Contact stress analysis and optimization of single crystal turbine blade tenon/disk mortise structure considering thermal-solid coupling

. Contact stress analysis and optimization design of single crystal turbine blade tenon/disk mortise structure considering thermal-solid coupling is proposed in this paper. Contact thermal conductivity analysis of turbine blade/disk mortise structure is carried out to obtain temperature distribution. Contact stress of mortise structure considering temperature influence is analyzed by FEM method. On basis of contact stress analysis, the optimization design method considering thermal-solid coupling is proposed. Broaching angle, wedge angle and gap distance are chosen as optimization design variables. The minimum Mises stress, average tensile stress and average compressive stress are chosen as optimization objectives. A three fir tree tenon/mortise structure is optimized to decrease the maximum Mises stress 14% by proposed method.


Introduction
The single crystal (SC) alloy has been widely applied for aircraft engine high pressure turbine blades, due to its fatigue and creep characteristics in high temperature. SC turbine blade always connect powder metallurgy (PM) disk with fir tree tenon/mortise structure. The blade tenon/disk mortise structure works at about 700 environment. High temperature working environment would reduce material properties of tenon/mortise structure. Meanwhile, blade tenon/disk mortise structure thermal deformations can cause contact load assign among blade tenon. So, analysis and design of SC turbine blade/PM disc fir tree tenon/mortise structure should consider thermal-solid coupling. Because contact stress is sensitive to size of tenon/ mortise structure , so it is important to optimize tenon/mortise structure to obtain minimum contact stress.
Cui [1] used finite element method to analyze contact stress of a coattail-type tenon/mortise structure at room temperature. Wang [2] studied the effect of processing tolerance on contact by finite element analysis. Wang [3] investigated effects of contact gap on contact properties of turbine blade tenon /mortise. Liao [4] introduced a collaborative optimization strategy to optimize a typical fir-tree mortise structure. Shen [5] optimized a three pairs of teeth fir-tree tenon/mortise structure and decreased the maximum equivalent stress by 12%. Yang [6] employed multi-island genetic algorithm and sequential quadratic programming to optimize turbine tenon/mortise. It can be seen from current literatures that most analysis and design of tenon/mortise structure do not considering effects of temperature. This paper aims to propose a SC blade tenon/PM disk mortise structure optimization method considering thermal-solid coupling. The main works include two sections. Firstly, the contact stress analysis considering thermal-solid coupling is carried out. Secondly, optimization of blade tenon/ disc mortise structure is studied. Finally, a SC blade tenon/PM disk mortise structure is optimized by method proposed 2 Contact analysis of SC blade tenon/PM disk mortise structure considering thermal-solid coupling The tenon/mortise structure which connected single crystal turbine blade and powder metallurgy disk is shown in Fig.1.The centrifugal load blade suffered is transferred to disk through contact surface of tenon/mortise structure. Because SC turbine blade tenon/PM disk mortise structure works at a high temperature about 700 , so the contact analysis considering temperature is necessary. In this work, the contact thermal analysis and contact stress analysis are carried out sequentially.

Contact thermal analysis
Turbine blade work around the high temperature combustion gas. Heat will transfer from blade to disk through contact surface. Relative low temperature air is used to reduce working temperature which flows through gaps between tenon and mortise.In this paper, the contact thermal analysis is carried out by FEM method. Thermal conductivity and specific heat capacity of blade material CMSX-2 and disk material Rene95 are shown in Table1-4.  The SC blade tenon/ PM disk mortise structure is divided to mesh grids for contact thermal analysis. Thermal contact coefficient 3000 TCC is applied on contact surface. Convective heat transfer coefficient is applied for heat exchange analysis when cooling air flows through gaps between tenon and mortise. The first thermal boundary condition 800 C q is applied on the top surface of blade tenon. In this paper, The FEM software Ansys is employed to contact thermal analysis. Fig.2-3 give the temperature distribution of blade and disk after contact thermal analysis. It can be shown that the top surface of blade tenon has the highest temperature. The maximum temperature of disk is about 750 , which locatedat region of mortise. The structure temperature decreases as radius decreases.

Contact stress analysis of SC blade tenon/PM disk mortise
Nickel-base single crystal alloy having face centered cubic is a classical anisotropy material. The elastic stress strain relationship of single crystal alloy can be expressed by following Eq.
C is a function of elastic modulus E , Poisson ration X and shear modulus G .
The material constants of CMSX2 alone <001> crystallographic orientation is shown in Table 5. The material constants of disk material Rene95 is shown in Table 6. FEM software Ansys is employed to analyze contact stress of single crystal turbine blade tenon/power disk mortise structure. Periodic boundary conditions are applied on the surface besides disk mortise in order to simulate the entire turbine disk. A equivalent pressure load 255.2 p M P a conversd by blade centrifugal load is applied on the top surface of blade tenon. Because contact stress has large gradient and sensitive to mesh grids on contact surface, so grids on contact surface is meshed very small. And the meshed grid is checked by grid-independent test in order to analyze accurately. Fig.3 gives the Mises stress distribution of SC blade tenon. It can be seen that the maximum contact stresses locate at the boundary regions of contact surface. In the three pairs of turbine blade tooth, the third pairs of tooth have the maximum Mises stress 809MPa. The contact stresses of first and second pairs of tooth are lower than the third pairs of tooth. The first pairs of tooth maximum stress is 493MPa, the second pairs of tooth maximum stress is 624MPa.

Optimization
Optimization of SC blade tenon/PM disk mortise structure to reduce structural stress is carried out on basis of contact thermal and stress analysis. Fig.5 gives the optimization flowchart of single crystal blade tenon/disk mortise structure optimization. Firstly, the parameterized blade tenon/disk mortise structure is created. Then, the automated contact thermal analysis and contact stress analysis are carried out orderly. Optimization algorithm is used to optimize turbine tenon/mortise. . . In this paper, Multi-island genetic algorithm is used to optimize turbine tenon/mortise. After optimization, the maximum Mises stress of SC blade tenon is decrease 14% relatively. The maximum Mises stress of disk mortise is decrease 3.2% relatively.

Conclusion
The blade tenon/disk mortise structure suffers centrifugal and thermal load at the same time. So, the contact analysis considering thermal-solid coupling is necessary. An optimization method which analyzing contact thermal and contact stress sequentially is introduced in this paper. A three fir tree SC blade tenon/PM mortise structure is optimized to decrease the maximum Mises stress 14% by proposed method