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The Mechanics of Tractor Performance and Their Impact on Historical and Future Device Designs by Guillermo Fabidn Diaz Lankenau B.S., Instituto Tecnologico y de Estudios Superiores de Monterrey (2012) Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering MA-As-US-T0Tr7INSTITUTE OF TECHNOLOGY at the JUN 21 2017 MASSACHUSETTS INSTITUTE OF TECHNOLOGY LIBRARIES June 2017 ARCHIVES @ Massachusetts Institute of Technology 2017. All rights reserved. ,4 0 Signature redacted Author Department of Mechanical Engineering May 12, 2017 Signature redacted C ertified by ...................... mo G. Winter, V Assistant Professor 6 ec anical Engineering Thesis Supervisor Signature redacted Accepted by ................................ Rohan Abeyaratne Chairman, Department Committee on Graduate Theses The Mechanics of Tractor Performance and Their Impact on Historical and Future Device Designs by Guillermo Fabian Diaz Lankenau Submitted to the Department of Mechanical Engineering on May 12, 2017, in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Abstract This thesis utilizes a terramechanics-based farm tractor model to predict machine performance. This model is used to reflect on tractor evolution throughout the last century and the physics-based principles that govern tractor performance. Insights from this model and reflection can help designers create new farm tractor embodi- ments, especially for markets where farming practices and industrial context differ significantly from those that shaped the conventional tractor's major evolutionary steps. It is shown how the small tractor evolved to its conventional modern form in in the early 1900s in USA pushed not only by suitability to domestic agriculture at the time but also efficiency in contemporary mass manufacturing and symbiosis with the burgeoning automotive industry. The farm tractor model as suggested in this thesis is proven to be in good agreement with published experimental data and historical standarized tractor testing. Inline drive wheels and mounting soil working implements between front and rear axles are identified as high potential design options for adapting the small tractor to modern emerging markets where draft animals are the dominant source of draft power. Thesis Supervisor: Amos G. Winter, V Title: Assistant Professor of Mechanical Engineering 3 4 Acknowledgments I am deeply grateful to for everyone and everything that has allowed me to be here now. I feel fortunate to have met amazing, supportive people throughout my life and to have been at the right place, at the right time more than once. Thank you Prof. Amos Winter for believing in me and helping me better realize my strengths and improve my weaknesses in work and in life. Thank you Jaya, my wife, for your patience, love, and advice. Your breathtaking awesomeness makes my life more splen- did than it has ever been and I look forward to sharing a lifetime of happiness with you. Thank you to Guillermo and Maga, my parents, for your unwavering support of my education and your rock-solid confidence in my ability to be an outstanding student even when results at times may have indicated otherwise. You have been the concrete that has allowed me build the life and achievements I now enjoy. iMuchas Gracias! 5 6 Contents 1 Introduction 15 1.1 Contributions ........... .................... 15 1.2 Tractors are ubiquitous in high productivity farming ........ 15 1.3 Brief History of the Farm Tractor ............ ........ 16 1.4 Evolution of small tractor to consolidated design .... ........ 20 1.5 There is an untapped market for which tractors could be designed . 25 1.6 We want to know how tractors work parametrically, reflecting on the strengths and drawbacks of previous designs .... .......... 26 2 Tractor Theory 27 2.1 Qualitative description of importance of soil-tire interaction in tractor design .... ........ ........ ........ ....... 27 2.2 Analytical model for interaction of single drive tire with soil ..... 30 2.3 M ulti-pass effect for tires ..... ......... ........ ... 33 2.4 Conventional tractor dimensions and relevant forces .. ........ 34 2.5 Proposed generalized vertical load per tire calculation . ........ 36 2.6 Proposed generalized horizontal load per tire calculation .... ... 40 2.7 Variable sensitivity of tractor-soil model as implemented ....... 41 2.8 Flowchart of tractor design exploration model ....... ...... 42 3 Validation of Tractor Model with Published Data 45 3.1 Comparison to specific tractor tests ... ........ ........ 45 3.2 Comparison to design trends .................. ..... 46 7 4 Insights into small tractor design 51 4.1 Comments on past and current tractor designs ....... ...... 51 4.1.1 "Fulcrum and Lever" towing adjusts drive tire vertical loading in proportion to pulling force. ... ........... .... 51 4.1.2 Central tool mounting increases safety but can be detrimental to traction in conventional tractors. ............... 55 4.1.3 Inline and side-by-side drive wheels each have their advantages. 61 4.1.4 Hypothetical inline drive wheels with centrally mounted tool . 63 4.2 Recommendations for future designs .................. 65 5 Conclusions 69 A 1910 to 1920 Production Vehicles Matched to Layouts in Ch. 1 71 B Evolution Steps, matched to vehicles in Ch. 1 75 8 List of Figures 1-1 Sample of tractor design layouts from 1910 to 1920. A list of some production tractors using each layout can be found in A ppendix A ........ ....................... 18 1-2 Graphic chronology of tractor evolution into conventional small tractor design. Connections (marked by letters) are described in section 1.4. More data on vehicles may be found in Ap- pendix B. The photo credits are referenced from the origin of each connection: A [171, C [18], E [19], G [20], H [21], I [22], J [23], L [24], N [25], P [26], Q [27], Q [28], V [29], W [30], B ottom [31] .............................. 21 2-1 Granular material flow under driven rigid tire. Arrows un- der soil represent flow speed and direction. The dotted line represents shear interface. .. ........... ........ 28 2-2 Stress under rigid tire. ...... ............ ...... 30 2-3 Parameters of tire perimeter for calculation of forces at inter- fa ce ....................... ............. 32 2-4 Illustration of tire-soil interaction and multi-pass effect used in analysis ................................ 34 2-5 Effect of repetitive loading on natural soil deformation and stiffness. Data from [36] ....................... 34 2-6 Full body diagram for farm tractor in 2D ............ 35 9 2-7 Sensitivity analysis of drawbar pull at 15% slip for a conven- tional small tractor [32]. Data generated using model created for this thesis. Note that drawbar pull (net horizontal force) is approximately linearly related to weight for a large range of values and different soils. ..... ...... ..... .... 42 2-8 Sensitivity analysis for tractive efficiency at a drawbar pull of 3000N. Data generated using model created for this thesis. Note that making a vehicle too heavy can be detrimental to efficiency. ..... ....... ........ ........ .... 43 2-9 Process flow in implemented MATLAB model to simulate a farm tractor on soil. ........ ....... ........ 44 3-1 Comparison of tractor model as described in Chapter 2 to published tractor experiments. Model has its best accuracy between 5% and 20% slip, which is the range recommended for farm tractor operation [36][371140][32]. ........ .... 46 3-2 Simulation data for one million tractor configurations. Demon- strates that optimal weight distribution for drawbar pull is about 70% on rear wheels. The semi-transparent purple fron- tier on the left on left represents where tractor wheels slip fully without generating progress or where any wheel sinks past its radius. The semi-transparent brown frontier on the right represents when the tractor flips backwards. ... ... 48 3-3 Data compiled from Nebraska Tractor Test archives. Notice that, for testing, company engineers would ballast their trac- tors place about 70 to 80% of the total weight on the rear w h eels. ........... ....................... 49 4-1 When a tractor tows a high draft tool, the angle and position of the towing chain can have a significant effect on perfor- m an ce. .................................. 52 10 4-2 Labeled standard conventional tractor like the Ford 8N (four wheels, rear wheel drive, and rigidly attached trailing tool) and conventional tractor with centrally mounted tool like the Allis Chalmers G. ... .. ................... 56 4-3 Examples of tractor layouts with inline wheels. Layouts are selection from those of Figure 1-1. ................ 63 4-4 A comparison of the drawbar pull of inline wheels vs. side-by- side wheels in a 500kg. In both cases, the horizontal drag from rolling idle wheels through the soil has been ignored. The model described in Chapter 2 was used. The drawbar pull of a bullock team (two animals) has been added for reference. 64 11 12 List of Tables 1.1 Data from FAO for farm sizes worldwide [citation needed]. The sample is from 460million farms in 111 countries. ........ ........ 25 1.2 Data from USDA agricultural census [citation needed] [citation needed]. 26 4.1 A comparison on some aspects of the 1948 to 1952 Ford 8N and the 1948 to 1955 Allis Chalmers G .. ...... ...... ...... .. 56 4.2 Values for side-by-side wheels and inline wheels used in Figure 4-4. Side-by-side wheels based on
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