DYNAMIC STUDIES OF ROLLING ELEMENT BEARINGS WITH WAVINESS AS A DISTRIBUTED DEFECT

Transcription

1 DYNAMIC STUDIES OF ROLLING ELEMENT BEARINGS WITH WAVINESS AS A DISTRIBUTED DEFECT by CHETTU KANNA BABU INDUSTRIAL TRIBOLOGY MACHINE DYNAMICS AND MAINTENANCE ENGINEERING CENTER Submitted in fulfillment of the requirements of the degree of Doctor of Philosophy to the INDIAN INSTITUTE OF TECHNOLOGY DELHI MARCH-2013

2 TO MY FATHER

3 Certificate This is to certify that the thesis entitled Dynamic Studies of Rolling Element Bearings with Waviness as a Distributed Defect being submitted by Mr. Chettu Kanna Babu (2006ITZ8049) to the Indian Institute of Technology Delhi, New Delhi, India, for the award of the degree of Doctor of Philosophy is a record of bonafide research work carried out by him under our guidance and the candidate has fulfilled the requirements for the submission of this thesis. The thesis, in our opinion has attained a standard required for a Ph.D. degree of this institute. As per our awareness the results contained in this thesis have not been submitted in part or in full to any other university or institute for award of any degree or diploma. Prof. N. Tandon (Supervisor) Professor Industrial Tribology, Machine Dynamics and Maintenance Engineering Centre (ITMMEC) I.I.T. Delhi, New Delhi , India Dr. R. K. Pandey (Supervisor) Associate Professor Department of Mechanical Engineering I.I.T. Delhi, New Delhi , India Date: Place: IIT Delhi, New Delhi i

4 Acknowledgements I wish to express my deep sense of gratitude and indebtedness to my thesis supervisors, Prof. N. Tandon and Dr. R. K. Pandey, for their constant support, inspiration and encouragement during the course of this endeavor. Their comments and suggestions at various stages have immensely improved my understanding of the subject and paved the way from time to time for solutions of governing equations and experimental studies reported in this thesis. I acknowledge all the supports provided by Prof. O. P. Gandhi (Head, Industrial Tribology, Machine Dynamics and Maintenance Engineering Centre) in completion of this thesis. I am highly thankful to Dr. A. K. Darpe (External expert in SRC), Department of Mechanical Engineering, Indian Institute of Technology Delhi, for his valuable suggestions and vital feedbacks during my presentations. I express my sincere gratitude to internal SRC members Prof. O. P. Gandhi and Prof. V. K. Agarwal for their kind technical suggestions and help time to time. I would also like to acknowledge the directly or indirectly help provided by other faculty members of IIT Delhi during perusal of this study. Vital helps rendered by Mr. Ashok Kumar, Mr. Avatar Singh and Mr. P. N. Jha in Machine Dynamics Laboratory (ITMMEC) during my experimental studies are gratefully acknowledged. I would also like to thankfully record the necessary helps extended by other staff members of the centre. I must mention and record my special thanks to my co-researchers Dr. Vinod Patel, Ms. Sidra Khanam and Mr. U. Sudeep at ii

5 ITMMEC, for their moral and academic interaction supports during pursue of this endeavor. I most respectfully record my gratitude to the management of Hindustan Aeronautics Limited, Bangalore, India, for granting needful permission and sponsoring me to pursue my Ph. D. programme at ITMMEC, IIT Delhi. My sincerely thank with great regards to Dr. V. Sridhara, Mr. P. V. Mustafa, Prof. B. Satyanarayana, Mr. M. N. Manjunatha, Mr. R. K. Bharati, Mr. P.R. Nagasubramanian, Mr. G. Harikrishnan, Mr. Girish K Degonkar and Prof. K. Ramji for their helping hands during pursuing of my research activities. I also thank Mr. R. P. Singh, Mr. Asit Behra, Mr. Viswanath, Dr. Ramkumar and Dr. G. V. Rao for their kind helps during pursuing of this research programme. I express my deep felt love and gratitude to my family members, wife (Umamaheswari), daughter (Shanmukha priya), and all nears and dears for having patiently put up with me and constantly encouraging me throughout this endeavor at the cost of their own sufferings. (Chettu Kanna Babu) Date: Place: IIT Delhi, New Delhi iii

6 Abstract Rolling bearings find wide applications in industrial and domestic machines/appliances. In spite of high precision manufacturing of the components of the rolling bearings, geometrical imperfections happen to arise in the bearings at the beginning (in new piece itself) due to manufacturing/assembly constraints or during the use of the bearings. The geometrical imperfections invite vibrations in the bearings during operation, which highly influence the rolling bearing s performance parameters such as temperature rise, wear and reliable life. Therefore, it is worth exploring the combined effects of the geometrical imperfections and frictional moments on the vibration behaviors of the rolling bearings. In this thesis attempts have been made to understand the role of the geometrical imperfection (distributed defect) on the vibrations of rolling bearings using theoretical and experimental approaches. The main objective of the study reported in this thesis is to develop a general and realistic non-linear 6-DOF dynamic model of a rotor-bearings system for investigations of vibrations of the rotorbearings system. The waviness on races and balls, frictional moments, shaft deflection, centrifugal force and gyroscopic moment of the balls has been accounted in this proposed analytical/numerical model for studies of the vibrations. However, the additional objective of this thesis is to investigate the combined influence of the lubricant starvation and waviness on the vibrations of the bearing-rotor system. Non-linear vibration analysis of angular contact ball bearings has been simulated herein considering load dependent and load independent components of frictional iv

7 moments in the bearing. Six degrees of freedom of rigid rotor is considered in the dynamic modeling of the rotor-bearing system. Moreover, surface waviness on inner race, outer race and ball is considered and has been incorporated in the model by representing it as sinusoidal function. The proposed model is validated with the experiments and published results of researchers by incorporating needful changes in degrees of freedom in the proposed model. Based on the computed results, it is observed that the load independent component of frictional moment significantly reduces the amplitudes of vibrations. The influence of inner race waviness is relatively more on the vibration in comparison to waviness of outer race and ball. Moreover, at large amplitude of waviness and increase in the order of waviness, vibration enhances considerably. Non-linear vibration model of the angular contact ball bearings supported rigid rotor has been simulated herein considering the combined influences of the lubricant starvation and waviness on the balls and races of the bearings. Based on the results of the proposed model, it is observed that for the same order of the waviness on the bearing components, the vibrations in the transverse direction of the rotational axis enhances considerably in case of starved contacts in comparison to fully flooded contacts of the bearings. Moreover, the influence of inner race waviness is relatively more on the vibrations in comparison to same orders and amplitudes of waviness present on outer race and balls. At large amplitudes of waviness and increase in the orders of waviness, vibrations enhance significantly. It is necessary to mention here that due to severity of lubricant s starvation; the amplitudes of vibrations reach the same order as due to increase in the orders of the waviness on the races and balls. Based on the proposed v

8 vibration model, authors found that the effects of starvation on vibrations are significant and it must be accounted for in the dynamic models of bearings for achieving accurate results. The model has also been used for vibration analysis of high speed angular contact ball bearings supporting the rotor bearing system under the effect of shaft deflection, centrifugal force and gyroscopic moment of the ball. Concepts pertaining to inner ring centrifugal displacement, frictional moments and waviness of balls and races have also been discussed. Three dimensional Timoshenko beam element with six degrees of freedom for each node has been adapted for computation of shaft deflection. Newton Raphson with centered finite divided difference formulae have been used to solve the deformation consistent equations. Nonlinear equations have been solved using the Runge-Kutta 4 th order method. Results have been validated through comparison with the research results established by predecessors. Based on the computed results, it is observed that the influence of outer race waviness on vibration is more as compared to the influence of inner race waviness and ball. Due to the centrifugal force and gyroscopic moment, side bands are observed around defect frequency and operating frequency in the spectrum. It is also important to note that the vibration enhances considerably owing to increase in the order and/or amplitude of waviness. Other major reasons attributing to change in vibration frequencies are seen as shaft deflection, centrifugal force and gyroscopic moment of the ball Experimental investigations of vibration response of deep groove ball bearings in presence of waviness on either of bearings races with fully flooded and starved condition vi

9 are attempted. Waviness on inner and outer races of bearings is created by electric discharge machining. Experimentations for vibration response of bearings with fully flooded and starved conditions have been conducted on a test rig using both healthy and defective (with waviness) bearings. The vibration signals have been acquired using accelerometer, signal conditioner and FFT. The acquired signals have been processed in time and frequency domains. Characteristic defect frequencies and its harmonics are broadly investigated in the frequency spectra. Comparisons of vibration responses of healthy and defective (with waviness on either of races) with fully flooded and starved bearings are provided and discussed the effect of starvation on vibrations. ************** vii

10 Contents Certificate Acknowledgements Abstract Contents List of Figures List of Tables Nomenclature i ii iv viii xii xxvii xxx Chapter-1 Introduction 1.1 Defects in Rolling Bearings Techniques of Defect Detection Scope of Study Organization of Thesis 11 Chapter-2 Literature Review Dynamic Models of Rolling Bearings/Rotor Systems with 13 Distributed Defects Models considering Lubricated Contacts Models neglecting Lubricated Contacts Dynamic Models of Rolling Bearings with Nonlinearity Effects Lubricated Rolling/Sliding Concentrated Contacts Conclusions of Literature Review 33 viii

11 2.5 Objectives of Studies in the Thesis 34 Chapter-3 Dynamic Model of Rotor Ball Bearing System with 6 DOF Rigid Rotor Supported on Lubricated Ball Bearing Deformed Rotor Supported on Lubricated Ball Bearings Waviness Models for Ball and Races Frictional Moments at the Contacts of Balls and Races Dynamic Coefficients between Bearing Elements Computational Procedure for Rigid Rotor Supported on 54 Lubricated Ball Bearing 3.7 Computational Procedure for Deformed Rotor Supported on 56 Lubricated Ball Bearing Chapter-4 Numerical Results of Dynamic Model for 6 DOF 58 Rigid Rotor Ball Bearing System 4.1 Numerical Results of Dynamic Model for Fully Flooded Condition Validation with Theoretical Models and Experimental Results Influence of Frictional Moments Influence of Frictional Moments with Inner race Waviness Influence of Frictional Moments with Outer race Waviness Influence of Frictional Moments with Ball Waviness Concluding Remarks Numerical Results of Dynamic Model for Starved Condition Starvation 101 ix

12 4.2.2 Damping Coefficients and Starved Film Thickness at Contacts Computational Procedure Inner race Waviness Outer race Waviness Ball Waviness Concluding Remarks 120 Chapter-5 Numerical Results of Dynamic Model for 6 DOF 141 Deformed Rotor Ball Bearing System 5.1 Numerical Results of Dynamic Model with Shaft deflection Validation of the Proposed Model Inner race Waviness Outer race Waviness Ball Waviness Conclusions Influence of Centrifugal Force and Gyroscopic Moment of the Ball 160 and Inner ring Centrifugal Displacement on Vibration Inner ring Centrifugal Displacement of Angular Contact 160 Ball Bearing Rolling Element Deflection and Load Analysis Calculation of Frictional Moment Bearing Force and Moments acting on the Shaft Computational Procedure Validation of the Proposed Model Outer race Waviness 171 x

13 5.2.8 Inner race Waviness Ball Waviness Conclusions 181 Chapter-6 Experimentation Experimental Setup and Instrumentation Experimental Results and Discussions Theoretical Model validation with Experimental Results of 197 Fully Flooded Condition Theoretical Model validation with Experimental Results of 219 Starved Condition 6.3 Concluding Remarks 237 Chapter-7 Conclusions and Scope for Future Work Vibration at Low Operating Speed of Bearings Vibration at High Operating Speed of Bearings Scope for Future Work 240 References 241 Appendix-A xi