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They represent the views of the individual to whom they are credited and are not binding on the Society as a whole. Traction and Tractor Performance Frank M. Zoz Retired John Deere Product Engineering Center Waterloo, Iowa, USA Robert D. Grisso Professor Virginia Tech Blacksburg, Virginia, USA For presentation at the 2003 Agricultural Equipment Technology Conference Louisville, Kentucky, USA 9-11 February 2003 Published by ASAE the Society for engineering in agricultural, food, and biological systems 2950 Niles Road, St. Joseph, MI 49085-9659 USA The Lecture Series has been developed by the Power and Machinery Division Tractor Committee (PM-47) of ASAE to provide in-depth design resource information for engineers in the agricultural industry. Topics shall be related to the power plant, power train, hydraulic system, and chassis components such as operator environment, tires, and electrical equipment for agricultural or industrial tractors or self-propelled agricultural equipment. ASAE is grateful to Deere & Co for sponsoring the ASAE Distinguished Lecture Series. Table of Contents INTRODUCTION .5 TRACTION MECHANICS .5 Solid Wheel on a Hard Surface .5 Soft Wheel on a Hard Surface .6 Deformable Wheel on a Soft Surface .7 Belt Drives .8 TRACTION PARAMETERS .9 Travel Reduction Ratio (TRR) .9 Net Traction Ratio (NTR) .10 Tractive Efficiency (TE) .11 Gross Traction Ratio (GTR) .11 Motion Resistance Ratio (MRR) .11 TRACTION DATA ANALYSIS .12 Pull Slip and NTR Slip .12 Tractive Efficiency .14 Regression Analysis .17 TRACTION TESTING .19 Single-Wheel Testing .20 Using Tractors to Test Tires .21 Speed Effects .23 TRACTION PERFORMANCE .24 Effects of Soil .24 Effects of Tire Pressure .25 Effects of Tire Size .25 Effects of Load on Tire .26 Belt and Tire Comparisons .26 SOIL, TIRE, AND TRACTION EQUATIONS .30 TRACTOR PERFORMANCE .33 Tractor Performance Spreadsheet .35 Estimated Drawbar Power .38 OPTIMIZING TRACTOR DRAWBAR PERFORMANCE .39 Tires .39 Ballasting .39 Ballasting Sensitivity .43 Ballasting Limitations .44 Ballast Optimization in the Tractor Performance Spreadsheet .44 CONCLUSIONS .45 ACKNOWLEDGEMENTS .45 REFERENCES .45 5 Traction and Tractor Performance Frank M. Zoz, P.E. Retired, John Deere Product Engineering Center, Waterloo, Iowa Robert D. Grisso, P.E. Professor, Biological Systems Engineering, Virginia Tech, Blacksburg, Virginia The primary purpose of agricultural tractors, especially those in the middle to high power ranges, is to perform drawbar work. The value of a tractor is measured by the amount of work accomplished relative to the cost incurred in getting the work done. Drawbar work is defined by pull and travel speed. Therefore, the ideal tractor converts all the energy from the fuel into useful work at the drawbar. In practice, most of the potential energy is lost in the conversion of chemical energy to mechanical energy, along with losses from the engine through the drivetrain and finally through the tractive device. Research shows that about 20% to 55% of the available tractor energy is wasted at the tractive device/soil interface. This energy wears the tires and compacts the soil to a degree that may cause detrimental crop production (Burt et al., 1982). Efficient operation of farm tractors includes: (1) maximizing the fuel efficiency of the engine and drivetrain, (2) maximizing the tractive advantage of the traction devices, and (3) selecting an optimum travel speed for a given tractor-implement system. Throughout the years, official tractor performance drawbar tests have been conducted on hard surfaces and in recent years (30+ years) on concrete. While this provides a valid comparison between tractors, the data does not provide much information about performance under field conditions. The primary difference between official tests and field conditions is the performance of the tires or other tractive devices. The understanding and prediction of tractor performance has been a major goal of many researchers. Tractor performance is influenced by traction elements, soil conditions, implement type, and tractor configuration (Brixius, 1987). It is necessary to understand traction performance to predict tractor performance in the field. Traction equations provide a basis for predicting tractor performance when combined with basic information from official tractor tests. Computer models allow researchers and designers to investigate many problems related to tractor performance under a wide range of conditions with the goal to improve tractor design, to optimize tractor operational parameters, and to improve the tractor/implement match. Relative importance of these factors affecting field performance of a tractor can be achieved without expensive field-testing. For teachers, models enhance the students ability to comprehend and compare various parameters that influence tractor performance. These models can also assist tractor operators to improve (fine-tune) and optimize their tractors setup to match operating conditions. 1. Traction Mechanics Solid Wheel on a Hard Surface An understanding of traction mechanics is fundamental to understanding differences between tractive performance and tractor performance. The basic forces involved in a powered wheel are shown in figure 1 for the simple case of a solid wheel on a hard surface. The torque input (T) develops a gross traction (GT) acting at the contact surface. Part of the gross traction is required to overcome motion resistance (MR), which is the resistance to the motion of the wheel, including internal and external forces. The remainder is equal to the net traction (NT) that the wheel develops, given by NT = GT - MR. 6 GT MR slr rr N T T W Va Wd rt W = Weight, static Wd = Weight, dynamic slr = Loaded radius, static rr = Rolling radius rt = Torque radius Vt = Velocity, theoretical Va = Velocity, actual T = Axle torque GT NT MR GT MR slr rr N T T W Va Wd rt W Wd slr rr rt Vt Va T GT = Gross traction (theoretical pull)NT = Net traction (actual pull) MR = Motion resistance Figure 1. Basic wheel forces for a solid wheel on a hard surface. Soft Wheel on a Hard Surface A soft wheel on a hard surface (fig. 2) is much the same as a solid wheel except that it becomes more obvious that the vertical reaction force (Wd) is not directly under the axle centerline but is offset by a distance designated eh. This offset is necessary for static equilibrium. The amount of the offset is a function of the motion resistance and is given by: ()()WdMRslr eh = (1) Three radii are shown in figures 1 and 2: slr is the static loaded radius, defined as the distance from the axle centerline to a hard surface; rr is the rolling radius, used for speed calculations. Rolling radius is derived from the rolling circumference (usually measured prior to a test but also included in tire manufacturer data tables). Static loaded radius and rolling radius are close but not equal. For a properly inflated agricultural tire, the rolling radius is about 6% greater than the static loaded radius. Rolling radius should be used for speed calculations. Static loaded radius is more appropriate to use for force or moment calculations. Both can be affected by the softness of the soil surface and are usually determined on a hard surface. The third radius shown in figure 1 is called the torque radius (rt). This is the effective radius where the gross traction (GT) and motion resistance (MR) forces act. It cannot be measured directly but can be determined by back calculating using energy calculations. This is explained in detail in section 2 of this paper under Gross Traction Ratio. 7 MR slr rr NT T W Va Wd GT eh rt W = Weight, static Wd = Weight, dynamic slr = Loaded radius, static rr = Rolling radius rt = Torque radius Vt = Velocity, theoretical Va = Velocity, actual T = Axle torque GT = Gross traction (theoretical pull) NT = Net traction (actual pull) MR = Motion resistance MR slr rr NT T W Va Wd GT eh rt W Wd slr rr rt Vt Va T GT NT MR Figure 2. Basic wheel forces for a soft wheel on a hard surface. Deformable Wheel on a Soft Surface In the real world, both the wheel and the (soil) surface are deformable and result in the forces and moments shown in figure 3. The result is both a vertical and a horizontal offset, designated ev and eh, respectively. The amount of the offsets depends on the motion resistance force (MR), the tire loaded radius (slr), and the vertical force resultant (Wd): ()()WdMRev -slr eh = (2) slr rr NT T W Va GT Wd eh MR ev Ground Line Ground Line rt W = Weight, static Wd = Weight, dynamic slr = Loaded radius, static rr = Rolling radiusrt = Torque radius Vt = Velocity, theoretical Va = Velocity, actual T = Axle torque GT = Gross traction (theoretical pull) NT = Net traction (actual pull) MR = Motion resistance slr rr NT T W Va GT Wd eh MR ev Ground Line Ground Line rt W Wd slr rr rt Vt Va T GT NT MR Figure 3. Deformable wheel on a soft surface. 8 Belt Drives The mechanics of the belt drive mechanism (fig. 4) is similar to the wheel in many respects; but the distribution of the load is dependent on vehicle parameters. The location of the dynamic load resultant, eh (dynamic balance ratio; Corcoran and Gove, 1985), depends on the static distribution, the design of the suspension mechanism supporting the bogie wheels, and vehicle weight transfer characteristics. MR slr rr NT T W 1 Va Wd GT W 2 W 3 W 4 W 5 Ground Line Dh rt Vt = Velocity, theoretical Va = Velocity, actual T = Axle torque GT = Gross traction (theoretical pull) NT = Net traction (actual pull) MR = Motion resistance W = Weight, static Wd = Weight, dynamic slr = Loaded radius, static rr = Rolling radius rt = Torque radius Vt Va T GT NT MR W Wd slr rr rt eh Figure 4. Belt drive. In general, the best tractive performance and the most uniform ground pressure on a belt drive can be obtained with a dynamic balance ratio of near 50%. Corcoran and Gove (1985) defined dynamic balance ratio as the ratio of the location of the vertical component of the dynamic load (external loads and tractor weight) from the front of the track divided by the track base length. Unlike a tire, where only the total dynamic weight (Wd) must be considered during a traction test, the dynamic balance of a track mechanism must be considered either in a belt test or a full vehicle test. The dynamic balance ratio obtained depends not only on tractor dimensional parameters and the location and angle of the line of draft but also on the magnitude of the drawbar pull. Figure 5 shows the effect of draft angle and vehicle traction ratio on the dynamic balance for a tractor with 60% of the static weight at the front. A generic wheel/belt tractor is shown for simplicity, but the weight transfer mechanics are the same for belted and wheel tractors. Note that it only takes a 5 draft angle to give a 50% dynamic balance ratio at a typical vehicle traction ratio of 0.40. Figure 5 is for implements hitched to the drawbar. Even higher weight transfer, and hence higher front weight requirements, may result from the use of three-point hitch equipment. 9 5 0 10 20 40 42 44 46 48 50 52 54 56 58 60 0 0.1 0.2 0.3 0.4 0.5 0.6 Vehicle Traction Ratio Dynamic Balance (% Front) Draft Angle With Dh/ Wb = 0.20 Dl/ Wb = 0.30 Wb Dl Draft Angle Dh 0.60 0.58 0.56 0.54 0.52 0.50 0.48 0.46 0.44 0.42 0.40 Dynamic Balance Ratio 5 0 10 20 40 42 44 46 48 50 52 54 56 58 60 0 0.1 0.2 0.3 0.4 0.5 0.6 With Dh/ Wb = 0.20 Dl/ Wb = 0.30 Wb Dl Draft Angle Dh 0.60 0.58 0.56 0.54 0.52 0.50 0.48 0.46 0.44 0.42 0.40 Figure 5. Tractor/belt drive dynamic weight distribution (when starting with 60% static front weight). 2. Traction Parameters Five dimensionless parameters are used to describe tractive performance: Travel reduction ratio (TRR), commonly called slip and expressed in percent. Net traction ratio (NTR), sometimes called pull/weight ratio. Tractive efficiency (TE), usually thought of as percent but used as a ratio in this paper. Gross traction ratio (GTR). Motion resistance ratio (MRR). The traction parameters involving forces are all normalized by dividing by Wd, the dynamic force reaction supporting the wheel or traction device. Wd includes static axle weight and any weight transfer that might take place during the testing process, i.e., the total reaction force. Dividing by Wd allows comparisons between tires and other tractive devices of different sizes and weights, and provides a dimensionless parameter for traction comparisons. Note that all the traction parameters are normally presented as ratios except travel reduction and tractive efficiency, which are commonly expressed as percentages. Working with traction data is easier if all parameters are presented as ratios. It will become more obvious later, but remember that the above parameters apply to a traction device and not necessarily to a vehicle. Travel Reduction Ratio (TRR) VtVa1Velocity lTheoreticaVelocity Actual1TRR= (3) Travel reduction has traditionally been called slip or % slip, but technically this is incorrect. Slip occurs between surfaces. Travel reduction is a reduction in distance traveled and/or speed that occurs because of: Flexing of the tractive device 10 Slip between the surfaces (rubber and concrete, for example) Shear within the soil. From a power efficiency standpoint, travel reduction is a power loss caused by a loss in travel speed or distance traveled. Slip (travel reduction) occurs any time a wheel or traction device develops pull (net traction) (Brixius and Wismer, 1978). Zero travel reduction can be defined using any of four methods (ASAE Standards, 2001b): 1. A self-propelled (zero net traction) condition on a non-deforming surface (recommended for rolling circumference data, as in published tire data). 2. A self-propelled (zero net traction) condition on the test surface. 3. A towed (zero gross traction, i.e., zero torque) condition on a non-deforming surface. 4. A towed (zero gross traction) condition on the test surface. There are arguments for using any of the above methods for a particular traction test. In any case, the zero condition used to define the rolling radius should always be stated. The most common zero condition is use of the self-propelled condition on the test surface (method 2). However, tire data are usually given for a non-deforming surface (method 1). The difference in measured rolling radii between a non-deforming (hard) surface and a test surface is small under normal agricultural soil conditions (dry and/or untilled soil) and thus makes little difference in the final results. In any case, errors of defining zero slip do not affect the final tractive efficiency results, as travel reduction does not enter directly into the equation. It only affects the results where the losses are assigned, that is, either to travel reduction or motion resistance. This will be discussed in more detail in section 3 of this paper. The authors preference is to use a self-propelled condition (zero net traction) on a hard surface, and this method is used throughout this paper. This method provides a repeatable test condition, results that should agree closely to published tire data, and data that can be replicated at other locations and test conditions. It is also easy to imagine a case of very soft soil where the zero condition may result in an apparent 100% slip, i.e., the vehicle gets stuck, while being assigned zero travel reduction. The rolling radius (rr) measured under one of the above methods is used to calculate the theoretical speed (Vt) of the wheel or tractive device: Vt (m/s) = (rpm) rr 2/60 (4) The actual forward velocity (Va) of the vehicle or wheel is usually measured directly using a fifth wheel or radar device. Both Vt and Va must use the same units of measurement. Net Traction Ratio (NTR) WdNTForceReaction DynamicTractionNet NTR= (5) The net traction ratio is sometimes referred to as pull/weight, P/W, dynamic traction ratio, or coefficient of traction. Most of these terms actually refer to a complete vehicle rather than to a simple traction device. The dynamic reaction force or dynamic weight (Wd) includes the effects of ballast and any weight transfer that may occur in the testing process. If a complete vehicle is used for the traction device testing, the weight may include front to rear transfer due to horizontal pull, and any transfer due to implement or load unit draft angle. The net traction force (NT) must be the force component in the direction of travel and perpendicular to the reaction force (Wd). As stated, the above equation applies to a tractive device and not to a complete vehicle. For a total vehicle (tractor), the equivalent to net traction ratio (NTR) is vehicle traction ratio (VTR), which is the vehicles drawbar pull divided by the total vehicle dynamic weight. This will be covered in more detail in section 7 of this paper. 11 Tractive Efficiency (TE) =VtVaGTRNTRVtVaWdGTWdNTVtVaGTNT Power AxleVa NTPowerInput PowerOutput (ratio) TE (6) Tractive inefficiency is caused by both velocity losses and pull losses. The loss in travel speed is commonly referred to as slip, although it is more accurately refered to as travel reduction. Travel reduction is the result of the theoretical travel speed (Vt) not being entirely converted to forward progress (Va) due to losses within the soil, between the soil surface and the traction device, and within the traction device (hysteresis, and tire windup or belt slippage). Travel reduction losses are visible, that is, the operator can see it happening. The other component of tractive inefficiency, which is less visible and often overlooked, is a loss of pull (net traction) when motion resistance reduces the amount of gross traction that is converted to useful output (net traction). This is part of what happens when a tractor is overballasted. Travel reduction is reduced, but motion resistance is increased. Motion resistance losses are especially relevant to belts, as internal losses within the belt drive mechanism, rollers, and bending of the belt are normally greater than those within a tire. On soft soils, the internal losses of belts are generally compensated for by lower external motion resistance than that of tires. Gross Traction Ratio (GTR) Wdrt T WdGT GTR = (7) Gross traction (GT) is sometimes referred to as rim pull, design drawbar pull, or theoretical pull. It is the axle torque input converted to a pull force. It is the pull you would develop if there were no motion resistance loss. The gross traction ratio (GTR) is the least understood of the traction parameters. Gross traction (GT) itself cannot be measured directly and is usually calculated from the axle torque and radius of the wheel or tractive device. The problem is that the correct radius to use is not well defined or directly measurable. There is no general agreement among traction researchers as to what radius to use, and an alternate method of calculating gross traction ratio is preferred using energy or power considerations. From equations 6 and 3: ()TRR1TENTRVtVaTENTRGTR= (8) Having thus determined the gross traction ratio (GTR), since Wdrt T W