Session #1566 A Hardware/Software Centered Approach to the Elements of Machine Design Course At a Four Year School of ET Howard A. Canistraro, Ph.D. Ward College of Technology University of Hartford Introduction: A particularly difficult course for many students in either Mechanical Engineering or MET is the Machine Design Course. One of the major problems they encounter is the vast range of diverse topics that must be covered which often tie into theories and principles that have been introduced over their entire academic careers.. Additionally, the idea of the course being open ended and without exact answers leads to confusion over the distinction between the textbook and the industrial world. In an attempt to unify and clarify this broad array of subject matter and provide some insight into the actual practices utilized in industry, our Machine Design Course now centers itself around mechanically complex commercial devices. These devices serve as an instrument to demonstrate much of the subject matter found in most texts. Computer software is also extensively used to ease in the calculation and aid in modelling the dynamic nature of mathematical relationships. The revised course has been taught for 5 semesters and in each case a gear transfer case has been analyzed in terms of the following: gear tooth design, shaft design, shaft vibration analysis, fracture and fatigue, bearing analysis, splines, keys and structural deflection. The hardware, along with complete prints and specifications have been donated by John Deere Inc. (A right angle gear box from commercial deck mower) and Mitsubishi Motors of America,(a transfer case from a 3000GT VR4). The students are required to disassemble the devices, make measurements (either from prints or directly), apply the principles presented in the course and determine the adequacy of the design. Specially designed student course evaluations have been overwhelmingly positive and performance on tests has been excellent. The use of the program MathCAD has also greatly eased the complex equation usage required. In general, the level of complexity and depth of course has been expanded. A detailed discussion of the application of the theory to the hardware, a description of the laboratory activities, a discussion of the use of MathCAD in machine design, and an evaluation of the student assessment of the course will be presented in the paper. Description of the Course: The primary goal of the course is to familiarize students with the common task of solving openended engineering design and analysis problems. Courses of this type cover all aspects of basic machinery with an emphasis on power transmission systems and advanced strength of materials. Page 5.28.1
Students are expected to be able to apply many of the theories and analytical methods that have been presented in their lower division courses, while being introduced to many new topics which may seem unrelated and diverse in their scope. These topics include spur gears, shaft design, tolerances and dimensioning and mechanical fatigue. Currently three text books (one required, two supplemental) are being used (references 1,2,3). In addition, the lecture portion of the course is supplemented by a weekly lab session in which many the presented theories are explored through a sequence of experiments. It is this component of the course that has lent itself well to the use of the hardware for analysis, but this technique could be exported to any conventional machine design sequence. Methodology of the Revised Curriculum In an effort to unite the diverse aspects of the machine design course curriculum, commercial pieces of engineering hardware are introduced to the student during the first few weeks of the semester. A good example has been a John Deere Inc. right angle transfer case, from a commercial grade deck lawn mower. The students are allowed to handle the device and physically measure some key dimensions, review the design prints, and study the operating specifications. The entire course syllabus is then reviewed and each subject area as it pertains to the given hardware is briefly reviewed. The course then covers the standards: various stress relationships for design such as modified endurance limits, print reading and dimensional interpretation. They are also introduced to the mathematical software package MathCAD,. As the analysis of the commercial hardware begins, a deliberate sequence of steps has been chosen in order to provide continuity in the presentation of the course material. A copy of the syllabus is given in Appendix A. The bevel gears are the logical first step; these are what cause the loads in a transfer case. First the basic laws of spur gears are introduced such as the relation between Diametral Pitch and pitch diameter, limits of interference, and the standard law of gearing. The concepts of tooth loads are then presented which relate the beam strength of individual teeth to the dynamic loads that they are subjected to. These relationships are then applied to the more complex right-angle bevel gear system found in the commercial hardware system. In this case, three dimensional loads must be considered and again fundamental aspects of statics are reinforced. A modified version of the Lewis Form Factor method as is pertains to bevel gears is employed. The students are required to conduct all computations using the program MathCAD and a factor safety for the bevel gear teeth are determined. Next the reactions at the bearing supports for the pinion and gear shafts are found which will be used in determining the equation for slope and deflection of each shaft as well as the loads that will be transmitted to bearings. Various methods can then be employed to find the slopes and deflections of the shafts. The primary method has been to utilize direct integration of the bending moment equation along with the use of McCaully brackets to ease in the computations. It is at this point that a brief introduction to the finite element method is given. The program ANSYS is utilized to conduct a Page 5.28.2
rudimentary analysis of the deflection of the pinion shaft and these results are compared with those obtained by the classical method. Once the loads on each shaft have been found, the concept of combined steady and dynamic stress loading is introduced through the use of the Distortion Energy Theory and the Maximum Shear Stress Theory. Again, the students are required to utilize the program MathCAD for all computations and a factor of safety for each shaft is found based on the applied torque and bending moment. Results in two planes must be found due to the three dimensional loading of the bevel gears and the moments and shears are added vectorally. The vibratory natural frequency of the pinion shaft is also found using the Rayleigh criteria in conjunction with results from the deflection relationships. Since the reactions at the bearings have been found, bearings lives are now evaluated. By using the standard L 10 life prediction methodology, the students compute the service life of each of the bearings. These values are then compared with the specified values provided by the manufacturer. Again, the program MathCAD is used to ease in calculations. Finally, the topic of keyways and splines can be explored since most every pinion or gear shaft is connected using one of these mechanisms. For the John Deere gear box, a Woodruff key has been used on both of the shafts. The students inspect the key system, conduct dimensional measurements and compute the capacity of the key. These results are then compared with the specified input torque provided by the manufacturer. Use of Software: By employing the ever expanding power of PC based mathematical software packages, today s students can explore many sophisticated relations with relative ease. The program MathCAD has proven to be quite intuitive and a typical student can be up and running in less than an hour. A sample laboratory handout and associated analysis using MathCAD 7.0 for evaluation of the fatigue strength of the pinion shaft is given in Appendix B. A recently introduced aspect of the course has been the use of the finite element program ANSYS. Several basic structural problem are considered including the modelling of a standard gear tooth subjected to power transmission loads. The students compare the stress values predicted using standard beam theory with the values delivered by the finite element program. Technical Communication Emphasis: For each major section (approximately 1 per week), a laboratory is required which requires a formal write up that is based upon the subject matter that is currently being covered and must be presented in standard technical report format. Students must include complete mathematical and simulations using either MathCAD or Microsoft EXCEL, appropriate prints of the subject matter under question using AutoCAD R14 and a master document created using Microsoft WORD. At the end of the course, all labs are combined into a complete technical report reviewing the engineering hardware that was investigated. Page 5.28.3
Course Evaluation: Machine Design I has been one of the most highly regarded courses in Ward College s MET program. A course specific post survey was developed and has been overwhelmingly positive a sample of which is given in Appendix C along with percentages of student responses. Students have especially enjoyed the use of an actual engineering system to illustrate the many concepts that are covered in the machine design course. They have also appreciated the invaluable experience of technical report writing that will ultimately lead to improved performance in professional practice. They also have the opportunity to integrate several types of software into a single report. A startling result has been the discovery of the conservative nature of the types of analyses that are presented in the typical machine design text, illustrating the first order nature of the material presented in the text. Conclusions and Future Plans: Given the open ended structure of the course, new commercial hardware can readily be evaluated in subsequent years providing additional subject matter and diversity in the course curriculum. The use of several software packages will continue including an expanded use of finite element modelling. References: 1. Deutschman A.D., Michels W.J., and Wilson C.E., Machine Design Theory and Practice, MacMillan Publishing, New York, 1975. 2. Hamrock B.J., Jacobson B. and Schmidt R., Fundamentals of Machine Elements, McGraw Hill, Boston, 1999. 3. Juvinall R.C. and Marshek K.M., Fundamentals of Machine Component Design 2 nd edition, New York, 1991. Acknowledgements: The author would like to thank John Deere Inc. and Mitsubishi of America Inc. for the donation of hardware, prints and design specifications. HOWARD CANISTRARO Howard Canistraro is currently the head of the Mechanical and Audio Engineering Technology programs, and the Assistant Dean of the Ward College of Technology. He received his B.S., M.S. and Ph.D. from the University of Connecticut. He has worked as an engineer at Pratt and Whitney Aircraft Inc. and holds several patents on devices ranging from indoor golf simulators to a novel method of mammography. His current research interests are in biomedical engineering and pedagogical development of the four year MET program. He is the principal investigator on an NSF ILI grant and has served as a co-p.i. on an NSF grant on Institution Wide Reform at the University of Hartford. He also serves as an expert witness in product liability cases. Page 5.28.4
APPENDIX A ELEMENTS OF MACHINE DESIGN - MET 363 SYLLABUS WEEK TOPIC SECTIONS HOMEWORK 1. Introduction and Definitions 1.1-1.6 Handout 3.1-3.22 2. Material Fatigue and Fracture 3.23-3.29 3.6a,6b,6c Lab #1: Use of MathCAD 3.7,23,24,28 3. Dimensions and Tolerances 4.6-4.9 3.30,31 Review of Commercial System Prints 4.28,29,30,31 (John Deere Gear Box) 4. Introduction to Spur Gears 10.1-10.4 10.1,3 Lab #2: Speed Reducing Gear System 5. Spur Gears 10.4-10.8 10.7,9a Lab #3: Evaluation of Bevel Gear Forces 10.10-10.15,10.18 10.19,21 On John Deere Gear Box 6. Stresses in Beams and Shafts 5.1-5.5 5.1, TBA Deflections 5.8-5.9 Lab #4: Evaluation of Shaft Stresses/ Deflections in John Deere Gear Box Shaft 7. Review and Exam #1 8. Shear and Torsion 5.6-5.7 5.1,4,6,8,12 Lab #5: Finite Element Method for deflection of John Deere Gear Box Shafts. 9. Buckling 5.10 5.34, 43,44 Failure Theories 6.1-6.4 Lab #6: Buckling of Brass Rods 10. Failure and Fatigue Lives 6.5 6.1,12,13 Soderberg Criteria Lab #7: Evaluation of the John Deere Gear Box pinion and gear shafts. 11. Introduction to Shaft Design 7.1-7.7 7.2.5.6.8 Page 5.28.5
12. Rolling Bearings 9.1-9.11 9.1-9.5 Lab #8: Evaluation of John Deere 9.12-9.20 9.7-9.17,24,26 Gear Box Bearings 13. Keys and Splines 16.1-16.6 16.1, 3,7,9 Lab #9: Evaluation of Woodruff Key on the John Deere Gear Box. 14. Review Final design review of the gear box. Final Exam APPENDIX B Laboratory Handout and Associated MathCAD Analysis Laboratory #7 Fatigue Analysis of the John Deere Gear Box Pinion Shaft Objective: Analyze the John Deere Gear Box shaft for fatigue at the location with the maximum bending moment a sustained torque loading. The maximum bending moment will be taken as the sum of the squares of the XY and XZ plane bending moments. Procedure: This lab will use the results for reactions and bending moments from the John Deere Gear box pinion shaft which were determined in the previous lab exercise. The following values will be needed: 1. Bending moment in each plane as a function of position down the shaft 2. The value of maximum sustained torque 2. All material properties of the shaft as given in the shaft specification handout. Other Values: Shock factor of Ks = 3.0 Analysis: Find the factor of safety for fatigue using both the general and simplified forms of the: -Maximum Shear Stress Theory -Distortion Energy Theory Page 5.28.6
MATHCAD 7.0 ANALYSIS OF THE PINION SHAFT Machine Design I - MET 363 John Deere Gear Box Analysis: Fatigue and Fracture Considerations of the Rotating Shaft - Laboratory #8 Maximum Shear Stress Theory, Distortion Energy Theory Define Material Input Variables for Pinion Shaft: Sy 52000 psi Material Yield Point (psi), p. 871 Deutschman Sn.5. 92000 psi Material Endurance Limit (psi), p. 106 Deutschman Sys 27000 psi Material Shear Yield Point Sns 0.58. Sn psi Material Endurance Limit in Shear Sn = 4.6 10 4 Cf.95 Finish Factor p. 111 Deutschman DMF 3.62 Deviation Multiplication Factor 99% Reliability p. 109 Deutschman Cr 1 0.08. ( DMF ) Reliability Factor P. 109 Deutschman Cr = 0.71 Cs.85 Size Factor p. 110 Deutschman Cw 1.0 Weld Factor p. 113 Deutschman Se Ses Cf. Cr. Cs. Cw. Sn psi Modified Endurance limit tension Se = 2.639 10 4 Cf. Cr. Cs. Cw. Sns psi Modified Endurance limit in shear Ks 3.0 Shock Factor Based on type of load p. 322 Deutschman q.2 Notch Sensitivity Factor p. 116 Deutschman Stress Concentration Factor (from Tables in Deutschman) Kt 1.5 Stress Concentration Factor Kf 1 q.( Kt 1) Fatigue Stress Concentration Factor Kf = 1.1 Kts 1.0 Torsional Stress Concentration Factor Kfs 1 q.( Kts 1) Torsional Fatigue Stress Concentration Factor Kfs = 1 Geometric considerations of the shaft are defined as: r 0.5 in. Radius of the pinion shaft I π. r 4 4 in 4 Area and polar moment of inertia of the shaft I = 0.049 in 4 J π. r 4 2 in 4 J = 0.098 in 4 c r in. Maximum distance from centroid of area Page 5.28.7
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The rest of the analysis includes the determination of the factors of safety using the simplified forms of the Maximum Shear Theory and Distortion Energy Theory for combined loading. APPENDIX C MACHINE DESIGN STUDENT EXIT SURVEY (Results presented are from 46 student surveys) Answer yes or no and include any comments: A. Did you feel the use of the commercial hardware aided in the presentation of the course material? 94% Yes, 6% No Page 5.28.9
B. Did the hardware help to unify the diverse aspects of the course? 98% Yes, 2% No C. Did the hardware aid in visualization of the concepts presented in the course? 100% Yes D. Were the limitations of the methods used in the course exposed by analyzing the commercial hardware? 75% Yes, 25% No E. Was the use of the computer programs helpful? 84% Yes, 16% No F. Do you think the hardware should continue to be used? 96% Yes, 4% No G. Do you think the use of MathCAD should continue? 100% Yes Page 5.28.10