Slip Measurement Using Dual Radar Guns

Introduction

Current farming economics reinforce the importance of efficiency in farm tractor operations. Maximizing the efficiency of a tractor requires the optimization of tractor weight, tire pressures, and operating speed for the given load and soil condition. Because maximum tractive efficiencies occur when tires operate within a narrow range of slip, slip at operating load can be used as an indicator of the optimum performance point. A problem is that accurate measurement of slip under working conditions can be difficult in farm situations. While slip measurement devices are available, many new tractors and most older ones do not have them. The result is that "on the farm" tire slip is often measured manually, estimated or simply ignored.

This paper reviews current and past slip measurement techniques, both in experimental work and in common farm practice, and describes a simple method of obtaining accurate slip values on a tractor by using a pair of radar guns. The system is universal, portable, quickly attached and requires no modifications to the tractor.

Slip Measurement Background

What slip is
Slip is defined as relative movement in the direction of travel at the mutual contact surface of a traction or transport device and the surface which supports it (ASAE 1983). Slip can also be considered as the reduction in actual vehicle travel speed when compared to the theoretical speed that should be attained from the speed of the tire or track surface. Slip is ultimately a measure of the relative motion between the surface of a tire or track and the ground plane where the tire or track is operating.

Slip and travel reduction are used interchangeably in some references, Collins et al. (1980), but they are not necessarily the same. The difference is in what is defined to be the zero condition to which vehicle speeds are compared. Collins et al. state that slip is measured when the actual speed under load is compared to the speed on a hard surface with zero input torque, and that travel reduction is measured when actual speed under load is compared to the unloaded speed on the same surface. Brixius and Wismer (1978) discuss the role of relative motion in traction and recommend zero pull on a hard surface as the basis for slip measurement in both the lab and the field.

Slip or travel reduction results when the horizontal force applied to the soil by a tire or track overcomes the internal shearing strength of the soil planes with the result that the soil displaces and moves in the opposite direction of the vehicle motion. Soil shear strength typically increases as soil is compressed, so slip is affected by the compressive load the tire or track transfers to the soil. Higher downward pressure over the same area tends to reduce slip for a given pull. Soil shear strength is a soil property that is constant throughout a given soil area, so slip is also affected by the area of the soil that is contacted by the tire or track. More contact area for the same downward pressure tends to reduce slip for a given pull.

What slip does
Slip serves two functions. When soil shear forces are higher than the friction force between the soil surface and the tire surface, additional pulling power can be developed by slipping the soil layers. Secondly, slip provides a fuse or safety valve in a traction drive train. As soil gives way or slides, the peak loads applied to the drive line components are limited. If a tractor is set so the slip level at operating load is too low, the drive train life will be significantly shortened.

Is slip important? Brixius and Wismer suggest slip is one of the most significant variables in traction and state that the effect of slip on tractive performance must be defined to adequately predict the traction process. Slip is better considered as a predictor of the tractive efficiency of a given tractor set-up, rather than as a dominant variable. Slip can be regarded as a measurable quantity that indicates the relative effectiveness of the traction delivery system. Since tires and tracks operate at their maximum effectiveness within a certain range of slip, an operator can use slip to determine if a tractor is within an optimum band for a specific soil and load condition.

What it Takes to calculate slip
Slip is not a directly measured value. It is calculated from two other measurements, usually speeds or distances traveled, one being the measurement under load and the other being the unloaded measurement. The value is commonly given as percent slip or percent travel reduction and the formula is commonly in one of two equivalent forms. Paulson and Zoerb (1971) or Collins et al. give the equation in the form:.
.

. Percent Slip =

unloaded quantity - loaded quantity ---------------------------------------------------- unloaded quantity

. x 100

Equation 1

The alternate form is:
.

Percent Slip = (

unloaded quantity - loaded quantity ---------------------------------------------------- unloaded quantity

)x 100

Equation 2

When speeds are used, the loaded quantity is true vehicle forward speed and the unloaded quantity is tire or track surface speed, either measured directly or computed from the rotational speed and the rolling radius. When distances are used, the loaded quantity is some measure of the distance traveled under load and the unloaded quantity the same measure of the distance traveled unloaded. The measure used can be tire revolutions over a given distance, distance traveled for a given number of tire revolutions or time to travel a given distance. Paulsen and Zoerb (1971) present a comprehensive discussion about slip measurement fundamentals and discuss using drive wheel revolutions, distance traveled and actual velocities for the calculation.

Measurement history
The different methods used to obtain the two measurements for slip calculation can be classified in two main groups, research project methods and on-farm methods. Research project methods are those where a specific tractor is used that can be modified before the tests, and where accurate measurements are important. On-farm methods apply where various unmodified farm tractors are used and less accuracy is required.

A literature review shows a wide variety of mechanisms have been used in research projects to obtain the measurements necessary to compute slip. Most involve some form of linear velocity measurement, either directly or through a combination of rotational speed and rolling radius.

Research methods used for measuring vehicle speed fall into three categories. One way has been to measure the rotation of a non-powered vehicle wheel, Lyne and Meiring (1976), Clark and Gillespie (1979), Jurek and Newendorp (1983). Another way has been to measure the wheel rotation of some form of an additional or fifth wheel device, Zoerb and Popoff (1967), Grevis-James et al. (1981), Erickson et al. (1982), Shropshire et al. (1983), Musonda et al. (1983). A third way has been to measure vehicle speed directly with a doppler effect device, either using microwave radar, Stuchly et al. (1975), Wang and Domier (1989), Grisso et al. (1991), or ultrasonics, Micro-Trak (1987), Freeland et al. (1988) and Khalilian et al. (1989).

There have been a number of different research methods used for measuring wheel surface speed. The driven axle rotational speed has been measured with a magnetic frequency generator, Shropshire et al., Musonda et al., Chancellor and Zhang (1987), Grogan et al. (1987); with an optical frequency generator, Lyne and Meiring, Grevis-James et al., Clark and Gillespie; with a voltage generator, Stange et al., (1982); and with a series of microswitches, Erickson et al., Shelton et al. (1987). The speed of the engine or a drive train component has been measured, Wang et al., Grisso et al. The speed of the PTO shaft has been measured, Zoerb and Popoff, Paulson and Elliot (1973). Tire mounted markers have been used in conjunction with high speed movies, Erickson et al. (1982). The surface speed of the tire has been measured with a doppler effect microwave radar, Stuchly et al.

On-farm slip measurement methods, as discussed in tractor operator manuals and various farm extension publications, can be classed in three groups: performance monitor usage, manual distance or wheel revolution counting, and visual inspection of the tire track in the soil.

If the tractor manufacturer supplies an optional performance monitor (most do) and if the farmer purchased it (many do not), this is the preferred on-farm method. Performance monitors typically use a doppler radar gun and a magnetic pick-up in the drive train in combination with a tire size switch setting or calibration value measured on a hard surface to measure tire surface speed.

If a monitor is not available the literature suggests some variation of a distance measurement. One commonly discussed method is referred to as the 10 turn method (Wyoming Energy Conservation Office, 1983). The distance the tractor under operating load moves in 10 turns of the drive tire is marked. The tractor is then operated over this same distance in a similar ground condition with the load removed and the number of tire revolutions is counted. The average percent slip is then calculated from a variation of Equation 1:

Percent Slip = (

10 - tire revolutions without load ---------------------------------------------------- 10

)x 100

Equation 3

Zoerb and Popoff, and Paulsen and Zoerb discuss the cumbersomeness and inaccuracies in this method.

Also in the literature are discussions about estimating slip by considering the appearance of the tread marks. At proper slip levels the soil between the cleats in the tire pattern will be shifted but the tread pattern will still be visible (Florida Cooperative Extension Service, 1978).

Interviews of farmers in Southern Alberta and Montana suggest the most common method of slip measurement is a visual estimation made by considering tire motion relative to the ground while the tractor is under load. The author’s experiences and other references suggest slip only becomes visually apparent at around 15 percent. This would indicate if an operator can see the tractor is slipping, it is already slipping too much.

Radar Gun Slip Measurement

The development of inexpensive microwave doppler radar units simplified the measurement of vehicle ground speed and such units are now offered as an option on most tractors. During field tests run in 1991 and 1992, a combination of two such radar units has been used successfully to measure instantaneous and average slip on a wide variety of tractors. The system proved to work well and was adaptable to various tractor models and types.

The operation principles, engineering compromises and relative accuracies of radar ground speed measurement on agricultural vehicles have been explained in detail in several papers, Stuchly et al., Tomkins et al., (1985) and Tsuha et al. (1982). The radar units transmit a known frequency of radiation towards a surface and receive reflections of the radiation from the surface. The doppler frequency, the difference in frequency between the transmitted radiation and received radiation, is proportional to speed. Figure 1 shows the geometry and the relationships for such a device. Whether the transmitting unit is moving in respect to the surface or the surface is moving in respect to the transmitting unit is immaterial; the signal is proportional to the difference in speed between the transmitter and the surface.

Figure 1. Diagram of radar principles

To measure wheel slip with two radar guns, one radar gun is used to obtain ground speed in the conventional way. The second radar gun is pointed at the surface of a drive tire. The curved tire surface results in a varying angle of the radar gun to the surface so this gun typically does not give an exact surface speed but it does give a value proportional to the surface speed. Although the mathematical relationship between frequency and speed is difficult to predict because of the curved surface, it is easy to calibrate the proportional tire surface gun against the exact ground speed gun. This is done by operating in a zero slip situation and measuring the difference between the two readings. Figure 2 shows the combination of two radar guns installed on a tractor.

Figure 2. Radar Guns Mounted on a Tractor

Experimental Verification and Usage

Two different types of commercially available radar guns have been used in this project. The first, the Dickey John Radar I, is an older design, operating at a microwave frequency of 10 GHz, with a relatively wide (30° cone angle) field of view. This field of view gives an oval footprint or received signal area of approximately 900 mm x 400 mm (35 in x 16 in) when the gun is mounted at 35° and 460 mm (18 in) above the target surface. The second type, the Dickey John Radar II, is a current design and operates at a microwave frequency of 24.125 GHz. This gun has a relatively narrow (15° cone angle) field of view. This results in an oval signal area of approximately 500 mm x 300 mm (20 in x 12 in) when it is mounted at 35° and 460 mm (18 in) above the surface. Both types of gun are designed to operate at a nominal angle of 35° from the horizontal and produce doppler shift frequencies of 26.41 Hz/km/h and 26.11 Hz/km/h (44.7 Hz/mph and 44.2 Hz/mph), respectively. The Radar II guns have additional electronic refinements and digital filtering to reduce the effect of wind generated crop motion on the signal. Either type is powered by the 12 volt power system of the vehicle.

The radar guns require a display system to convert the frequency output to a displayed velocity and this project used a data acquisition system instead of the manufacturer’s standard monitor. The frequency from each of the guns was passed to a frequency to voltage (F/V) converter and the resulting voltages were recorded and displayed using an on-board data acquisition system developed previously, Turner (1992). The on-board system was programmed to accept and store the signals from each gun and to compute, display and store the corresponding slips, using a wheel speed calibration value determined from an initial run on a hard surface.

At the beginning of the project a series of experiments were carried out to determine if there was an optimum angle or location for the gun relative to the tire. The basic geometry relationships are shown in Figure 3.

Figure 3. Tire radar gun location

Tests showed satisfactory function as long as the nominal tire angle (Ø) was at least 10° away from the perpendicular from the tire surface to the gun. As the angle moved farther away from perpendicular the level of the signal increased. By trial and error it was usually possible to find an angle where the net signal gave exact readings. This was typically not at a nominal gun-to-tire angle of 35° and seemed to be influenced by the tread pattern of the tire. It was also found to be preferable for the gun to illuminate the upper part of the tire. In this position there was less tendency for the beam to encounter the ground and give a ground speed reading. Tests showed satisfactory function for distances from 300 mm to 1200 mm (12 in to 48 in) away from the tire. As the distance increased beyond 1200 mm it became more difficult to receive only reflections from the tire.

Some differences were noted between the two types of radar units. The Radar I guns gave the most uniform tire speed signal. These guns were the best to use on the tire providing they were pointed up and away from the ground. If tractor geometry made it necessary to point the tire gun down and towards the ground it was better to use a Radar II gun. While the smaller footprint of these guns made it easier to focus only on the tire, the tire surface signal from these guns typically had more variation than did the signal from the Radar I guns. The Radar II guns were preferable to the Radar I in the ground speed position because they were less affected by crop motion on windy days.

The radar slip measurement system has been installed on some 30 different two-wheel drive, mechanical front-wheel drive and four-wheel drive tractors. The main variable in the set-up procedure has been finding a convenient place on the tractor to attach the radar gun set. At various times this has been in front or behind the front tires, in front or behind the rear tires, at various distances from the tires and above or below the tire centre line. All variations worked acceptably. Once the guns were attached, the angle on the ground speed gun was set to the nominal 35°. The second gun was adjusted in or out to be on the same centre line as the tire and was then set by "eyeball" to have the approximate edge of its field of view cone just inside the tangent edge of the tire surface. For calibration, the tractor was operated on a hard surface at zero pull over a range of speeds and the ratio of the tire signal to the ground speed signal was recorded. This ratio was then used during data acquisition to adjust the signal of the tire gun to give the actual tire surface speed.

A series of tests were run to compare the accuracy of the radar slip reading to other methods. Comparison with the 10 turn method showed average radar obtained slips to be well within the reported ±5 percent accuracy of the 10 turn method. Radar slip readings compared to factory slip monitors on several different tractors showed good correlation. On one tractor, signals from the factory slip meter transducers (radar gun and magnetic pick-up on a transmission shaft in front of the differential) and the radar slip readings were recorded and compared. Again, the readings showed good correlation. Figure 4 is a time history of wheel speed from the magnetic tape and uncorrected wheel speed from the wheel radar gun and shows the similarity between the two signals.

Figure 4. Data from tire surface and magnetic pick-up

Figure 5 is a time history plot of slip computed from the magnetic pick-up and from the radar gun. The two methods give identical average and very close instantaneous results. The short term differences that occur are probably attributable to the radar method measuring the instantaneous speed of only one wheel, while the magnetic pick-up measured the driveline input.

Figure 5. Radar slip time histories

While the dual radar gun concept has worked effectively as a slip measurement system on many different tractors in many different field conditions, there are some limitations. The system only measures slip on one wheel, one quarter of a four-wheel drive tractor or one half of a two-wheel drive tractor. Because of differential action, the instantaneous slip on other wheels of the tractor may vary. Test results have shown average slip from one wheel to another does not usually vary significantly and that a 2 to 4 second average on the single wheel is a good reflection of the overall average slip. Tests with two sets of radar guns, one on each side of a tractor, showed a tendency for the instantaneous slips to be opposite each other, as one wheel slip went up, the other went down.

The radar system does not give correct slip readings while the tractor is being steered to any significant degree. Two things happen during steering that affect the readings. First, the sideways motion from the steering changes the net ground speed reading and second, the wheel speeds are different from side to side as the tractor turns.

The radar system will work in sticky mud conditions but there are some concerns. Since calibration occurs at a given tire surface radius, if the radius changes from mud build-up, the calibration will change. When the build-up on the tire was relatively constant and when the calibration could be done with the mud build-up on the tire, the system worked fine.

There were a few instances where the ground speed radar gun was affected by the motion of dense crop materials in the wind. This was more noticeable with the Radar I guns than with the Radar II guns.

Future Work

This system could be developed into a self-contained slip meter that an extension agent, district agriculturist or college could use as a farm productivity tool. The system could be a single box magnetically attached to the vehicle, powered either internally or from the vehicle, with two radar antenna cones and the necessary electronics to calibrate, compute and display vehicle speed and slip. Such a system would make it easier for an operator to consider slip while optimizing a given tractor and could also be used as an extension tool for presentations about the value and effect of optimization on tractor performance.

Conclusion

To summarize, a combination of two radar guns was used successfully on various tractors to measure slip at operating load. The first radar unit was used to measure vehicle speed unit and the second was used to measure tire or track surface speed. The tire or track signal was calibrated against the vehicle speed signal in a zero slip condition. The calibration procedure removed the need for a specific mounting and viewing angle and compensated for any effect of curved surfaces on the tire or track. Continuous readings of slip at the given drive wheel were possible and there was excellent correlation with other slip measurement techniques, either average or instantaneous. The set-up required no modifications to a tractor, was quickly portable between tractors and was universally applicable to traction units.

References

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