Analysis of Composite Blade/Casing Rub Stability Through Delayed Differential Equations

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Jiaguangyi Xiao ◽  
Yong Chen ◽  
Jie Tian ◽  
Hua Ouyang ◽  
Anjenq Wang
Keyword(s):  
Differential Equations ◽  
Machine Tool ◽  
Experimental Investigations ◽  
Reduced Order ◽  
Composite Blade ◽  
Characteristic Roots ◽  
Engine Industry ◽  
Delayed Differential Equations ◽  
Inner Surface ◽  
Aero Engine

Abstract To improve aerodynamic efficiencies, the clearances between blades and casings are becoming smaller and smaller in the aero-engine industry, which might lead to the interactions between these components. These unexpected interactions are known as the so-called blade/casing rubs. Abradable materials are implemented on the inner surface of the casings to reduce the potential damages caused by it. However, failures may still arise from blade/casing rubs according to experimental investigations and actual accidents. In this paper, a reduced-order delayed differential equations (DDEs) are used to simplify the rubbing process between composite blade and casing. It is assumed that the removal of the abradable material in blade/casing rubbing process shares a resemblance with machine tool chatters encountered in machining. The DDEs are established with centrifugal stiffness and the impacts of stacking sequences on the blade damping taking into consideration. Semidiscretization method (SDM) is used to study the stabilities of the simplified system, which is verified by cluster treatment of characteristic roots (CTCR) and direct integrations. The results show that the stacking sequences, rub positions, blade damping, and stiffness could have much impact on the relatively dangerous interaction regimes. With the help of this method, one can assist the design processes of the composite blade-casing interface in initial aero-engine structural designs.

Analysis of Composite Blade/Casing Rub Stability Through Delayed Differential Equations

2019 ◽  
Author(s):  
Jiaguangyi Xiao ◽  
Yong Chen ◽  
Jie Tian ◽  
Hua Ouyang ◽  
Anjenq Wang
Keyword(s):  
Differential Equations ◽  
Experimental Investigations ◽  
Discretization Method ◽  
Reduced Order ◽  
Composite Blade ◽  
Characteristic Roots ◽  
Engine Industry ◽  
Delayed Differential Equations ◽  
Inner Surface ◽  
Aero Engine

Abstract To improve aerodynamic efficiencies, the clearances between blades and casings are becoming smaller and smaller in the aero-engine industry, which might lead to the interactions between these components. These unexpected interactions are known as the so called blade/casing rubs. Abradable materials are implemented on the inner surface of the casings to reduce the potential damages caused by it. However, failures may still arise from blade/casing rubs according to experimental investigations and actual accidents. In this paper, a reduced-order delayed differential equations are used to simplify the rubbing process between composite blade and casing. It is assumed that the removal of the abradable material in blade/casing rubbing process shares a resemblance with machine tool chatters encountered in machining. The delayed differential equations are established with centrifugal stiffness and the impacts of stacking sequences on the blade damping taking into consideration. Semi-Discretization Method (SDM) is used to study the stabilities of the simplified system, which is verified by Cluster Treatment of Characteristic Roots (CTCR) and direct integrations. The results show that the stacking sequences, rub positions, blade damping and stiffness could have much impact on the relatively dangerous interaction regimes. With the help of this method, one can assist the design processes of the composite blade-casing interface in initial aero-engine structural designs.

A General Ply Design for Aero Engine Composite Fan Blade

2017 ◽  
Author(s):  
Jiaguangyi Xiao ◽  
Yong Chen ◽  
Qichen Zhu ◽  
Jun Lee ◽  
Tingting Ma
Keyword(s):  
Composite Laminates ◽  
Composite Structures ◽  
Stacking Sequence ◽  
Composite Blade ◽  
Arduous Task ◽  
Aero Engine ◽  
Margin Of Safety ◽  
Fan Blade ◽  
The Impact ◽  
Ply Orientation

Composite fan blade ply lay-up design, which includes ply drop-off/shuffle design and stacking sequence design, makes fan blade structures different from traditional composite structures. It gives designers more freedom to construct high-quality fan blades. However, contemporary fan blade profiles are quite complex and twisted, and fan blade structures are quite different from regular composite structures such as composite laminates and composite wings. The ply drop-off design of a fan blade, especially for a fully 3D fan blade, is still an arduous task. To meet this challenge, this paper develops a ply lay-up way with the help of a software called Fibersim. The fully 3D fan blade is cut into ply pieces in Fibersim. As a result, an initial ply sequence is created and ply shuffle could revise it. Because of the complexity of ply shuffling, the ply shuffle table developed in this paper mainly refers to the design experience gained from simple plate-like laminate structures and some criterion. Besides, the impact of different ply orientation patterns on the reliability of composite fan blade is studied through static and modal numerical analysis. The results show that this ply lay-up idea is feasible for aero engine composite fan blade. Under the calculated rotating speeds, the ply stacking sequence 4 (i.e.[−45°/0°/+45°/0°] with the outer seven groups are [−45°/0°/−45°/0°]) shows the greatest margin of safety compared with other stacking sequences. Modal analysis shows that plies with different angles could have relatively big different impacts on blades vibration characteristics. The composite fan blade ply design route this paper presents has gain its initial success and the results in this paper might be used as basic references for composite blade initial structural design.

Numerical and Experimental Investigations on Liner Heat Transfer in an Aero Engine Combustion Chamber

2017 ◽  
Author(s):  
Korukonda Venkata Lakshmi Narayana Rao ◽  
B. V. S. S. S. Prasad ◽  
Ch. Kanna Babu ◽  
Girish K. Degaonkar
Keyword(s):  
Combustion Chamber ◽  
Structural Integrity ◽  
Operating Conditions ◽  
Experimental Investigations ◽  
Numerical Computations ◽  
Combustion Gases ◽  
Flow Characterization ◽  
Aero Engine ◽  
Straight Flow ◽  
Flow Variables

The Gas turbine combustion chamber is the highest thermally loaded component where the temperature of the combustion gases is higher than the melting point of the liner that confines the gases. Combustor liner temperatures have to be evaluated at all the operating conditions in the operating envelope to ensure a satisfactory liner life and structural integrity. On experimental side the combustion chamber rig testing involves a lot of time and is very expensive, while the numerical computations and simulations has to be validated with the experimental results. This paper is mainly based on the work carried out in validating the liner temperatures of a straight flow annular combustion chamber for an aero engine application. Limited experiments have been carried out by measuring the liner wall temperatures using k-type thermocouples along the liner axial length. The experiments on the combustion chamber testing are carried out at the engine level testing. The liner temperature which is numerically computed by CHT investigations using CFX code is verified with the experimental data. This helped in better understanding the flow characterization around and along the liner wall. The main flow variables used are the mass flow rate, temperature and the pressure at the combustor inlet. Initially, the fuel air ratio is used accordingly to maintain the same T4/T3 ratio. The effect of liner temperature with T3 is studied. Since T4 is constant, the liner temperature is only dependent on T3 and follows a specific temperature distribution for the given combustor geometry. Hence this approach will be very useful in estimating the liner temperatures at any given T3 for a given combustor geometry. Further the liner temperature is also estimated at other fuel air ratios (different T4/T3 ratios) by using the verified CHT numerical computations and found that TL/T3 remains almost constant for any air fuel ratio that is encountered in the operating envelope of the aero engine.

Reduced Order Finite Element Modeling of Thermally Induced Bearing Loads in Machine Tool Spindles

1999 ◽  
Author(s):  
Alex O. Gibson ◽  
Jeffrey L. Stein
Keyword(s):  
Finite Element ◽  
Thermal Expansion ◽  
Machine Tool ◽  
Mechanical Load ◽  
Machining Process ◽  
Thermally Induced ◽  
Reduced Order ◽  
Wide Range ◽  
Bearing Load ◽  
Bearing Loads

Abstract Machine tool spindle bearings are subjected to a large range of axial and radial loads due to the machining process. Further the rotating spindle must be extremely stiff to minimize the cutting tool’s deflection. The high spindle stiffness is achieved by applying a mechanical load to the bearings, the preload. In fixed preload spindles the bearing loads tend to increase with increasing spindle speed due to thermal expansion and it is well established that these thermally induced loads can lead to premature bearing failure. A model of thermally induced bearing load in angular contact bearing spindles is developed that includes an axis-symmetric reduced order finite element model of the heat transfer and thermal expansion within the spindle’s housing and shaft and the bearing and shaft dynamics. Nodal reduction is used in the reduced order model to minimize the number of temperature states and the computational load. The reduced order model’s calculated temperature and bearing load values are shown to closely match experimentally measured values over a wide range of spindle speeds. The paper ends with a parameter variation study which predicts a dramatic decrease in the thermally induced bearing load when silicon nitride balls are substituted for steel balls.

Nonlinear Delay Equations With Fluctuating Delay: Application to Regenerative Chatter

2002 ◽  
Author(s):  
Ali Demir ◽  
N. Sri Namachchivaya ◽  
W. F. Langford
Keyword(s):  
Differential Equations ◽  
Machine Tool ◽  
Periodic Solutions ◽  
Stability Boundary ◽  
Spindle Speed ◽  
Regenerative Chatter ◽  
Machine Tool Chatter ◽  
Tool Motion ◽  
Nonlinear Delay ◽  
Tool Chatter

The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. The suppression of regenerative chatter by spindle speed variation is attracting increasing attention. In this paper, we study nonlinear delay differential equations with periodic delays which models the machine tool chatter with continuously modulated spindle speed. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. We make use of Lyapunov-Schmidt Reduction method to determine the periodic solutions and analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions close to the new stability boundary.

Effects of Chip Seizure on Steady State Motion of a Machine-Tool

2009 ◽  
Author(s):  
Brandon C. Gegg ◽  
Steve S. Suh
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Machine Tool ◽  
Systems Theory ◽  
Degree Of Freedom ◽  
Continuous Systems ◽  
Discontinuous Systems ◽  
Mechanical Analogy ◽  
Steady State Motion ◽  
Two Degree Of Freedom

The steady state motion of a machine-tool is numerically predicted with interaction of the chip/tool friction boundary. The chip/tool friction boundary is modeled via a discontinuous systems theory in effort to validate the passage of motion through such a boundary. The mechanical analogy of the machine-tool is shown and the continuous systems of such a model are governed by a linear two degree of freedom set of differential equations. The domains describing the span of the continuous systems are defined such that the discontinuous systems theory can be applied to this machine-tool analogy. Specifically, the numerical prediction of eccentricity amplitude and frequency attribute the chip seizure motion to the onset or route to unstable interrupted cutting.

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