Weight Optimization of Turbine Blades - Technical Paper

Weight Optimization of Turbine Blades

J.S. Rao
Chief Science Officer, Altair Engineering
Mercury 2B Block, 5th Floor, Prestige Tech Park, Sarjapur Marathahalli
Outer Ring Road, Bangalore, Karnataka, 560103, India
js.rao@altair.com

Bhaskar Kishore
Project Engineer, Altair ProductDesign
bhaska.chirravuri@altair.com

Vasantha Kumar
Project Manager, Altair ProductDesign
vasanthakumar.mahadevappa@altair.com

www.altairproductdesign.com
copyright Altair Engineering, Inc. 2011


Abstract

Optimization of aircraft structures and engines for minimum weight has become important in
the recent designs. Topology optimization of airframe structures, wings, and fuselage … is
now practiced since last 3-4 years to reduce weight considerably in ribbed members, rotating
structures in engines is of much more recent origin.

Advanced engine rotating components such as blades and disks operate as globally elastic
but locally plastic structures. The shape of the notch in these structures where yield occurs
can be optimized to reduce peak strain levels considerably that can significantly increase life
of the component.

In addition, designers have been practicing to remove some material in the blade platform
area by analysis. This weight removal can be optimized to obtain maximum reduction without
compromising the structural integrity. This procedure is illustrated in this paper by using two
optimization codes, Altair OptiStruct for linear structures and Altair HyperStudy for nonlinear
structures using Ansys platform as the main solver. Using this procedure nearly 10% weight
reduction is achieved.

1.0 Introduction

Bladed Disks are most flexible elements in steam and gas turbines used in land based and
aerospace applications. While the average stress in the mating areas of these bladed disks is
fully elastic and well below yield, the peak stress at singularities in the groove shape can
reach yield values and into local plastic region. Last stage LP turbine blades and first stage LP
compressor blades are the most severely stressed blades in the system. Usually these are the
limiting cases of blade design allowing the peak stresses to reach yield or just above yield
conditions. Failures can occur with crack initiation at the stress raiser location and
propagation, two cases can be cited. The last stage blades in an Electricite de France B2 TG
Set failed in Porcheville on August 22, 1977 during over speed testing Frank (1982). On
March 31,1993 Narora machine LP last stage blades suffered catastrophic failures, see Rao
(1998). These blades have stresses well beyond yield. On Narora machine blade, initial fully
elastic analysis has shown a peak stress value 3253 MFa though the average stress is only
318 MFa. An elasto plastic analysis for the same case showed that the peak stress is 1157
MFa well beyond the yield. While it is not possible to eliminate the yield and keep the structure
fully elastic to achieve the last stage blades in limiting cases, it will be advisable to achieve the
yield conditions to be as low as possible. Invariably all the earlier long blade designs in last
stage LP turbines or first stage LP compressors operate in local plastic regions.

Until recently, the dynamic stress field under nonlinear conditions is determined using energy
methods and one dimensional beam models as given by Rao and Vyas (1996). A serious
disadvantage in this approach is the inability to model the stress field in the regions of
discontinuities or stress raisers. Today's commercial finite element codes can handle large
mesh sizes and can be used as solvers not only for an accurate assessment of the stress and
strain field Rao et. al., (2000) but also for applications

Copyright Altair Engineering, Inc., 2011 2


in optimization.

The shape optimization in recent years depended on determining strain energy density and
based on the location where it is high, different shapes were chosen and models are
generated. Rao (2003) discussed these developments from an industry perspective. Because
the problem is highly nonlinear due to centrifugal stiffening and spin softening, considerable
time is taken to achieve an optimized root.

Optimization has become a necessity in the recent years to achieve an optimal design in
stress or strain, stiffness and weight etc. In earlier practices, dedicated codes are developed
to achieve a specific optimization problem. For example, Bhat, Rao and Sankar (1982) used
the method of feasibility directions to achieve optimum journal bearings for minimum
unbalance response.

OptiStruct (2003) has been developed recently to perform linear structural optimization and
successfully applied for topology, topography, gauge and shape optimizations of automotive
and airframe structures, e.g., Schuhmacher (2006), Taylor et. al., (2006) discussed the weight
optimization achieved in aircraft structures. HyperStudy (2003) is a multi-purpose DOE/
Optimization/ Stochastic tool used to perform 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, HyperMesh (2003), it has become
somewhat easier in shape optimization.

Advanced engine rotating components such as blades and disks operate as globally elastic
but locally plastic structures. The shape of the notch in these structures where yield occurs
can be optimized to reduce peak strain levels considerably that can significantly increase life
of the component. In advanced military aircraft engines the weight removal can be a major
objective even if it is small. This paper illustrates shape and weight optimization in the blade
root region.

2.0 Shape Optimization of a Steam Turbine Blade Root Notch

The Bladed Disk considered has 60 pre-twisted blades each with a height of 290 mm placed
on the disk with the bottom of the blade root at a radius of 248 mm from the axis of the rotor.
Asector of rotor disc is modeled to make use of cyclic symmetry condition. Fig. 1 shows the 3-
D finite element model having 8 noded brick elements with finer mesh in all the critical regions
around the singularities in the dovetail root fillet regions with 2 to 3 layers of elements and size
as low as 0.235 mm. The mesh shown in Fig. 1 consists of 305524 elements and 344129
nodes.

Baseline Analysis
Before attempting a shape optimization of the given root, a base line stress analysis is first
carried out. For this purpose the blade along with disk effect is considered by modeling a 1/60
sector of the disk with one blade and using cyclic symmetry boundary conditions applied on
both the partition surfaces as shown in Fig. 1. The common nodes on the pressure faces at
six positions, shown in Fig. 1, where the load transfer between blade and disc takes place are



joined together to make it as a single entity. The blade and disc are assumed to be made up
of same material with Yield stress 585 MPa, Young's Modulus 210 GPa, Density 7900 Kg/m 3
and Poisson's Ratio OJ.

Figure 1: Bladed Disk Model Showing the FE Mesh

Elastic Analysis
An elastic stress analysis is conducted for a centrifugal load at full speed 8500 RPM, using
ANSYS solver (2004). The Von Mises elastic stress field near the root region is shown in Fig.
2. The root fillet in the first landing area experiences a severe stress of 1825 MPa at node
153608 well beyond Yield 585 MPa, with an average sectional stress 256 MPa. Stress
contour beyond yield is shown to be spread across 3 elements over a depth of 1.22 mm.

Figure 2: Von Mises Stress in Elastic domain at 8500 RPM

Elasto Plastic Analysis



The hardening property of the material in the plastic region is given in Fig. 3. The elasto-
plastic analysis result for the von Mises stress is given in Fig. 4. The root fillet now
experiences a peak Von Mises stress 768 MPa at a node 176017 in the same region which is
beyond the yield value 585 MPa. The peak stress value has dropped considerably from the
elastic analysis result 1825 MPa to a value 768 MPa just above the yield.

The peak strain observed at the node 153608 in the same region closer to peak stress
location is 0.0153.

Figure 4: Material hardening characteristic in the plastic region

Figure 4: Results of Elasto-Plastic analysis at 8500 RPM



3.0 Shape Optimization

The peak stress in the root region being plastic, the strain gets hardened while stress relaxes
due to yielding. An optimization for minimum peak stress is carried out that will substantially
decrease plastic strain. With decreased local strain, life gets enhanced.

HyperStudy
HyperStudy can be applied in the multi-disciplinary optimization of a design combining
different analysis types. Once the finite element model and shape variables are developed, an
optimization can be performed by linking HyperStudy to a particular solver of choice that can
include nonlinear analyses.

Global optimization methods used in HyperStudy use higher order polynomials to approximate
the original structural optimization problem over a wide range of design variables. The
polynomial approximation techniques are referred to as Response Surface methods. A
sequential response surface method approach is used in which, the objective and constraint
functions are approximated in terms of design variables using a second order polynomial. One
can create a sequential response surface update by linear steps or by quadratic response
surfaces. The process can also be used for non-linear physics and experimental analysis
using wrap-around software, which can link with various solvers.

Optimization through HyperStudy
Here, HyperStudy is linked with ANSYS solver used in base line analysis. Shape optimization
is carried by using the baseline model, having the cyclic symmetry boundary conditions
imposed on the disc, with the objective to minimize the peak stresses. Shape variables are
given in Table 1, as depicted in Fig. 5. These parameters are taken as the design variables in
the optimization problem.

Table 1: Shape Variable Definitions



Figure 5: Parameters used for defining the shape variables

The details of mesh are given in Fig. 6 which is morphed with the parameters as continuous
variables using HyperMesh.

Figure 6: Morphed Mesh for the Design Variables



Figure 7: Shape Optimization in 21 Iterations



Figure 8: Optimized Shape

The objective function and shape variables during the optimization process are given in Fig. 7
and the final optimized shape is shown in Fig. 8. Table 2 gives the optimized shape compared
with the base line.

Table 2: Comparison of Optimized Shape with Baseline

Maximum stress has decreased marginally from 768 to 746 MPa by 22 MPa (2.86%) from
baseline elastoplastic analysis for 8500 RPM; however the peak plastic strains reduced from
0.0153 to 0.01126 by 26.4%. This is the major advantage in optimization for a blade root
shape.

4.0 Weight Optimization

Shape optimization was discussed in the previous section where the main aim is to increase
life when the blades are subjected to local plastic conditions. If the local plastic conditions are
to be avoided, one may have to sacrifice the blade length so as to decrease the centrifugal
loads with a corresponding loss in extraction of power from the turbine. The case of military
aircraft engines, on the other hand, is different; here the life can be limited, but weight is an



important criterion. Usually considerable material sits near the platform region taking very little
load and can be easily removed without endangering the structural integrity. Here, such a
weight optimization problem is illustrated.

LP Compressor Blade for Weight Optimization Fig. 9 shows the CAD model of a typical
aircraft engine LP compressor blade made of a Ti-alloy; Mass Density = 4.42x10-9
N.sec2/mm4, Poisson's ratio = 0.3, Young's modulus = 102 GPa, Yield strength = 820 MPa.

Figure 9: CAD Model ofA LP Compressor Bladed Disk

The blade separated from the disk is shown in Fig. 10. The FE model of the disk is shown in
Fig. 11. It has 106066 Solid 45 elements with 121948 nodes. The FE model of the blade is
given in Fig. 12 with 46970 Solid 45 elements and 41811 nodes. Loads and boundary
conditions are given in Fig. 13.

The nonlinear material property of the bladed-disk is shown in Fig. 14.



Figure 10: CAD Model of Blade

Figure 11: FE Model of Disk



Figure 12: FE Model of Blade

Figure 13: Loads and Boundary Conditions



Figure 14: Material Stress-Strain Characteristics

Baseline Results
The baseline results are given in Figs. 15 and 16 for the disk and blade respectively.

The peak stress in the disk is 787 MPa below the yield strength of the material. The maximum
value of stress in the blade is 721 MPa.

Optimization
HyperStudy is used to optimize the blade for weight reduction by limiting the peak stress to
the yield value, 820 MPa in the blade-disk system. Ansys is the solver used to determine the
elasto-plastic stress condition with HyperStudy calling Ansys for optimization.



Figure 15: Disk Baseline Stress Results

Figure 16: Blade Baseline Stress Result

The blade root and shank have considerable regions of stress well below yield and a baseline
for optimization is chosen as given in Fig. 17. As shown, 8 holes with radius R=1.75 nun are
provided in the blade root and two cutouts in the shank are allowed to reduce the weight. Fig.
18 gives the cutout proposed in the shank. The blade root in Fig. 18 originally without any
cutouts was 7890.34 mm3. The objective function is chosen to be this volume and it was
minimized subject to the condition that the peak stress is limited to the yield value, namely
820MPa.



Fig. 19 gives the design variables chosen; the front shank has Dl=1.1, Wla=4.75, Wlb=13.94
nun, while the rear shank D2-1.1, W2a=4.44, W2b=13.64 nun. Table 3 gives the range of
design variables allowed in optimization.

Figure 17: Baseline for Weight Optimization

Figure 18: Baseline Root Region of the Blade



Figure 19: Design Variables on the Front Shank

Table 3: Range of Design Variables

Fig. 20 gives the objective function for minimum volume during optimization; In 16 steps the
result was achieved. The objective function value decreased from 7890.34 to 7098.93 mm3,
i.e., a reduction of 10.03%.

The progress of the design variables in this process is shown in Fig. 21. Optimum design
variables are given in Table 4.

Fig. 21 and 22 give the optimized stress results for the disk and blade respectively. In the disk,
the peak stress increased from 787 to 810 MPa, while in the blade, the stress increased from
721 to 798 MPa.



Figure 20: Objective Function, Volume of Blade Root

Figure 21: Design Variables in Optimization



Table 4: Optimized Design Variables

Figure 22: Optimized Disk Stress Result



Figure 23: Optimized Blade Stress Result

The weight reduction in the root region achieved is 10.03%. This will be considerable
reduction in the bladeddisk stage of this compressor. Such a reduction can be achieved in all
compressor and turbine stages for minimum weight objective.

5.0 Conclusions

In this paper turbomachinery blade optimization is performed to increase life and minimize
weight.

Shape optimization is carried out in the peak stress regions to determine the most appropriate
shape of the blade root in the stress raiser location. Peak stress was the objective function
and the shape was varied with several variables in the region. This optimization showed that
the local strain can be reduced considerably by as much as 26%. This reduction will have
significant influence on the life of the bladed disk.

Next a case of weight optimization of the blades is considered. In the root region where there
is a considerable material with less stress load distribution, several holes and cutouts in the
shank region are used as design variables. The weight of the blade root region where the
cutouts are made is taken as the objective function. The shank cutouts and the holes in the



root are used as design variables. The root region could be optimized to reduce weight by as
much as 10%.

6.0 Acknowledgements

The authors are thankful to Altair Engineering India for their support.

7.0 References

ANSYS, (2004) Release 9.0 Documentation, Ansys Inc., USA

Bhat, R B., Rao, J S and Sankar, T S, (1982), Optimum Journal Bearing Parameters for
Minimum Rotor Unbalance Response in Synchronous Whirl, Journal of Mechanical Design,
TransASME, v.104, p.339

Frank, W (1982), Schaden Speigel, 25, No.1, 20

HyperMesh, (2003) User's Manual v7.0, Altair
Engineering Inc., Troy, MI, USA

HyperStudy, (2003) Users Manual v7.0, Altair
Engineering Inc., Troy, MI, USA

OptiStruct, (2003) User's Manual v7. 0, Altair Engineering Inc., Troy, MI, USA

Rao, J S. (1998), Application of Fracture Mechanics in the Failure Analysis of A Last Stage
Steam Turbine Blade, Mechanism and Machine Theory, vol. 33, No.5, p. 9

Rao, J S. (2003), Recent Advanced in India for Airframe & Aeroengine Design and Scope for
Global Cooperation, Society of Indian Aerospace Technologies & Industries, 11th Anniversary
Seminar, February 8, 2003, Bangalore

Rao, J. S. and vyas, N. S (1996), Determination of Blade Stresses under Constant Speed and
Transient Conditions with Nonlinear Damping, J of Engng. for Gas Turbines and Power, Trans
ASME, voL 116, p. 424

Rao, J S., et. al. (2000), Elastic Plastic Fracture Mechanics of a LP Last Stage Steam Turbine
Blade Root, ASME-2000-GT-0569

Schuhmacher, G (2006), Optimizing Aircraft Structures, Concept to Reality, Winter Issue, p.
12

Taylor, R. M, et. al.(2006), Detail Part Optimization on the F-35 Joint Strike Fighter, AIAA
2006-1868, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Material
Conference, Newport, Rhode Island.


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