Engineering Principles of Agricultural Machines PDF

Engineering Principles of Agricultural Machines 2nd Edition Ajit K. Srivastava Michigan State University Carroll E. Goering University of Illinois Roger P. Rohrbach North Carolina State University Dennis R. Buckmast...

Engineering Principles of Agricultural Machines 2nd Edition Ajit K. Srivastava Michigan State University Carroll E. Goering University of Illinois Roger P. Rohrbach North Carolina State University Dennis R. Buckmaster The Pennsylvania State University  Copyright  2006 by the American Society of Agricultural and Biological Engineers All rights reserved. ASABE is an educational and scientific organization dedicated to the advancement of engineering applicable to agricultural, food, and biological systems. Editing by Peg McCann Cover design by Melissa Miller Production assistance by Patricia Howard and Marcia Stults McCavit Cover photo of a Massey Ferguson combine courtesy of AGCO Corporation. This book may not be reproduced in whole or in part by any means without the permission of the publisher. For information, contact the American Society of Agricultural and Biological Engineers 2950 Niles Road, St. Joseph, MI 49085-9659 USA Phone: 269-429-0300 Fax: 269-429-3852 E-mail: [email protected] Library of Congress Card Number (LCCN) 2005937948 International Standard Book Number (ISBN) 1-892769-50-6 ASAE Publication 801M0206 The American Society of Agricultural and Biological Engineers is not responsible for the statements and opinions advanced in its meetings or printed in its publications. They represent the views of the individuals to whom they are credited and are not binding on the Society as a whole. PREFACE We are pleased to offer the second edition of the textbook Engineering Principles of Agricultural Machines. To arrive at the revisions in the second edition, we called some instructors of the first edition and conducted lengthy phone interviews to seek their thoughts and suggestions for revisions. We interviewed Dr. Dennis Buckmaster of Penn State University, Dr. Dan Humburg of South Dakota State University, Dr. Lei Tian of the University of Illinois, and Dr. Ranal Taylor of Kansas State University. Based on their input we prepared a survey form listing the many changes suggested. The survey forms were sent to all instructors, in the U.S. and abroad, who were using the textbook. We compiled the responses and rated each suggestion. We also held a user forum during the 2005 ASABE conference in Tampa, Florida to share the results of our survey and to seek additional input. Items receiving a 3 or higher score on a 5- point scale were marked for inclusion in the revised edition. The changes can be divided in four categories. These are: reorganization of chap- ters into shorter modules to allow instructors greater flexibility in selecting topics to match their needs; the addition of a new chapter on agricultural information systems in response to the growth in precision agriculture technology since the first edition; addition of simulation problems; and adding a supplemental CD that includes a spreadsheet and many simulations. We feel the CD will add a new dimension to student learning and give them the opportunity to develop a deeper understanding of the process under study as affected by the various system parameters. We are very pleased that Dr. Dennis Buckmaster has joined the list of authors. Dennis has been an avid user of the textbook and has developed much supplemental simulation material during the course of teaching principles of agricultural machines at Penn State University. We have included much of his material in the accompanying CD. Dennis also revised the chapter on hay and forage harvesting. Finally, we would like to thank the many people who have been helpful in the process of preparing this edition. We thank Monte Dickson for providing a thorough review of the new chapter on agricultural information systems (Chapter 6). We would also like to acknowledge Frank Zoz for letting us include his traction prediction model in the CD, and Al Hanson for letting us use his engine simulator in the CD. As always, we welcome your feedback and suggestions for improvement. Please feel free to contact any of us. Additions and changes will be posted to the ASABE Technical Library at http://asae.frymulti.com/toc.asp (scroll down to the listing of textbooks). For specific questions we ask that you direct your inquiries to Ajit Srivastava for Chapters 1, 4, 8, 10, 12, and 14; to Carroll Goering for Chapters 2, 3, 5, 6, 7, 9, and 15; to Roger Rohrbach for Chapter 13; and to Dennis Buckmaster for Chapter 11 and the accompanying CD. Ajit Srivastava ([email protected]) Carroll Goering ([email protected]) Roger Rohrbach ([email protected]) Dennis Buckmaster ([email protected])  The authors wish to dedicate this edition to their wives Barbara Srivastava, Carol Goering, Jeanette Rohrbach, and Corinne Buckmaster for their unwavering support and encouragement throughout our lives. CONTENTS Chapter 1 Agricultural Mechanization and Some Methods of Study 1 Introduction.............................................................................................................. 1 1.1 History of Mechanized Agriculture................................................................. 1 1.2 Farming Operations and Related Machines................................................... 3 1.3 Functional Analysis of Agricultural Machines............................................... 4 1.3.1 Basic processes of agricultural machines................................................. 5 1.3.2 Process diagrams...................................................................................... 6 1.4 Dimensional Analysis..................................................................................... 7 1.4.1 Scope........................................................................................................ 7 1.4.2 Physical dimensions................................................................................. 7 1.4.3 Units of measurement.............................................................................. 8 1.4.4 Developing a prediction equation............................................................ 9 1.4.5 Buckingham’s Theorem......................................................................... 10 1.4.6 Systematic calculation of the dimensionless products............................. 12 1.4.7 Transformation of dimensionless products............................................ 13 Problems................................................................................................................. 14 Chapter 2 Engine Power for Agricultural Machines 15 Introduction............................................................................................................ 15 2.1 The power in fuel.......................................................................................... 15 2.2 Combustion................................................................................................... 16 2.2.1 Combustion chemistry........................................................................... 16 2.2.2 Energy release in combustion................................................................ 19 2.3 Thermodynamic limits to Engine Performance............................................ 21 2.4 Heat Losses and Power at the Pistons.......................................................... 25 2.5 Mechanical Losses and Power at the Flywheel............................................. 26 2.6 Engine Torque and Efficient Engine Loading.............................................. 28 2.7 Control of Engine Speed............................................................................... 29 2.8 Engine performance simulator..................................................................... 33 2.9 Turbocharging and Intercooling Engines..................................................... 35 2.9.1 Operation of turbochargers.................................................................... 36 2.9.2 Intercoolers............................................................................................ 39  2.9.3 Turbocharging and intercooling for versatility...................................... 39 Problems................................................................................................................. 41 Simulation Problems............................................................................................... 43 Chapter 3 Electrical Power for Agricultural Machines 45 Introduction............................................................................................................ 45 3.1 Motor Components........................................................................................ 45 3.2 Motor Classifications.................................................................................... 46 3.3 Principles of Operation Of Induction Motors............................................... 47 3.4 Types of Single-Phase Induction Motors..................................................... 49 3.4.1 Split-phase induction motors.................................................................. 49 3.4.2 Capacitor-start, induction-run motors.................................................... 50 3.4.3 Two-value-capacitor, induction-run motors........................................... 52 3.4.4 Repulsion-start, induction-run motors.................................................... 52 3.5 Three-Phase Induction Motors..................................................................... 53 3.6 Dual-Voltage Motors.................................................................................... 54 3.7 Torque-Speed Characteristics of Induction Motors....................................... 56 3.8 Motor Nameplate Information..................................................................... 57 3.9 Motor Starters............................................................................................... 59 3.10 Motor Enclosures.......................................................................................... 59 3.11 Variable- Speed Electric Motors.................................................................. 59 3.12 Motor Efficiency........................................................................................... 60 Problems................................................................................................................. 61 Simulation Problems............................................................................................... 63 Chapter 4 Mechanical Power Transmission 65 Introduction............................................................................................................ 65 4.1 V-Belt Drives................................................................................................ 65 4.1.1 V-belt types and standardization............................................................ 66 4.1.2 V-belt drive geometry............................................................................ 67 4.1.3 Kinematics of V-belt drives................................................................... 68 4.1.4 Mechanics of V-belt drives.................................................................... 69 4.1.5 Stresses and service life......................................................................... 72 4.1.6 Variable-speed V-belt drives.................................................................. 74 4.1.7 V-belt drive design................................................................................. 76 4.2 Chain Drives................................................................................................. 76 4.2.1 Types of chains and standardization...................................................... 76 4.2.2 Geometry of chain drives....................................................................... 79 4.2.3 Kinematics of chain drives..................................................................... 79 4.2.4 Design of chain drives............................................................................ 82  4.3 Power-Take-Off Drives................................................................................. 83 4.4 Overload Safety Devices............................................................................... 87 4.4.1 Shear devices......................................................................................... 87 4.4.2 Jump clutch devices............................................................................... 88 4.4.3 Friction devices...................................................................................... 89 Problems................................................................................................................. 90 Chapter 5 Fluid power, mechatronics, and control 91 Introduction............................................................................................................ 91 5.1 Basic Principles and Elements Of Fluid Power............................................ 91 5.2 Pumps............................................................................................................ 92 5.3 Valves........................................................................................................... 96 5.3.1 Pressure control valves........................................................................... 96 5.3.2 Volume control valves........................................................................... 98 5.3.3 Directional control valves...................................................................... 99 5.4 Actuators..................................................................................................... 102 5.4.1 Hydraulic motors................................................................................. 102 5.4.2 Hydraulic cylinders.............................................................................. 102 5.5 Reservoirs, Fluids, Filters, and Lines......................................................... 104 5.6 Types of Fluid Power Systems................................................................... 107 5.6.1 Open-center systems............................................................................ 107 5.6.2 Pressure-compensated systems............................................................ 109 5.6.3 Load-sensing systems.......................................................................... 109 5.7 Pressure Transients...................................................................................... 111 5.8 Hydrostatic Transmissions.......................................................................... 112 5.9 Mechatronics and System Control............................................................. 114 5.9.1 An introduction to mechatronics.......................................................... 114 5.9.2 System control..................................................................................... 115 Problems............................................................................................................... 117 Simulation Problems............................................................................................. 121 Chapter 6 Precision agriculture 123 Introduction.......................................................................................................... 123 6.1 Sensors........................................................................................................ 124 6.1.1 Sensor types......................................................................................... 124 6.1.2 Sensor applications.............................................................................. 124 6.1.3 Advanced sensors................................................................................. 124 6.2 Global Positioning System.......................................................................... 125 6.2.1 GPS for civilian use............................................................................. 125 6.2.2 Military GPS........................................................................................ 125  6.2.3 Differential GPS................................................................................... 125 6.2.4 Carrier-phase GPS............................................................................... 126 6.2.5 Real-time kinematic GPS..................................................................... 126 6.2.6 Accuracy measures.............................................................................. 126 6.2.7 Coordinate transformation................................................................... 127 6.3 Geographic Information System................................................................. 130 6.3.1 Data input to a FIS............................................................................... 130 6.3.2 Map coordination................................................................................. 131 6.3.3 Data analysis in the FIS....................................................................... 133 6.3.4 Data persistence................................................................................... 133 6.4 Variable Rate Applications......................................................................... 133 6.4.1 Approaches.......................................................................................... 133 6.4.2 Applications......................................................................................... 134 6.4.3 Application resolution.......................................................................... 134 6.4.4 Control systems.................................................................................... 134 6.4.5 Automatic guidance............................................................................. 135 6.5 Controller Area Networks........................................................................... 135 Problems............................................................................................................... 137 Chapter 7 Tractor Hitching, Traction, and Testing 139 Introduction.......................................................................................................... 139 7.1 Hitching Systems........................................................................................ 139 7.1.1 Principles of hitching........................................................................... 139 7.1.2 Types of hitches................................................................................... 139 7.1.3 Hitching and weight transfer................................................................ 142 7.1.4 Control of hitches................................................................................. 144 7.2 Tires and Traction....................................................................................... 144 7.2.1 Basic tire design................................................................................... 146 7.2.2 Traction models................................................................................... 149 7.2.3 Traction predictor spreadsheet............................................................. 153 7.3 Soil Compaction.......................................................................................... 154 7.4 Traction Aids............................................................................................... 155 7.5 Tractor Testing............................................................................................ 156 7.5.1 Basic principles of tractor testing......................................................... 156 7.5.2 Official tractor tests.............................................................................. 158 Problems............................................................................................................... 165 Simulation Problems............................................................................................. 166 Chapter 8 Soil Tillage 169 Introduction.......................................................................................................... 169  8.1 Tillage Methods and Equipment................................................................ 169 8.1.1 Primary tillage in conventional tillage systems.................................... 170 8.1.2 Secondary tillage in conventional tillage systems................................ 179 8.1.3 Tillage in conservation tillage systems................................................ 184 8.2 Mechanics of Tillage Tools......................................................................... 185 8.2.1 Soil texture........................................................................................... 185 8.2.2 Physical properties of soils.................................................................. 187 8.2.3 Mechanical properties of soils............................................................. 189 8.2.4 Mechanics of a simple tillage tool....................................................... 200 8.3 Performance of Tillage Implements........................................................... 207 8.3.1 Moldboard plows................................................................................. 207 8.3.2 Disk implements.................................................................................. 209 8.3.3 Cultivators............................................................................................ 211 8.3.4 Rotary tillers......................................................................................... 214 8.4 Hitching of Tillage Implements................................................................. 215 8.4.1 Forces on tillage tools.......................................................................... 215 8.4.2 Pull- type implements........................................................................... 221 8.4.3 Mounted implements............................................................................ 226 Problems............................................................................................................... 229 Chapter 9 Crop Planting 231 Introduction.......................................................................................................... 231 9.1 Methods and Equipment............................................................................. 231 9.1.1 Broadcast seeding................................................................................ 231 9.1.2 Drilling................................................................................................. 232 9.1.3 Precision planting................................................................................. 233 9.1.4 Transplanting....................................................................................... 234 9.2 Functional Processes................................................................................... 235 9.2.1 Seed metering....................................................................................... 235 9.2.2 Seed transport....................................................................................... 245 9.2.3 Furrow opening and covering.............................................................. 255 9.2.4 Transplanting....................................................................................... 258 9.3 Evaluating Planter and Transplanter Performance...................................... 262 9.3.1 Broadcast seeders................................................................................. 262 9.3.2 Drills.................................................................................................... 264 9.3.3 Precision planters................................................................................. 264 9.3.4 Transplanters........................................................................................ 265 Problems............................................................................................................... 265 Chapter 10 Chemical Application 269 Introduction.......................................................................................................... 269 10.1 Application of Granular Chemicals............................................................ 269 10.1.1 Methods for application of granular chemicals.................................... 270 10.1.2 Equipment for application of granular chemicals................................ 270 10.1.3 Functional processes of granular chemical applications..................... 273 10.2 Application of Liquid Chemicals............................................................... 280 10.2.1 Methods for application of liquid chemicals........................................ 280 10.2.2 Equipment for application of liquid chemicals.................................... 280 10.2.3 Functional processes of applying liquid chemicals.............................. 286 10.3 Performance Evaluation.............................................................................. 310 10.3.1 Uniformity of coverage of granular chemical application.................. 310 10.3.2 Calibration of fertilizer spreaders......................................................... 312 10.3.3 Liquid chemical application................................................................. 315 10.3.4 Sprayer calibration............................................................................... 321 Problems............................................................................................................... 322 Chapter 11 Hay and Forage Harvesting 325 Introduction.......................................................................................................... 325 11.1 Methods and Equipment............................................................................. 325 11.2 Functional Processes................................................................................... 331 11.2.1 Cutting mechanics and plant structure................................................. 331 11.2.2 Cutting and chopping........................................................................... 343 11.2.3 Curing and preservation of forage........................................................ 370 11.2.4 Windrowing......................................................................................... 374 11.2.5 Baling................................................................................................... 380 11.3 Performance Evaluation.............................................................................. 392 Problems............................................................................................................... 395 Chapter 12 Grain Harvesting 403 Introduction.......................................................................................................... 403 12.1 Methods and Equipment............................................................................. 403 12.1.1 Direct harvesting.................................................................................. 403 12.1.2 Cutting and windrowing....................................................................... 408 12.2 Functional Processes................................................................................... 409 12.2.1 Gathering, cutting, pickup, and feeding............................................... 410 12.2.2 Threshing............................................................................................. 415 12.2.3 Separation............................................................................................ 420 12.2.4 Cleaning............................................................................................... 427  12.2.5 Power requirements.............................................................................. 433 12.3 Combine Testing......................................................................................... 433 Problems............................................................................................................... 435 Chapter 13 Fruit, Nut, and Vegetable Harvesting 437 Introduction.......................................................................................................... 437 Natural constraints............................................................................................ 438 Economic constraints........................................................................................ 438 13.1 The Functional Processes............................................................................ 439 13.1.1 Removal............................................................................................... 439 13.1.2 Control................................................................................................. 440 13.1.3 Selection............................................................................................... 440 13.1.4 Transportation...................................................................................... 441 13.2 Methods and Equipment............................................................................. 441 13.2.1 Root crops............................................................................................ 442 13.2.2 Surface crops........................................................................................ 447 13.2.3 Bush and trellis crops........................................................................... 452 13.2.4 Tree crops............................................................................................. 459 13.3 Theoretical Considerations.......................................................................... 464 13.3.1 Aerodynamic concepts......................................................................... 464 13.3.2 Fundamentals of bush and tree shakers................................................ 468 13.3.3 Vibrational detachment during harvest................................................ 475 13.3.4 Impact models and mechanical damage............................................... 476 13.4 Performance Factors.................................................................................... 483 13.4.1 Damage................................................................................................ 484 13.4.2 Efficiency............................................................................................. 484 13.4.3 Reliability............................................................................................. 484 Problems............................................................................................................... 486 Chapter 14 Conveying of Agricultural Materials 491 Introduction.......................................................................................................... 491 14.1 Screw Conveyors........................................................................................ 491 14.1.1 Screw conveyor methods and equipment............................................. 491 14.1.2 Theory of screw conveyors.................................................................. 492 14.1.3 Screw conveyor performance............................................................... 494 14.2 Pneumatic Conveyors.................................................................................. 499 14.2.1 Pneumatic conveyor methods and equipment...................................... 499 14.2.2 Theory of pneumatic conveyors........................................................... 502 14.2.3 Pneumatic conveyor performance........................................................ 510 14.3 Bucket Elevators......................................................................................... 511  14.3.1 Theory of bucket elevators................................................................... 512 14.3.2 Bucket elevator capacity...................................................................... 514 14.3.2 Bucket elevator power......................................................................... 514 14.4 Forage Blowers........................................................................................... 515 14.4.1 Theory of forage blowers..................................................................... 516 14.4.2 Energy requirements of forage blowers............................................... 519 14.4.3 Forage blower performance................................................................. 521 14.5 Miscellaneous Conveyors........................................................................... 521 14.5.1 Belt conveyors..................................................................................... 521 14.5.2 Bulk or mass conveyors....................................................................... 523 Problems............................................................................................................... 524 Chapter 15 Machinery Selection and Management 525 Introduction.......................................................................................................... 525 15.1 Field Capacity and Efficiency..................................................................... 525 15.1.1 Field capacity....................................................................................... 525 15.1.2 Field efficiency.................................................................................... 526 15.2 Draft and Power Requirements................................................................... 529 15.3 Machinery Costs.......................................................................................... 535 15.3.1 Ownership costs................................................................................... 535 15.3.2 Operating costs..................................................................................... 538 15.3.3 Timeliness costs................................................................................... 540 15.4 Machinery Selection and Replacement......................................................... 545 15.4.1 Machinery selection............................................................................. 545 15.4.2 Machinery replacement........................................................................ 548 Problems............................................................................................................... 549 Simulation Problems............................................................................................. 551 Selected Bibliography.......................................................... 553 Appendix A............................................................................. 566 Appendix B.......................................................................... 568 Subject Index...................................................................... 571  Srivastava, Ajit K., Carroll E. Goering, Roger P. Rohrbach, and Dennis R. Buckmaster. 2006. Agricultural mechanization and some methods of study. Chapter 1 in Engineering Principles of Agricultural Machines, 2nd ed., 1-14. St. Joseph, Michigan: ASABE. Copyright American Society of Agricultural and Biological Engineers. AGRICULTURAL MECHANIZATION AND SOME METHODS OF STUDY INTRODUCTION Many factors have contributed to agricultural mechanization. Reducing human drudgery, increasing productivity, improving timeliness of agricultural operations such as planting and harvesting, and reducing peak labor demands are among the most com- pelling. Farm work is physically demanding and the working conditions are often harsh. It is less strenuous to drive a tractor than to till the soil with a spade all day long. A trac- tor pulling a plow can cultivate a larger area than a human with a spade in the same amount of time, thereby increasing productivity and timeliness. Timeliness is an impor- tant factor in agricultural production. Completing certain farming operations such as planting and harvesting in a timely manner increases yields and improves profitability. Farming operations are seasonal with fluctuating labor demand. More labor is needed during planting and harvesting than during other periods of plant growth. This fluctua- tion in labor demand creates labor management problems. With mechanization it is pos- sible to reduce peak labor demand and maintain a more stable labor force on the farm. 1.1 HISTORY OF MECHANIZED AGRICULTURE Even though great changes have taken place in the field of agriculture, soil still has to be tilled; seeds still have to be planted in the soil; the growing crop still has to be tended and cared for; and the crops still have to be harvested and threshed. However, the manner in which these operations are performed have changed drastically. One of the earliest plows used to till soil was a wooden plow pulled either by hu- mans or draft animals. As we learned to work with steel, moldboard plows were de- veloped. The moldboard plow was a major development, since it turned the soil for better weed control and soil aeration. The seeds were planted by broadcasting them by hand. A major development in planting occurred when we learned to plant seeds in rows using dibble sticks in the early stages and later on with planters. Planting in rows had the advantage of controlling the plant population and facilitated better weed con- trol during the plant growth period. 2 CHAPTER 1 AGRICULTURAL MECHANIZATION AND SOME METHODS OF STUDY Crop harvesting was done by hand using sickles or scythes. The cut crop was bun- dled and carried to a central location where it was threshed either by beating it with a stick or by having hoofed animals walk on it. The threshed crop was separated from chaff and straw by winnowing in natural wind. The threshed crop mixture would be slowly dropped from a height and the wind would blow the chaff and small pieces of straw away leaving the clean grains to fall in a pile. The process was repeated until the grain was totally free of chaff and other debris. Later, the grain was cut by mowers that used a reciprocating sicklebar. The crop was still bundled by hand. Reapers com- bined the cutting and binding process in one machine. The development of steam en- gines made it possible to develop stationary threshers. Stationary threshers were used to thresh a bundled crop at a central location. The cleaning operation was still done by winnowing but it was done by a fan instead of the natural wind. The development of the internal combustion engine made it possible to combine the cutting, threshing, and cleaning functions. The name “combine” became popular because the machine com- bined the three operations. The power for early farming operations was primarily human labor. Later, draft animals were used as the source of power. Horses, water buffalo, oxen, camels, and even elephants were used as power sources. Mechanical power became the primary source with the development of steam engines in 1858. In 1889 the first tractor with an internal combustion engine was built. Tractors powered by internal combustion en- gines were lighter and more powerful than steam-powered tractors. In the 1930s the high compression diesel engine was adopted for tractors and became very popular. Today’s modern tractor is a very sophisticated machine with hydrostatic drive, elec- trohydraulic servos to control draft force and the operating depth, and an ergonomi- cally designed, climate-controlled operator’s station. Developments in technologies such as global positioning systems (GPS) and geospacial information systems (GIS) have led to the development of what is commonly known as precision agriculture in which soil variability and fertility data are stored in an on-board computer that con- trols the application rate of chemicals such as fertilizers, pesticides, and herbicides. It needs, however, to be pointed out that in many parts of the world, especially the Third World countries, animal and human labor continue to be the major source of power for farming operations. Even in the most advanced countries, manual labor is still used for fresh-market fruit and vegetable harvesting operations because of the delicate nature of the products. The level of mechanization depends upon the availabil- ity of human labor and the level of industrialization within each country. Mechanization of agriculture was an important factor in reducing labor demands for farming and making it available to develop other industries. In 1900 nearly two- thirds of the U.S. population was engaged in farming. While only 3% of the American population is engaged in production agriculture now, an American farmer produces enough food to feed 60 people and one farm family can manage up to 1200 ha of farmland. Agricultural mechanization has transformed American agriculture from sub- sistence farming to a major industry. Today, in monetary value, exports from the agri- culture sector are second only to the sale of weapons to foreign countries. Mechanized agriculture is, however, energy and capital intensive. Energy costs and the availability of capital to buy machines determine the level of mechanization in a ENGINEERING PRINCIPLES OF AGRICULTURAL MACHINES 3 society. Thus, production agriculture is facing many challenges. Rising energy costs, greater competition in the global marketplace, and the growing concerns for the envi- ronment pose new challenges that agricultural engineers must face to keep agriculture productive and affordable. The area of agricultural machines is dynamic and will con- tinue to evolve to meet the changing needs of production agriculture. 1.2 FARMING OPERATIONS AND RELATED MACHINES Plants are the primary production units of agriculture. They receive carbon dioxide from the air through their leaves, and receive water and nutrients from the soil through their roots. Using carbon dioxide, water, nutrients, and solar energy, plants produce seeds, fruits, roots, fibers, and oils that people can use. The growth of plants happens in nature without any human intervention. However, agriculture arises when people exert control over plant growth. Machines are used as an extension of people’s ability to produce and care for plants. This book focuses on many of the machines used by farmers to produce crops in plant agriculture. A crop is a group of similar plants which are growing within the same land area. For example, if a farm produces rice and wheat, that farm is said to produce two crops. A farmer must complete certain operations in order to successfully produce a crop. The first operation is a mechanical stirring of the soil, called tillage, to prepare the seed bed. The second operation is called planting and it places the seeds in the tilled soil at the correct depth with the appropriate spacing between seeds. When the re- quired soil temperature and soil water content are present, the seeds will germinate and then grow leaves and roots. For some crops the seeds are planted in a small area called a nursery and then the small plants are transplanted to the fields where they will grow to maturity. As the plants grow the farmer must protect them from pests such as weeds (un- wanted plants), insects, other animals, and diseases. Mechanical cultivation (tillage between the plants) is used to control weeds in some cases. Chemicals are frequently used to control weeds, insects, and diseases. Fences and/or noise-making devices may be used for protection from larger animals. The final crop production operation is the harvesting of the plant parts which have economic value for the farmer. In some cases, more than one part of the plant may have economic value. For example, a farmer may use rice straw (stems and leaves) as an energy resource after the rice seeds have been removed from the plants. In other cases, the crop residue (unused plant parts) is stirred into the soil during tillage for the next crop. The period of time on the calendar which passes from the beginning of the planting operation until the end of the harvest operation is called the growing season. The weather in some tropical farming areas is such that the growing season is continuous. In these areas, a crop can be planted any time during the year, and it can be harvested whenever it is mature. In many farming areas, however, the growing season is re- stricted because of weather conditions. For example, the planting operation may begin during spring when the soil temperature is increasing, and the harvest operation is 4 CHAPTER 1 AGRICULTURAL MECHANIZATION AND SOME METHODS OF STUDY Table 1.1. Example of a crop rotation with four crops. Year Area 1 Area 2 Area 3 Area 4 1 Crop A Crop B Crop C Crop D 2 Crop B Crop C Crop D Crop A 3 Crop C Crop D Crop A Crop B 4 Crop D Crop A Crop B Crop C completed during fall before cold weather begins. In other climates, the growing sea- son depends on rainfall patterns with the planting operation done at the beginning of the rainy season so that the plants have adequate water for growth. Some farming ar- eas have weather conditions which cause a short growing season that allows only one crop per calendar year, while other areas have a longer growing season which allows two or more crops each year from a given field. When the growing season is weather dependent, the planting and harvesting operations are very labor intensive in order to complete these operations in a timely way. If planting and harvesting are not com- pleted in a timely way, the crop yield will be lowered. Agricultural crops such as rice and wheat are annual plants which have one harvest after each planting. The annual plants die after they reach maturity and a new crop must be planted before another harvest can be achieved. Crops like hay (used for live- stock feed) are perennial plants which live for several years and can be harvested sev- eral times after a single planting operation. Field crops include grains, hay, and sugar beets, while horticultural crops include fruit and vegetables. The crops which farmers choose for their own farm depends on soil type, climate, labor availability, machine availability, profit potential, social cus- toms, government programs, and the farmer’s skills. Many farmers produce more than one type of crop during each calendar year. For example, a farm may be divided into four land areas with a different crop grown on each of the four areas. Alternating these crops in a fixed sequence is called a crop ro- tation and an example is illustrated in Table 1.1. Using a crop rotation spreads the farmer’s work load over a longer period of time and reduces the economic risk in case one crop fails. A good crop rotation can also improve crop yield and the soil. Crop rotation affects the set of machines that must be available on the farm. For example, if wheat, corn, and soybeans are all grown, then the farmer needs a grain drill and a row- planter to plant crops, and a grain head and a row crop head as attachments to the combine to harvest crops. A broad selection of machines adds to capital cost and must be taken into account when selecting a crop rotation system. 1.3 FUNCTIONAL ANALYSIS OF AGRICULTURAL MACHINES An agricultural machine has components that work together as a system in order for the machine to perform its intended function. Any machine, however simple, may be divided into many subcomponents. To understand how a machine works, consider the machine as a collection (or system) of several subsystems made up of components and subcomponents. In this section, we will learn how to identify the various systems found in a modern agricultural machine and the functions performed by the subsystems. ENGINEERING PRINCIPLES OF AGRICULTURAL MACHINES 5 SYSTEMS OF AN AGRICULTURAL MACHINE Agricultural Machine Support System Process System Frame Power Control Revers- Non-re- Non-di- ible versible rectional Figure 1.1 – Systems of agricultural machines. It is often useful to look at a complex machine, such as an agricultural machine, as including two kinds of systems: process systems and support systems. The process systems are those components of the machine that actually perform the function(s) that the machine is designed to perform, i.e., cut, separate, mix, etc. The support systems are the parts that support or aid the process systems in performing their functions. Process systems may be divided into three types: reversible, non-reversible, and non-directional. Reversible processes include processes such as separation and com- paction. Non-reversible processes include cutting and grinding. Examples of non- directional processes are conveying, metering, and storing materials. Support systems may be divided into three subsystems: the framing, control, and power subsystems. The framing system consists of all structural parts of the machine that hold pieces together so they function properly. The control system provides con- trol over the process system. Controls may be automatic or manual. Power systems supply the power to the process systems. Self-propelled machines contain both the power source (the engine) and the power transmission devices (the drivetrain). Ma- chines that depend on the tractor as a power source contain power transmission de- vices such as chains, belts, gears, PTO shafts, etc. Together these devices form the power system, which drives the process system. A breakdown of the types of systems found in an agricultural machine is given in Figure 1.1. This illustration should aid in developing the concept of the agricultural machine as a system. 1.3.1 Basic processes of agricultural machines In this book we will concentrate on process systems of agricultural machines. The process systems of a machine include all parts that perform reversible, non-reversible, or non-directional processes, whereas these processes are the functions the machine was designed to perform. For example, the hay baler was designed to package hay material in the form of a bale so it can be transported and stored for later feeding to animals. In order to perform this task, several processes must be performed on the hay 6 CHAPTER 1 AGRICULTURAL MECHANIZATION AND SOME METHODS OF STUDY Table 1.2. Basic processes of agricultural machines. Non-Reversible Non-Directional Reversible Processes Processes Processes Mix Separate Dissociate Convey Fluff Pack Cut Meter Pickup Deposit Crush Store Scatter Position Grind material. They include non-reversible processes such as cutting, reversible processes such as pickup and compaction, and non-directional processes such as conveying and metering of hay. Table 1.2 lists the processes commonly found in various agricultural machines. The reversible processes are listed in opposing pairs under the appropriate category in the table. The list is not comprehensive, but it includes most commonly found processes in modern agricultural machines. 1.3.2 Process diagrams An exercise that can be helpful in understanding the operation of an agricultural machine is to draw a diagram of the processes that occur in the machine. The diagram is formed by following the flow of material through the machine and listing the proc- esses in order. The processes can be connected with lines to indicate the flow of the material through the machine. Any of the processes can occur either totally within the machine or with machine mobility as part of the process. For example, the forward motion of a baler is essential to pick up hay. However, after hay is picked up, it will be baled regardless of the for- ward motion of the machine. When machine mobility is a part of the process, the process is, in this book, enclosed in a box. A process occurring totally within the ma- chine is enclosed in a circle or an oval. A few examples should be helpful in understanding the concept of process dia- gramming. A good first example is the moldboard plow. The first step is to determine what processes occur as the plow moves through the soil. As the plow moves forward, the soil is cut, picked up, positioned, and deposited. The second step is to determine whether the processes are dependent upon forward motion. In the case of a moldboard plow, all functions would cease as soon as the plow is stopped. The process diagram for the moldboard plow is given in Figure 1.2. The processes of picking up and posi- tioning occur simultaneously and, therefore, are diagrammed as a pair. A more complex machine to diagram is the conventional hay baler. The processes that occur in the machine are pickup, convey, meter, cut, pack, bind, convey, and de- posit. The process which is dependent upon forward motion of the baler is pickup. The process diagram is given in Figure 1.3. Pick up Cut Deposit Position Figure 1.2 – Process diagram for a moldboard plow. ENGINEERING PRINCIPLES OF AGRICULTURAL MACHINES 7 Convey Pick up Cut Pack Bind Deposit Meter Figure 1.3 – Process diagram of for a hay baler. The concepts of machine systems and process diagramming are introduced here as tools to aid students in learning more about the makeup and operation of agricultural machines. It is hoped that these concepts will provide a new and more interesting way to study agricultural machines, or any machine for that matter. 1.4 DIMENSIONAL ANALYSIS Engineers like to develop predictive models to study a process or a phenomenon. Ide- ally we would like to develop a model that is based on the natural laws that govern the process. For example, to predict the droplet size and its distribution in a sprayer nozzle we need to understand basic fluid mechanics and the physics of a jet breakup in another fluid such as air. However, this can be a very complex process and does not lend itself to easy modeling. In cases like these another technique which is often useful is dimensional analysis. In dimensional analysis we need only to identify all pertinent physical quanti- ties that influence the process. We then combine these quantities in groups so that each group is dimensionless. Experiments are then carried out to develop a power law model to relate the dependent dimensionless group to the independent ones. Dimensional analysis can be applied to highly complex processes to develop a prediction equation; however, the basic underlying natural laws are not necessarily revealed. It is, however, better than regression models in that the number of variables that must be studied are reduced substantially. Below is an abbreviated discussion of dimensional analysis. 1.4.1 Scope Dimensional analysis is a method by which we deduce information about a phe- nomenon from the single premise that the phenomenon can be described by a dimen- sionally correct equation among pertinent variables. The result of a dimensional analysis of a problem is a reduction in the number of variables in the problem. This results in a considerable savings in both cost and labor during the experimental determination of the function. 1.4.2 Physical dimensions Scientific reasoning is based on such abstract entities such as force, mass, length, time, accelerations, velocity, temperature, specific heat, and electric charge. Each of these entities is assigned a unit of measurement. Of these entities, mass, length, time, temperature, and electric charge are in a sense independent and their units of meas- urement are specified by international standards. Furthermore, specified units of these entities determine the units of all other entities. There is, however, nothing fundamen- tal in the set of entities, mass, length, time, temperature, and electric charge. A great many possibilities exist for choosing five mutually independent entities. Frequently, unit of force is prescribed, rather than the unit of mass. The unit of mass is determined 8 CHAPTER 1 AGRICULTURAL MECHANIZATION AND SOME METHODS OF STUDY by Newton’s law, F = ma. In this case the system of measurement is called a force system. Dimensions are a code for telling us how the numerical value of a quantity changes when the basic units of measurement are subjected to prescribed changes. The symbols [F], [M], [L], [T], and [θ] have been employed to denote dimensions of force, mass, length, time, and temperature, respectively, and any entity that has no units is denoted by (Table 1.3). Table 1.3. Dimensions of entities. Mass System Force System Length L L Time T T Temperature θ θ Force MLT-2 F Mass M FL-1T-2 Mass density ML LF-4T2 Pressure and stress ML-1T-2 LF-2 Energy, work ML2T-2 FL Viscosity ML-1T-1 FL-2T Mass movement of inertia ML2 FLT Surface tension MT-2 FL-1 Strain 1 1 Poisson’s ratio[a] 1 1 [a] Any ratio of like-dimensioned quantities (i.e., unitless) has the dimension of one. 1.4.3 Units of measurement CGS (Centimeter Gram Second) System SI (International) System Force, measured in dynes, is defined as the Force, measured in Newtons, is defined force required to accelerate a 1 gram mass as the force required to accelerate a 1 kg with 1 cm/s2 acceleration. Thus, the weight mass with 1 m/s2 acceleration. Thus, the of a gram mass is: weight of a kilogram mass is: W = mg W = mg = (1 g) (981 cm/s2) = (1kg) (9.81 m/s2) = 981 (g. cm/s2) = 9.81 kg m/s2 = 981 dynes = 9.81 Newtons U.S. Customary System Conversion Factors Force = pound (lb) 1 m = 3.281 ft Length = foot (ft) 1 ft = 0.0348 m Time = second (s) 1 kg = 0.06852 slug Mass, measured in slugs, is defined as that 1 slug = 14.594 kg mass which will require a 1 lb force in 1 Newton = 0.2248 lb order to accelerate with 1 ft/s2 accelera- 1 lb = 4.448 Newtons tion. Thus, the weight of 1 slug is: W = mg 1º C = 1.9º F = (1 slug) (32.2 ft/s2) = 32.2 (slug ft/s2) = 32.2 lb ENGINEERING PRINCIPLES OF AGRICULTURAL MACHINES 9 1.4.4 Developing a prediction equation A critical step in dimensional analysis is to decide what physical quantities enter the problem. It is important that there be no redundancy and that no pertinent quantities are left out. To list pertinent variables, it is useful to develop an understanding of the basic phenomena or laws that affect the system. For example, let us consider that we want to develop an equation to predict the period of oscillation of a simple pendulum, that is, a mass is attached to one end of a string while the other end is attached to a support in a way such that the mass is allowed to swing with no friction. We will also neglect the aerodynamic effects. An equation of the following form may be written: Τ = Cα la mb gc (1.1) where T = period, a time entity denoted by dimension [T] Cα = a dimensional coefficient denoted by dimension l = string length, a length entity denoted by dimension [L] m = mass, an entity denoted by dimension [M] g = acceleration due to gravity, denoted by dimension [LT-2] a, b, and c = dimensionless exponents Substituting the dimension of each physical quantity in Equation 1.1 we get: [T] = [L]a [M]b [LT-2]c (1.2) It may clarify the next step to place the [L] and [M] dimensions on both sides of the equation, each with a zero exponent: [M]0 [L]0 [T] = [L]a [M]b [LT-2]c Then, collecting and equating the exponents of the above equation we get: for [M]: 0 = b, because the [M] exponent on the left is 0 and the [M] exponent on the right is b; for [L]: 0 = a + c, thus a = – c, because the [L] exponent on the left is 0 and on the right the collected [L] exponents are a + c; and similarly, for [T]: 1 = – 2c c = – 1/2 a = 1/2 Substituting the values of a, b, and c in Equation 1.1 we get 1 -1/2 Τ = Cα l /2 m0 g or T = Cα 1/ g T or = Cα (1.3) l/g Note that the quantity on the left hand side of Equation 1.3 is a dimensionless group. Also note that mass, m, dropped off. This is true since we know that the period of oscillation does not depend on mass as heavier objects do not fall faster. The coeffi- cient Cα needs to be determined experimentally. We know from mechanics that the 10 CHAPTER 1 AGRICULTURAL MECHANIZATION AND SOME METHODS OF STUDY value of the constant is 2π. Also note that we began with four physical quantities and we reduced the equation by three (a number equal to the number of basic dimensions in the problem) to one dimensionless term in Equation 1.3. 1.4.5 Buckingham’s Theorem Buckingham’s Theorem states that “If an equation is dimensionally homogeneous, it can be reduced to a relationship among a complete set of dimensionless products.” Suppose that we are interested in the drag force, F, acting on a sphere of diameter, D, submerged in a fluid with an average velocity, V, and having density, ρ, and vis- cosity, µ. Consider tentatively the relationship: F = Cα Va Dbρc µd (1.4) where Cα = dimensionless coefficient; and a, b, c, d = dimensionless exponents. In order for the equation to be dimensionally homogeneous both sides of the equa- tion should have the same dimensions. This is similar to checking your units in a com- plicated equation; they must be the same on each side. This is accomplished by replac- ing the variables by their dimensions (Table 1.3) in the above equations. (Note that we use the force system since our objective is to develop a prediction equation for drag force. This can be done in the mass system, but the result will not be intuitive since force will need to be expressed as mass times the acceleration.) Replacing the vari- ables by their dimensions results in: [F] = [LT-1]a [L]b [FL-4T2]c [FL-2T]d (1.5) for [F]: 1 = c + d for [L]: 0 = a + b – 4c – 2d for [T]: 0 = – a + 2c + d a=2–d b=2–d c=1–d Substituting the values in Equation 1.4 we get: d  µ  F = Cα V 2 D 2   (1.6)  VDP  η  F   PVD  rearranging,   = C α   (1.7)  PV 2 D 2   µ   F  Note that the pressure coefficient, Ρ =  2 2  , and the Reynolds number,  PV D   PVD  N Re =   , can be substituted into the rearranged equation, which then simplifies to:  µ  Ρ = f (N Re ) (1.8) where f is any general function. ENGINEERING PRINCIPLES OF AGRICULTURAL MACHINES 11 Both Ρ , the pressure coefficient, and NRe, Reynolds number, are dimensionless quantities. In general, a dimensional equation can be reduced to dimensionless quanti- ties (call the pi-terms) related by a general function f. Notice that there are only two terms in the dimensionless form of the equation (Equation 1.8) whereas there are five variables in the dimensional form (Equation 1.7). Stated generally, Buckingham’s Theorem allows us to conclude that if n variables are connected by an unknown dimensionally homogeneous equation, it can be ex- pressed in the form of n – r dimensionless products, where r is the number of basic dimensions. We follow up with Equation 1.7 while noting that the projected area of a sphere is A = (1/4) π D2. Substituting, we obtain:  F  1 8  = f (N Re ) (1.9)  PV 2 A  2 π 8 The term f (N Re ) is called the drag coefficient, CD. Thus, the equation for drag on a π sphere can be written as: 1 F = C D PV 2 A (1.10) 2 where CD is a function of NRe. It is plotted in Figure 1.4. The figure is an experimental graph for smooth spherical bodies. It gives complete information concerning the drag forces on smooth spherical bodies of all sizes in an incompressible fluid with any speed of flow. To provide the same information without using dimensional analysis would require about 25 graphs that would show separately the effects of each of the variables V, D, ρ, and µ. 3 2 Log CD 1 0 -1 -2 -2 -1 0 1 2 3 4 5 6 7 Log NRe Figure 1.4 – Drag coefficient as a function of Reynolds number for smooth spherical bodies. 12 CHAPTER 1 AGRICULTURAL MECHANIZATION AND SOME METHODS OF STUDY 1.4.6 Systematic calculation of the dimensionless products Consider the problem of computing dimensionless products of variables P, Q, R, S, T, U, V, whose dimensional matrix is given below: k1 k2 k3 k4 k5 k6 k7 P Q R S T U V M 2 –1 3 0 0 –2 1 L 1 0 –1 0 2 1 2 T 0 1 0 3 1 –1 2 The first step is to calculate the r, rank of the matrix. The determinant to the right hand side of the matrix is: 0 −2 1 2 1 2 =1 (1.11) 1 −1 2 Since the determinant is not zero, r = 3. The number of dimensionless groups is the number of variables minus the rank of the dimensional matrix, i.e., the number of di- mensionless groups, or 7 – 3 = 4. The corresponding algebraic equations are: 2k1 – k2 + 3k3 – 2k6 + k7 = 0 k1 – k3 + 2k5 + k6 + 2k7 = 0 k2 + 3k4 + k5 – k6 + 2k7 = 0 There are seven variables in the above three equations. This implies that four vari- ables may be assigned any arbitrary values and the other three may be solved using the above equation. Since the value of the determinant as computed above corresponds to k5, k6, and k7, is non-zero, we will use these as dependent variables. In other words, k1, k2, k3, and k4 may be assigned arbitrary values and k5, k6, and k7 may be solved explic- itly. While any value may be assigned to k1 through k4, it is prudent to select a set of values that results in simplicity in calculations. Let k1 = 1 and k2 = k3 = k4 = 0 and find k5 = – 11, k6 = 5, and k7 = 8. Similarly, let k2 = 1 and k1 = k3 = k4 = 0 and find k5 = 9, k6 = – 4, and k7 = – 7. The above procedure can be repeated and the solutions arranged as follows: Solution Matrix k1 k2 k3 k4 k5 k6 k7 P Q R S T U V π1 1 0 0 0 – 11 5 8 π2 0 1 0 0 9 –4 –7 π3 0 0 1 0 –9 5 7 π4 0 0 0 1 15 –6 – 12 ENGINEERING PRINCIPLES OF AGRICULTURAL MACHINES 13 From the above matrix the dimensionless products can be written as follows: PU 5 V 8 QT 9 π1 = π2 = T11 U4V7 RU 5 V 7 ST15 π3 = π4 = T9 U 6 V12 These products are linearly independent of each other. Using these dimensionless terms the following prediction equation can be written: π1 = C α π a2 π3b π c4 (1.12) 1.4.7 Transformation of dimensionless products New dimensionless products can be determined by forming the products of powers of the old terms. For example, the following set of dimensionless products may be transformed if necessary: PF P P 2g π1 = π2 = V3 π3 = L3 µ2 µg µ2 Suppose we have determined that µ is not important. Even so, we cannot drop all terms containing µ. Instead, we transform the existing set in such a way that µ appears only in one group, which can then be discarded if necessary. This is done as follows: π1 F π1* = = π 2 π 32 PV 2 L2 VLP π*2 = π 2 π 3 = µ π 22 V 2 π*3 = = π3 µ where π* denotes the transformed dimensionless products. Now µ appears only in one term, which we may decide to disregard in order to simplify the investigation. PROBLEMS 1.1 Show by dimensional analysis that the centrifugal force of a particle is propor- tional to its mass, proportional to the square of its velocity, and inversely propor- tional to radius of curvature of its path. 14 CHAPTER 1 AGRICULTURAL MECHANIZATION AND SOME METHODS OF STUDY 1.2 Complete a dimensional analysis to predict the traction force of a wheel on soil. With the help of your instructor identify soil properties that should be included in dimensional analysis. Express the prediction equation as a function of dimen- sionless groups. 1.3 Suppose it is desired to obtain an expression of the draft force of a tillage tool operating in soil. List all variables that affect the draft force and complete a di- mensional analysis of the problem suitable for plotting data from experimental tests. 1.4 An agricultural spray nozzle is used to atomize fluid in air. Complete a dimen- sional analysis to predict the droplet mean diameter of the spray. Srivastava, Ajit K., Carroll E. Goering, Roger P. Rohrbach, and Dennis R. Buckmaster. 2006. (rev.) Engine power for agricultural machines. Chapter 2 in Engineering Principles of Agricultural Machines, 2nd ed., 15-44. St. Joseph, Michigan: ASABE. Copyright American Society of Agricultural and Biological Engineers. ENGINE POWER FOR AGRICULTURAL MACHINES INTRODUCTION The earliest farm equipment made use of human power and, for a period in the 19th and 20th centuries, animals supplied the power needs of farm equipment. Modern agricultural equipment, however, is powered by internal combustion (IC) engines and, since the 1970s, nearly all new agricultural engines have been compression ignition (CI) engines that burn diesel fuel. The engine can be a part of the machine itself, as on a self-propelled combine, or can provide the power for an agricultural tractor. Engines consume fuel to produce power. The power is delivered to some load through the crankshaft and flywheel of the engine. Much of the energy in the fuel is lost before it is converted to useful power. The purpose of this chapter is to clarify the processes by which an IC engine produces power and to provide insights into how engines may be made to operate efficiently. By reading this chapter, you will also learn the important terminology of diesel engines. 2.1 THE POWER IN FUEL Liquid fuels are a highly concentrated form of chemical energy storage. Burning the fuel at even a modest rate releases a large amount of energy that can be calculated using Equation 2.1: Hgm &f Pfe = (2.1) 3600 where Pfe = fuel equivalent power, kW Hg = gross heating value of the fuel, kJ/kg m& f = fuel consumption rate, kg/h The heating values are measured by burning a sample of fuel in a calorimeter. The heating values are defined as gross (Hg) or net (Hn) depending on whether the water created in combustion is recovered as liquid or vapor, respectively. The terms higher 16 CHAPTER 2 ENGINE POWER FOR AGRICULTURAL MACHINES Figure 2.1 – Energy flows through an engine. and lower are sometimes used instead of gross and net, respectively. Heating values tabulated in books (see Table 2.1) are gross values unless otherwise indicated. Less than half of the fuel equivalent power is available for useful work at the flywheel of an engine (see Figure 2.1). In the remainder of this chapter, the various power losses are identified. 2.2 COMBUSTION Combustion is a very complex process, particularly in a CI engine. The fuel must vaporize and mix with air to form a combustible mixture. Burning of the fuel-air mixture generates exhaust emissions, but also generates increased pressure to drive the pistons. The rate of pressure rise affects engine performance and durability. 2.2.1 Combustion chemistry Insights that are very useful in understanding engines can be obtained by making two simplifying assumptions regarding combustion chemistry. The first is that all of the hydrogen in the fuel links with oxygen to form water. The second is that all of the carbon in the fuel is converted to carbon dioxide (CO2) and carbon monoxide (CO), so that no free carbon appears in the combustion products. Most conventional, petroleum- based engine fuels are mixtures of a variety of hydrocarbon molecules, but representative molecules are given in Table 2.1 for each of the common petroleum- based fuels. Alcohols, which may become engine fuels of the future, are also listed. Atomic weights of 12 for carbon, 1 for hydrogen, 16 for oxygen and 14 for nitrogen may be used in the combustion calculations. Although various gases are in the earth’s atmosphere, it is common practice in combustion calculations to neglect all gases except oxygen and nitrogen. The composition of earth’s atmosphere is such that 3.76 molecules of nitrogen (N2) accompany every molecule of oxygen (O2). Combustion chemistry then becomes a simple matter of counting atoms, as indicated in Example Problem 2.1. ENGINEERING PRINCIPLES OF AGRICULTURAL MACHINES 17 Table 2.1. Comparison of properties of several fuels. Higher Stoichio- API Heating Research Boiling metric Gravity, Density, Value, Octane Range, Air-Fuel Fuel degrees kg/m3 kJ/kg Number °C Formula Ratio Butane 112 580 49.500 98 0 C4H10 15.5 Propane 146 509 50,300 111 – 42 C3H8 15.7 Reg.gasoline 61 735 47,600 93 30 - 230 C6H18 15.2 No. 1 diesel 40 823 45,700 40[a] 160 - 260 C12H26 15.0 No. 2 diesel 38 834 45,500 40[a] 200 - 370 C16H34 15.0 Methanol --- 792 22,700 110 65 CH4O 6.49 Ethanol --- 785 29,700 110 78 C2H6O 9.03 Methyl --- 885 38,379 51[b] C19H36O2 12.5 soyate [a] Minimum cetane rating for diesel fuel [b] Cetane rating Example Problem 2.1 Calculate the stoichiometric (chemically correct) air/fuel ratio when diesel fuel is burned with air. Also analyze the products of combustion when No. 2 diesel is burned. Solution From Table 2.1, the cetane molecule (C16H34) is used to represent diesel fuel. Under the standard simplifying assumptions, the complete combustion reaction becomes: C16H34 + 24.5 O2 + 92.12 N2 → 92.12 N2 + 16 C02 + 17 H2O The reaction is balanced on the basis of one molecule of fuel. The hydrogen balance determines the amount of water in the combustion products, while the carbon balance determines the amount of CO2. Then enough O2 must be supplied to form the CO2 and H2O; each mole of O2 is accompanied by 3.76 moles of N2. The nitrogen is nearly inert and simply appears in the combustion products. The stoichiometric air/fuel ratio is: A/F = (24.5 × 32 + 92.12 × 28) / 226 = 14.9 Note that 17 moles of water appear in the exhaust for each mole of fuel burned or, on a mass basis, 1.35 kg of water appear per kilogram of fuel burned. The difference between the gross and net heating values of the fuel is exactly equal to the latent energy of the water produced by combustion, i.e., the energy needed to convert that liquid water to vapor. A major reason why quick warm up of engines is important is to cause the combustion water to exit the engine as vapor rather than liquid. If the fuel contains sulphur impurities, the sulphur compounds created in combustion can react with liquid water to form sulfuric acid and corrode the engine. 18 CHAPTER 2 ENGINE POWER FOR AGRICULTURAL MACHINES Engine exhaust gases are normally analyzed on a dry, volume basis. Since the exhaust gases are intermingled at the same temperature and pressure, each molecule occupies the same volume according to Avogadro’s Law. Thus, the analysis of the dry exhaust gases in Example Problem 2.1 is: 92.12 / (92.12 + 16) = 0.852 volume fraction (85.2%) is occupied by N2, and 16 / (92.12 + 16) = 0.148 volume fraction (14.8%) is occupied by CO2. The equivalence ratio, φ, is a measure of mixture richness. It is defined as follows: ( F / A) actual φ= (2.2a) ( F / A) stoichiometric ( A / F) stoichiometric or φ= (2.2b) ( A / F) actual Note that the F/A ratio is just the inverse of the A/F ratio. Thus, in Example Problem 2.1, the stoichiometric ratios were A/F = 14.9 or F/A = 0.0671. An air-fuel mixture is rich if φ >1, stoichiometric if φ =1, or lean if φ 1, not enough oxygen is available to convert all the carbon in the fuel to CO2; consequently, CO appears in the exhaust. When φ 1 Ψ3 = 0 for φ < 1 2Ψ1 (1 – 1/ φ) for φ >1 Ψ4 = Ψ1 (1 / φ – 1) for φ < 1 0 for φ > 1 ENGINEERING PRINCIPLES OF AGRICULTURAL MACHINES 19 Note that the Combustion Reaction 2.3 accommodates oxygenated fuels, such as the alcohols in Table 2.1. The number of carbon, hydrogen, and oxygen atoms need not be integer numbers. The stoichiometric air/fuel ratio for the combustion is: 137.3ψ1 A/F = (2.4) φ(12 x + y + 16z ) The theoretical concentrations of the dry exhaust products on a volume basis are: Conc. N2 = 3.76 Ψ1/(φ T) (2.5a) Conc. C02 = Ψ2/T (2.5b) Conc. CO = Ψ3/T (2.5c) Conc. O2 = Ψ4/T (2.5d) where T = Ψ2 + Ψ3 + Ψ4 + 3.76Ψ1/φ. Equations 2.5a through 2.5d give good approximations to actual exhaust emissions, except that minute amounts of other gases also appear. A small amount of oxygen and nitrogen react with each other to form oxides of nitrogen, i.e., NO and NO2. The combined NO and NO2 gases are commonly referred to as NOx. Also, φ is typically not uniform throughout all of the combustion chambers of an actual engine. Thus, small amounts of CO and O2 may appear in the exhaust whether the overall φ is less than or greater than one. Some free carbon may also appear, as well as trace amounts unburned hydrocarbons (HC), hydrogen, and other gases. 2.2.2 Energy release in combustion The purpose of the combustion reaction is to release energy to drive the pistons. A cross section of a typical diesel engine is shown in Figure 2.2. The combustion process can be carried out in either two or four strokes of the piston, but the four-stroke cycle is most common. Unless otherwise indicated, all engines discussed in this book will be assumed to use the four-stroke cycle. Through a combined experimental and analytical technique, it is possible to infer the rate of energy release throughout the combustion process. The technique relies on measurement of combustion chamber pressures in a running engine while simultane- ously measuring the crankshaft rotation, and computing the volume within the combustion chamber. The spatially averaged temperature in the combustion chamber can be calculated from the pressure and volume. Then, from changes in pressure, volume, and temperature, the heat loss through the chamber walls, work done on the piston, and changes in internal energy of the mixture in the combustion chamber can be calculated. The energy released from the fuel is equal to the sum of the heat loss, work, and increases in internal energy. Figure 2.3 shows a typical energy release diagram for a diesel engine; the rate of energy release is plotted versus crankshaft position. 20 CHAPTER 2 ENGINE POWER FOR AGRICULTURAL MACHINES Figure 2.2 – Cross section of a typical diesel engine. Figure 2.3 – Rate of energy release from fuels in a compression ignition engine. ENGINEERING PRINCIPLES OF AGRICULTURAL MACHINES 21 In a diesel engine, air without fuel is taken in during the intake stroke and com- pressed. Late in the compression stroke, at approximately 20° before HDC (Head Dead Center), injection of fuel into the combustion chamber begins. An apparent negative energy release rate appears initially as energy is withdrawn from the chamber to evaporate the injected fuel. The evaporated fuel mixes with air and undergoes certain pre-reactions during an ignition delay period. Then ignition occurs and all of the air-fuel mixture prepared during the ignition delay burns suddenly to produce a sharp, triangular-shaped energy release pattern identified as premixed combustion. For combustion to continue, fuel vapor and air must diffuse toward each other across the regions burned out in the premixed combustion. The rate of diffusion limits the latter combustion, which is identified as diffusion combustion. The total energy release is the sum of the premixed and diffusion combustion. Premixed combustion is efficient and, except for the production of NOx, is also clean combustion. However, the rapid release of energy produces the greatest stress on the engine and also most of the combustion noise. The slower diffusion burning is quieter and less stressful on the engine, but produces exhaust smoke and most of the CO emissions and is less efficient. Using fuels of higher cetane rating and less-advanced injection timing shifts more of the combustion from the premixed to the diffusion mode; the converse is also true. In a diesel engine, the air supply is never throttled to control the engine speed. Rather, control is achieved by controlling only the fuel delivery rate. Consequently, φ is close to zero when the engine is idling without load and increases as more fuel is injected with increasing load. To limit smoke emissions and avoid excessive engine temperatures, it is necessary to operate a diesel engine with φ below approximately 0.7. As Reaction 2.3 and Equation 2.5d would show, considerable free oxygen appears in the exhaust when φ = 0.7 or less. Engine users sometimes increase the fueling rate to diesel engines to take advantage of the extra oxygen and boost the power output of the engine, but at the cost of reduced engine life. For their own protection, engine manufacturers put a seal on the injector pumps of their engines; if the seal is broken to increase the fueling rate, the engine warranty is automatically voided. 2.3 THERMODYNAMIC LIMITS TO ENGINE PERFORMANCE The effective pressure that can be obtained from fuel to drive the pistons and also the combustion efficiency have thermodynamic limits which are defined in this section. The engine is designed to carry out the combustion cycle in four strokes of the piston. As is required in an engine with a four-stroke cycle, the timing gears in Figure 2.2 are arranged such that the crankshaft makes two revolutions for each revolution of the camshaft. Valve timing in a four-stroke cycle is shown on a valve-timing spiral, as illustrated in Figure 2.4. Valve timing is designed to maximize airflow through the engine and may differ somewhat from that shown in Figure 2.4. The cycle begins just before HDC (Head Dead Center) with the opening of the intake valve, and the air intake process ends well after CDC (Crank Dead Center) with the closing of the intake valve. As the piston approaches HDC on the compression stoke, fuel is injected and, after a short delay, ignites and forces the piston down on the power stroke. The 22 CHAPTER 2 ENGINE POWER FOR AGRICULTURAL MACHINES exhaust process begins with the opening of the intake valve late in the power stroke and ends with the closing of the exhaust valve soon after HDC. Thus, the four strokes of the cycle are intake, compression, power, and exhaust. Note that there is valve overlap, i.e., both valves are open simultaneously during a brief part of the cycle. Alternate terms used in the literature are TDC (Top Dead Center) instead of HDC and BDC (Bottom Dead Center) instead of CDC. The dual cycle of Figure 2.5 is the best thermodynamic model of the modern diesel engine. It illustrates the theoretical variations in combustion gas pressure and cylinder volume during an engine cycle. The dual cycle is a combination of the Otto cycle, which represents spark ignition engines, and the original Diesel cycle that Dr. Rudoph Diesel proposed to represent his engine. Parameter γ defines the relative proportion of energy input to the dual cycle at constant pressure, i.e.: qp γ= (2.6) qp + qv where qp = energy input at constant pressure qv = energy input at constant volume Figure 2.4 – Valve timing spiral showing typical valve timing. ENGINEERING PRINCIPLES OF AGRICULTURAL MACHINES 23 Figure 2.5 – The theoretical dual cycle. When γ = 0, the dual cycle becomes the Otto cycle with points 2a and 3 becoming coincident (Figure 2.5). When γ = 1, the dual cycle becomes the original Diesel cycle with points 2 and 2a becoming coincident. In the dual cycle, 0-1 is the intake process, followed by compression, 1-2. Process 2-2a is energy input to the cycle at constant volume and 2a-3 is constant-pressure energy input. Work is extracted from the cycle between points 2a and 3, followed by heat rejection, 4-1. Process 1-0 is exhaust, at which point the cycle starts over. The cylinder volume at CDC, V1, is the maximum gas volume. The cylinder volume at HDC, V2, is called the clearance volume. The displacement of a single cylinder is: Vc = V1 − V2 (2.7) The displacement, Ve, of a multi-cylinder engine is simply Vc times the number of cylinders. The compression ratio of the engine is: V1 r= (2.8) V2 The cycle mean effective pressure is the net area within the p-v diagram of Figure 2.5 divided by Vc. Multiplying the cycle mean effective pressure by the piston area and stroke length gives the actual work performed by each power stroke. The cycle mean effective pressure can be calculated from: 24 CHAPTER 2 ENGINE POWER FOR AGRICULTURAL MACHINES p cme r − r k + Θ r ( r − r 2− k rco k −1 −1 + r rco ( k − 1)( rco − 1)) = (2.9) p1 ( k − 1)( r − 1) where pcme = cycle mean effective pressure, kPa p1 = absolute pressure at beginning of compression, kPa Θr = Θ3/Θ1 λ = k(γ -1 – 1) rco = (λ +1)/( λ + (Θ3/Θ1)rk-1) = fuel cutoff ratio k = 1.4 for air standard cycle The pressure, p1, is very nearly equal to the atmospheric pressure unless the engine is turbocharged. The fuel cutoff ratio is defined as the proportion of the power stroke during which energy is being released into the cycle from the burning fuel. The cycle efficiency is defined as: q v + q p − q out ηcy = qv + qp where each heat transfer quantity is calculated from the mass (M) in the combustion chamber, multiplied by the appropriate specific heat and temperature difference, i.e.: q v = Mc v (T2a − T2 ) q p = Mc p (T2a − T3 ) q out = Mc v (T4 − T1 ) where cv = specific heat at constant volume, J/kg °K cp = specific heat at constant pressure, J/kg °K k = cp/cv The temperatures are those at the corresponding points in the cycle of Figure 2.5. Note that the mass (M) cancels out in the efficiency equation. Through use of the definition of k, the specific heats also cancel out of the efficiency equation. Then, in a lengthy derivation making use of the ideal gas law, the temperatures can be reduced to volume ratios (r or rco) and the inlet pressure, p1. The result is the following equation for cycle efficiency: γ ( r k − 1) + k( rco − 1)(1 − γ ) r 1− k ηcy = 1 − co (2.10) k( rco − 1) The theoretical values, pcme and ηcy, cannot be achieved in practice, but are thermodynamic upper limits and targets against which practical designs can be compared. ENGINEERING PRINCIPLES OF AGRICULTURAL MACHINES 25 Example Problem 2.2 Assume that the compression ratio of a NA (naturally aspirated, i.e., not turbocharged) diesel engine is r = 14.5. For typical conditions, estimate the cycle mean effective pressure and the cycle efficiency if γ = 0.2. Solution An estimate is needed for the ratio, Θ3 /Θ1. If the ambient temperature is 27°C, then Θ1 = 300°K. It is common practice to estimate Θ3 as being equal to the equilibrium flame temperature for hydrocarbon fuels, i.e., Θ3 = 2700°K. Thus, for a NA diesel engine, a good estimate is Θ3 / Θ1 = 9. Then, using Equations 2.9, 2.10, and the supplementary equations that support them: Θr = 8.078 rco = 1.114 pcme/p1 = 11.36 ηcy = 0.655 Theoretically, the specified cycle can convert 65.5% of the input energy to useful work. For a NA diesel engine, p1 is approximately equal to barometric