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Development of a Flow Model for the Design of a Momentum Type Beet Mass Flow Sensor
ARTICLE IN PRESS Available online at www.sciencedirect.com
Biosystems Engineering (2003) 85 (4), 425–436 doi:10.1016/S1537-5110(03)00095-3 AE}Automation and Emerging Technologies
Development of a Flow Model for the Design of a Momentum Type Beet Mass Flow Sensor D. Hennens; J. Baert; B. Broos; H. Ramon; J. De Baerdemaeker Laboratory of Agricultural Machinery and Processing, Katholique Universiteit Leuven, Kasteelpark Arenberg 30, Heverlee 3001, Belgium; e-mail of corresponding author: [email protected] (Received 19 July 2002; accepted in revised form 9 May 2003; published online 21 June 2003)
A lot of research is done to monitor yield during harvesting. Combined with a positioning system, this information can be used to produce yield maps. Based on the yields of successive years, site-specific field management can be done, aiming for higher local economic and ecological yield efficiencies. In this research, a curved plate mass flow sensor for sugar beet is designed with the aid of a mathematical model. The principle is based on measuring the impulse flow colliding with the plate. For granular materials, an accuracy of 2% is achieved. The mass flow sensor for sugar beet is integrated as a curved side rack in the cleaning channel of the harvester. The side rack is mechanically isolated from the frame. A theoretical model of the beet flow over the turbines of the cleaning unit is calculated and incorporates all physical parameters that influence the mass flow measurement by the momentum sensor. The flow density and friction coefficients with the rack and the turbine characterise the mass flow. From the model, the influence of the different parameters (slope, beet velocity, friction, length of the plate) on the momentum is investigated. The force exerted on the rack of the cleaning unit is measured, from which the momentum can be indirectly calculated. A measurement device is constructed, minimising the influence of the harvesting conditions and the material properties. After calibration, measurements are carried out on the cleaning unit of a Dewulf R6000T (two-phase system) and an Agrifac ZA 215 EH (one-phase system). Research is done to construct the sensor independent on friction properties between beets and the rack. Major influence comes from the velocity of the transported material. Variations in beet speed have to be registered continuously with a Doppler radar meter. Influences of a varying slope can also be corrected regarding the instantaneous beet velocities. More accurate measurements are done when the sensor is installed on bigger spinning wheels because of higher momentum due to a higher centrifugal force and hence a higher signal to noise ratio. To evaluate the model, only average mass flows and flow speeds could be used to predict the executed moments. When comparing the integrated measured momentum and the scale weight of the harvester bin, the error never exceeds 3% when using the derived equation. # 2003 Silsoe Research Institute. All rights reserved Published by Elsevier Science Ltd
1. Introduction For many thousands of years, farmers cultivated their own small fields looking to the local needs of the plants. By mechanisation and the consequential expansion of farms, farmers lost the knowledge of those local needs. Homogeneous treatment was the only technological solution to manage the arable land. Adaptation to the site-specific needs can decrease the input and gives rise to increasing profits. Today’s technology creates the 1537-5110/03/$30.00
possibility to collect data of a lot of crop parameters, soil conditions and yield variations. Although totally integrated systems are available on the market, the profits of the whole system are questionable (Dampney et al., 1999). Englisch et al. (1998) indicate that, to evaluate the profitability of precision agriculture, the variability in the field over different years is the most important step. Yield maps are the most useful tools to visualise this variability. Most of the time, farmers can indicate the causes of low yield areas but they rarely 425
# 2003 Silsoe Research Institute. All rights reserved Published by Elsevier Science Ltd
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Notation a b C dmax ERMS Fcf FD FDr Fg Fg,x Fg,y Frack Frad Ftan g h FN M m n Q R2 r rc
rc,
corr
linearised parameter of the velocity correction linearised parameter of the velocity correction original calibration factor maximal size of the holes in the beet flow, m root mean square error of calibration, kg s1 centrifugal force, N frictional (driving) force between the turbine and the sugar beets, N radial component of the driving force, N gravitational force, N radial component of the gravitational force, N tangential component of the gravitational force, N frictional force acting between the sugar beets and the side-rack, N radial projection of the forces acting on an elementary mass particle, N tangential projection of the forces acting on an elementary mass particle, N gravitational acceleration, m s2 height of the beet flow on the turbine, m the normal force acting perpendicular on the contact surface, N momentum acting on a small part of the side rack, N m mass particle, kg number of measurements mass flow rate, kg s1 coefficient of determination radius of the friction independent pivot axis, m regression coefficient for the calibration curve between measured voltage and mass flow rate, kg V1 s1 velocity-corrected regression coefficient, kg V1 m1
know the quantitative losses. Comparing the yield of successive years, it is possible to indicate crop, soil or environment dependent causes of the variability (Auernhammer & Demmel, 1997). For measuring and mapping yield and other crop properties on harvesters, several systems have been developed (Reyns et al., 2001). Kutzbach and Schneider (1997) give an overview of all existing grain flow measurement concepts involving the measurement of a weight, volume, impacts or other indirect parameters. Besides yield, also lodged grain, weeds, straw yield and the moisture and protein content are recorded and mapped. For non-combinable products, such as potatoes and sugar beet, few yield measurement systems are
rm
mean radius of the mass centreline of the material flow along the side-rack, m rmin mean radius of the mass centreline till the first beet, m ru radius of the turbine, m U mass flow related output voltage, V Ucorr corrected mass flow related output voltage, V Un net output voltage of the load cell, V v material velocity, m s1 vavg average material velocity, m s1 v0 initial beet flow velocity, m s1 x, y, z coordinates yi ith value of a response variable yi,pred value of the ith measured variable predicted by the linear regression model a angle of the rotation point referred to the driving direction, 8 aopt angle of the rotation point referred to the driving direction minimising the influence of the friction on the momentum, 8 b angle between driving direction and the beginning of the mass flow sensor, 8 d longitudinal slope of the harvester, 8 ds standard value of longitudinal slope of 9208 g lateral slope of the harvester, 8 j angle of the spokes of the turbine, 8 mrack friction coefficient between the sugar beet and the side-rack msun friction coefficient between the sugar beet and the rotating turbine y angle from the start of the mass flow sensor to the position of the mass particle, 8 ye total angle of the mass flow sensor, 8 r density of the sugar beet flow, kg m3
available. The non-smoothed flow, the high mass yields and the large range of harvesting conditions cause major problems. Ehlert (1999) tried an impact plate to measure the mass flow of potatoes. The angle of the impact, flow speed variation, machine vibration and dirt affect the accuracy of the measurements, while the impacts damage the potatoes. The sensor was only tested under laboratory conditions. Durrence (1998) measured the bin weight of a peanut harvester. Hien and Kromer (1995) tried to predict the mass flow by measuring continuously the thickness of sugar beets. An exponential relation was found between the maximum diameter of the beets and the weight. The diameter was measured by different means, such as ultrasonic distance sensors,
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optical sensors, Doppler radar sensors, tactile sensors and a force measurement on the knives while topping the beets. Auernhammer and Demmel (1997) isolated a part of a conveyor belt. They replaced one of the rollers with a load cell and a slide bar. A continuous overload was necessary and the slope of the conveyor had to be constant. Most of the beet harvesters used in Belgium, Germany and the Netherlands are not provided with the appropriate conveyor belt. They all have a cleaning system of rotating turbines and one or more conveyor belts that turn around the bin. In this research, a measurement system is integrated in the cleaning system. Its concept is based on a mass flow sensor for harvesters, developed by Strubbe (1997). The mass flow is obtained indirectly by measuring the forces on a curved plate such that all impact forces are excluded. For the development of the sensor, a model was derived to reduce the influences of the product properties. This means that one calibration each harvest season must be sufficient for all types of crops.
An elementary mass particle dm in kg experiences four different forces (Fig. 1): (1) the centrifugal force dFcf in N caused by the turning of the turbine with rm in m, the mean radius of the mass centreline of the material flow along the siderack and v the velocity of the beets in m s1 dFcf ¼ dm
v2 rm
ð1Þ
(2) the gravitational force dFg in N, with g in m s2 defined as the gravitational acceleration dFg ¼ dm g
ð2Þ
which can be decomposed in a radial component dFg,x in N and a tangential component dFg,y in N dFg;x ¼ g dm½sinðy þ bÞcos d sin g þ cosðy þ bÞsin d ð3Þ dFg;y ¼ g dm½cosðy þ bÞsin d cos g sinðy þ bÞsin d ð4Þ
2. Theory of the model 2.1. Development of the model For the development of the model, three-dimensional coordinates (x, y, z) are used. The Z-axis is situated in the centre of the turbine, pointing upwards. The X-axis goes through the considered mass particle. To describe the forces acting on the side-rack it is necessary to first evaluate the forces on the mass flow.
where: y in degrees is defined as the angle from the start of the mass flow sensor to the position of the mass particle; b in degrees as the angle between the driving direction and the beginning of the mass flow sensor; d in degrees as the longitudinal slope of the harvester; and g in degrees as the lateral slope of the harvester; (3) the driving force of the curved spokes dFD in N, with msun the friction coefficient between the beets and the rotating turbine and FN in N, the normal force acting perpendicular to the
ϕ
β
θe
FD
ϕ cos
θ
ϕ
FD
FD sinϕ
FD k
F rac (a)
(α,r)
Fcf
Fcf (b)
Fig. 1. (a) Top view of the different forces acting on an elementary mass particle dm rotating on a cleaning turbine; (b) detail of the forces in the radial and tangential direction; a, angle of the rotation point referred to the driving direction; b, angle between driving direction and the beginning of the mass flow sensor; j, angle of the spokes of the turbine; y, angle from the start of the mass flow sensor to the position of the mass particle; ye, total angle of the mass flow sensor; Fcf, centrifugal force; FD, frictional (driving) force between the turbine and the sugar beets; Frack, frictional force acting between the sugar beets and the side-rack
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contact surface dFD ¼ msun
FN ¼ msun dm g
ð5Þ
the frictional force between the mass flow and the side rack dFrack in N, with mrack defined as the friction coefficient between the sugar beets and the side-rack; dFcf in N as the centrifugal force and dFDr in N as the radial component of the driving force dFrack ¼ mrack ðdFcf þ dFDr Þ
ð6Þ
Due to the rotation and the slope of the turbine, it is necessary to transform the forces to the initial coordinate system. To evaluate the mass speed, the different forces are split into a radial component, perpendicular to the side-rack and a tangential component, parallel with the moving direction. The projection of the forces in the radial direction Frad and in the tangential direction Ftan can be formulated as Frad ¼ Fcf þ Fg;x þ FD sin j
ð7Þ
Ftan ¼ Fg;y Frack þ FD cos j
ð8Þ
where: the parameter j in degrees is defined as the angle of the turbine spokes; Fg,x in N as the radial component of the gravitational force and Fg,y in N as the tangential component of the gravitational force. The residual force in the tangential direction can also be defined as dv dm ¼ dFtan ð9Þ dt
impulse. The elementary momentum dM on a small part of the side-rack can be expressed by (Fig. 2): Q rm dyðr sinðy þ b aÞ v þ mrack ðr cosðy þ b aÞ ru ÞÞ 2 v þ sinðy þ bÞsin g cos d grm
dM ¼ g
þ cosðy þ bÞsin d þ msun cos d cos g sin j
where: a in degrees is the angle of the rotation point referred to the driving direction, r in m is defined as the radius of the friction independent pivot axis; ru in m is the radius of the turbine; and Q in kg s1 is the mass flow rate. Integrating the momentum over the total length of the side-rack will result in the momentum measured with the sensor.
2.2. Sensitivity analysis In this section, the theoretical influences of the different model parameters on the momentum are investigated. With the developed model it is possible to optimise the construction of the mass flow sensor, by taking care that all considered influences are minimised.
Substituting Eqns (1)–(6) into Eqns (7)–(9) and combining both formulae (also see in Appendix A), an expression for the speed of the mass flow during the transport over the turbines is derived: dv2 ¼ 2grm msun cos d cos g cos j sinðy þ bÞsin d dy þcosðy þ bÞsin g cos d mrack 2 v þ sinðy þ bÞcos d sin g þ cosðy þ bÞsin d grm þ msun cos d cos g sin j ð10Þ where: b in degrees is the angle between the driving direction and the beginning of the mass flow sensor; d in degrees is the longitudinal slope angle of the harvester; g in degrees is the lateral slope of the harvester; and y in degrees is the angle from the start of the mass flow sensor to the position of the mass particle. From Eqn (10), it follows that the mass velocity is independent from the total mass flow rate. The side-rack forces the sugar beets to make a circular movement, which results in a continuously changing
ð11Þ
ru β α
θ
θe r cos(+−) −ru
Frack Frad r M
r sin(+−)
Fig. 2. Momentum and forces acting on the rack with their lever; a, angle of the rotation point referred to the driving direction; b, angle between driving direction and the beginning of the mass flow sensor; y, angle from the start of the mass flow sensor to the position of the mass particle; ye, total angle of the mass flow sensor; r, radius of the friction independent pivot axis; ru, radius of the turbine; Frack, frictional force acting between the sugar beets and the side-rack; Frad, radial projection of the forces acting on an elementary mass particle; M, momentum acting on a small part of the side-rack
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Table 1 Construction parameters for the different cleaning units
Big turbine (Agrifac ZA EH 215) Construction parameters 095 ru, m r, m 1 d, deg 813 g, deg 0 ye, deg 3769 b, deg 90 j, deg 17 aopt, deg 11986
Small turbine (Agrifac ZA EH 215) 063 0675 813 0 4138 90 17 12095
Dewulf (R6000T)
070 085 79 0 4337 10183 20 1092
Default flow parameters 3 v0, m s1 Q, 40 kg s1 r, 600 kg m3 mrack 055 msun 035 h, m 035
The effect caused by a change in one parameter will be compared to the reference value of the momentum, calculated with the standard values of the parameters, shown in Table 1. The measure in % that will be used further is defined as DM ðparameter; reference value parameterÞ Mð parameterÞ Mðreference valueÞ 100 Mðreference valueÞ
60 40 20 0 −20
0
1
2
3
4
5
−40 −60
Mass flow density , ms−1
Fig. 3. Influence of the beet velocity on the momentum (&, small turbine; ^, big turbine)
and a diameter of 063 m for the smaller turbine. The considered influence is quadratic and smaller for bigger turbines. This can be explained because of a higher force and by this a higher momentum, resulting in a better signal-to-noise ratio Big turbine:
ru, radius of the turbine; r, radius of the friction independent pivot axis; d, longitudinal slope of the harvester; g, lateral slope of the harvester; ye, total angle of the mass flow sensor; b, angle between driving direction and the beginning of the mass flow sensor; j, angle of the spokes of the turbine; aopt, angle of the rotation point referred to the driving direction minimising the influence of the friction on the momentum; v0, initial beet flow velocity; Q, mass flow rate; r, density of the sugar beet flow; mrack, friction coefficient between the sugar beet and the siderack; msun, friction coefficient between the sugar beet and the rotating turbine and h, height of the beet flow on the turbine.
¼
80 Moment sensitivity, %
Design value
100
ð12Þ
2.2.1. Influence of the beet velocity From experiments the beet velocity varied between 15 and 3 m s1, an average initial mass velocity v0 of 25 m s1 was chosen. Varying this value (Fig. 3) indicate that the beet velocity has significant influence on the measured momentum. The size of the turbines depends on the type of harvester. In this study, two types are compared with a diameter of 095 m for the big turbine
DMðv0 ; 25 m s1 Þ ¼ 195v20 þ 1493v0 4940
ð13Þ
Small turbine: DMðv0 ; 25 m s1 Þ ¼ 224v20 þ 1649v0 5526
ð14Þ
It is concluded that a continuous correction of the speed is required to achieve sufficient accuracy. 2.2.2. Influence of the slope During the cleaning of the beets, the turbines of the cleaning unit already have an angle of inclination d of 8138. Figures 4 and 5 show that both angles, longitudinal d and lateral g have a major influence on the measured momentum. Both can be explained by changing mass velocities on the rotating turbines corresponding to a changing slope. The gravitational force dFg changes the speed of the beets when the slope varies and causes a major influence on the centrifugal force dFcf. The effect of the slope due to the mass of the sensor itself is negligible when installing a counter weight. 2.2.3. Influence of the mass flow density The mass density of sugar beets can vary because of changing conditions during the growing season. This will be reflected in the apparent mass flow density. Measurements indicate an average value of the apparent mass flow density of 600 kg m3 and a standard deviation of 20 kg m3 (Weyne, 2000). The most important influence here is the size of the beets that is influenced by soil and weather parameters. Figure 6 shows that the influence on the momentum is very small and can be neglected.
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25 20 Momentum sensitivity, %
15 10 5 −15
−5
−10
0 −5
0
5
10
15
−10 −15 −20 Lateral slope , deg
Fig. 4. Influence of the longitudinal slope on the momentum (&, big turbine; ^, small turbine)
25 20 Momentum sensitivity, %
15 10 5 −15
−10
−5
0 −5
0
5
10
15
−10 −15 −20 Lateral slope , deg
Fig. 5. Influence of the lateral slope on the momentum (&, big turbine; ^, small turbine)
0.20
Momentum sensitivity, %
0.15 0.10 0.05 0 500 . −0 05
550
600
650
700
750
−0.10 −0.15 −0.20 −0.25
Apparent mass flow density , kg m−3
Fig. 6. Influence of the mass flow density on the momentum (&, small turbine; ^, big turbine)
2.2.4. Influence of the angle of the spokes To keep contact with the beets for as long as possible, the spokes make an angle with the radial direction
(Figs. 1 and 7 ). Different values of the angle j are chosen for different type of crops. In practice, turbines with spokes varying between 15 and 258 will be used.
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431
Momentum sensitivity, %
4 3 2 1 0 −1
15
17
19
21
23
25
−2 −3 −4
Angle of the spokes , deg
Fig. 7. Influence of the angle of the spokes on the momentum (&, small turbine; ^, big turbine) Fig. 8. Construction of the side-rack with the parallel round bars (Dewulf R6000T)
Figure 7 shows major influence of the spoke angle on the momentum. This influence minimises when using a friction-compensated sensor, which can be explained by stating that j only has an effect on the components of the driving force dFD [Eqn (5)]. Simulations confirm that errors made without using a friction-compensated sensor, are small compared to the cost of the accompanying construction of the sensor. The constructive adaptations associated with this friction independency can be neglected. Variations in the flow speed have great influence on the measured moment. Therefore, a continuous correction of the mass velocity is necessary, taking into account variations in field slope. Comparisons between big and small turbines indicate that variations in momentum have minor influence in case of a large radius ru because of a higher momentum created by a more structured beet flow.
Fig. 9. Construction of the mass flow sensor: the side-rack (top view) is mechanically isolated from the frame and a load cell registers the exerted momentum
rotation and translation of the harvester. A construction with a counter weight is made to realise latter objective. The mass flow is continuous and enters the considered part of the rack in a tangential way. The flow follows the radius of the rack and no impact is caused.
3. Materials and methods 3.2. Method 3.1. Positioning of the sensor A side-rack of one of the turbines was chosen as a curved plate. This rack is an original part of the harvester. Its function is to guide the beet flow through the cleaning unit and to clean the beets. Table 1 summarises the construction parameters of the turbines used in this research. Two different cleaning units were enclosed in the laboratory arrangement, an Agrifac ZA EH 215 (one-phase system) and a Dewulf R6000T (collector of a two-phase system). Figure 8 shows that the side-rack is made of parallel round bars with a space of 5 cm in between. The rack is mechanically isolated from the frame of the harvester and can pivot around an axis. The momentum executed on the side-rack is measured by a load-cell (Sensy 2712 C3), shown in Fig. 9. The centre of gravity of the sensor has to be on the pivot axis to minimise the influences of the slope,
3.2.1. Theory of friction compensation In the field, properties of the sugar beets will vary due to changing growing conditions. A more heavy soil will cause the beets to branch off more than beets grown in a sandy soil. In wet zones, beets will attach more soil than those from more dry parts of the field. All this gives origin to a variation in friction coefficient. Strubbe (1997) found that the position of the rotation axis of the mass flow sensor is determining when desiring friction independent grain flow measurements. The determination of the angle a, in which the effect on the measurement of the momentum is minimal, involves an optimisation problem with a as a parameter (Anthonis et al., 2003). (a) Determination of the optimal pivot position. Strubbe (1997) indicated that based on the momentum balance on a chute in free flow conditions, a zone can be derived
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msun ¼ mrack
035 055
ð15Þ
Equation (15) makes it possible to determine an optimal pivot position aopt for a given set of construction parameters and with a minimised influence of friction. To examine the influence of the friction on the measured momentum, in Eqn (16) a new measure is defined as DMðmrack Þ Mðmrack Þ Mð055Þ 100 ð16Þ ¼ Dmrack Mð055Þ 10ðmrack 055Þ This measure is dimensionless. The first part of the right term is a measure for the relative deviation of the momentum when using another friction coefficient then the reference value. The second part of the right term gives the percentage change of momentum per change of 01 in the value of mrack. Specific, aopt is chosen minimizing the difference for the new defined measure, varying mrack between 045 and 065. The position of aopt is also influenced by the initial velocity of the beet mass flow. Reybrouck (1998) found that the velocity varied between 22 and 3 m s1. (b) Comparison between the chosen and the friction independent pivot position. Owing to constructional considerations, the pivot position was situated at about 908. The influence of the friction coefficient on the moment was investigated. Therefore DM was calculated, taking Mðmrack ¼ 055Þ as a reference value. One can conclude that the impact of the friction coefficient on the momentum is negligible (Fig. 10). Maximal variance is changing between 15% for small turbines and 1% for big turbines. As the accuracy of the mass flow sensor is expected to be in the range of 3%, these values can be ignored. 3.2.2. Measurements During the time of the first sensor construction, the real parameter settings were unknown. In the first step of the sensor development, there was no intention of changing the original configuration of the cleaning unit and only the side-rack was mechanically isolated. The momentum on the pivot point was continuously recorded and the flow speed at the entrance of the
2.0 Moment sensitivity,%
in which the optimal pivot position aopt in degrees is located. The exact position of aopt can be determined solving the optimisation problem. Out of constructional limitations, r is chosen equal to ru. Reybrouck (1998) indicated that the friction coefficient mrack, between beet and rack varies between 045 and 065. A reference value of 055 was chosen. For the friction coefficient between beet and turbine the following relationship was derived based on experiments (Weyne, 2000):
1.5 1.0 0.5 0 −0.5
0.45
0.50
0.55
0.60
0.65
−1.0 −1.5 −2.0
Friction coefficient µrack
Fig. 10. Influence of the friction coefficient on the momentum (&, small turbine; ^, big turbine; m, big turbine friction compensated)
curved plate measured by a Doppler radar sensor. Measurements were done dynamically in the field and statically on a laboratory cleaning unit of a Dewulf R6000T beet harvester.
4. Results and discussion Finally, tests were carried out to optimise and evaluate the chosen configuration. First, stationary experiments were carried out. Next measurements were done in the field, resulting in general calibration equations for three different crops (sugar beets, chicory and turnips).
4.1. Calibration The time-integrated momentum signal M is compared with the scale weight of the total load to calibrate the model. By measuring the harvesting time, an average mass flow and flow speed can be calculated. Using these average values and the known construction parameters, a comparison between the predicted and the measured moment can be made. Optimising the sensor for having low influence of flow properties, the sensor signal was corrected for the velocity of the mass flow. The corrected signal is defined as the ‘velocity-corrected momentum’. Comparing the average mass flow and the time-integrated momentum, a correlation of 97% was found. Using only the momentum to predict the mass flow errors up to 20% are found. Higher flow speeds indicate a higher momentum than predicted by the model and therefore, a flow speed correction is introduced. Using the immediate rotational speed in s1 to correct the flow sensor signal the error is reduced to 5%. Measurements were done with an inductive
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Table 2 Summary of the most important calibration results for sugar beet, chicory and turnips Number of fields harvested
Number of measurements
Calibration error, kg s1
Standard deviation, kg s1
Coefficient of determination (R2)
Sugar beet Chicory Turnips
3 1 1
31 25 24
073 041 028
105 050 037
097 080 087
4.2. Comparison between the different crops A statistical linear regression is used to derive the different calibration equations. In Table 2, a summary of the most important calibration parameters is given. The lower value of the correlation coefficient of chicory and turnips can be explained by the smaller spreading of the dataset. The bigger value of the root mean square error of calibration of sugar beets ERMS in kg s1 is caused by higher mass flow rates. From Fig. 11, it follows that for the same mass flow rate, sugar beets have lower output voltage U in V. Correcting the data for the variation in mass flow speed can ignore this problem. The relation between the mass flow speed and the measured momentum is quadratic [Eqns (13) and (14)]. On the other hand variations in mass flow speed for each of the crops are maximal 1 m s1, creating the opportunity to linearise the quadratic relation without introducing a substantial error. From this Eqn (18) follows, where C is the original dimensionless calibration factor; v in m s1 is the beet flow speed; Un is the net output voltage in V and a and b are linearised parameters of the velocity
y = 5.1264x −1.4839 R2 = 0.9677 ERMS = 0.73 kg s−1
30 25 20 15 10 5 0 0
1
(a)
2
3 4 5 Measured voltage U, V
16 . . 14 y = 2 8681x −1 0601 2 = 0.8808 R 12 . −1 10 ERMS = 0 41 kg s 8 6 4 2 0 0 1 2 3 (b) Measured voltage U, V
6
7
Mass flow rate Q, kg s−1
where ERMS in kg s1 is defined as the root mean square error of calibration, yi in kg s1 as the ith value of a response variable, yi,pred in kg s1 as the value of the ith measured variable predicted by the linear regression model and n as the number of measurements. Table 2 specifies more details from the field test executed. Resulting from these tests, three calibration curves (Fig. 11) are derived.
35
4
5
12 Mass flow rate Q, kg s−1
sensor placed on the drive shaft. The result gives an indication of the flow speed but is dependent on the flow properties. A Doppler sensor is used for measuring the immediate flow speed. When continuously correcting the time-integrated signal with the immediate flow speed a correlation of 099 was obtained and the prediction error of a maximum load of 9000 kg is reduced to 3%. The root mean square error of calibration ERMS in kg s1, is calculated by Eqn (17) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðyi yi;pred Þ ERMS ¼ ð17Þ n2
Mass flow rate Q, kg s−1
Crop type
y = 3.0369x −0.783 R2 = 0.8747 8 ERMS = 0.28 kg s−1
10
6 4 2 0 0
(c)
0.5
1.0
2.5 1.5 2.0 Measured voltage U, V
3.0
3.5
Fig. 11. Experimental calibration curves: (a) for sugar beets; (b) for chicory; (c) for turnips; ERMS, root mean square error of calibration; R2 coefficient of determination
correction: Q ¼ CUcorr ¼ C
Un av þ b
ð18Þ
Determination of the exact position of the Doppler radar sensor has a major influence here. Incorrect placement will lead to wrong velocity measurements caused by registering rolling of the beets or the turbine speed (Fig. 12).
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20
Table 3 Regression and correlation coefficients of the calibration curves for different longitudinal slopes
15 Error, %
10
Longitudinal slope (d) deg
5 0 −5
20
30
40
50
60
70
421 920 1310 1706
−10
Error, %
(a)
Error, %
(b)
(c)
−15 4 3 2 1 0 −120 −2 −3 −4
10 8 6 4 2 0 −2 20 −4 −6 −8 −10
Mass flow by scale weight, kg s−1
30
40
50
60
70
Mass flow by scale weight, kg s−1
30
40
50
60
70
Mass flow by scale weight, kg s−1
Fig. 12. Comparison between the sensor-predicted weight and the measured scale weight of the bunker: (a) measured moment; (b) velocity-corrected momentum; (c) rotational speed-corrected momentum
4.3. Stationary measurements Following Eqn (11), both the longitudinal and lateral slope would have an influence on the measured value of the mass flow rate. During the test sessions on a Dewulf R6000T cleaning unit, different values were used for both slopes. 4.3.1. Influence of the slope Most of the attention was paid to the longitudinal slope d, since fields are harvested in this direction. Values for standard slopes of the turbines of the cleaning unit are presented in Table 1. Identical conclusions as the model [Eqn (11)] are drawn for large longitudinal slopes (Table 3). For larger slopes, the measured momentum decreases. This can be explained as a decreasing velocity of the sugar beets. Slopes smaller than the standard value lead to contradictory results. No logical explanation was found. Compensating for the average measured velocity of the beets,
Regression coefficient of calibration curve, kg V1 s1
Coefficient of determination (R2)
00783 00828 00724 00541
0482 0917 0872 0345
a velocity corrected regression coefficient rc,corr is developed rc ð19Þ rc;corr ¼ v The influence of this speed correction is determined by calculating the influence in % of the slope on the regression coefficient of the calibration curve relative to a standard value ds of 9208 (Table 4). rc ðdÞ rc ðds Þ ð20Þ Drc ¼ rc ðds Þ These differences are much smaller than for nonvelocity-corrected calibration curves. Longitudinal slopes smaller than the standard value require more tests. The deviation of the measured momentum compared with the momentum predicted by the model is presented in Table 5. Other experiments were carried out varying the value of the lateral slope g between 11928 and 1388. Reliable conclusions require more tests under different situations.
5. Conclusion The objective of the study was to develop a mass flow sensor that is universal for all types of beet harvesters and independent of the crop properties. Existing sensor technologies experience many disadvantages: low accuracy, difficulty of use, excessive machine modifications and intolerance of variation in harvesting conditions. A method based on the use of a curved plate to measure the momentum was chosen. The sensor was installed in the cleaning unit of a beet harvester. A side-rack at the border of a rotating turbine was chosen because of the continuous beet flow and the universality on the beet harvesters. A mathematical model of the beet flow was developed by analysing the different kind of forces acting on the beets. The big differences compared with combine harvester yield sensors are: (a) the beet flow is continuously undergoing the driving force exerted by the turbine;
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Table 4 The influence of a velocity correction on the regression coefficient of calibration curves for different longitudinal slopes Longitudinal Regression coefficient slope (d), deg of calibration curve (rc), kg V1 s1 920 1310 1706 421
Average material velocity (vavg), m s1
00828 00724 00541 00783
Velocity-corrected regression coefficient (rc,corr), kg V1 s1
17246 16515 12224 14767
00480 00438 00425 00530
Table 5 The deviation of the measured momentum compared with the momentum predicted by the model for different longitudinal slopes Longitudinal slope (d), deg
No correction
Correction
0 1250 3717 538
0 862 1136 1050
lijk-Technologisch Onderzoek in de Industrie, project number IWT 990202) and is done in association with the company Dewulf nv.
Deviation of measured momentum, %
References Relative to model Relative to test Difference for ds ¼ 9208 for ds ¼ 9208 model}test
1310 1706 421
Change in regression coefficient (rc), %
1096 2019 817
1250 3717 538
154 1698 1355
ds, standard value of longitudinal slope of 9208.
(b) the thickness of the beet flow in relation to the diameter of the turbine cannot be ignored; and (c) the pivot point is vertical in beet harvesters whereas combine harvesters have a horizontally oriented pivot axis. By numerical integration of the formula for the momentum, the total momentum on the side-rack is obtained and then influences of the different parameters can be calculated. From these calculations, the optimal position of the pivot point can be determined and the effect of the slope can be quantified. Field measurements were carried out to test the accuracy of the simulations and resulted in the side-rack before the sensor being pivoted, to guide the beet flow tangentially to the sensor. Calibrations were carried out by comparing the scale weight of the bunker with the integrated sensor signal. Errors of more than 15% were detected without a velocity compensation. With a linear correction for the beet velocity; errors below 3% were detected. Corrections for rotational speeds of the turbine contributed an improvement in accuracy of 5%.
Acknowledgements This research is financed by the IWT (Vlaams Instituut voor de Bevordering van het Wetenschappe-
Anthonis J; Maertens K; Strubbe G; De Baerdemaeker J; Ramon H (2003). Design of a friction independent mass flow sensor by force measurement on a circular chute. Biosystems Engineering 84(2), 127–136 Auernhammer H; Demmel M (1997). The stability of yield patterns in a year-by-year comparison. Landtechnik 1997, VDI-berichte 1356, VDI-Du. sseldorf, VDI-verlag, S.245–248 Dampney P; Froment M; Moore M; Stafford J; Miller P (1999). Yield mapping and precision farming, an appraisal of potential benefits based on recent research and farmer experience. Silsoe Research Institute, UK, 17pp Durrence J S (1998) Mapping peanut yield variability with an experimental load cell yield monitoring system. 4th International Conference on Precision Agriculture, St. Paul, Minnesota, USA, July Ehlert D (1999). Measuring mass flow of potatoes for yield mapping. Proceedings Precision Agriculture 1999, Odense, SI, Part B, pp 797–804 Englisch B C; Roberts R K; Mahajanashetti S B (1998). Spatial break-even variability for variable technology adoption, 4th International Conference on Precision Agriculture, St. Paul, Minnesota, USA, July Hien P; Kromer K H (1995). Sensortechnologie zur Ertragsbestimmung und Ertragskartierung von Zu. ckerruben. [Sensor technology for yield determination and yield mapping for sugar beets.] VDI-berichte 1211, pp 187–190 Kutzbach H D; Schneider H (1997). Scientific challenges of grain harvesting. ASAE Paper No 97-1080 Reybrouck S (1998). Massadebietmeting op een bietenrooier. [Mass flow measurements on a beet harvester.] MSc Thesis, KULeuven, Belgium Reyns P; Missotten B; Ramon H; De Baerdemaeker J (2001). A review of combine sensors for precision farming. Precision Agriculture 3(2), 169–175 Strubbe G (1997). Mechanics of friction compensation in mass flow measurement of bulk solids. PhD Thesis, Katholieke Universiteit Leuven, Faculteit Toegepaste Wetenschappen, Belgium Weyne V (2000). Optimalisatie van een massadebietsmeter op een bietenrooier. [Optimization of a mass flow sensor on a beet harvester.] MSc Thesis, KULeuven, Belgium
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The apparent mass flow density is used because of the spacing between the beets.
Appendix A A.1. The relation between rm and Q When assuming a rectangular flow profile next equation can be derived: ru þ rmin or rmin ¼ 2rmin ru ðA1Þ rm ¼ 2 where: rm in m is defined as the distance of the turbine centre to the mass centre point of the beet flow, ru in m as the radius of the turbine and rmin in m as the distance between the border of the turbine and the first beet. The mass flow rate Q in kg s1 can also be written as Q ¼ rvðru rmin Þh ¼ rv2ðru rm Þh
ðA2Þ
where: r in kg m3 is defined as the apparent beet flow density, v in m s1 as the beet velocity and h in m as the height of the beets on the turbine wheel.
A.2. The derivation of Eqn (10) The forces acting in the radial and tangential directions are given in Eqns (7) and (8). The tangential; Fg,y in N; and radial; Fg,x in N; components of the gravitational force are defined as Fg;x ¼ g dm½sinðy þ bÞcos d sin g þ cosðy þ bÞsin d
ðA3Þ
Fg;y ¼ g dm½cosðy þ bÞsin d cos g sinðy þ bÞsin d
ðA4Þ
Substitution of both formulae in Eqns (7) and (8) gives an expression for both the radial and tangential acting forces.
Biosystems Engineering (2003) 85 (4), 425–436 doi:10.1016/S1537-5110(03)00095-3 AE}Automation and Emerging Technologies
Development of a Flow Model for the Design of a Momentum Type Beet Mass Flow Sensor D. Hennens; J. Baert; B. Broos; H. Ramon; J. De Baerdemaeker Laboratory of Agricultural Machinery and Processing, Katholique Universiteit Leuven, Kasteelpark Arenberg 30, Heverlee 3001, Belgium; e-mail of corresponding author: [email protected] (Received 19 July 2002; accepted in revised form 9 May 2003; published online 21 June 2003)
A lot of research is done to monitor yield during harvesting. Combined with a positioning system, this information can be used to produce yield maps. Based on the yields of successive years, site-specific field management can be done, aiming for higher local economic and ecological yield efficiencies. In this research, a curved plate mass flow sensor for sugar beet is designed with the aid of a mathematical model. The principle is based on measuring the impulse flow colliding with the plate. For granular materials, an accuracy of 2% is achieved. The mass flow sensor for sugar beet is integrated as a curved side rack in the cleaning channel of the harvester. The side rack is mechanically isolated from the frame. A theoretical model of the beet flow over the turbines of the cleaning unit is calculated and incorporates all physical parameters that influence the mass flow measurement by the momentum sensor. The flow density and friction coefficients with the rack and the turbine characterise the mass flow. From the model, the influence of the different parameters (slope, beet velocity, friction, length of the plate) on the momentum is investigated. The force exerted on the rack of the cleaning unit is measured, from which the momentum can be indirectly calculated. A measurement device is constructed, minimising the influence of the harvesting conditions and the material properties. After calibration, measurements are carried out on the cleaning unit of a Dewulf R6000T (two-phase system) and an Agrifac ZA 215 EH (one-phase system). Research is done to construct the sensor independent on friction properties between beets and the rack. Major influence comes from the velocity of the transported material. Variations in beet speed have to be registered continuously with a Doppler radar meter. Influences of a varying slope can also be corrected regarding the instantaneous beet velocities. More accurate measurements are done when the sensor is installed on bigger spinning wheels because of higher momentum due to a higher centrifugal force and hence a higher signal to noise ratio. To evaluate the model, only average mass flows and flow speeds could be used to predict the executed moments. When comparing the integrated measured momentum and the scale weight of the harvester bin, the error never exceeds 3% when using the derived equation. # 2003 Silsoe Research Institute. All rights reserved Published by Elsevier Science Ltd
1. Introduction For many thousands of years, farmers cultivated their own small fields looking to the local needs of the plants. By mechanisation and the consequential expansion of farms, farmers lost the knowledge of those local needs. Homogeneous treatment was the only technological solution to manage the arable land. Adaptation to the site-specific needs can decrease the input and gives rise to increasing profits. Today’s technology creates the 1537-5110/03/$30.00
possibility to collect data of a lot of crop parameters, soil conditions and yield variations. Although totally integrated systems are available on the market, the profits of the whole system are questionable (Dampney et al., 1999). Englisch et al. (1998) indicate that, to evaluate the profitability of precision agriculture, the variability in the field over different years is the most important step. Yield maps are the most useful tools to visualise this variability. Most of the time, farmers can indicate the causes of low yield areas but they rarely 425
# 2003 Silsoe Research Institute. All rights reserved Published by Elsevier Science Ltd
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Notation a b C dmax ERMS Fcf FD FDr Fg Fg,x Fg,y Frack Frad Ftan g h FN M m n Q R2 r rc
rc,
corr
linearised parameter of the velocity correction linearised parameter of the velocity correction original calibration factor maximal size of the holes in the beet flow, m root mean square error of calibration, kg s1 centrifugal force, N frictional (driving) force between the turbine and the sugar beets, N radial component of the driving force, N gravitational force, N radial component of the gravitational force, N tangential component of the gravitational force, N frictional force acting between the sugar beets and the side-rack, N radial projection of the forces acting on an elementary mass particle, N tangential projection of the forces acting on an elementary mass particle, N gravitational acceleration, m s2 height of the beet flow on the turbine, m the normal force acting perpendicular on the contact surface, N momentum acting on a small part of the side rack, N m mass particle, kg number of measurements mass flow rate, kg s1 coefficient of determination radius of the friction independent pivot axis, m regression coefficient for the calibration curve between measured voltage and mass flow rate, kg V1 s1 velocity-corrected regression coefficient, kg V1 m1
know the quantitative losses. Comparing the yield of successive years, it is possible to indicate crop, soil or environment dependent causes of the variability (Auernhammer & Demmel, 1997). For measuring and mapping yield and other crop properties on harvesters, several systems have been developed (Reyns et al., 2001). Kutzbach and Schneider (1997) give an overview of all existing grain flow measurement concepts involving the measurement of a weight, volume, impacts or other indirect parameters. Besides yield, also lodged grain, weeds, straw yield and the moisture and protein content are recorded and mapped. For non-combinable products, such as potatoes and sugar beet, few yield measurement systems are
rm
mean radius of the mass centreline of the material flow along the side-rack, m rmin mean radius of the mass centreline till the first beet, m ru radius of the turbine, m U mass flow related output voltage, V Ucorr corrected mass flow related output voltage, V Un net output voltage of the load cell, V v material velocity, m s1 vavg average material velocity, m s1 v0 initial beet flow velocity, m s1 x, y, z coordinates yi ith value of a response variable yi,pred value of the ith measured variable predicted by the linear regression model a angle of the rotation point referred to the driving direction, 8 aopt angle of the rotation point referred to the driving direction minimising the influence of the friction on the momentum, 8 b angle between driving direction and the beginning of the mass flow sensor, 8 d longitudinal slope of the harvester, 8 ds standard value of longitudinal slope of 9208 g lateral slope of the harvester, 8 j angle of the spokes of the turbine, 8 mrack friction coefficient between the sugar beet and the side-rack msun friction coefficient between the sugar beet and the rotating turbine y angle from the start of the mass flow sensor to the position of the mass particle, 8 ye total angle of the mass flow sensor, 8 r density of the sugar beet flow, kg m3
available. The non-smoothed flow, the high mass yields and the large range of harvesting conditions cause major problems. Ehlert (1999) tried an impact plate to measure the mass flow of potatoes. The angle of the impact, flow speed variation, machine vibration and dirt affect the accuracy of the measurements, while the impacts damage the potatoes. The sensor was only tested under laboratory conditions. Durrence (1998) measured the bin weight of a peanut harvester. Hien and Kromer (1995) tried to predict the mass flow by measuring continuously the thickness of sugar beets. An exponential relation was found between the maximum diameter of the beets and the weight. The diameter was measured by different means, such as ultrasonic distance sensors,
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optical sensors, Doppler radar sensors, tactile sensors and a force measurement on the knives while topping the beets. Auernhammer and Demmel (1997) isolated a part of a conveyor belt. They replaced one of the rollers with a load cell and a slide bar. A continuous overload was necessary and the slope of the conveyor had to be constant. Most of the beet harvesters used in Belgium, Germany and the Netherlands are not provided with the appropriate conveyor belt. They all have a cleaning system of rotating turbines and one or more conveyor belts that turn around the bin. In this research, a measurement system is integrated in the cleaning system. Its concept is based on a mass flow sensor for harvesters, developed by Strubbe (1997). The mass flow is obtained indirectly by measuring the forces on a curved plate such that all impact forces are excluded. For the development of the sensor, a model was derived to reduce the influences of the product properties. This means that one calibration each harvest season must be sufficient for all types of crops.
An elementary mass particle dm in kg experiences four different forces (Fig. 1): (1) the centrifugal force dFcf in N caused by the turning of the turbine with rm in m, the mean radius of the mass centreline of the material flow along the siderack and v the velocity of the beets in m s1 dFcf ¼ dm
v2 rm
ð1Þ
(2) the gravitational force dFg in N, with g in m s2 defined as the gravitational acceleration dFg ¼ dm g
ð2Þ
which can be decomposed in a radial component dFg,x in N and a tangential component dFg,y in N dFg;x ¼ g dm½sinðy þ bÞcos d sin g þ cosðy þ bÞsin d ð3Þ dFg;y ¼ g dm½cosðy þ bÞsin d cos g sinðy þ bÞsin d ð4Þ
2. Theory of the model 2.1. Development of the model For the development of the model, three-dimensional coordinates (x, y, z) are used. The Z-axis is situated in the centre of the turbine, pointing upwards. The X-axis goes through the considered mass particle. To describe the forces acting on the side-rack it is necessary to first evaluate the forces on the mass flow.
where: y in degrees is defined as the angle from the start of the mass flow sensor to the position of the mass particle; b in degrees as the angle between the driving direction and the beginning of the mass flow sensor; d in degrees as the longitudinal slope of the harvester; and g in degrees as the lateral slope of the harvester; (3) the driving force of the curved spokes dFD in N, with msun the friction coefficient between the beets and the rotating turbine and FN in N, the normal force acting perpendicular to the
ϕ
β
θe
FD
ϕ cos
θ
ϕ
FD
FD sinϕ
FD k
F rac (a)
(α,r)
Fcf
Fcf (b)
Fig. 1. (a) Top view of the different forces acting on an elementary mass particle dm rotating on a cleaning turbine; (b) detail of the forces in the radial and tangential direction; a, angle of the rotation point referred to the driving direction; b, angle between driving direction and the beginning of the mass flow sensor; j, angle of the spokes of the turbine; y, angle from the start of the mass flow sensor to the position of the mass particle; ye, total angle of the mass flow sensor; Fcf, centrifugal force; FD, frictional (driving) force between the turbine and the sugar beets; Frack, frictional force acting between the sugar beets and the side-rack
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contact surface dFD ¼ msun
FN ¼ msun dm g
ð5Þ
the frictional force between the mass flow and the side rack dFrack in N, with mrack defined as the friction coefficient between the sugar beets and the side-rack; dFcf in N as the centrifugal force and dFDr in N as the radial component of the driving force dFrack ¼ mrack ðdFcf þ dFDr Þ
ð6Þ
Due to the rotation and the slope of the turbine, it is necessary to transform the forces to the initial coordinate system. To evaluate the mass speed, the different forces are split into a radial component, perpendicular to the side-rack and a tangential component, parallel with the moving direction. The projection of the forces in the radial direction Frad and in the tangential direction Ftan can be formulated as Frad ¼ Fcf þ Fg;x þ FD sin j
ð7Þ
Ftan ¼ Fg;y Frack þ FD cos j
ð8Þ
where: the parameter j in degrees is defined as the angle of the turbine spokes; Fg,x in N as the radial component of the gravitational force and Fg,y in N as the tangential component of the gravitational force. The residual force in the tangential direction can also be defined as dv dm ¼ dFtan ð9Þ dt
impulse. The elementary momentum dM on a small part of the side-rack can be expressed by (Fig. 2): Q rm dyðr sinðy þ b aÞ v þ mrack ðr cosðy þ b aÞ ru ÞÞ 2 v þ sinðy þ bÞsin g cos d grm
dM ¼ g
þ cosðy þ bÞsin d þ msun cos d cos g sin j
where: a in degrees is the angle of the rotation point referred to the driving direction, r in m is defined as the radius of the friction independent pivot axis; ru in m is the radius of the turbine; and Q in kg s1 is the mass flow rate. Integrating the momentum over the total length of the side-rack will result in the momentum measured with the sensor.
2.2. Sensitivity analysis In this section, the theoretical influences of the different model parameters on the momentum are investigated. With the developed model it is possible to optimise the construction of the mass flow sensor, by taking care that all considered influences are minimised.
Substituting Eqns (1)–(6) into Eqns (7)–(9) and combining both formulae (also see in Appendix A), an expression for the speed of the mass flow during the transport over the turbines is derived: dv2 ¼ 2grm msun cos d cos g cos j sinðy þ bÞsin d dy þcosðy þ bÞsin g cos d mrack 2 v þ sinðy þ bÞcos d sin g þ cosðy þ bÞsin d grm þ msun cos d cos g sin j ð10Þ where: b in degrees is the angle between the driving direction and the beginning of the mass flow sensor; d in degrees is the longitudinal slope angle of the harvester; g in degrees is the lateral slope of the harvester; and y in degrees is the angle from the start of the mass flow sensor to the position of the mass particle. From Eqn (10), it follows that the mass velocity is independent from the total mass flow rate. The side-rack forces the sugar beets to make a circular movement, which results in a continuously changing
ð11Þ
ru β α
θ
θe r cos(+−) −ru
Frack Frad r M
r sin(+−)
Fig. 2. Momentum and forces acting on the rack with their lever; a, angle of the rotation point referred to the driving direction; b, angle between driving direction and the beginning of the mass flow sensor; y, angle from the start of the mass flow sensor to the position of the mass particle; ye, total angle of the mass flow sensor; r, radius of the friction independent pivot axis; ru, radius of the turbine; Frack, frictional force acting between the sugar beets and the side-rack; Frad, radial projection of the forces acting on an elementary mass particle; M, momentum acting on a small part of the side-rack
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Table 1 Construction parameters for the different cleaning units
Big turbine (Agrifac ZA EH 215) Construction parameters 095 ru, m r, m 1 d, deg 813 g, deg 0 ye, deg 3769 b, deg 90 j, deg 17 aopt, deg 11986
Small turbine (Agrifac ZA EH 215) 063 0675 813 0 4138 90 17 12095
Dewulf (R6000T)
070 085 79 0 4337 10183 20 1092
Default flow parameters 3 v0, m s1 Q, 40 kg s1 r, 600 kg m3 mrack 055 msun 035 h, m 035
The effect caused by a change in one parameter will be compared to the reference value of the momentum, calculated with the standard values of the parameters, shown in Table 1. The measure in % that will be used further is defined as DM ðparameter; reference value parameterÞ Mð parameterÞ Mðreference valueÞ 100 Mðreference valueÞ
60 40 20 0 −20
0
1
2
3
4
5
−40 −60
Mass flow density , ms−1
Fig. 3. Influence of the beet velocity on the momentum (&, small turbine; ^, big turbine)
and a diameter of 063 m for the smaller turbine. The considered influence is quadratic and smaller for bigger turbines. This can be explained because of a higher force and by this a higher momentum, resulting in a better signal-to-noise ratio Big turbine:
ru, radius of the turbine; r, radius of the friction independent pivot axis; d, longitudinal slope of the harvester; g, lateral slope of the harvester; ye, total angle of the mass flow sensor; b, angle between driving direction and the beginning of the mass flow sensor; j, angle of the spokes of the turbine; aopt, angle of the rotation point referred to the driving direction minimising the influence of the friction on the momentum; v0, initial beet flow velocity; Q, mass flow rate; r, density of the sugar beet flow; mrack, friction coefficient between the sugar beet and the siderack; msun, friction coefficient between the sugar beet and the rotating turbine and h, height of the beet flow on the turbine.
¼
80 Moment sensitivity, %
Design value
100
ð12Þ
2.2.1. Influence of the beet velocity From experiments the beet velocity varied between 15 and 3 m s1, an average initial mass velocity v0 of 25 m s1 was chosen. Varying this value (Fig. 3) indicate that the beet velocity has significant influence on the measured momentum. The size of the turbines depends on the type of harvester. In this study, two types are compared with a diameter of 095 m for the big turbine
DMðv0 ; 25 m s1 Þ ¼ 195v20 þ 1493v0 4940
ð13Þ
Small turbine: DMðv0 ; 25 m s1 Þ ¼ 224v20 þ 1649v0 5526
ð14Þ
It is concluded that a continuous correction of the speed is required to achieve sufficient accuracy. 2.2.2. Influence of the slope During the cleaning of the beets, the turbines of the cleaning unit already have an angle of inclination d of 8138. Figures 4 and 5 show that both angles, longitudinal d and lateral g have a major influence on the measured momentum. Both can be explained by changing mass velocities on the rotating turbines corresponding to a changing slope. The gravitational force dFg changes the speed of the beets when the slope varies and causes a major influence on the centrifugal force dFcf. The effect of the slope due to the mass of the sensor itself is negligible when installing a counter weight. 2.2.3. Influence of the mass flow density The mass density of sugar beets can vary because of changing conditions during the growing season. This will be reflected in the apparent mass flow density. Measurements indicate an average value of the apparent mass flow density of 600 kg m3 and a standard deviation of 20 kg m3 (Weyne, 2000). The most important influence here is the size of the beets that is influenced by soil and weather parameters. Figure 6 shows that the influence on the momentum is very small and can be neglected.
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25 20 Momentum sensitivity, %
15 10 5 −15
−5
−10
0 −5
0
5
10
15
−10 −15 −20 Lateral slope , deg
Fig. 4. Influence of the longitudinal slope on the momentum (&, big turbine; ^, small turbine)
25 20 Momentum sensitivity, %
15 10 5 −15
−10
−5
0 −5
0
5
10
15
−10 −15 −20 Lateral slope , deg
Fig. 5. Influence of the lateral slope on the momentum (&, big turbine; ^, small turbine)
0.20
Momentum sensitivity, %
0.15 0.10 0.05 0 500 . −0 05
550
600
650
700
750
−0.10 −0.15 −0.20 −0.25
Apparent mass flow density , kg m−3
Fig. 6. Influence of the mass flow density on the momentum (&, small turbine; ^, big turbine)
2.2.4. Influence of the angle of the spokes To keep contact with the beets for as long as possible, the spokes make an angle with the radial direction
(Figs. 1 and 7 ). Different values of the angle j are chosen for different type of crops. In practice, turbines with spokes varying between 15 and 258 will be used.
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431
Momentum sensitivity, %
4 3 2 1 0 −1
15
17
19
21
23
25
−2 −3 −4
Angle of the spokes , deg
Fig. 7. Influence of the angle of the spokes on the momentum (&, small turbine; ^, big turbine) Fig. 8. Construction of the side-rack with the parallel round bars (Dewulf R6000T)
Figure 7 shows major influence of the spoke angle on the momentum. This influence minimises when using a friction-compensated sensor, which can be explained by stating that j only has an effect on the components of the driving force dFD [Eqn (5)]. Simulations confirm that errors made without using a friction-compensated sensor, are small compared to the cost of the accompanying construction of the sensor. The constructive adaptations associated with this friction independency can be neglected. Variations in the flow speed have great influence on the measured moment. Therefore, a continuous correction of the mass velocity is necessary, taking into account variations in field slope. Comparisons between big and small turbines indicate that variations in momentum have minor influence in case of a large radius ru because of a higher momentum created by a more structured beet flow.
Fig. 9. Construction of the mass flow sensor: the side-rack (top view) is mechanically isolated from the frame and a load cell registers the exerted momentum
rotation and translation of the harvester. A construction with a counter weight is made to realise latter objective. The mass flow is continuous and enters the considered part of the rack in a tangential way. The flow follows the radius of the rack and no impact is caused.
3. Materials and methods 3.2. Method 3.1. Positioning of the sensor A side-rack of one of the turbines was chosen as a curved plate. This rack is an original part of the harvester. Its function is to guide the beet flow through the cleaning unit and to clean the beets. Table 1 summarises the construction parameters of the turbines used in this research. Two different cleaning units were enclosed in the laboratory arrangement, an Agrifac ZA EH 215 (one-phase system) and a Dewulf R6000T (collector of a two-phase system). Figure 8 shows that the side-rack is made of parallel round bars with a space of 5 cm in between. The rack is mechanically isolated from the frame of the harvester and can pivot around an axis. The momentum executed on the side-rack is measured by a load-cell (Sensy 2712 C3), shown in Fig. 9. The centre of gravity of the sensor has to be on the pivot axis to minimise the influences of the slope,
3.2.1. Theory of friction compensation In the field, properties of the sugar beets will vary due to changing growing conditions. A more heavy soil will cause the beets to branch off more than beets grown in a sandy soil. In wet zones, beets will attach more soil than those from more dry parts of the field. All this gives origin to a variation in friction coefficient. Strubbe (1997) found that the position of the rotation axis of the mass flow sensor is determining when desiring friction independent grain flow measurements. The determination of the angle a, in which the effect on the measurement of the momentum is minimal, involves an optimisation problem with a as a parameter (Anthonis et al., 2003). (a) Determination of the optimal pivot position. Strubbe (1997) indicated that based on the momentum balance on a chute in free flow conditions, a zone can be derived
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msun ¼ mrack
035 055
ð15Þ
Equation (15) makes it possible to determine an optimal pivot position aopt for a given set of construction parameters and with a minimised influence of friction. To examine the influence of the friction on the measured momentum, in Eqn (16) a new measure is defined as DMðmrack Þ Mðmrack Þ Mð055Þ 100 ð16Þ ¼ Dmrack Mð055Þ 10ðmrack 055Þ This measure is dimensionless. The first part of the right term is a measure for the relative deviation of the momentum when using another friction coefficient then the reference value. The second part of the right term gives the percentage change of momentum per change of 01 in the value of mrack. Specific, aopt is chosen minimizing the difference for the new defined measure, varying mrack between 045 and 065. The position of aopt is also influenced by the initial velocity of the beet mass flow. Reybrouck (1998) found that the velocity varied between 22 and 3 m s1. (b) Comparison between the chosen and the friction independent pivot position. Owing to constructional considerations, the pivot position was situated at about 908. The influence of the friction coefficient on the moment was investigated. Therefore DM was calculated, taking Mðmrack ¼ 055Þ as a reference value. One can conclude that the impact of the friction coefficient on the momentum is negligible (Fig. 10). Maximal variance is changing between 15% for small turbines and 1% for big turbines. As the accuracy of the mass flow sensor is expected to be in the range of 3%, these values can be ignored. 3.2.2. Measurements During the time of the first sensor construction, the real parameter settings were unknown. In the first step of the sensor development, there was no intention of changing the original configuration of the cleaning unit and only the side-rack was mechanically isolated. The momentum on the pivot point was continuously recorded and the flow speed at the entrance of the
2.0 Moment sensitivity,%
in which the optimal pivot position aopt in degrees is located. The exact position of aopt can be determined solving the optimisation problem. Out of constructional limitations, r is chosen equal to ru. Reybrouck (1998) indicated that the friction coefficient mrack, between beet and rack varies between 045 and 065. A reference value of 055 was chosen. For the friction coefficient between beet and turbine the following relationship was derived based on experiments (Weyne, 2000):
1.5 1.0 0.5 0 −0.5
0.45
0.50
0.55
0.60
0.65
−1.0 −1.5 −2.0
Friction coefficient µrack
Fig. 10. Influence of the friction coefficient on the momentum (&, small turbine; ^, big turbine; m, big turbine friction compensated)
curved plate measured by a Doppler radar sensor. Measurements were done dynamically in the field and statically on a laboratory cleaning unit of a Dewulf R6000T beet harvester.
4. Results and discussion Finally, tests were carried out to optimise and evaluate the chosen configuration. First, stationary experiments were carried out. Next measurements were done in the field, resulting in general calibration equations for three different crops (sugar beets, chicory and turnips).
4.1. Calibration The time-integrated momentum signal M is compared with the scale weight of the total load to calibrate the model. By measuring the harvesting time, an average mass flow and flow speed can be calculated. Using these average values and the known construction parameters, a comparison between the predicted and the measured moment can be made. Optimising the sensor for having low influence of flow properties, the sensor signal was corrected for the velocity of the mass flow. The corrected signal is defined as the ‘velocity-corrected momentum’. Comparing the average mass flow and the time-integrated momentum, a correlation of 97% was found. Using only the momentum to predict the mass flow errors up to 20% are found. Higher flow speeds indicate a higher momentum than predicted by the model and therefore, a flow speed correction is introduced. Using the immediate rotational speed in s1 to correct the flow sensor signal the error is reduced to 5%. Measurements were done with an inductive
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Table 2 Summary of the most important calibration results for sugar beet, chicory and turnips Number of fields harvested
Number of measurements
Calibration error, kg s1
Standard deviation, kg s1
Coefficient of determination (R2)
Sugar beet Chicory Turnips
3 1 1
31 25 24
073 041 028
105 050 037
097 080 087
4.2. Comparison between the different crops A statistical linear regression is used to derive the different calibration equations. In Table 2, a summary of the most important calibration parameters is given. The lower value of the correlation coefficient of chicory and turnips can be explained by the smaller spreading of the dataset. The bigger value of the root mean square error of calibration of sugar beets ERMS in kg s1 is caused by higher mass flow rates. From Fig. 11, it follows that for the same mass flow rate, sugar beets have lower output voltage U in V. Correcting the data for the variation in mass flow speed can ignore this problem. The relation between the mass flow speed and the measured momentum is quadratic [Eqns (13) and (14)]. On the other hand variations in mass flow speed for each of the crops are maximal 1 m s1, creating the opportunity to linearise the quadratic relation without introducing a substantial error. From this Eqn (18) follows, where C is the original dimensionless calibration factor; v in m s1 is the beet flow speed; Un is the net output voltage in V and a and b are linearised parameters of the velocity
y = 5.1264x −1.4839 R2 = 0.9677 ERMS = 0.73 kg s−1
30 25 20 15 10 5 0 0
1
(a)
2
3 4 5 Measured voltage U, V
16 . . 14 y = 2 8681x −1 0601 2 = 0.8808 R 12 . −1 10 ERMS = 0 41 kg s 8 6 4 2 0 0 1 2 3 (b) Measured voltage U, V
6
7
Mass flow rate Q, kg s−1
where ERMS in kg s1 is defined as the root mean square error of calibration, yi in kg s1 as the ith value of a response variable, yi,pred in kg s1 as the value of the ith measured variable predicted by the linear regression model and n as the number of measurements. Table 2 specifies more details from the field test executed. Resulting from these tests, three calibration curves (Fig. 11) are derived.
35
4
5
12 Mass flow rate Q, kg s−1
sensor placed on the drive shaft. The result gives an indication of the flow speed but is dependent on the flow properties. A Doppler sensor is used for measuring the immediate flow speed. When continuously correcting the time-integrated signal with the immediate flow speed a correlation of 099 was obtained and the prediction error of a maximum load of 9000 kg is reduced to 3%. The root mean square error of calibration ERMS in kg s1, is calculated by Eqn (17) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðyi yi;pred Þ ERMS ¼ ð17Þ n2
Mass flow rate Q, kg s−1
Crop type
y = 3.0369x −0.783 R2 = 0.8747 8 ERMS = 0.28 kg s−1
10
6 4 2 0 0
(c)
0.5
1.0
2.5 1.5 2.0 Measured voltage U, V
3.0
3.5
Fig. 11. Experimental calibration curves: (a) for sugar beets; (b) for chicory; (c) for turnips; ERMS, root mean square error of calibration; R2 coefficient of determination
correction: Q ¼ CUcorr ¼ C
Un av þ b
ð18Þ
Determination of the exact position of the Doppler radar sensor has a major influence here. Incorrect placement will lead to wrong velocity measurements caused by registering rolling of the beets or the turbine speed (Fig. 12).
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20
Table 3 Regression and correlation coefficients of the calibration curves for different longitudinal slopes
15 Error, %
10
Longitudinal slope (d) deg
5 0 −5
20
30
40
50
60
70
421 920 1310 1706
−10
Error, %
(a)
Error, %
(b)
(c)
−15 4 3 2 1 0 −120 −2 −3 −4
10 8 6 4 2 0 −2 20 −4 −6 −8 −10
Mass flow by scale weight, kg s−1
30
40
50
60
70
Mass flow by scale weight, kg s−1
30
40
50
60
70
Mass flow by scale weight, kg s−1
Fig. 12. Comparison between the sensor-predicted weight and the measured scale weight of the bunker: (a) measured moment; (b) velocity-corrected momentum; (c) rotational speed-corrected momentum
4.3. Stationary measurements Following Eqn (11), both the longitudinal and lateral slope would have an influence on the measured value of the mass flow rate. During the test sessions on a Dewulf R6000T cleaning unit, different values were used for both slopes. 4.3.1. Influence of the slope Most of the attention was paid to the longitudinal slope d, since fields are harvested in this direction. Values for standard slopes of the turbines of the cleaning unit are presented in Table 1. Identical conclusions as the model [Eqn (11)] are drawn for large longitudinal slopes (Table 3). For larger slopes, the measured momentum decreases. This can be explained as a decreasing velocity of the sugar beets. Slopes smaller than the standard value lead to contradictory results. No logical explanation was found. Compensating for the average measured velocity of the beets,
Regression coefficient of calibration curve, kg V1 s1
Coefficient of determination (R2)
00783 00828 00724 00541
0482 0917 0872 0345
a velocity corrected regression coefficient rc,corr is developed rc ð19Þ rc;corr ¼ v The influence of this speed correction is determined by calculating the influence in % of the slope on the regression coefficient of the calibration curve relative to a standard value ds of 9208 (Table 4). rc ðdÞ rc ðds Þ ð20Þ Drc ¼ rc ðds Þ These differences are much smaller than for nonvelocity-corrected calibration curves. Longitudinal slopes smaller than the standard value require more tests. The deviation of the measured momentum compared with the momentum predicted by the model is presented in Table 5. Other experiments were carried out varying the value of the lateral slope g between 11928 and 1388. Reliable conclusions require more tests under different situations.
5. Conclusion The objective of the study was to develop a mass flow sensor that is universal for all types of beet harvesters and independent of the crop properties. Existing sensor technologies experience many disadvantages: low accuracy, difficulty of use, excessive machine modifications and intolerance of variation in harvesting conditions. A method based on the use of a curved plate to measure the momentum was chosen. The sensor was installed in the cleaning unit of a beet harvester. A side-rack at the border of a rotating turbine was chosen because of the continuous beet flow and the universality on the beet harvesters. A mathematical model of the beet flow was developed by analysing the different kind of forces acting on the beets. The big differences compared with combine harvester yield sensors are: (a) the beet flow is continuously undergoing the driving force exerted by the turbine;
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Table 4 The influence of a velocity correction on the regression coefficient of calibration curves for different longitudinal slopes Longitudinal Regression coefficient slope (d), deg of calibration curve (rc), kg V1 s1 920 1310 1706 421
Average material velocity (vavg), m s1
00828 00724 00541 00783
Velocity-corrected regression coefficient (rc,corr), kg V1 s1
17246 16515 12224 14767
00480 00438 00425 00530
Table 5 The deviation of the measured momentum compared with the momentum predicted by the model for different longitudinal slopes Longitudinal slope (d), deg
No correction
Correction
0 1250 3717 538
0 862 1136 1050
lijk-Technologisch Onderzoek in de Industrie, project number IWT 990202) and is done in association with the company Dewulf nv.
Deviation of measured momentum, %
References Relative to model Relative to test Difference for ds ¼ 9208 for ds ¼ 9208 model}test
1310 1706 421
Change in regression coefficient (rc), %
1096 2019 817
1250 3717 538
154 1698 1355
ds, standard value of longitudinal slope of 9208.
(b) the thickness of the beet flow in relation to the diameter of the turbine cannot be ignored; and (c) the pivot point is vertical in beet harvesters whereas combine harvesters have a horizontally oriented pivot axis. By numerical integration of the formula for the momentum, the total momentum on the side-rack is obtained and then influences of the different parameters can be calculated. From these calculations, the optimal position of the pivot point can be determined and the effect of the slope can be quantified. Field measurements were carried out to test the accuracy of the simulations and resulted in the side-rack before the sensor being pivoted, to guide the beet flow tangentially to the sensor. Calibrations were carried out by comparing the scale weight of the bunker with the integrated sensor signal. Errors of more than 15% were detected without a velocity compensation. With a linear correction for the beet velocity; errors below 3% were detected. Corrections for rotational speeds of the turbine contributed an improvement in accuracy of 5%.
Acknowledgements This research is financed by the IWT (Vlaams Instituut voor de Bevordering van het Wetenschappe-
Anthonis J; Maertens K; Strubbe G; De Baerdemaeker J; Ramon H (2003). Design of a friction independent mass flow sensor by force measurement on a circular chute. Biosystems Engineering 84(2), 127–136 Auernhammer H; Demmel M (1997). The stability of yield patterns in a year-by-year comparison. Landtechnik 1997, VDI-berichte 1356, VDI-Du. sseldorf, VDI-verlag, S.245–248 Dampney P; Froment M; Moore M; Stafford J; Miller P (1999). Yield mapping and precision farming, an appraisal of potential benefits based on recent research and farmer experience. Silsoe Research Institute, UK, 17pp Durrence J S (1998) Mapping peanut yield variability with an experimental load cell yield monitoring system. 4th International Conference on Precision Agriculture, St. Paul, Minnesota, USA, July Ehlert D (1999). Measuring mass flow of potatoes for yield mapping. Proceedings Precision Agriculture 1999, Odense, SI, Part B, pp 797–804 Englisch B C; Roberts R K; Mahajanashetti S B (1998). Spatial break-even variability for variable technology adoption, 4th International Conference on Precision Agriculture, St. Paul, Minnesota, USA, July Hien P; Kromer K H (1995). Sensortechnologie zur Ertragsbestimmung und Ertragskartierung von Zu. ckerruben. [Sensor technology for yield determination and yield mapping for sugar beets.] VDI-berichte 1211, pp 187–190 Kutzbach H D; Schneider H (1997). Scientific challenges of grain harvesting. ASAE Paper No 97-1080 Reybrouck S (1998). Massadebietmeting op een bietenrooier. [Mass flow measurements on a beet harvester.] MSc Thesis, KULeuven, Belgium Reyns P; Missotten B; Ramon H; De Baerdemaeker J (2001). A review of combine sensors for precision farming. Precision Agriculture 3(2), 169–175 Strubbe G (1997). Mechanics of friction compensation in mass flow measurement of bulk solids. PhD Thesis, Katholieke Universiteit Leuven, Faculteit Toegepaste Wetenschappen, Belgium Weyne V (2000). Optimalisatie van een massadebietsmeter op een bietenrooier. [Optimization of a mass flow sensor on a beet harvester.] MSc Thesis, KULeuven, Belgium
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The apparent mass flow density is used because of the spacing between the beets.
Appendix A A.1. The relation between rm and Q When assuming a rectangular flow profile next equation can be derived: ru þ rmin or rmin ¼ 2rmin ru ðA1Þ rm ¼ 2 where: rm in m is defined as the distance of the turbine centre to the mass centre point of the beet flow, ru in m as the radius of the turbine and rmin in m as the distance between the border of the turbine and the first beet. The mass flow rate Q in kg s1 can also be written as Q ¼ rvðru rmin Þh ¼ rv2ðru rm Þh
ðA2Þ
where: r in kg m3 is defined as the apparent beet flow density, v in m s1 as the beet velocity and h in m as the height of the beets on the turbine wheel.
A.2. The derivation of Eqn (10) The forces acting in the radial and tangential directions are given in Eqns (7) and (8). The tangential; Fg,y in N; and radial; Fg,x in N; components of the gravitational force are defined as Fg;x ¼ g dm½sinðy þ bÞcos d sin g þ cosðy þ bÞsin d
ðA3Þ
Fg;y ¼ g dm½cosðy þ bÞsin d cos g sinðy þ bÞsin d
ðA4Þ
Substitution of both formulae in Eqns (7) and (8) gives an expression for both the radial and tangential acting forces.