modeled as a cavity, filled with a compressible fluid with injection from the solid-propellant surface, the problem is a standard one in steady computational aerodynamics. For large rockets, the problem of quasi-steady solid rocket motor core flow is analogous to the steady aerodynamic flow past a large aircraft flying at speeds such that compressible flow effects must be included. One can adopt advanced time-integration strategies that have been applied to commercial or military aircraft to solid rocket motor grain burning to compute a series of steady flows as the grain burns back to near completion. The slow regression of the burning solid-propellant surface is analogous to the motion of control surfaces on the aircraft. With straightforward two-timing, multiscale asymptotic analysis we develop a reduced quasi-steady description of the quasi-steady burning that is extensible to three dimensions. We show how to integrate reduced equations for stable quasi-steady motor burning and use the multigrid method as a representative method to obtain the steady flows in the frozen configurations.

Pseudodomain Fracture Analysis of Instrumented Analog Rocket Motors

An advanced stress analysis technique has been developed for evaluating propellant fracture in solid-rocket motors subjected to thermal cooling. When a strain-to-pseudostrain transformation is performed, it is shown that the time- and temperature-dependent relaxation of the solid propellant can be taken into account to yield a nonlinear elastic material model. This material model can be used in a finite element analysis of a solid-rocket motor grain to quantify the driving force for quasi-static crack propagation under a variety of thermal loads by using elastic-plastic fracture mechanics. The analysis technique was assessed by subjecting analog rocket motors instrumented with miniature bond-stress sensors to a sequence of quasi-isothermal temperatures. The data measured by the sensors allowed the stress predictions to be verified and the crack length and fracture resistance of the propellant to be deduced. It is hypothesized that compatibility must be maintained between the crack tip constraint conditions in the fracture specimen used to characterize a propellant and the crack tip constraint conditions in the structure being analyzed to use this analysis technique in a predictive manner.

Direct Evidence of Spatial Burning Rate Variation as Cause of Midweb Anomaly

With the use of the ultrasonic pulse-echo technique, local burningrates aremeasured at different radial locations across the web during static tests of center-perforated solid propellant rocket motor grains. The measurement shows a higher burning rate in the midweb region and a lower burning rate toward the port and motor case. The measured motor pressure history could be very well simulated by using the measured local burning rates. Thus, direct evidence is provided that the variationof the burning rate across the web is the cause of themidweb anomaly in chamber pressure widely reported in solid motors with center-perforated grains.

Solid-propellant grain-to-case bond-stress measurement

To satisfy the need for better definition of solid rocket-motor grain stress state, a through-the-case bond-stress gage* which provides for measurement of the radial stress induced at the propellant/liner/case interface during environmental-temperature variations has been developed. This paper describes a study† designed to evaluate theoretical approaches to grain stress analysis using experimental data from these gages. Four analog motors were cast with cylindrical-bore propellant grains in steel sleeves using a mechanically characterized solid propellant. The analog motors were exposed to thermal changes typical of prototype rocket motors. Radial stresses at the propellant-case interface were monitored using the stress gages during propellant cure and subsequent thermal testing. Correlation of the monitored results with state-of-the-art analytical methods reveals the need for improved analytical treatments and further application of experimental techniques.