Dept.of Mechanical Engg, Defence Institute of Advanced Technology, Pune. India

Transcription

1 Applied Mechanics and Materials Submitted: ISSN: , Vols , pp Revised: doi: / Accepted: Trans Tech Publications, Switzerland Online: Influence of applied misalignment on the balanced high speed flexible coupling of fighter aircraft S.Nagesh 1, a, A.M. Junaid Basha 2,b and G Thakur Dinesh singh 3,c 1,2 Combat Vehicles Research and Development Establishment, DRDO, Chennai.India 3 Dept.of Mechanical Engg, Defence Institute of Advanced Technology, Pune. India a nge0207@gmail.com, b junaidbashaam@yahoo.com, c dinnu74@yahoo.com Keywords: Rotating machinery, Misalignment, Vibration, Campbell diagram, Critical speed, unbalance response, Dynamic balancing, Abstract. The fighter aircraft transmission system consists of a light weight, High Speed Flexible Coupling (HSFC), used to transmit power from engine gear box to accessory gear box at speed ranging from 10,000 to 18,000 rpm. The HSFC accommodates larger parallel and axial misalignment resulting from differential thermal expansion of the aircraft engine and mounting arrangement. As the HSFC operates at higher rotational speeds close to critical velocities, it is important to analyze, the unbalance exciting forces considering the misalignment. In the present work, prediction of critical speed by camp bell diagram and unbalance response of the HSFC has been carried out using FEA. An experimental investigation also been carried out to study the influence of applied misalignment on a bi- plane dynamically balanced HSFC. The study shows that lower reaction forces are transmitted to HSFC end supports with the applied misalignments, as they are accommodated by the elastic material flexure of flexible plates. Introduction The Fighter aircraft transmission system consists of a light weight, High Speed Flexible Coupling (HSFC) known as power take-off shaft for connecting engine gearbox with accessory gear box. The HSFC transmits the power at speed ranging from 10,000 to 18,000 rpm through series of specially contoured metallic annular thin flexible plates whose planes are normal to the torque axis. The HSFC is also catered for accommodating larger angular and axial misalignment. In the aircraft transmission system, the engine and accessories drives are mounted on different bases. Under dynamic conditions it results in parallel misalignment of HSFC and axial misalignment occurs due to the thermal expansion of engine. The misalignments are accommodated by the thin cross sectional contoured titanium alloy flexible plates by bending. The Fig.1 shows Configuration of HSFC and Fig.2 shows cross section of flexible plate. Fig. 1 Configuration of HSFC Fig.2 Flexible Plate cross section The HSFC was bi-plane dynamic balanced. The unbalance of the rotor system will create unbalanced couple which results in higher bearing thrust. This which will reduce the life of the support end bearings and fatigue failure may occur. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-06/03/16,13:02:25)

2 Applied Mechanics and Materials Vols Fischer, Jonas, and Jens Strackeljan [1] investigated steady state deflections, bearing loads and dynamic run-ups by simulation using open code FERAN. Luneno, Jean-Claude, et.al. [2] have presented the effects of shaft flexibility and gyroscopic coupling on instability threshold speeds of rotor-bearing systems. Lee Sunung, Chris leontopoulos, and Colin Besant [3] have investigated backward whirl in isotropic and anisotropic systems with gyroscopic effects. In the present study, prediction of critical speed by camp bell diagram and unbalance response of the HSFC has been carried out using FEA. An experimental investigation also been carried out to study the influence of applied misalignment on a bi- plane dynamically balanced HSFC. The equation of motion of axially symmetric rotor The HSFC is an axially symmetric rotor. The equation of motion, in generalized matrix form, for an axially symmetric rotor rotating at a constant spin speed Ω is given by Eq.1 [4]. Where, M = Symmetric mass matrix C = Symmetric damping matrix G = Skew-symmetric gyroscopic matrix K = Symmetric bearing stiffness matrix N = Gyroscopic matrix of deflection for inclusion of e.g., centrifugal elements. q = Generalized coordinates of the rotor in inertial coordinates f = Forcing function including the unbalance Ω = Angular velocity of the rotor The gyroscopic matrix G is proportional to spin speed Ω. The general solution to the above equation involves complex eigenvectors which are spin speed dependent. Critical speed analysis The balancing of HSFC has to be done at the speed range away from the critical speed. The spin speeds at which one of the forcing functions has a frequency coinciding with one of the natural frequencies of the system are usually referred to as critical speeds and can be identified on the Campbell diagram by the intersections of the curves related to the natural frequencies with those related to the forcing frequencies [5]. The critical speed analysis of the HSFC was carried out using the commercial Finite element code Ansys The Fig.3 shows finite element model of HSFC. The solid element rotor dynamic model was used carried out considering the effects of gyroscopes and spin softening. For the analysis, stationary frame of reference is used in which HSFC is Fig. 3 Finite element model of HSFC (1) modeled along with a stationary support structure. This facilitates spinning at different rotational speeds about different axes of rotation and generation of Campbell plot for computing rotor critical speeds [6]. In dynamic condition, the rotor tends to bend and follows an orbital or elliptical motion due to centrifugal force acting upon the rotor during rotation known as whirl. In this analysis, a number of Eigen frequency analyses are performed on HSFC for the speed range from 0 rpm to rpm using multiple load steps. Since the model undergoes rotation on this analysis, it is possible to extract Eigen frequencies at any speed between the specified speed ranges with the defined increment. The critical speed of 15,632 rpm of HSFC predicted by Campbell diagram is shown in Fig.4.

3 1086 Dynamics of Machines and Mechanisms, Industrial Research Fig. 4 Campbell plot of HSFC From the Campbell analysis it can be seen that the gyroscopic moment stiffens the HSFC stiffness, shifts forward whirl frequencies and gyroscopic moment softening the HSFC stiffness, shifts down the backward whirl frequencies. Unbalance response analysis The uneven mass distribution and elastic bending misalignment of the HSFC in dynamic condition induce unbalance. The harmonic response analysis has been performed using FEA code Ansys 14.5 [5] to determine maximum force and displacement transmitted to the end supports by applied unbalance loading. The unbalance loading conditions are defined as force input and frequency of excitation synchronous with the rotational velocities. The maximum force and moment reaction of HSFC transmitted at the critical speed is shown in Fig.5 and Fig.6.The frequency response at center tube and at end flange at the critical speed are shown in Fig.7 and Fig.8. The results show that lower end moments and reaction forces are offered by HSFC. This is due to the misalignment accommodation by flexible plates by elastic material flexure which offers lower reaction forces being transmitted to the support ends [7]. Experimental investigations on residual unbalance of HSFC As the HSFC operates below its critical speed, it is dynamic balanced as rigid rotor. For HSFC, the desired balance quality grade is G 2.5 as per ISO: 1940 standard [8]. The balancing was carried out by material removal method on the balancing collars provided on HSFC at either ends of center tube. For carrying out the dynamic balancing of the HSFC, bi-plane balancing method with simply supported mounting as shown in Fig. 9 was used. The total unbalance in the HSFC can be visualized as two unbalanced weights on the HSFC input side (plane-i) and output end (plane- II), respectively. The experiments are conducted with three test units of HSFC with indexing of mounting bolts to evaluate residual unbalance level of HSFC. The HSFC without misalignment has been examined for magnitude of residual unbalance level and results are as given in Fig.10.

4 Applied Mechanics and Materials Vols Fig: 5 Force reaction of HSFC Fig: 6 Moment reaction of HSFC Fig: 7 Frequency response at center tube Fig: 8 Frequency response at end flange In the HSFC, the axial misalignment was applied by moving the one pedestal of the balancing machine axially in steps of 1 mm extension. The residual unbalance levels of HSFC with axial misalignment are shown in Fig.11. The HSFC the parallel misalignment was applied by raising the one pedestal of the balancing machine by shims of known thickness in steps, while other end pedestal was fixed. The residual unbalance levels of HSFC with parallel misalignment are given in Fig.12. The applied misalignment has resulted in increase in magnitude of residual unbalance compared to HSFC without misalignment. But the residual unbalance level per plane of HSFC is well within the specified balancing quality requirements. HSFC Plane - I Plane - II Fig.9 Test Setup Fig.10 HSFC without misalignment

5 1088 Dynamics of Machines and Mechanisms, Industrial Research Fig.11 HSFC with Axial misalignment Fig.12 HSFC with parallel misalignment Conclusion The critical speed of HSFC has been predicted by Campbell diagram. The unbalance response analysis shows that the lower end moments and reaction forces are offered by HSFC due to accommodation of misalignment by flexible plates. The experimental investigation of influence of applied misalignment on the magnitude of residual unbalance of HSFC shows that there is no significant variation in residual unbalance level because of flexible nature of HSFC. It is concluded that, it is always advantageous to design the HSFC with the lower bending stiffness to reduce the corresponding bending stress induced on the flexible plates. This will enable greater bending deflection can be accommodated by HSFC before flexible plate material fatigue and endurance limits are reached. References [1] Fischer, Jonas, and Jens Strackeljan: FEM-Simulation and stability analyses of high speed rotor systems, 7 th International Conference on Rotor Dynamics. Conference Proceedings, Vienna University of Technology. (2006) [2] Luneno, Jean-Claude, Jan-Olov Aidanpää, and Rolf Gustavsson, in Effects of Shaft Flexibility and Gyroscopic Coupling on Instability Threshold Speeds of Rotor-Bearing Systems, Proc. of thirteenth International symposium on Transport phenomena and Dynamics of rotating machinery, Waikiki, Hawaii. (2010) [3] Lee Sun Ung, Chris Leontopoulos, and Colin Besant in "Backward whirl investigations in isotropic and anisotropic systems with gyroscopic effects" IMAC -Proc. of International Modal Analysis Conference, Vol. 2, (1999) p [4] Muszyńska Agnieszka : Rotor dynamics. (CRC Press. 2005) [5] Giancarlo Genta: Dynamics of Rotating Systems,(Springer Science 2005). [6] ANSYS Inc: ANSYS Mechanical User Guide Release 14.5 (2012) [7] Nagesh.S and A.M. Junaid Basha : Effects of Misalignment of High Speed Flexible Coupling on the Fighter Aircraft Transmission Characteristics, International Journal of Fluid Machinery and Systems. Vol. 5, No. 2, (2012) [8] ISO standard: Mechanical Vibration-Balancing Quality Requirements of Rigid Rotor- part I, Determination of permissible residual unbalance, ISO 1940/1 (1986)

6 Dynamics of Machines and Mechanisms, Industrial Research / Influence of Applied Misalignment on the Balanced High Speed Flexible Coupling of Fighter Aircraft /