Energy Requirement Model for a Combine Harvester, Part I: Development of Component Models

ARTICLE IN PRESS Biosystems Engineering (2005) 90 (1), 9–25 doi:10.1016/j.biosystemseng.2004.08.017 PM—Power and Machinery

Energy Requirement Model for a Combine Harvester, Part I: Development of Component Models D.C. Baruah1; B.S. Panesar2 1

Department of Agricultural Engineering, AAU Jorhat, India; e-mail of corresponding author: [email protected] 2 School of Energy Studies for Agriculture, PAU Ludhiana, India; e-mail: [email protected] (Received 15 April 2003; accepted in revised form 23 August 2004; published online 22 December 2004)

Energy is an important input of production agriculture. The timeliness of operation depends on energy availability. Energy input for harvesting and threshing of grain crops constitutes a major part of the total energy input. The combine harvester is a widely used harvesting machine for grain crops. The components of combine harvester have been modelled for power and energy requirements by using a number of processes and knowledge of physics, mechanics and mathematics. These models incorporate the crop, machine and soil parameters. The modulus of elasticity, moment of inertia of the transverse section, height and linear density of the crop stem, and crop throughput are some of the crop parameters identified in the models. Forward travel speed of the machine, total weight of the machine, peripheral speed of the respective components and several design parameters are the machine parameters identified in the models. The models are expected to be a useful tool for optimisation of energy use for harvesting operation by combine harvester. r 2004 Silsoe Research Institute. All rights reserved Published by Elsevier Ltd

requirements of harvesting and threshing machines were related to basic laboratory or field studies and the effect of a few selected operating parameters on energy, power or force requirements has been studied for a specific system (Burrough, 1954; Arnold & Lake, 1964; Lotey & Singh, 1975; Spokas & Lideikis, 1996). These studies do not include operational parameters, which are of paramount importance for farmers/machine operators from energy management aspect. Therefore, though the results of such studies have been useful for the similar situations, neither these become representative for other situations nor a thorough picture of the harvesting and threshing phenomenon is obtained from these studies. The effect of geometry and velocity of cutting blade, stem size and moisture contents of crop on the energy requirements behaviour of cutting crop stem drew attention of some other researchers (McRandal & McNulty, 1978, 1980; Chattopadhyay & Pandey, 1999). Much useful information relating to cutting blade and stem interaction, such as optimum blade angle, blade velocity, mode of cutting, were obtained through these studies. However, these studies have

1. Introduction Harvesting and threshing of grain crops are two major farm operations requiring considerable energy. Besides being major energy-consuming operations, these operations are also critical operations, as delay in completion of these operations result in huge grain loss (Bector & Singh, 1999). Mechanisation of these operations maintains the timeliness and hence prevents loss. However, the supply of sufficient amount of energy must be ensured for timely operation of harvesting and threshing machines. For that purpose, realistic assessment of energy demand is to be made so that ways and means to meet that energy demand are identified. Energy model may be an efficient tool to forecast the energy demand (Panesar, 1998). Several parameters, relating to soil, crop and machine effect the energy requirements of harvesting and threshing machines. Identification of these system parameters and the knowledge of their role in the energy requirement of machine are required to develop energy demand model of a machine. Most of the previous research on energy 1537-5110/$30.00

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r 2004 Silsoe Research Institute. All rights reserved Published by Elsevier Ltd

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D.C. BARUAH; B.S. PANESAR

Notation Ac Acc Ar At amr

b br , bf bmr

Cd Ci cc cf cmr

di dr , df ds dsw E eb esw F Fh, Fv

Fkd Fpc Fr Fs Ftr Ftt

cross-sectional area of crop stem, m2 effective area of concave, m2 projected area of the reciprocated portion of the knife, m2 total projected area of the cutter bar over which crop mass flows, m2 coefficient of the motion resistance formula involving wheel geometry, cone penetration resistance and centre of gravity position distance between front and rear wheel, m widths of rear and front tyre section, respectively, m coefficient of the motion resistance formula involving wheel geometry, cone penetration resistance, centre of gravity position and material flow characteristics through combine harvester crop stand density, number/m2 soil cone penetration resistance, kPa cylinder concave clearance, m ratio of mass agitated by sieves to throughput coefficient of the motion resistance formula involving material flow characteristics through combine harvester deflection of the crop stem, m diameter of the rear and front wheel, respectively, m rearward displacement of the crop mass over sieve per oscillation, m rearward straw displacement per oscillation over the straw walker, m modulus of elasticity of the crop stem, kPa energy expended to bend a single stem by knife, kJ energy expended per oscillation, kJ crop feed rate, Mg/h frictional resistances over horizontal and vertical bearing surfaces respectively, kN resistance force against bending of crop stem at the interference of knife, kN resistance force against movement of crop mass in the auger, kN resisting force against deflection of crop stem, kN average shearing resistance per unit length of stroke, kN/m tangential force experienced by the reel bat due to crop stem deflection, kN tangential force on threshing cylinder periphery, kN

f

forward movement of the machine per stroke of the knife, m frequency of oscillation of straw walker, s
1 fsw ft1, ft2, ft3 tangential forces due to impact, compression and motion resistance, respectively, at threshing cylinder periphery, kN g acceleration due to gravity, m/s2 h height of the crop stem, m hal lift of auger conveyor, m hc height of cut, m hf height of the feed conveyor, m hgc height of grain elevator, m hs lift of agitation over the sieve, m hsw effective lift of the straw mass in the straw walker, m I moment of inertia of the transverse section of the crop stem, m4 K elasticity of the crop mass, kPa kibearing proportionality coefficient for bearing friction kdcb ; kfcb1 kfcb2 kfcb3 ; kscb crop deflection, frictional and shear energy coefficients for the cutter bar t2 w kt1 k ; k cy cy cy threshing and windage energy coefficients for the threshing cylinder klfc crop lifting energy coefficient for the feeder conveyor kcpc ; klpc crop conveying and lifting energy coefficients for the platform conveyor kbr ; kwr crop bending and windage energy coefficients for the reel kwb proportionality coefficient for blower power requirement kasw ; kas energy coefficients for agitating the material by the straw walker and sieve katc ; ketc proportionality coefficients for tailings conveyor power requirements kagc ; kegc coefficients for grain conveyor power requirements la length of the auger section, m lgc length of auger-type grain conveyor, m lk length of the cutter bar section, m lmf path length of the material flow through the combine harvester, m lp length of the auger pitch, m ls equivalent length of sieves, m lsw length of straw walker, m mk mass of the reciprocating knife, kg mrcb mass of the crop mass supported by the reciprocating portion of the cutter bar, kg n number of crop stems deflected by a reel bat ns number of stalk deflected per second

ARTICLE IN PRESS ENERGY INPUT FOR A COMBINE HARVESTER

np rotational speed of auger conveyor, r s
1 Pb power requirement by the blower, kW Pbearing power expenditure due to bearing friction at the ith component, kW Pcb power requirement by the cutter bar, kW Pcy power requirement by the threshing cylinder, kW Pgc power requirements by the grain conveyor, kW Pfc power requirement of the feeder conveyor, kW Ppc power requirement of the platform conveyor, kW Pr power requirement by the reel, kW Ps power requirements by the sieves, kW Psw power requirement at the straw walker, kW Pt power required for propulsion, kW Ptc power requirement by the tailings conveyor, kW Pbr power requirement by the reel for bending crop stems, kW Pwr power due to windage at the reel, kW Pdcb power expended for stalk deflection by the knife, kW Pscb power required by the knife for shearing the stems, kW P0fcb instantaneous power required to overcome friction at the sliding bearing surfaces, kW Pcpc ; Plpc power required for material conveying and lifting through auger section, kW Ptcy ; Pwcy power required to thresh crop mass and for windage in the threshing cylinder, kW Pagc ; Pegc power requirements by auger grain conveyor and elevator, kW pz pitch of the reel bat, m Rm motion resistance to driving wheel, kN Rmf, Rmr motion resistances to front and rear wheels, kN Rv normal reaction to the vertical sliding surface at the cutter bar, kN r radius of the reel bat, m rc radius of the knife driving crank, m Sg ratio of non-grain to grain s knife stroke length, m sf ratio of straw mass in the straw walker to throughput Dt reduction in the thickness of the crop stream, m tc thickness of the incoming crop stream, m u1, u2 speed of crop mass before and after impact in threshing cylinder, m/s ub peripheral speed of the blower fan, m/s

ucb

11

peripheral velocity of the knife driving pulley, m/s ucy peripheral speed of threshing cylinder, m/s ui peripheral velocity of the ith rotating component, m/s ur reel peripheral velocity, m/s vf forward velocity of the machine, km/h vk knife velocity, m/s vmf average speed of flow of material through the combine harvester, m/s vsw average speed of the straw movement over the straw walker, m/s W load due to crop mass flowing within a pitch length, kN Wgc load carried by the grain conveyor, kN/s Wr, Wf vertical load borne by rear and front wheel, respectively, kN Wt weight of grain in the grain tank, kN w cutting width of the machine, m wc width of the cylinder, m xcg distance of the centre of gravity of the combine harvester ahead of the rear axle, m Z number of reel bat d deflection of the crop stem due to action of the reel bat, m y angle made by a reel bat with a horizontal plane passing through the reel centre, rad l reel speed index ms coefficient of sliding friction between the crop mass and the auger surface mc coefficient of friction of the crop mass over the concave surface mdh dynamic coefficient of friction between knife and horizontal bearing surface mdv dynamic coefficient of friction between knife and vertical bearing surface msg coefficient of sliding friction between the grain mass and the auger surface r linear density of the crop stem, g/m Dr increase in density of the entrapped crop mass, kg/m3 ri bulk density of the entrapped crop in the cylinder concave clearance, kg/m3 ro bulk density of the incoming crop stream, kg/ m3 j angle made by the crank, rad ts shear strength of the crop stem, kN/m2 c; c1 angles made by an imaginary plane oriented in the path of whole crop and grain movement, respectively, passing through the bottom and top of the auger, rad or angular velocity of the reel, rad/s

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D.C. BARUAH; B.S. PANESAR

limited application due to the fact that these studies do not consider the harvesting and threshing phenomenon. Some models are available for the estimation of energy for harvesting and threshing operations. These are average unit energy or unit power requirement models (Singh et al., 1997; Michael & Ojha, 1996; Kepner et al., 1987; Quick, 1998). These are very simple models and independent of system description and therefore, are not functions of system parameters. Thus, these models have very limited application. Klenin et al. (1985) made an attempt to estimate energy requirements of harvesting machines using multiple linear model of two system parameters, i.e. weight of the machine and crop throughput. This model is empirical and thus had limited application. The combine harvester has been widely used for harvesting and threshing of grain crops and its population has been increased in India in recent time (Singh, 1999). Development of the energy requirement models of the machine components of combine harvester will enable to identify appropriate design parameters and, thus, the optimisation of these parameters will ensure energy saving. Such models will also help to assess the energy demand of different machine components and the machine as a whole. The choosing of optimal harvesting timing pertaining to specific soil or crop parameter will also be easier if such parameters are identified and described in the models. Therefore, the present investigation has been undertaken to identify different system parameters effecting the energy requirements of the processes of combine harvester components and then develop energy models.

2. Methods of model development A combine harvester machine consists of several sub units or functional components. During the working of the machine, the components interact with each other, crop and/or terrain to achieve the main goal of harvesting and/or threshing. Energy expenditure takes place because of such interaction. The power is supplied from the prime mover using power transmission devices to meet energy demand of these components. Some energy is lost in the transmission device and other parts to overcome bearing friction of the respective components. The present investigation assumes that the power expenditure at transmission devices is independent of the execution of the intended function and therefore, independent of the system parameters. The components of a combine harvester are the reel, cutter bar, platform conveyor, feeder conveyor, threshing cylinder, straw walker, cleaning sieve, blower, grain conveyors, tailings feeding unit and traction device. The power expenditure

in bearing friction is a common feature for all the components and therefore, separately modelled. The requirement of power for performing the intended functions by these machine components including bearing friction have been modelled using the physical laws governing their functions and differentiating their working into distinct processes as discussed below. 2.1. Reel The reel in a combine harvester machine delivers the stalks to the cutting mechanism, holds them upright during cutting and pushes the cut crop towards the platform conveyor. The power input into the shaft of the reel is spent in pushing the crop stem and in overcoming air friction. These two processes are modelled as given below. 2.1.1. Power required for deflecting the crop In an ideal condition, the top of the crop stem experiences a deflection d in m due to action of the reel bat as shown in Fig. 1. The stem resists the deflection by generating a resisting force Fr. The following classical formula for the deflection of cantilever beam is used to estimate Fr in kN: 3nEId (1) h3 where: E is the modulus of elasticity of the crop stem in kPa; I is the geometrical moment of inertia of the transverse section of the crop stem in m4; h is the height of the crop stem in m; and n is the number of crop stems deflected by a reel bat. The reel bat undergoes a complex cycloid motion resulting from translatory motion of the harvesting machine and a rotary motion of the reel with respect to the machine. The number of crop stems deflected by a reel bat is governed by crop stand density, travel speed Fr ¼

Fr




h

Fig. 1. Action of a reel bat on crop stem; h, stem height; d; stem deflection and Fr, resisting force against deflection of crop stem

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ENERGY INPUT FOR A COMBINE HARVESTER

of the machine, angular speed of the reel and geometry of the reel. From the operational geometry of the reel, n can be expressed as given below: 5pC d wvf n¼ 9or Z

l¼ (2)

where: Cd is the crop stand density in number/m2; w is the cutting width of the machine in m; vf is the forward velocity of the machine in km/h; or is the angular velocity of the reel in rad/s and Z is the number of reel bats. The deflection of the stalks varies depending on their positions. As the resistance of stalks against bending is linearly proportional to deflection, the mean value of the deflection is considered as estimated below: 0 þ pz pz ¼ (3) 2 2 where pz is the pitch of the reel bat in m. The pitch of the reel bat, which is function of the travel speed of the machine, angular speed of the reel and number of reel bat, is expressed as given below: d¼

pz ¼

5pvf 9or Z

(4)

The tangential force Ftr in kN experienced by the reel bat due to crop stem deflection can be expressed as given below: Fr (5) sin y The angle y is the angle made by a reel bat with a horizontal plane passing through the reel centre. Similar to the variation of the deflection d, angle y also varies. However, from geometry it can be shown that, the angle y corresponding to the assumed average deflection is function of the position of the reel centre with respect to the ground surface and cutter bar, radius of the reel, crop height and reel speed index. Using the geometry of the reel, functional relationship can be obtained for y relating the above parameters. Now, the power requirement by the reel for bending crop stems is obtained by multiplying Ftr with reel peripheral velocity ur. Thus, combining Eqns (1)–(5) and simplifying power requirement by the reel for bending crop stems is obtained as given below: F tr ¼

5p2 EIr2 wC d vf 1 (6) sin y 3h3 Z 2 l where: Pbr is power requirement by the reel for bending crop stems in kW; r is the radius of the reel bat in m; Z is the number of reel bats; l is the reel speed index; and y is an angle made by the reel bat with respect to horizontal plane in radian. The angle y is function of reel geometry and crop height. The reel speed index l is the ratio of Pbr ¼

peripheral speed of reel to the forward travel speed of the combine harvester and is given by 18ror 5vf

(6a)

The crop feed rate or throughput can be expressed in terms of crop stand density, cutting width of the machine, travel speed of the machine, and other crop and operational parameters as given below F ¼ wC d vf rðh
hc Þ  10
3

(7)

where: hc is the height of cut in m; r is the linear density of the crop stem in g/m; and F is the crop feed rate in Mg/h. Finally, incorporating Eqn (7) into Eqn (6), the power requirements by the reel for bending crop stems is expressed as below:   5  103 p2 EIr2 1 Pbr ¼ F (8) 3rðh
hc Þh3 Z 2 l sin y

2.1.2. Power required to overcome air resistance In addition to bending the crop stem, power is also spent while overcoming the air resistance. Klenin et al. (1985) stated that windage loss is proportional to the cube of the peripheral speed. The following relationship is used to estimate the power required to overcome air resistance using a proportionate coefficient: Pwr ¼ kwr ður Þ3

(9)

Pwr

where: is the power loss due to windage in kW; ur is the peripheral speed of the reel in m/s; kwr is the coefficient used to estimate the power requirement due to air resistance. 2.1.3. Total power requirement for working of the reel The total power requirement for the operation of reel Pr in kW is the sum total of the power required for overcoming resistance against stem bending and air resistance as given below: Pr ¼ kwr ður Þ3 þ kbr F

(10) kbr

where the bending energy coefficient for the reel is given by   5  103 p2 EIr2 1 kbr ¼ (10a) 3rðh
hc Þh3 Z2 l sin y

2.2. Cutter bar Crop stems are first deflected and then sheared off in cutter bar. Apart from the energy expenditure for

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D.C. BARUAH; B.S. PANESAR

deflecting and shearing the crop stem, energy is also required to overcome friction at sliding surfaces of the reciprocating knife. The power expenditure for all three processes are discussed below.

2.2.1. Power required for stalk deflection The component of the stalk deflection along the path of reciprocation of the knife is considered for modelling the power requirement for this phenomenon. The deflection of an individual crop stem due to knife movement is schematically shown in Fig. 2. Considering a crop stem as a simply supported beam where bottom end is supported by ground surface and the top end is by a reel bat, the resistance force against bending Fkd in kN is estimated using the following classical formula (Gaylord & Gaylord, 1968) by F kd ¼

12EIh3 d i ð4h
hc Þðh
hc Þ2 h3c

(11)

eb ¼

3EIh3 s2 ð4h
hc Þðh
hc Þ2 h3c

(12)

where s is the stroke length in m. The average power required by knife section for stalk deflection is the product of eb and the number of stalk deflected per second. The number of stalks deflected per second ns is estimated by 5 wC d vf (13) 18 Therefore, the average power required for stalk deflection is obtained from Eqns (12), (13) and finally by the substitution of Eqn (7) as given below: ns ¼

Pdcb ¼

5  103 EIh3 s2 F 6rð4h
hc Þðh
hc Þ3 h3c

(14)

or Pdcb ¼ kdcb F

where: di is the deflection of the plant stem in m. The magnitude of deflection depends on the location of the stem within the stroke length of the cutter bar. Half of the stroke length is considered as an approximate estimate of deflection. If a stem offers resistance for an average distance of half of stroke length, then the energy expended to bend a single stem eb in kJ can be

(15)

where Pdcb is the power expended for stalk deflection in kW and kdcb is the deflection energy coefficient for the cutter bar given by kdcb ¼

5  103 EIh3 s2 6rð4h
hc Þðh
hc Þ3 h3c

(15a)

2.2.2. Power required for shearing of stem Power required for shearing of stem is estimated from the average shearing force during the stroke. Considering that the stems are sheared off at a linearly increasing rate from the beginning of the stroke to the end of the stroke, the average shearing resistance per unit length of stroke is expressed by the following relationship:

Bat

Crop stem

estimated by

h−hc

Knife

hc

ts Ac wC d f (16) s where: Fs is the average shearing resistance per unit length of stroke in kN/m; ts is the shear strength of the crop stem in kN/m2; Ac is the cross-sectional area of crop stem in m2 and f is the forward movement of the machine per stroke of the knife in m. Now, the average power per unit stroke length of the knife to overcome the shear resistance can be obtained by multiplying Fs with knife velocity. The knife velocity vk in m/s for a reciprocating cutter bar can be expressed with the help of the following expression: Fs ¼

vk ¼ ucb sin j di Fig. 2. Deflection of a plant stalk due to knife movement; h, stem height; hc, height of cut; di, deflection of crop stem

(17)

where, ucb is the peripheral velocity of the knife driving pulley in m/s and j is the angle made by the crank in radian.

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ENERGY INPUT FOR A COMBINE HARVESTER

Substituting the expression for knife velocity and then integrating the average power so obtained over the stroke length and finally simplifying the results of integration, the total power Pscb in kW required by the knife for shearing the stems are obtained as given below:

Crop pressure Reciprocating knife

Pscb ¼

5p  10 ts Ac rc F 36rðh
hc Þ

(18)

or Pscb ¼ kscb F

Fv

(19)

where, kscb is the shear energy coefficient for the cutter bar, given by kscb ¼

5p  103 ts Ac rc 36rðh
hc Þ

(19a)

and rc is the radius of the knife driving crank in m. 2.2.3. Power required for overcoming friction at sliding surfaces The knife sections slide over two surfaces during its reciprocating motion. Power is spent due to friction at these surfaces. The instantaneous power required to overcome friction is estimated using the following relationship: P0fcb ¼ ðF h þ F v Þ  jvk j

where: is the instantaneous power required to overcome friction at the sliding bearing surfaces in kW; Fh and Fv are the frictional resistances over horizontal and vertical bearing surfaces, respectively, in kN and vk is the knife velocity in m/s (Figs. 3 and 4). Using the law of friction, Fh and Fv can be obtained from the normal reaction and the dynamic coefficient of friction between the knife and the sliding bearing surfaces. The normal reaction at the horizontal sliding surface arises due to self-weight of the knife and weight of the

r

mcb + mk Reciprocating knife vK Fh

Rv Fig. 4. Frictional forces acting on vertical sliding surface of reciprocating knife (top view of knife section); Fv, resistance over vertical bearing surface; vk, knife velocity; Rv, reaction force against crop pressure

crop mass supported by the reciprocating knife. If Ar in m2 is the projected area of the reciprocated portion of the knife and At in m2 is the total projected area of the cutter bar over which crop mass flows then the crop mass supported by the reciprocating knife can be expressed as given below:

(20)

P0fcb

Bearing surface

Bearing surface

vk

3

vK Fh

Fig. 3. Frictional forces acting on horizontal sliding surface of reciprocating knife (front view of knife section); Fh, resistance over horizontal bearing surface; vk, knife velocity; mrcb ; crop mass supported by reciprocating portion of cutter bar; mk, mass of reciprocating knife

mrcb ¼

10
3 Ar l k F vf At

(21)

where: mrcb is the mass of the crop mass supported by the reciprocating portion of the cutter bar in kg and lk is the length of the cutter bar section in m. Now, if mk is the mass of the reciprocating knife in kg, then Fh can be expressed as below:   10
3 Ar l k F h ¼ mdh g mk þ F vf A t

(22)

where: g is the gravitational acceleration in m2/s; and mdh is the dynamic coefficient of friction between knife and horizontal bearing surface. Similarly, the frictional resistance Fv over the vertical bearing surface is the product of dynamic coefficient of friction and the normal reaction to the vertical bearing surface. The normal reaction to the vertical sliding surface for a combine harvester is estimated from the crop pressure exerted by the reel. Combining Eqns (1)–(4), (6a) and (7) the pressure exerted by reel is used to estimate the normal reaction Rv in kN to vertical sliding surface as given below:  Rv ¼

 5  103 p2 EIr2 F 3rðh
hc Þh3 Z 2 l ur

(23)

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The frictional resistance on the vertical bearing surface is obtained as given below: F v ¼ mdv Rv ¼

5  103 mdv p2 EIr2 F 3rðh
hc Þh3 Z 2 l ur

(24)

where, mdv is the dynamic coefficient of friction between the knife and the vertical bearing surface. Incorporating the Fh, Fv and vk into Eqn (20) and then integrating in the interval of 0pjpp=2; the average power required to overcome frictional resistance can be obtained as given below: Pfcb

2 2 ¼ mdh mk gucb þ p 4

10
3 mdh Ar l k g pAt

F pc ¼

ucb F vf

pEIr2 mdv

10 ucb þ F 3 2 3 h ðh
hc ÞZ rl ur

ð25Þ

or, Pfcb ¼ kfcb1 ucb þ kfcb2

ucb F þ kfcb3 F vf

(26)

where the three coefficients for the energy components kfcb1 ; kfcb2 and kfcb3 are given by 2 d m mk g p h

(26a)

kfcb2 ¼

2  10
3 mdh Ar l k g pAt

(26b)

kfcb3 ¼

104 mdv pEIr2 ucb 3 h3 ðh
hc ÞZ2 rl ur

(26c)

kfcb1 ¼

and

Pcb ¼ ðkdcb þ kscb þ

þ

kfcb2

ucb F þ kfcb1 ucb vf

la s ðm W cos cÞ lp

(28)

where: W is the load due to crop mass flowing within a pitch length in kN; c is the angle made by an imaginary plane oriented in the path of material movement which passes through the bottom and top of the platform auger in radian; la is the length of the auger section in m; lp is the length of the auger pitch in m; and ms is the coefficient of sliding friction between the crop mass and the auger surface. The pitch of the auger governs the value of the angle c where cos c is always positive and less than one. The load on the platform conveyor is due to the crop mass entering into the machine. Further, the load at any point is proportional to distance from the outer end where the load is zero. The expression for W in kN can be obtained from the average value of loading rate as given below: W¼

2.2.4. Total power requirement for cutter bar The power requirements of the cutter bar is the sum total of the power requirements of stalk deflection, stalk shearing and sliding friction as given by Eqns (15), (19) and (26), respectively. Therefore, adding the power requirements for these three processes, the power requirements of the cutter bar Pcb in kW can be written as given below: kfcb3 ÞF

2.3.1. Power required for conveying crop mass to the centre of the auger Ignoring the curvature of the auger, the movement of crop mass within a pitch length can be visualised as the movement over a sliding surface (Fig. 5). During half of its pitch length the crop mass undergoes upward movement while in the other half it undergoes downward movement. The total resistance against the movement of crop mass in the auger Fpc in kN can be obtained using the law of mechanics and physics as given below:

gl a F 7200wnp

(29)

la 2

Spike section lp

Auger section

lp

(a)

W cos  2

(27)

W sin  2

2.3. Platform conveyor



s W cos  s W cos  2 2 W cos  2 W 2

W 2



W sin  2

(b)

On a grain combine harvester, the platform conveyor gathers the crop mass from the sides to the centre of the platform. The platform conveyor consists of left and right augers with open flight and central sections with spikes. Power is needed to convey the crop mass from both sides of the platform to the centre and also to lift the crop mass by the central spikes.

Fig. 5. Platform auger conveyor: (a) three sections of a platform conveyor; la, length of auger section; lp, pitch length of auger; (b) movement of crop mass within a pitch length and forces acting on it; W, vertical load due to crop mass within a pitch length; ms ; coefficient of sliding friction between the crop mass and the auger surface; c; angle made by an imaginary plane oriented in the path of material movement which passes through the bottom and top of the platform conveyor

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ENERGY INPUT FOR A COMBINE HARVESTER

where: np is the rotational speed of the conveyor s
1. Now substituting W from Eqn (29) into Eqn (28) and then multiplying the resistance Fpc by the velocity of the crop mass and finally simplifying, the power Pcpc in kW required for material conveying is obtained as given below:   gðl a Þ2 ms Pcpc ¼ cos c F (30) 7200w

Driving pulley Feeder conveyor Components of the gravitational force on the crop mass

hf

or, Pcpc ¼ kcpc F

(31)

where the crop conveying energy component coefficient kcpc is given by   gðl a Þ2 ms cos c (31a) kcpc ¼ 7200w

2.3.2. Power required for lifting the material through the central spike section The central spiked portion of the platform conveyor lifts the crop mass from the platform to the feeder conveyor. If the effective height of lift is hal in m and F is the crop throughput in Mg/h, then power required to lift the material by the spike section Plpc in kW is given by the following expression: Plpc ¼

ghal F 3600

(32)

or Plpc ¼ klpc F

(33)

where the crop lifting energy component coefficient klpc is given by klpc ¼

ghal 3600

(33a)

2.3.3. Total power requirements for operation of platform conveyor The total power requirement of the platform conveyor Ppc in kW for handling the crop mass is the sum of Pcpc and Plpc as given below Ppc ¼ ðkcpc þ klpc ÞF

(34)

2.4. Feeder conveyor The crop mass delivered by platform conveyor is transferred to threshing cylinder by feeder conveyor. Generally, power is consumed for conveying the crop mass by a slat type of endless chain. A free body

Fig. 6. Crop mass passing through feeder conveyor; hf, height of feeder conveyor

diagram of the feeder conveyor is shown in the Fig. 6. The model used to estimate the power required to convey the crop mass Pfc in kW is based on potential energy required and is given below: Pfc ¼

ghf F 3600

(35)

or Pfc ¼ klfc F

(36)

where: hf is the height of the feeder conveyor in m, and the crop lifting energy coefficient for the feeder conveyor is given by klfc ¼

ghf 3600

(36a)

2.5. Threshing cylinder The shaft of the rotating cylinder is powered to perform threshing function. The power is expended to thresh the grain and also to overcome air resistance. The procedure of the model development for threshing cylinder is discussed below. 2.5.1. Power for threshing the crop The free body diagram of the threshing mechanism of a cross flow thresher is shown in Fig. 7. The flow of crop mass is maintained through the clearance between cylinder and concave. The revolving cylinder imparts impact force required to dislodge the grain from nongrain portion. The internal resistance amongst the plants of the flowing crop mass and frictional resistance at the concave surface resists the movement of the crop mass. In addition, the thresher also compresses the crop

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ucy Cylinder

Crop mass Ftt Concave

where: cc is the cylinder concave clearance in m; tc is the thickness of the incoming crop stream in m; ro is the bulk density of the incoming crop stream in kg/m3; and wc is the width of the threshing cylinder in m. The resistance due to crop compression is estimated considering the crop mass as an elastic body undergoing changes in volume due to compression (Mohsenin, 1980). If Dr is the increase in density in kg/m3 due to compression of the entrapped crop mass between cylinder and concave, the resistive force experienced by the cylinder at its periphery is estimated using the following relationship:

Fig. 7. Cylinder-concave arrangement of a cross flow type threshing cylinder; ucy, peripheral speed of threshing cylinder; Ftt, tangential force on threshing cylinder periphery

masses. Thus, the cylinder needs to be powered to provide the tangential force at cylinder periphery which comprises the forces of (i) impact of threshing member on crop mass, (ii) compression of crop mass and (iii) resistance against movement of crop mass. The following expression is written for estimation of the power Ptcy in kW to overcome tangential force: Ptcy ¼ F tt ucy

(37)

where: Ftt is the tangential force in kN; and ucy is the peripheral speed of threshing cylinder in m/s. The tangential force Ftt is the sum of the three component forces due to impact, crop compression and crop movement resistances, respectively, as given by F tt ¼ f t1 þ f t2 þ f t3

(38)

The tangential force due to impact action ft1 in kN can be obtained from the principle of conservation of momentum and is given below f t1 ¼

5 ðu2
u1 ÞF 18

(39)

where u1 and u2 are speed of the crop mass before and after impact, respectively, in m/s. The speeds of crop mass before and after impact are estimated based on flow rate, bulk density and thickness of the crop stream. For simplification, the change in density of the crop mass due to impact is ignored and maintenance of the increased speed due to reduction of the thickness of flow path is assumed to be the only result of the impact. With these assumptions Eqn (39) is modified as given below:   25 1 1 f t1 ¼
(40) F2 324wc ro cc tc

f t2 ¼ Kcc wc

Dr ri

(41)

where: K is the elasticity of the crop mass in kPa; wc is the width of the cylinder in m; ri is the bulk density of the entrapped crop stream in kg/m3. The resistance against the movement of the crop mass ft3 in kN is estimated based on the frictional resistance over the concave surface with an area Acc in m2. The normal reaction to the concave surface is the result of the compression pressure and force of gravity on the crop mass occupying the clearance volume. The mass of the entrapped crop is estimated using density ri ; and clearance volume. Incorporating the different parameters the resistance against the movement of the crop mass ft3 is expressed as given below:   Dr f t3 ¼ K þ gri cc Acc mc (42) ri where: Acc is the effective area of concave in m2; mc is the coefficient of friction of the crop mass over the concave surface. Combining Eqns (38), (40)–(42) the tangential force Ftt can be written as given below: F tt ¼

25Dt Dr F2 þ K cc w c 324wc ro cc tc ri Dr þK Acc mc þ gri cc Acc mc ri

ð43Þ

where Dt is the reduction of the thickness of the crop stream as it enters the cylinder concave clearance, m. Now, substituting Eqn (43) into Eqn (37), the power required to thresh can be written as  25Dt Dr Ptcy ¼ F 2 ucy þ K cc wc 324wc ro cc tc ri  Dr þK Acc mc þ gri cc Acc mc ucy ð44Þ ri

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or t2 2 Ptcy ¼ kt1 cy ucy F þ k cy ucy

where the threshing energy coefficient threshing cylinder is given by: kt1 cy ¼ kt2 cy ¼ K

kt1 cy

(45) and

kt2 cy

25Dt 324wc r0 cc tc

Dr Dr cc wc þ K Acc mc þ gri cc Acc mc ri ri

oscillation esw is estimated using the following relationship. esw ¼

for the

(45a)

(45b)

Pwcy ¼ kwcy ðucy Þ3

(46)

Psw ¼ kasw F

(47)

(50)

(51)

where dsw is the rearward straw displacement per oscillation over the straw walker expressed by the ratio of vsw to fsw, m and kasw is the energy coefficient for straw walker given by kasw ¼

where: is a proportionality coefficient considered to estimate the power requirements to overcome air resistance.

t2 w 3 2 Pcy ¼ kt1 cy ucy F þ k cy ucy þ k cy ðucy Þ

sf l sw hsw g F 3600d sw

or

kwcy

2.5.3. The total power requirement at threshing cylinder The total power requirement Pcy in kW of a threshing cylinder, which is equal to the sum of the power requirements given by Eqns (45) and (46) is as follows.

(49)

where: sf is the ratio of straw mass in the straw walker to throughput; lsw is the length of straw walker in m; hsw is the effective lift of throw of the straw mass in m; and vsw is the average speed of the straw movement over the straw walker in m/s. Now substituting Eqn (49) into Eqn (48): Psw ¼

2.5.2. Power required to overcome air resistance Power required to overcome air resistance depends upon the surface, shape, size and speed of the cylinder and air properties. Simplified proportionate relationship (Klenin et al., 1985) is used to estimate the cylinder power Pwcy in kW required to overcome air resistance as given below:

sf l sw hsw gF 3600vsw

sf l sw hsw g 3600d sw

(51a)

2.7. Blower Power requirement of the blower Pb in kW depends upon the peripheral speed of the fan and fan design parameters. The following relationship (Baumeister & Marks, 1958) is used to estimate blower power requirements: Pb ¼ kwb ðub Þ3

(52)

kwb

2.6. Straw walker Power given to the straw walker driving pulley is utilised to agitate the straw mass by throwing it in a rearward and upward direction. The throwing of the crop mass is achieved by reciprocating motion of the straw walker racks. The average power required at straw walker driving shaft depends upon the design and operational parameters of the straw walker such as the length of the racks, crank throw, the load of the crop mass over the straw walker at any time and speed of operation. Power requirement for operation of straw walker Psw in kW is estimated using the following relationship: Psw ¼ esw f sw

(48)

where: esw is the energy expended per oscillation and is directly proportional to crop throughput F, lift of oscillation; and fsw is the frequency of oscillation of straw walker in s
1. The energy expenditure per

is the coefficient of blower power requirement where: involving design parameters of the blower and ub is the peripheral speed of the fan in m/s. 2.8. Sieves A set of sieves ensures cleaning of the grains from the non-grain part with the help of mechanical agitation. The mechanical agitation is achieved by a special drive arrangement given from the sieve drive pulley. The power requirement for mechanical agitation depends on crop and machine factors. The rate of flow of material through the sieve, which depends upon the feed rate of the crop and its condition, effects the power requirements. Considering the set of sieves as an equivalent single sieve, a relationship similar to the straw walker [Eqn (50)] is used to estimate power requirements by the sieves Ps in kW as given below. Ps ¼ kas F

(53)

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where: kas is the coefficient of power requirements by the cleaning sieves given by kas ¼

c f l s hs g 3600d s

(53a)

where: cf is the ratio of mass agitated by sieves to throughput; ls is the equivalent length of sieves in m; hs is the lift of agitation in m; and ds is the rearward displacement of the crop mass over sieve per oscillation in m.

Generally grain-conveying unit of a combine harvester consists of (i) lower grain conveyor, (ii) grain elevator and (iii) upper grain conveyor. The lower and upper grain conveyors are of screw auger type, which delivers the grain to the grain elevator and grain tank, respectively. A chain- and pad-type grain elevator lifts the grain from the lower grain conveyor to the upper grain conveyor. 2.9.1. Power requirements for auger type (lower and upper) grain conveyor The load carried by grain conveyor can be expressed using the following relationship: gF ¼ 3600ð1 þ S g Þ

ghgc F 3600ð1 þ S g Þ

gl gc msg cos c1 F 3600ð1 þ S g Þ

or Pegc ¼ kegc F

kegc ¼

ghgc 3600ð1 þ S g Þ

Pgc ¼ ðkagc þ kegc ÞF

Pagc ¼ kagc F

(55)

(56)

where the energy coefficient for the grain auger kagc is given by 3600ð1 þ S g Þ

(58a)

(59)

2.10. Tailings feed unit The un-threshed heads are passed through the sieves and these constitute the major portion of the tailings. Tailings are re-directed to the inlet of the threshing cylinder for re-threshing using a similar conveying unit as used for grain conveyor. The working of the threshing cylinder and condition of the crop affect the loading rate of the tailings conveyor. Under normal working condition, loading rate may be assumed to be proportional to the feed rate and a similar model as used for grain conveyor unit can be applied to give the power requirement Ptc in kW for the tailings feed unit: Ptc ¼ ðkatc þ ketc ÞF

kagc ¼

(58)

2.9.3. Total power requirements of grain conveyor Now adding the power requirements given by Eqns (56) and (58), the total power requirements Pgc in kW of the grain conveyor units can be obtained as given below

or

gl gc msg

(57)

(54)

where, Wgc is the load carried by the grain conveyor in kN/s and Sg is the ratio of non-grain to grain. The power requirement model developed for the platform auger is suitably modified for the lower and upper grain conveyors using the loading rate given by Eqn (54) to obtain the power requirement for the grain conveyor auger Pagc in kW: Pagc ¼

Pegc ¼

where the energy coefficient kegc for the elevator is given by

2.9. Grain-conveying unit

W gc

2.9.2. Power requirements of the elevator section If hgc is the effective lift height of grain conveyor in m, then using Eqn (54), the following relationship can be used to model the power requirements Pegc in kW of the elevator section:

cos c1

and: msg is the coefficient of sliding friction between the grain mass and the auger surface; c1 is the angle made by an imaginary plane oriented in the path of material movement which passes through the lower and top of the auger conveyor in radian; and lgc is the length of the auger section in m.

(60)

where: katc and ketc are the proportionality coefficients. 2.11. Traction unit The traction unit of a combine harvester consists of two pairs of pneumatic tyres—one pair on the frontdriven wheels and the other pair on the steered wheels. The power expenditure model for propulsion or traction developed in the present study assumes the combine harvester travelling at uniform velocity on level ground. Thus, power is required to overcome motion resistance experienced by these wheels. Size of the driven wheels

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are larger than the size of the steered wheels and therefore, motion resistances for both the wheels have been separately estimated and added together to obtain the total motion resistance of the machine. The relationship given in ASAE Data, D497 3 (Anonymous, 1996) is used to estimate motion resistance Rm in kN as given below: Rm ¼ Rmf þ Rmr 1 2 1 2 ¼ ðW f Þ2 þ ðW r Þ2 C i bf d f C i br d r þ 0 04ðW f þ W r Þ

ð61Þ

where: Rmr and Rmf are the motion resistances to rear and front wheel, respectively, in kN; Ci is the soil cone penetration resistance in kPa; br and bf are the widths of rear and front tyre section, respectively, in m; dr and df are the diameters of the rear and front wheel, respectively, in m; Wr and Wf are the vertical loads borne by rear and front wheel, respectively, in kN. The relationship incorporates the parameters which affect the motion resistance, viz. diameter of the wheels, distribution of the vertical load in the wheels and soil cone penetration resistance. The vertical loads supported by the wheels consist of self-weight of the machine, weight of crop mass passing over the machine and weight of the grain in the grain tank. The distribution of the vertical loads amongst the wheels is expressed in terms of the position of the centre of gravity of the machine and the wheelbase. The weight of the crop mass passing over the machine is expressed in terms of the length of the material flow path lmf in m, the average speed of flow vmf in m/s and the crop feed rate F. Again, in a combine harvester, weight of grain in the grain tank varies—increasing from zero to a maximum value given by the capacity of the tank. An average value of the weight of the grain in the tank is assumed and added for calculating the vertical wheel load Wt in kN. Incorporating these parameters and then simplifying, Eqn (61) is written as given below: Rm ¼ amr ðW t Þ2 þ bmr W t F þ

bmr F 2 þ 0 04W t þ cmr F 2 (62)

where the motion resistance coefficients amr, bmr, and cmr are given by: amr ¼

1 2x2cg 1 2ðb
xcg Þ2 þ bbf d f C i bbr d r C i

(62a)

5  10
3 gamr l mf 9vmf

(62b)

bmr ¼

cmr ¼

10
4 gl mf 9vmf

(62c)

and: b is the distance between front and rear wheel in m; and xcg is the distance of the centre of gravity of the combine harvester ahead of the rear axle in m. The harvesting machine also experiences the resistance due to crop pressure from the front. The longitudinal pressure experienced by the cutter bar given by Eqn (23) is used to estimate the resistance due to crop pressure. The total resistance against propulsion of combine harvester is the sum total of motion resistance [Eqn (62)] and crop resistance [Eqn (23)]. Thus, multiplying the sum of the resistances with the forward travel speed and then simplifying, the power requirement for propulsion Pt in kW is obtained by as given below: Pt ¼

5 5 amr ðW t Þ2 vf þ bmr W t Fvf 18 18 5 1 bmr F 2 vf þ W t vf þ 36 90   5 5  103 p2 EIr2 Fvf ur cmr þ þ 18 3rðh
hc Þh3 Z2 l ur

ð63Þ

2.12. Bearing friction The power from the prime mover is transmitted to the rotating shafts of the respective components. Power expenditure takes place to overcome friction at the shaft bearings. Considering a uniform phenomenon of power expenditure at the bearings, the flowing relationship, proposed by Klenin et al. (1985) is written to estimate this component of power expenditure. Pbearing ¼ kibearing ui

(64)

kibearing

where: is the proportionality coefficient for bearing friction, ui is the peripheral velocity of the ith component in m/s and Pbearing is the power expenditure due to bearing friction at the ith component, in kW.

3. Discussion The experimental works conducted by earlier researchers (Burrough, 1954; Arnold & Lake, 1964) indicated that different units of a combine harvester, viz. threshing cylinder, cutter bar, separating–cleaning and reel consumed different amounts of power. It was also observed that threshing cylinder was the highest

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D.C. BARUAH; B.S. PANESAR

power-consuming unit (requiring up to 50% of the total power) amongst the working units of a combine harvester followed by traction, separating–cleaning, cutting, reel and conveying (Burrough, 1954). The effect of certain system parameters on power requirements was also investigated by these studies. Although the results of such tests are still useful indicator of power requirements by different processes of a combine harvester, neither all of the parameters involved in the processes nor their interactions were fully explained by such studies. In the present study, power requirement models have been developed conceptualising 11 different processes concerning 12 machine components of the combine harvester. Mechanistic models have been developed for nine processes, identifying system parameters relating to crop, machine and soil. Proportionate relationships have been considered for the remaining two processes, viz., air resistance on the revolving member and bearing friction. The models of the different processes are discussed below in order of their power share, as indicated by earlier researchers, starting with the highest power-consuming process.

3.1. Threshing the crop by threshing cylinder Experiments conducted by earlier research workers observed that not only crop throughput but also the way in which the crop is fed has pronounced influence on energy expenditure of threshing cylinder (Pedersen, 1963; Dolling, 1957). In addition to these, type of crop was also found to affect the energy expenditure of threshing cylinder. The parameters identified in the mechanistic model of threshing process, viz. operational parameters (throughput F and peripheral speed of threshing cylinder ucy), crop parameters (bulk modulus of elasticity K, mass density r and coefficient of sliding friction mc ) and parameters involving mode of feeding given by Dt=tc seem to support the above facts. Particularly the findings of Arnold and Lake (1964) that much less power is required to thresh a fast-moving thin stream of crop than a slow-moving thick one is appropriately supported by the presence of the parameters, such as Dt=tc ; Dr=ri in the model of threshing process. A thicker stream would result in a higher reduction of stream thickness Dt associated with increase in Dr and thus cause an increase in the power requirement. The model also indicated that an increase in the cylinder concave clearance area given by wccc would result in a decrease in power requirement. Dolling (1957) observed that head first feeding took more power than parallel feeding of the crop stem into the cylinder. The presence of the longitudinal fibres in the crop stem would result in a higher value for K on

axial loading than on parallel loading. Thus, the appearance of K in the model of the threshing process supports Dolling’s observation. However, no relevant literature could be consulted on the variation of the parameter K with changes in the loading mode. The model of the threshing process also indicated that for a given throughput F, the power requirement linearly varies with the peripheral speed of threshing cylinder ucy, which is supported by the experimental work of Arnold and Lake (1964). Another observation of Arnold and Lake, that increasing the length of concave increased the power requirement for threshing is also supported by the parameter Acc appearing in the model. From the above discussion it is seen that although the model has not been validated through experiments, the various parameters identified in the model of the threshing process are in line with the findings of earlier research works. The sliding friction mc and bulk modulus of elasticity K are dependent on crop moisture content. The moisture content on the other hand is a function of crop maturity. Thus, scheduling harvesting operation to achieve minimum values of mc and K seems to reduce the power consumption for threshing. However, the knowledge of the frictional and elastic behaviour of the crop mass with changing moisture content vis-a`-vis maturity will be a pre-requisite for such scheduling.

3.2. Propulsion of the combine harvester The ground conditions, wheel size and total weight supported by wheels influence the power consumption for propulsion of a combine harvester. This has been observed in earlier experimental works (Burrough, 1954; Spokas & Lideikis, 1996) and also reflected by the model developed for power requirement of traction unit in the present study. The power requirement is a quadratic function of the total weight Wt. Thus, a lighter machine will be useful in cutting down the energy required for propulsion provided all the functionally required components are accommodated. Again, a larger grain tank and/or delay in unloading will also increase the power requirements for propulsion of the combine harvester as Wt includes the weight of grain in the tank. The model may be a useful tool to decide the size of the grain tank vis-a`-vis unloading frequency of grain on the basis of optimal energy expenditure for traction. The value of cone penetration resistance Ci appearing in the model reflects the ground condition. Similar to the threshing operation, scheduling of harvesting time to avoid poor soil conditions may lead to a saving of

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energy. However, such decisions should be based on the comprehensive economic analysis taking into consideration of the loss of grain due to delay (or early) harvesting. Crop loss models are already available and the present model of propulsion power for combine harvester may be a useful tool for assessment of variation of power requirements due to variation of ground conditions. 3.3. Power required for separation and cleaning by straw walker and sieve Burrough (1954) observed in his experiment that proportion of power requirements for the processes of separation and cleaning of grain from the non-grain material in a combine harvester was more than the cutting process under all throughputs and for both soya bean and wheat crops. Separating and cleaning involve three components, viz. straw walker, sieve and blower. Burrough’s work, however, did not give separate accounts for these three components. The working of the straw walkers and the sieves are similar and therefore, separating processes by these two components are modelled using the similar mechanistic models. The design parameters appearing in the power requirement models of straw walker and sieve, viz. lengths lsw, ls; heights of throw hsw, hs and rearward displacements per throw dsw, ds are decided by the functional requirements of these units. However, the non-grain to throughput ratio over the straw walker and sieve sf and cf, respectively, are governed by crop and operating conditions. It appears from the models that any effort to reduce the non-grain to grain ratio would reduce the power requirements for separation and cleaning. 3.4. Power required due to deflection, shearing and frictional resistance at cutter bar Research work on the power requirements of mower cutter bar conducted by Elfes (1954) differentiated the cutting power from the inertia and friction power, stating that out of 1 90 kW of the power take-off (PTO) power spent for mowing, only 0 63 kW was required for cutting, while remaining 1 27 kW was consumed by inertia and friction. The action of mower harvesting is similar to that of grain harvesting and bending of crop stems occur during cutting. However, Elfes did not show any account for the process of crop bending by the movement of the reciprocating cutter bar in his experimental works. The power requirement models of three processes, viz. bending, shearing and frictional resistance between

23

moving members of the cutter bar identified several system parameters. The model indicated that for a given forward velocity vf and throughput F, the power expenditure at cutter bar due to friction is a linear function of crank speed ucb. The increased power requirement due to increased knife friction has been the observation of earlier research worker (Prince et al., 1958). Self-weight mk of the reciprocating cutter bar is another parameter which appeared in the model. Thus, selection of cutter bar material to reduce self-weight mk as well as to reduce sliding friction mdh and mdv may be useful design considerations to cut down the power expenditure of the cutter bar. Similar to the processes of threshing and propulsion, adjustment of the harvesting schedule to ensure minimum values for E and ts of the crop stem so as to reduce cutter bar power may also be a matter of further investigation, provided the information on variation these parameters with time is obtained. 3.5. Power required to convey the crop mass before threshing The energy models of the platform auger and feeder conveyor indicate that power required for conveying crop mass from header platform to threshing cylinder linearly varies with the crop throughput F. However, no experimental results on the power required for conveying crop mass to threshing cylinder could be consulted. Height of the threshing cylinder above the header platform is a design parameter of the combine harvester. The higher the level of the cylinder, the more will be the power requirement for conveying the crop mass for a given throughput F. The increase in the coefficient of sliding friction of crop mass over the auger surface ms would cause increase in the auger power requirement. The scheduling of harvesting operations to ensure optimum crop moisture content may be a consideration to minimise the power expenditure of the conveyor, as positive correlation of the sliding friction with crop moisture content was observed by many research workers (Blevins & Hansen, 1956; Wieneke, 1956; Dernedde, 1970). 3.6. Power requirement by reel Burrough (1954) found that minor amount of power was required for the operation of the reel which comprises the power at load as well as power at no load, i.e. throughput independent component. The reel power was found to vary linearly with throughput F for a given value of reel peripheral speed while harvesting

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wheat. Neither the slope nor the intercept of the linear relationship was explained by the experimental results. The power requirement model for a reel developed in this study agrees with the experimental results. Moreover, the gradient of the linear relationship has also been explained. The gradient comprises several parameters relating to crop, reel design and operating conditions. The model indicates that the increase in the reel diameter would result increase in power requirements—both at load as well at no load, even if rotational speed is kept constant. From the model, it also appears that increasing the number of bats would reduce the power at load. At constant travel speed, an increase in the peripheral speed would cause a reduction in power requirement, as the value of the reel speed index l; which appears in the denominator of the model, would increase. 3.7. Power required for conveying grain and tailings The working of tailings conveyor is similar to the grain conveyor with a difference in the characteristics of the materials being conveyed. Mechanistic models have been developed for grain conveyor, while transferring of tailings by conveyors, have been modelled using proportionate relationships with katc and ketc as the coefficients. The moist grain with higher sliding friction msg associated with a longer auger section would demand more power for conveying through lower and upper conveyors. Similarly, higher the elevation of the grain tank more would be the power for elevator section. With a given non-grain–grain ratio, an increase in the throughput would necessitate more power for both the auger and elevator section of the grain conveyor. 3.8. Air resistance and bearing friction The revolving members of the combine harvester, viz. threshing cylinder, blower and reel have been considered as fans. The models have been developed considering the power expenditure due to air resistance as functions of the cube of the peripheral speed and using proportionality coefficients kwcy ; kwb and kwr for cylinder, blower and reel, respectively. The parameters involved in these proportionality coefficients are remained undetermined. It is expected that these coefficients are functions of shape, size and the surface conditions of the respective components besides the air pressure around the revolving members. Burrough (1954) revealed the influence of surface condition of the threshing cylinder on power requirement due to air resistance. Investigating the blower power, Burrough (1954) identified static pressure around the fan blade as the air property to influence the

blower power requirement. Higher static pressure reduced the blower power requirement. It was also observed that an increase in crop material over the cleaning shoe resulted in an increase in static pressure and thus reduction of the power requirement. From the well-known fan laws, it can also be said that blade number, shape and size influence the blower power requirements. The proportionality coefficient kibearing used to model the power expenditure due bearing friction also remains undetermined. The design parameters including shape and size of the bearing would influence the coefficient kibearing : 3.9. Utility of the models The models for high-energy processes such as threshing and traction may be used as tools for optimisation of the operating conditions or for optimising design parameters. The models of other processes may also be useful to assess the energy demands of the respective components and design the power transmission elements accordingly. The parameters appearing in the models are the result of mathematical analysis of the processes involving biological and mechanical elements. Accurate evaluation of the biological parameters is itself a subject of investigation. Thus, the prediction accuracies of the power requirement models of different processes of combine harvester developed in this study should be the subject for further study.

4. Conclusion The several system parameters are identified in the models of power requirements by the processes of combine harvester. Most of the models and associated parameters are found to agree with the previous experimental works on power requirement of combine harvester processes. However, the examinations of the predictive accuracy of the models still remain as a matter of future investigation. Selection of optimal harvesting schedule and optimal design parameters with an aim to reduce the energy requirements of combine harvester operation would be the possible uses of the models. It is also anticipated that reduction in the high-energy processes, viz. threshing and traction would give substantial energy savings, whereas, the models of lowenergy processes would enable to select the appropriate elements of power transmission to the respective components based on the forecasted energy demands. Crop-metal sliding friction, elasticity of the crop material, shear strength of the stalk, soil cone penetration resistance, etc. are some of the temporally varying

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parameters appearing in the models which would help scheduling of harvesting operation. The models may also be useful tools for optimisation of the cylinderconcave area, mass of reciprocating knife, capacity of the grain tank, mass of the combine harvester, etc. with an objective of energy reduction. References Anonymous (1996). Agricultural Machinery Management Data. ASAE data D497.3. 2950 Niles Rd., St Joseph, MI 49085-9659, USA Arnold R E; Lake J R (1964). Experiments with rasp bar threshing drum, III power requirement. Journal of Agricultural Engineering Research, 9, 348–355 Baumeister T; Marks L S (eds) (1958). Mechanical Engineering Hand Book. pp 73–74. McGraw-Hill Book Company, New York. Bector V; Singh S (1999). Timeliness loss factor for different operations of major crops in Punjab. Journal of Institution of Engineers of India, 79, 32–35 Blevins F Z; Hansen H J (1956). Analysis of forage harvester design. Agricultural Engineering, 37, 21–27,29 Burrough D E (1954). Power requirements of combine drives. Agricultural Engineering, 35, 15–18 Chattopadhyay P S; Pandey K P (1999). Effect of knife and operational parameters on energy requirements in flail forage harvesting. Journal of Agricultural Engineering Research, 73, 3–12 Dernedde W (1970). Technological properties of grass and their influence on the cutting process. Landbauforschung Voelkenrode, 8, 53–57 Dolling C (1957). The power requirement of combine-harvesters. Landtech. Forsch., 7(2), 33 Elfes L E (1954). Design and development of a high speed mower. Agricultural Engineering, 35, 147–153 Gaylord E H; Gaylord G N (eds) (1968). Structural Engineering Hand Book. pp 26–30. McGraw-Hill Book Company, New York Kepner R A; Bainer R; Barger E L (1987). Principles of Farm Machinery. pp 424–426. CBS Publishers and Distributors, Delhi 110032

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Klenin N I; Popov I F; Sakun V A (1985). Agricultural Machines. pp 280–293, 400–411 and 542–545. Amerind Publishing Co. Pvt. Ltd, New Delhi Lotey J S; Singh C P (1975). Studies on cutting force requirements and shattering losses incurred in harvesting of wheat. Journal of Agricultural Engineering, 12, 10–16 McRandal D M; McNulty P B (1978). Impact cutting behaviour of forage crops: I mathematical models and laboratory tests. Journal of Agricultural Engineering Research, 23, 313–328 McRandal D M; McNulty P B (1980). Mechanical and physical properties of grasses. Transactions of the ASAE, 23, 816–821 Michael A M; Ojha T P (1996). Principles of Agricultural Engineering. pp 284–287. Jain Brothers, New Delhi 110005 Mohsenin N N (1980). Physical Properties of Plant and Animal Materials, pp 90–100. Gordon and Breach Science Publishers, New York Panesar B S (1998). Integrating spatial and temporal models: an energy example. In Agricultural System Modeling and Simulation (Peart R M; Curry R B eds), pp 93–112. Marcel Dekker, Inc., New York Pedersen T T (1963). Power requirements of combine-harvesters. Meddr 7, Afdel. Landbrugsmask., jordbrugstek. Inst., Kbh., 39 Prince R P; Wheeler W C; Fisher D A (1958). Discussion on energy requirements for cutting forage. Agricultural Engineering, 39, 638–639, 652 Quick G R (1998). Global assessment of power thresher for rice. Agricultural Mechanization in Asia Africa and Latin America, 29, 47–54 Singh S; Mittal J P; Verma S R (1997). Energy requirements for production of major crops in India. Agricultural Mechanization in Asia Africa and Latin America, 28, 13–17 Singh G (1999). Relationship between mechanization and productivity in various parts of India. Paper presented during XXXIV Annual Convention Indian Society of Agricultural Engineers, CCSHAU, Hisar, 16–18, December, 1999 Spokas L; Lideikis A (1996). Study of fuel consumption of harvester. Zemes-Ukio-Inzinerija, 28, 27–36 Wieneke F (1956). Coefficient of friction of plants and fibers. Landtechnische Forchung, 5, 146–151