Studies and Analysis of the Rack and Pinion. Steering Gear

Transcription

1 Studies and Analysis of the Rack and Pinion Steering Gear by Naresh Dayanand Kamble Mechanical Engineering Department Submitted in fulfillment of the requirements of the degree of Doctor of Philosophy to the Indian Institute of Technology Delhi August 2006

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3 CERTIFICATE This is to certify that the thesis entitled, "Studies and Analysis of Rack and Pinion Steering Gear" being submitted by Mr. Naresh Dayanand Kamble to the Indian Institute of Technology Delhi for the award of the degree of Doctor of Philosophy in Mechanical Engineering is a bonafide record of original research work carried out by him under my supervision in conformity with the rules and regulations of the institute. The results presented in this thesis have not been submitted, in part or full, to any other university or institute for the award of any degree or diploma. Dr. S. K. Saha Professor Mechanical Engineering Department Indian Institute of Technology Delhi New Delhi , India

4 Acknowledgements I would like to express my sincere thanks and deep sense of gratitude to my supervisor Dr. S. K. Saha, Professor, Mechanical Engineering Department for his constant encouragement, inspiring guidance, and vigilance without which this thesis could not have been completed. His knowledge of the subject and wealth of experience steered me to the completion of the work. His dedication, punctuality, hard work, determination, and lifestyle have a great influence on my life. His approach to cope up with the work pressure is rather technical and systematic. I would like to thank Dr. I. N. Kar for his valuable suggestions and sharing his experience during the course of this research work. I also take this opportunity to express my heartfelt thanks to the respected SRC members Prof. K. Athre, Dr. P. V. M. Rao and Dr. R. K. Pandey for their valuable suggestions. I acknowledge the financial support extended by Sona Koyo Steering Systems Ltd. (SKSSL), Gurgaon, and appreciate the initiative taken by Dr. Surinder Kapoor for the collaborative research work to be conducted at IIT Delhi. I wish to express my deepest sense of gratitude to Mr. K. M. Deshmukh, Mr. A. D. Rao, and Mr. R. Priyadarshi of SKSSL for the technical support to this research work. I also express my thanks to Mr. Anudeep, Mr. Ashish, Mr. Kamaldeep, Mr. Sameer and Mr. Sanjay, all from SKSSL for their support. Many thanks to my family, Kajal and Manasi, who spared me to do the research work. I express my sincere thanks to Mr. D. Jaitly of Mechatronics Lab. at IIT Delhi for his technical and logistic support. I admire his liveliness and cheering discussion, which usually relieved me from stress. I acknowledge the expert tips and sharing of knowledge by my coresearchers, Mr. Prasad, Mr. Ashish, Mr. Himanshu, and Mr. Ali. I also acknowledge the fruitful discussions on the research topic I had with Mr. Shrikanth, Mr. Adil, Mr. Shankar and Mr. Gopal. I convey my thanks to all those who have contributed to the realization of my thesis. 6 14gEsq KA (lima) ii

5 Abstract Passenger cars cover a large share of the automobile market. The rack and pinion steering (RPS) system is a unique choice for the majority of the passenger cars available in the world market. Varying the constructional features, viz., zero backlash, crossed helical gearing, and profile modification, a rack and pinion pair is adapted to work as a steering gear So, an RPS gear can be easily distinguished from the conventional gearing, and it has distinct torque characteristics. The torque characteristics of the RPS gear is important from the view point of the steering effort required to drive the vehicle, and the ability to steer the vehicle along the desired path. This is evident from the mandatory testing of Free Pinion Torque (FPT) as per the standards used by the industry. In this thesis, a comprehensive study of the rack and pinion steering gear is carried out, along with its geometry and mechanics. The FPT characteristics being the benchmark for the satisfactory functioning of a steering gear, and a mandatory test for every steering gear, an approach to model the RPS gear using a CAD tool, namely, the ADAMS software, is undertaken. It is followed by an exclusive analytical approach to estimate the FPT of the RPS gear. Both the virtual prototype and analytical models are validated against the experimental data. Finally, a novel concept of variable radius steering gear to achieve variable ratio steering is proposed. The pitch profile of the variable radius gear is synthesized to provide the desired variation in the steering ratio. The gear pair is then assembled in a compound gear box which can be attached to the existing pinion to provide variable ratio steering system. The results of the proposed system are compared with commercially available variable ratio steering based on variable pitch rack. iii

6 Contents Page No. Certificate Acknowledgements Abstract Contents List of Figures List of Tables List of salient Symbols and Abbreviations ii iii iv viii xii xiii 1. Introduction Background The RPS gear and its modeling Variable ratio steering gear Thesis contributions Thesis organization 7 2. Literature Survey Standards and testing Gear mechanics Recent developments Rack and Pinion Steering Gear Gear parameters Helix angles on rack and pinion 28 Contd. iv

7 Page No. 3.3 Interference Roll angle Subtended angles of teeth Topping up Contact ratio Rack and pinion geometry RPS gear errors Profile errors Helix errors Runout errors Rack bend error Experimental setup for FPT Summary Virtual Prototyping Limitations in ADAMS Remedies Gear generation Modeling of RPS gear components Rack Pinion Yokenut assembly Constraints Translation joint of rack 62 Contd.

8 Page No Pinion motion Modeling of gear errors Simulation Free pinion torque Effect of gear errors Summary Analytical Modeling Mesh geometry Tooth loads Frictional force Teeth meshing force Other tooth loads Free pinion torque Gear errors Profile error Helix error Rack bend error Runout error on pinion Total center distance variation Yoke clearance effect Analytical results Summary 105 Contd. vi

9 Page No. 6. Variable Ratio Steering Gears Improvement requirements Overall steering ratio Variable pitch rack Variable radius gear systems Noncircular gear pair Pitch curve of a noncircular gear Pitch curve of the conjugate gear Involute profiles for the teeth Noncircular compound gear with conventional rack Summary Analyses of variable ratio RPS gears Variable pitch rack Virtual prototype of VPR Analytical model of the VPR Noncircular compound gears with conventional rack Virtual prototype of NCGCR Analytical model of NCGCR Summary Conclusions Future scope 149 References 151 Appendix A: Packaging size of NCGCR 159 vii