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Tractor stability indicator
Applied Ergonomics 1985, 16.3, 187-191
Ergonomics in agriculture
Tractor stability indicator D.J. Murphy, D.C. Beppler and H.J. Sommer Faculty membersof The Pennsylvania State University, University Park, Pennsylvania, 16802, USA
Tractor overturns are a major cause of death in farm operations. The overturns are the result of interactions between the tractor operator, the tractor and the environment. Numerous variables involved in tractor overturn have been identified. Previous stability analyses have resulted in attempts to design devices to warn or prevent tractor rollover but to date nothing has proved successful. A newer approach to the rollover problem is to develop instrumentation that will give the operator instantaneous cues concerning the tractor's stability as it is operated. The device is perceived as a learning instrument which will increase both cognitive and motor skills.
Keywords: Agricultural safety, accidents, tractors I ntroduction In 1982, the last year for which records are available, tractor overturns accounted for 49% (approximately 300 deaths) of all on-the-farm tractor fatalities reported by the National Safety Council (1983). The underlying intent of tractor rollover research is to understand better when and why tractors overturn. Presumably, if impending overturn can be predicted, then a device, system or procedure could be incorporated to prevent it. If the overturn is not predictable explicitly, some way of interrupting the sequence leading to the problem might still be possible.
Man and the machine Most experienced tractor operators have a general understanding of the forces that affect tractor stability. For instance, most know that a force acts on the tractor and tries to roll it over during a turn. But is a 'general understanding' adequate? Would it not be more useful if the operator could know exactly how much centrifugal force increased with higher tractor speeds concomitantly with a decrease in allowable turning radius? How are those factors affected by mounted equipment? Likewise, with rear overturns the operator can understand that when he or she engages the clutch, a twisting force is applied and the wheels are supposed to move forward. They know the tractor drawbar is the only safe point from which to pull a load, but does he or she understand the interplay among gear ratios, engine speed, height of hitching point, and of clutch release?
Man and the environment Tractor stability is reduced by environmental factors such as rough terrain, slopes, mud and ice, particularly as they interrelate to tractor speed and turning angle. Although
knowledge of these factors adds greatly to the engineer's understanding of tractor rollover, it has yet to be translated to the operator in a usable form. Thus he or she must use their skill and intuition in evaluating the effects of various environmental factors encountered during tractor operation. Ability to operate a tractor safely is further reduced by adverse stressors such as vibration, noise, fumes, cold and heat. A noisy environment can cause confusion and fatigue. High temperature also causes fatigue and slows reaction time; cold temperature causes physical stiffness and decreases touch sensitivity. These problems make it more difficult for a tractor operator continually to make good operating decisions. This is particularly true if the stressors build up for hours or for days at a time, as is often the case. The human nervous system collects information via sensory systems. The information is then transmitted to the brain, evaluated and acted upon. Information overload occurs when information or stimuli'are transmitted to the brain faster than can be properly evaluated. Both the natural environment and man-made environments are sources of information or stimuli. The human sensory systems pick up much more information in any given second than can ever be used by the human brain. A single glance will provide so much information that it simply cannot all be recorded by the human mind. The eyes serve as one example. For instance, when observing a freshly ploughed field, the eyes pick up detailed information on the size, shape, position and colour of hundreds of dirt clods as well as a general impression of the field. But the brain can only remember, or absorb, the general impression of the field, and perhaps some detailed information about a few clods of particular interest. Consequently, even though a great deal of information is presented to us, the brain can make use of only a very small amount of that information.
0003-6870/85/03 0187-05 $03.00 (~ 1985 Butterworth & Co (Publishers) Ltd
AppliedErgonomics September 1985
187
Ergonomics in agriculture Which bits of information are absorbed, evaluated and acted upon is a lengthy subject all its own and will not be discussed here. The important point is that humans have limitations on tile quantity and speed with which they can absorb information. Tractor operators can easily be put into situations in which they are overloaded with pertinent information. As a consequence, operating judgements and decisions are often made that do not represent reality. As an example, a tractor operator is baling hay with a large round baler. He is operating the tractor at 6 km/h on ground that starts out with a 5% slope at the outer edges of tile field. The path of the windrows on the outside of the field is sufficiently curved so that he has not decreased speed to make turns. But as he moves toward the centre of the field the slope has gradually increased to 20% and the turns have grown slightly tighter. He hasn't reduced his speed yet, but he has noticed that there is less time to correct his steering after the turn to stay on the windrow. On the next round a narrow ridge, where the inside rear tyre travels, raises the slope to 23%. And the turning angle is tightening once again. Unbeknown to the operator, the slight increase in slope, decrease in turning radius, and constant speed puts his tractor right on the brink of overturn. As he starts into the turn of this new round, the operator, from previous experience, senses that he needs to slow down. But just as he reaches for the throttle his eye catches sight of a rodent hole that the front wheel is about to drop into. The presentation of this new bit of stimulus causes the slightest hesitation as it is transmitted to the brain and analysed. Almost instinctively, the operator quickly turns the steering wheel tighter to avoid the hole. This final act results in the tractor rolling over. A cursory analysis of this scenario could lead one to conclude that the tractor operator used poor judgement. He was simply going too fast for the slope, not realising the tightness of the turn. But an analysis from the information processing point of view would direct us to examine how many bits of information had to be processed and acted upon at the instant several critical variables came together. The conclusion would be that it was more than the operator could properly handle. And remember, our scenario has not even considered the effects of a long working day, a hot sun or an inexperienced operator.
Overturn warning and prevention system Agricultural engineers and safety educators have long harboured the idea that there should be some device or instrumentation to prevent automatically a tractor from rolling over. Early studies by McKibben (1927) followed by McCormack (1941 ) and Worthington (1949) established the basis for stability analysis. Many of the critical variables, such as tractor speed, mass, wheel traction, slope, surface roughness, etc, were identified. Application of the stability theory was reported by Mitchell et al (1972), Griss (1981 ) and Spencer and Owen (1981) all of whom designed devices to prevent or warn of overturn. A major stumbling block has been the influence of the hidden hole and the unexpected bump. Real-time processing of this information is a critical problem. For an automatic
188
AppliedErgonomics September 1985
device to be effective it has to }lave sufficien~ ttmc ~,, evaluate all relevant variables and then effect a response. A response such as cutting off the tractor fucl supply o~ ignition system is typically proposed. Even ihough this ma). take only a fraction of a second, e~lough lllotneJHLml tllay have already been developed to allow tile ~racto~ tt~ tip over.
If such a device or instrumentation were to warn tile person of impending overturn, the time factor becomes even more of a problem because a human cannot possibly react as fast or as correctly as can specifically designed instrumentation. This problem could possibly be overcome by building a safety factor that could compensate for variable human reaction times, but the safety factor would have to be so great that operators would soon learn to ignore the warnings.
Mathematical basis for stability Recently the basic theory cited in the previous section has been greatly expanded in reports from Gilfillan (1967), Pershing and Yoerger (1969), Gibson and Bille r (1971 ), Smith et al (1974) and Davis and Rehkugler (1974). Studies reported herein are based upon the logic that if a tractor side overturn can be predicted, it should then be possible to design and build an information processing system to inform the operator of impending rollovers. In pursuing this objective, the effects that gravity, centrifugal force and ground roughness have on tractor overturn are examined. The simplistic mathematical model which has been developed by Johnson (1983) is capable of predicting side overturn at various speeds and turns on any slope and for any ground roughness. It will be used, however, to monitor relative stability rather than as a predictor of rollover. The model was not developed for use in designing safer vehicles, nor for studying vehicular motion after the instant of instability has occurred.
Liner motion The stability base for the tractor was assumed to be a triangle with elevated apex as defined by two rear tyre prints and the front axle articulation point, and is shown in Fig. 1. This assumption implies that the front axle of an articulating axle wide-front-end tractor has not contacted the frame at the axle stop. This contact normally occurs at an axle rotation, relative to the frame, in the range of 10° to 15 °. Because the model developed for this study is used to monitor relative stability, certain additional simplifying assumptions have been made in application of the model. Inertia forces from the rotating tractor chassis prior to contact with axle stops are not included, nor are inertia forces from rotating components. Tyre roll-under and rear axle torque are not considered although their value in describing the motion of the tipping tractor is recognised. By describing each of the three sides (lines) of the stability pattern in vector notation and then describing the local co-ordinate system with respect to the global co-ordinate system as shown in Fig. 2, the conditions under which the acceleration vector at the centre of mass
Ergonomics in agriculture
intersects any side of the stability pattern can be determined. Three forces originating from the influence of gravity, turning the tractor and ground roughness all act through the centre of mass and thus affect the lateral stability. The basic stability equation derived by Johnson (1983) for this model is:
X
TW
S3rTt ~ - + S3r 1LC
Y TIC = S2r 3 -~ + S I r 3 L C + S l r 2 H C - S2r I HC
I-
LW
. . . (1)
where S~, S 2 and S 3 denote the x, y and z components of the stability pattern and r 1 , r 2 and r 3 denote respective components of the acceleration at the mass centre.
-I
The critical ground slope angle at which a motionless tractor tips due to its own weight and geometry is determined by passing only the gravity vector through the centre of mass. This critical ground slope angle A is given as follows for tractor heading angle B and various geometric descriptors as shown in Fig. 1 :
Z
tan A = TW(LW- L ~ / / / / / / / / / / f
Fig. 1
f//-///~-
ff/-~-
f~- r r~./f/-f
...(2)
2 [TWI2 (sin B ) ( H P - H C ) - (cosB)(HPx L C - LWx HC)]
/ ~- s- ~- / i g / / /
Stability base for hinge point condition
the tractor When centrifugal force is added to the gravity vector, the resultant equation can be rearranged to predict the limiting forward velocity for stability operation on a given slope with turning radius R. Turning
• V 2 = gR x l(sm
+
Hill contour hne
~
TW (sin B) (lip - HC) a)(~x//~~C) ) - cos B
TW ( c o s A ) ( L C - LW)]
...
(3)
2 ( H P x L C - L WxHC)
This equation gives the critical velocity at which a tractor of given geometry can travel while making a turn of radius R on a given smooth ground slope and tractor attitude.
Hitting a b u m p
t
i
co.,ou
r
Global coordinate system
Fig. 2
Tractor orientation on ground slope
When a tractor is operated on rough ground, these irregularities produce a rolling motion on the tractor. The rolling motion decreases the ground slope on which a tractor can safely operate. In order to model the rolling motion, the effect of a tractor hitting a bump was examined. A ground roughness component has been added to the components o f gravity and centrifugal force. To obtain values for this component the vertical accelerations at the rear axle were assumed by Johnson (1983) to be proportional to the square of the tractor forward velocity and a roll roughness coefficient designated as C. In other words, A R - A L = C * V a . The net vertical acceleration, (A R - A L ) , is measured by two accelerometers mounted on the rear axle equidistant from the tractor centreline. Vector addition of the forces
Applied Ergonomics
September1985
189
Ergonomicsin agriculture acting at the centre of mass produces this expression for stable tractor velocity: V2= (; lT'3(sinA)r-2
where
TIC
3:
(cosA)(LIC-L63I
CxHC + .... ) (HPxLC R DA
72 = (1
(HP-- H C ) -
2
and
DA =
(4)
..... DA
(LC-
i t,,,,I,,,,ll,,, I,,,,I,,,,l,,,,I,,,, II |
F
6"x TIC2 -LICxHC)+
SA
LW)
(cos B )
(HPxLC - L WxHC)
Distance from roll axis to furthest accelerometer.
The gravitational constant has been designated by g.
G
~ / / / / / / / / / / / / / / / A Hill
T
Roughness
A
A
N
•
E
S
TIC
73 = --. (sin B )
'
E
R
////////A
Turn
E
Speed
N
S T
A
/////////////]
B L
U
///A
B L
E
I n f o r m a t i o n and display system
The eventual goal of the current study is to develop an information processing system that will help the operator understand the interrelationship of critical variables that result in overturn. This information processing system is designed to increase the tractor operator's skill. It is actually a learning tool to tell the operator what is happening to the tractor. It is expected that this system would result in the development of cognitive and motor skills.
Fig. 3
Example of i n f o r m a t i o n display to provide operator w i t h stability i n f o r m a t i o n
and observe the maximum magnitudes for that time period. This eliminates the need to watch the panel constantly.
The display must present two types of information. First, it must give relative tractor stability. Relative stability means the proximity to impending instability. Secondly, it must give the reason for proximity to impending instability due to a turn, hill inclination, ground roughness, tractor speed or a combination of these factors.
This type of display can be called a human-machine system as described by Hutchinson (1981). It is known as a semi-automatic system. This means that the operator senses what is happening from the display as well as from sensual contact with the surrounding environment.
Relative stability should be given with a trend information display. An example is a moving pointer along a fixed scale as shown at the top of Fig. 3. The reasons for the pointer movement should also be given with additional indicators as shown by the four lower portions of Fig. 3. The lower portions should differ from that showing relative stability because they must allow for comparisons between each other. An example would be several movin~ solid lines each along a fixed scale. Fig. 3 gives an example of the type of instrument necessary to provide both types of information.
The acceleration interpolation network processes the output from accelerometers to yield the components of acceleration at the centre of gravity. Low pass 1 kHz filters are used to remove noise from the system.
Generally, the tractor operator will not be observing the instrument, but instead watches the field or equipment. If suddently he were to hit a large rock or hole causing a sudden jolt his eyes would not be on the instrument. This means he would not see the change in tractor stability. Therefore all components of the instrument should have a feature that retains the peak value of each individual component. This should be retained for a certain time period to allow the operator to glance at the instrument
Acceleration transformation network
Stability determination network
A block diagram of the physical system is given in Fig. 4. The system consists of three basic components. These are the acceleration interpolation network, stability determination network and information delivery network.
The stability determination network processes the information from the acceleration interpolation network according to Eqn.l. For the most stable condition, a condition when the resultant of the accelerations through the centre of gravity is parallel to the Z axis, the value for the left-hand side of the equation is zero. When the resultant of the accelerations through the centre of gravity intersects the perimeter of the stability base. both sides of the equation are equal. The information delivery network consists of a division of the left side of Eqn.1 by the right side of Eqn.l. This is possible since the right side never becomes zero. The
Information delivery
Fig. 4
190
Applied Ergonomics
September 1985
The system components
Ergonomics in agriculture absolute function is needed since there are times when the left side has a negative value. The information is then provided to a display similar to that of Fig. 3. A display value of 0 corresponds to the most stable conditions. A display value of 1 corresponds to a condition iust as the tractor becomes unstable.
Griss, R. 1981 Vehicle upset warning device. In Farmsafe, Ontario Farm Safety Association, Guelph, Ontario, Canada.
Hutehingson, R.D. 1981 'New horizons for human factors in design'. McGrawHill, Inc, New York.
The displays showing reasons for the changes in stability are also controlled from information obtained through the accelerometers.
Johnson, S.R.
Summary
McCormack, E. 1941 Agric Engr, 22.5:166-167. Some engineering aspects
A mathematical model has been developed to measure the relative stability of a farm tractor. This model is based upon the premise that the tractor becomes unstable when a modified weight vector intersects a stability baseline. The weight vector is modified by vectorially adding it to a centrifugal force vector and a ground roughness vector. The ground roughness vector is defined in terms of the net acceleration of the rear axle. The concept of an electronic surveillance system for monitoring stability is presented. The surveillance system is primarily an information processor to aid the tractor operator in learning safe tractor operation. The essential features of a display panel for this system are specified.
References Davis, D.C., and Rehkugler, G.E. 1974 Trans of the ASAE, 17.3: 477-488. ~ e e l - t r a c t o r overturns, Parts I, II.
Gibson, H.G., and Biller, C.J. 1971 Side-slope stability of logging tractors and forwarders. ASAE Paper No 71-611. American Society of Agricultural Engineers, St Joseph, Michigan. Gilfdlan, G. i967 JAgricEngrRes, 12.40: 293-296. Attitude of a tractor on sloping land.
1983 'Mathematical model for use in tractor side overturns prevention'. Unpublished MS thesis. The Pennsylvania State University.
of high speed farming. McKibben, E.G. 1927 Agric Engr, 8: 15-16, 39-40, 58-60, 90-93, 119-122, 155-160, 187-189. The kinematics and dynamics of the wheel type farm tractor. Mitchell, B.W., Zachariah, G.L., and Liljedahl, J.B. 1972 Trans oftheASAE, 15.5: 838-844, 848. Prediction and control of tractor stability to prevent rearward overturning. National Safety Council, The 1983 'Accident Facts'. p 87. The Council, Chicago, Illinois. Pershing, R.L., and Yoerger, R.R. 1969 TransoftheASAE, 12.5: 715-719. Simulation of tractors for transient response.
Smith, D.W., Perumpral, J.V., and Liljedahl, J.B. 1974 Trans o/the ASAE, 17.1: 1-3. The kinematics of tractor sideways overturning.
Spencer, H.B., and Owen, G.M. 1981 JAgricEngngRes, 26. 277-286. A device for assessing the safe descent slope of agricultural vehicles. Worthington, W.H. 1949 Agri¢ Engr, 30. 119-123, 179-183. Evaluation of factors affecting the operational stability of wheel tractors.
Applied Ergonomics September1985
191
Ergonomics in agriculture
Tractor stability indicator D.J. Murphy, D.C. Beppler and H.J. Sommer Faculty membersof The Pennsylvania State University, University Park, Pennsylvania, 16802, USA
Tractor overturns are a major cause of death in farm operations. The overturns are the result of interactions between the tractor operator, the tractor and the environment. Numerous variables involved in tractor overturn have been identified. Previous stability analyses have resulted in attempts to design devices to warn or prevent tractor rollover but to date nothing has proved successful. A newer approach to the rollover problem is to develop instrumentation that will give the operator instantaneous cues concerning the tractor's stability as it is operated. The device is perceived as a learning instrument which will increase both cognitive and motor skills.
Keywords: Agricultural safety, accidents, tractors I ntroduction In 1982, the last year for which records are available, tractor overturns accounted for 49% (approximately 300 deaths) of all on-the-farm tractor fatalities reported by the National Safety Council (1983). The underlying intent of tractor rollover research is to understand better when and why tractors overturn. Presumably, if impending overturn can be predicted, then a device, system or procedure could be incorporated to prevent it. If the overturn is not predictable explicitly, some way of interrupting the sequence leading to the problem might still be possible.
Man and the machine Most experienced tractor operators have a general understanding of the forces that affect tractor stability. For instance, most know that a force acts on the tractor and tries to roll it over during a turn. But is a 'general understanding' adequate? Would it not be more useful if the operator could know exactly how much centrifugal force increased with higher tractor speeds concomitantly with a decrease in allowable turning radius? How are those factors affected by mounted equipment? Likewise, with rear overturns the operator can understand that when he or she engages the clutch, a twisting force is applied and the wheels are supposed to move forward. They know the tractor drawbar is the only safe point from which to pull a load, but does he or she understand the interplay among gear ratios, engine speed, height of hitching point, and of clutch release?
Man and the environment Tractor stability is reduced by environmental factors such as rough terrain, slopes, mud and ice, particularly as they interrelate to tractor speed and turning angle. Although
knowledge of these factors adds greatly to the engineer's understanding of tractor rollover, it has yet to be translated to the operator in a usable form. Thus he or she must use their skill and intuition in evaluating the effects of various environmental factors encountered during tractor operation. Ability to operate a tractor safely is further reduced by adverse stressors such as vibration, noise, fumes, cold and heat. A noisy environment can cause confusion and fatigue. High temperature also causes fatigue and slows reaction time; cold temperature causes physical stiffness and decreases touch sensitivity. These problems make it more difficult for a tractor operator continually to make good operating decisions. This is particularly true if the stressors build up for hours or for days at a time, as is often the case. The human nervous system collects information via sensory systems. The information is then transmitted to the brain, evaluated and acted upon. Information overload occurs when information or stimuli'are transmitted to the brain faster than can be properly evaluated. Both the natural environment and man-made environments are sources of information or stimuli. The human sensory systems pick up much more information in any given second than can ever be used by the human brain. A single glance will provide so much information that it simply cannot all be recorded by the human mind. The eyes serve as one example. For instance, when observing a freshly ploughed field, the eyes pick up detailed information on the size, shape, position and colour of hundreds of dirt clods as well as a general impression of the field. But the brain can only remember, or absorb, the general impression of the field, and perhaps some detailed information about a few clods of particular interest. Consequently, even though a great deal of information is presented to us, the brain can make use of only a very small amount of that information.
0003-6870/85/03 0187-05 $03.00 (~ 1985 Butterworth & Co (Publishers) Ltd
AppliedErgonomics September 1985
187
Ergonomics in agriculture Which bits of information are absorbed, evaluated and acted upon is a lengthy subject all its own and will not be discussed here. The important point is that humans have limitations on tile quantity and speed with which they can absorb information. Tractor operators can easily be put into situations in which they are overloaded with pertinent information. As a consequence, operating judgements and decisions are often made that do not represent reality. As an example, a tractor operator is baling hay with a large round baler. He is operating the tractor at 6 km/h on ground that starts out with a 5% slope at the outer edges of tile field. The path of the windrows on the outside of the field is sufficiently curved so that he has not decreased speed to make turns. But as he moves toward the centre of the field the slope has gradually increased to 20% and the turns have grown slightly tighter. He hasn't reduced his speed yet, but he has noticed that there is less time to correct his steering after the turn to stay on the windrow. On the next round a narrow ridge, where the inside rear tyre travels, raises the slope to 23%. And the turning angle is tightening once again. Unbeknown to the operator, the slight increase in slope, decrease in turning radius, and constant speed puts his tractor right on the brink of overturn. As he starts into the turn of this new round, the operator, from previous experience, senses that he needs to slow down. But just as he reaches for the throttle his eye catches sight of a rodent hole that the front wheel is about to drop into. The presentation of this new bit of stimulus causes the slightest hesitation as it is transmitted to the brain and analysed. Almost instinctively, the operator quickly turns the steering wheel tighter to avoid the hole. This final act results in the tractor rolling over. A cursory analysis of this scenario could lead one to conclude that the tractor operator used poor judgement. He was simply going too fast for the slope, not realising the tightness of the turn. But an analysis from the information processing point of view would direct us to examine how many bits of information had to be processed and acted upon at the instant several critical variables came together. The conclusion would be that it was more than the operator could properly handle. And remember, our scenario has not even considered the effects of a long working day, a hot sun or an inexperienced operator.
Overturn warning and prevention system Agricultural engineers and safety educators have long harboured the idea that there should be some device or instrumentation to prevent automatically a tractor from rolling over. Early studies by McKibben (1927) followed by McCormack (1941 ) and Worthington (1949) established the basis for stability analysis. Many of the critical variables, such as tractor speed, mass, wheel traction, slope, surface roughness, etc, were identified. Application of the stability theory was reported by Mitchell et al (1972), Griss (1981 ) and Spencer and Owen (1981) all of whom designed devices to prevent or warn of overturn. A major stumbling block has been the influence of the hidden hole and the unexpected bump. Real-time processing of this information is a critical problem. For an automatic
188
AppliedErgonomics September 1985
device to be effective it has to }lave sufficien~ ttmc ~,, evaluate all relevant variables and then effect a response. A response such as cutting off the tractor fucl supply o~ ignition system is typically proposed. Even ihough this ma). take only a fraction of a second, e~lough lllotneJHLml tllay have already been developed to allow tile ~racto~ tt~ tip over.
If such a device or instrumentation were to warn tile person of impending overturn, the time factor becomes even more of a problem because a human cannot possibly react as fast or as correctly as can specifically designed instrumentation. This problem could possibly be overcome by building a safety factor that could compensate for variable human reaction times, but the safety factor would have to be so great that operators would soon learn to ignore the warnings.
Mathematical basis for stability Recently the basic theory cited in the previous section has been greatly expanded in reports from Gilfillan (1967), Pershing and Yoerger (1969), Gibson and Bille r (1971 ), Smith et al (1974) and Davis and Rehkugler (1974). Studies reported herein are based upon the logic that if a tractor side overturn can be predicted, it should then be possible to design and build an information processing system to inform the operator of impending rollovers. In pursuing this objective, the effects that gravity, centrifugal force and ground roughness have on tractor overturn are examined. The simplistic mathematical model which has been developed by Johnson (1983) is capable of predicting side overturn at various speeds and turns on any slope and for any ground roughness. It will be used, however, to monitor relative stability rather than as a predictor of rollover. The model was not developed for use in designing safer vehicles, nor for studying vehicular motion after the instant of instability has occurred.
Liner motion The stability base for the tractor was assumed to be a triangle with elevated apex as defined by two rear tyre prints and the front axle articulation point, and is shown in Fig. 1. This assumption implies that the front axle of an articulating axle wide-front-end tractor has not contacted the frame at the axle stop. This contact normally occurs at an axle rotation, relative to the frame, in the range of 10° to 15 °. Because the model developed for this study is used to monitor relative stability, certain additional simplifying assumptions have been made in application of the model. Inertia forces from the rotating tractor chassis prior to contact with axle stops are not included, nor are inertia forces from rotating components. Tyre roll-under and rear axle torque are not considered although their value in describing the motion of the tipping tractor is recognised. By describing each of the three sides (lines) of the stability pattern in vector notation and then describing the local co-ordinate system with respect to the global co-ordinate system as shown in Fig. 2, the conditions under which the acceleration vector at the centre of mass
Ergonomics in agriculture
intersects any side of the stability pattern can be determined. Three forces originating from the influence of gravity, turning the tractor and ground roughness all act through the centre of mass and thus affect the lateral stability. The basic stability equation derived by Johnson (1983) for this model is:
X
TW
S3rTt ~ - + S3r 1LC
Y TIC = S2r 3 -~ + S I r 3 L C + S l r 2 H C - S2r I HC
I-
LW
. . . (1)
where S~, S 2 and S 3 denote the x, y and z components of the stability pattern and r 1 , r 2 and r 3 denote respective components of the acceleration at the mass centre.
-I
The critical ground slope angle at which a motionless tractor tips due to its own weight and geometry is determined by passing only the gravity vector through the centre of mass. This critical ground slope angle A is given as follows for tractor heading angle B and various geometric descriptors as shown in Fig. 1 :
Z
tan A = TW(LW- L ~ / / / / / / / / / / f
Fig. 1
f//-///~-
ff/-~-
f~- r r~./f/-f
...(2)
2 [TWI2 (sin B ) ( H P - H C ) - (cosB)(HPx L C - LWx HC)]
/ ~- s- ~- / i g / / /
Stability base for hinge point condition
the tractor When centrifugal force is added to the gravity vector, the resultant equation can be rearranged to predict the limiting forward velocity for stability operation on a given slope with turning radius R. Turning
• V 2 = gR x l(sm
+
Hill contour hne
~
TW (sin B) (lip - HC) a)(~x//~~C) ) - cos B
TW ( c o s A ) ( L C - LW)]
...
(3)
2 ( H P x L C - L WxHC)
This equation gives the critical velocity at which a tractor of given geometry can travel while making a turn of radius R on a given smooth ground slope and tractor attitude.
Hitting a b u m p
t
i
co.,ou
r
Global coordinate system
Fig. 2
Tractor orientation on ground slope
When a tractor is operated on rough ground, these irregularities produce a rolling motion on the tractor. The rolling motion decreases the ground slope on which a tractor can safely operate. In order to model the rolling motion, the effect of a tractor hitting a bump was examined. A ground roughness component has been added to the components o f gravity and centrifugal force. To obtain values for this component the vertical accelerations at the rear axle were assumed by Johnson (1983) to be proportional to the square of the tractor forward velocity and a roll roughness coefficient designated as C. In other words, A R - A L = C * V a . The net vertical acceleration, (A R - A L ) , is measured by two accelerometers mounted on the rear axle equidistant from the tractor centreline. Vector addition of the forces
Applied Ergonomics
September1985
189
Ergonomicsin agriculture acting at the centre of mass produces this expression for stable tractor velocity: V2= (; lT'3(sinA)r-2
where
TIC
3:
(cosA)(LIC-L63I
CxHC + .... ) (HPxLC R DA
72 = (1
(HP-- H C ) -
2
and
DA =
(4)
..... DA
(LC-
i t,,,,I,,,,ll,,, I,,,,I,,,,l,,,,I,,,, II |
F
6"x TIC2 -LICxHC)+
SA
LW)
(cos B )
(HPxLC - L WxHC)
Distance from roll axis to furthest accelerometer.
The gravitational constant has been designated by g.
G
~ / / / / / / / / / / / / / / / A Hill
T
Roughness
A
A
N
•
E
S
TIC
73 = --. (sin B )
'
E
R
////////A
Turn
E
Speed
N
S T
A
/////////////]
B L
U
///A
B L
E
I n f o r m a t i o n and display system
The eventual goal of the current study is to develop an information processing system that will help the operator understand the interrelationship of critical variables that result in overturn. This information processing system is designed to increase the tractor operator's skill. It is actually a learning tool to tell the operator what is happening to the tractor. It is expected that this system would result in the development of cognitive and motor skills.
Fig. 3
Example of i n f o r m a t i o n display to provide operator w i t h stability i n f o r m a t i o n
and observe the maximum magnitudes for that time period. This eliminates the need to watch the panel constantly.
The display must present two types of information. First, it must give relative tractor stability. Relative stability means the proximity to impending instability. Secondly, it must give the reason for proximity to impending instability due to a turn, hill inclination, ground roughness, tractor speed or a combination of these factors.
This type of display can be called a human-machine system as described by Hutchinson (1981). It is known as a semi-automatic system. This means that the operator senses what is happening from the display as well as from sensual contact with the surrounding environment.
Relative stability should be given with a trend information display. An example is a moving pointer along a fixed scale as shown at the top of Fig. 3. The reasons for the pointer movement should also be given with additional indicators as shown by the four lower portions of Fig. 3. The lower portions should differ from that showing relative stability because they must allow for comparisons between each other. An example would be several movin~ solid lines each along a fixed scale. Fig. 3 gives an example of the type of instrument necessary to provide both types of information.
The acceleration interpolation network processes the output from accelerometers to yield the components of acceleration at the centre of gravity. Low pass 1 kHz filters are used to remove noise from the system.
Generally, the tractor operator will not be observing the instrument, but instead watches the field or equipment. If suddently he were to hit a large rock or hole causing a sudden jolt his eyes would not be on the instrument. This means he would not see the change in tractor stability. Therefore all components of the instrument should have a feature that retains the peak value of each individual component. This should be retained for a certain time period to allow the operator to glance at the instrument
Acceleration transformation network
Stability determination network
A block diagram of the physical system is given in Fig. 4. The system consists of three basic components. These are the acceleration interpolation network, stability determination network and information delivery network.
The stability determination network processes the information from the acceleration interpolation network according to Eqn.l. For the most stable condition, a condition when the resultant of the accelerations through the centre of gravity is parallel to the Z axis, the value for the left-hand side of the equation is zero. When the resultant of the accelerations through the centre of gravity intersects the perimeter of the stability base. both sides of the equation are equal. The information delivery network consists of a division of the left side of Eqn.1 by the right side of Eqn.l. This is possible since the right side never becomes zero. The
Information delivery
Fig. 4
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September 1985
The system components
Ergonomics in agriculture absolute function is needed since there are times when the left side has a negative value. The information is then provided to a display similar to that of Fig. 3. A display value of 0 corresponds to the most stable conditions. A display value of 1 corresponds to a condition iust as the tractor becomes unstable.
Griss, R. 1981 Vehicle upset warning device. In Farmsafe, Ontario Farm Safety Association, Guelph, Ontario, Canada.
Hutehingson, R.D. 1981 'New horizons for human factors in design'. McGrawHill, Inc, New York.
The displays showing reasons for the changes in stability are also controlled from information obtained through the accelerometers.
Johnson, S.R.
Summary
McCormack, E. 1941 Agric Engr, 22.5:166-167. Some engineering aspects
A mathematical model has been developed to measure the relative stability of a farm tractor. This model is based upon the premise that the tractor becomes unstable when a modified weight vector intersects a stability baseline. The weight vector is modified by vectorially adding it to a centrifugal force vector and a ground roughness vector. The ground roughness vector is defined in terms of the net acceleration of the rear axle. The concept of an electronic surveillance system for monitoring stability is presented. The surveillance system is primarily an information processor to aid the tractor operator in learning safe tractor operation. The essential features of a display panel for this system are specified.
References Davis, D.C., and Rehkugler, G.E. 1974 Trans of the ASAE, 17.3: 477-488. ~ e e l - t r a c t o r overturns, Parts I, II.
Gibson, H.G., and Biller, C.J. 1971 Side-slope stability of logging tractors and forwarders. ASAE Paper No 71-611. American Society of Agricultural Engineers, St Joseph, Michigan. Gilfdlan, G. i967 JAgricEngrRes, 12.40: 293-296. Attitude of a tractor on sloping land.
1983 'Mathematical model for use in tractor side overturns prevention'. Unpublished MS thesis. The Pennsylvania State University.
of high speed farming. McKibben, E.G. 1927 Agric Engr, 8: 15-16, 39-40, 58-60, 90-93, 119-122, 155-160, 187-189. The kinematics and dynamics of the wheel type farm tractor. Mitchell, B.W., Zachariah, G.L., and Liljedahl, J.B. 1972 Trans oftheASAE, 15.5: 838-844, 848. Prediction and control of tractor stability to prevent rearward overturning. National Safety Council, The 1983 'Accident Facts'. p 87. The Council, Chicago, Illinois. Pershing, R.L., and Yoerger, R.R. 1969 TransoftheASAE, 12.5: 715-719. Simulation of tractors for transient response.
Smith, D.W., Perumpral, J.V., and Liljedahl, J.B. 1974 Trans o/the ASAE, 17.1: 1-3. The kinematics of tractor sideways overturning.
Spencer, H.B., and Owen, G.M. 1981 JAgricEngngRes, 26. 277-286. A device for assessing the safe descent slope of agricultural vehicles. Worthington, W.H. 1949 Agri¢ Engr, 30. 119-123, 179-183. Evaluation of factors affecting the operational stability of wheel tractors.
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