10th International Conference on Vibrations in Rotating Machinery

11-13 September 2012, Imeche London, UK

Institution of Mechanical Engineers

• Publisher: Woodhead Publishing
• Year: 2012
• Print ISBN:
  9780857094520
• eBook ISBN:
  9780857094537
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

This book presents the papers from the 10th International Conference on Vibrations in Rotating Machinery. This conference, first held in 1976, has defined and redefined the state-of-the-art in the many aspects of vibration encountered in rotating machinery. Distinguished by an excellent mix of industrial and academic participation achieved, these papers present the latest methods of theoretical, experimental and computational rotordynamics, alongside the current issues of concern in the further development of rotating machines. Topics are aimed at propelling forward the standards of excellence in the design and operation of rotating machines. - Presents latest methods of theoretical, experimental and computational rotordynamics - Covers current issues of concern in the further development of rotating machines

Blades

3D Blade root shape optimization

J.S. Rao*, KL University and Altair Engineering,India

B. Kumar, Pricol Technologies Ltd, India

ABSTRACT

A turbine blade with a curved entry root shape is optimized to achieve minimum plastic strain. Using the baseline finite element model two shapes are defined as shape variables by assigning the lower and upper bounds. Three different DOE studies Latin Hypercube, Hammersley and Box-Behnken with three approximations, Least Square Regression, Moving Least Square Method and Hyperkriging were made. 3D response surfaces for the stress as a function of the two shape variables were generated. Then an optimization study was performed. The combination of Box-Behnken with Hyperkriging is found to give the best result.

1 INTRODUCTION

Last stage steam turbine blades are subjected to locally plastic and globally elastic stress field near the stress raiser locations of the blade root. In these regions local strain controls the life. A blade root with lowest strain field is the best in providing maximum possible fatigue life. The conventional design procedure is to depend on test results and the best possible from a set of experiments is used as final design. Presently the general trend is to use simulation and optimization methods using DOE and Metamodel approach.

Optimization goes back to scientific revolution period with Isaac Newton discovering Variational Calculus, see Rao [1]. Optimization has advanced since then; see Rao [2]; however its industrial applications were limited because of lack computational power until recent times. The pioneering work of modern structural topology can be traced back to 1981 when Cheng and Olhoff, see Keng-Tuno [3] introduced the concept of microstructure to structural optimization in studying the optimum thickness design of a solid elastic plate for minimum compliance. A continuum approach to structural topology optimization was first introduced by Bendsoe and Kikuchi [4]. Optimization of Finite Element-based structures is acknowledged as a useful methodology for achieving important improvements in product design and is widely used in aerospace industries.

Prior to commercial code development, conventional optimization in structures was achieved by determining the strain energy density and identifying the material areas where a removal can be made or a component is required to be strengthened [5]. This is a tedious and time consuming process requiring skilled engineers.

Bendsøe et al [6] developed an alternative to using strain energy density as a measure, SIMP (Solid Isotropic Material with Penalization) which is also called the density method. In this method, the stiffness of the material is assumed to be linearly dependent on the density. The material density of each element is directly used as the design variable, and is normalized to have a value between 0 and 1, representing the state of void and solid, respectively. The topology of the structure can be altered by removing these low density areas, thus this method became to be known as Topology method.

The classical topology optimization setup involves the objective of minimizing the compliance with volume fraction as constraint. The compliance is the strain energy of the structure and can be considered a reciprocal measure for the stiffness of the structure. Volume fraction constraint specifies what fraction of the volume is to be removed. The remaining material is redistributed within the design space to obtain an optimal load path.

In earlier practices, dedicated codes are developed to achieve a specific optimization problem. For example, Bhat, Rao and Sankar [7] used the method of feasibility directions to achieve optimum journal bearings for minimum unbalance response. While many commercial codes have optimization modules built in to them in recent years, some are dedicated to topology optimization, e.g., OptiStruct [8] to perform structural optimization limited to linear problems. HyperStudy [9] is a multipurpose DOE/Optimization/Stochastic tool that can perform a wide cross-section of optimizations in CFD, Heat Transfer, Structures or multi physics problems using available commercial code platforms. With additional advances in mesh morphing techniques, see [10] it has now become somewhat easier to handle advanced large size industrial problems.

Taking advantage of these developments an effective method of shape optimization of blade roots is described here to keep the peak stress and strain levels to a minimum in the plastic region of limiting blade cases. An LP stage blade with a curved entry root operating at 8500 rpm is considered. The baseline model is first analysed to determine the peak stress location and corresponding plastic strain using an elasto plastic analysis.

Using the baseline finite element model two shapes are generated by morphing (by modifying the grid point locations and saved as perturbation vectors) within the available design space and without remeshing. Each shape is then defined as a shape variable by assigning the lower and upper bounds to it. To find the optimum shape of the root, three different DOE studies are first made, viz., Latin Hypercube, Hammersley and Box-Behnken. In the first two cases the DOE matrix runs were 12 and 13 in the case of Box-Behnken. The run with least stress wa...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Keynote Addresses
• Rotordynamics
• Cracks
• Blades
• Rotordynamics Balancing
• Ambs and Control
• Dampers and Seals
• Bearings
• Rub, Whirl, Instability
• Condition Monitoring
• Diagnostics and Faults - Fault Detection
• Electrical Machines
• Torsional Vibration
• Author Index