


Chapter 3Rice Threshing and Separation Method
The threshing unit is a key device of combine harvester,which determines the working performance of the other devices. Straw characteristics of movement in the threshing process are an important way to improve threshing performance of combine harvester. The thorough investigation of both grain threshing and grain separating processes is also a crucial consideration for effective structural design and variable optimization of threshing unit. 

3玩1Threshing and Separate Model of Rice Grain

Three types of threshing and separation units have reached common use over the last century of innovation and development of combine harvesters within the agricultural industry. The first is a single or multiple transversely玨arranged threshing cylinder unit. The second is a single or multiple vertically arranged threshing cylinder unit. The third type is the combined structure of transversely玨arranged threshing cylinders and vertical arranged threshing cylinders. The combined threshing and separation structure of single transversely玨arranged threshing cylinders and single vertically玨arranged threshing cylinders was proven suitable for Asian small combine harvesters,due to its simple structure,small size,and flexibility. As of now,the combined threshing and separation structure of single transversely玨arranged threshing cylinders and single vertically玨arranged threshing cylinders is the primary mechanical structure of combine harvesters in the Asian region.


In this book,we attempt to deduce and develop theoretical models of the threshing and separation process of both tangential or longitudinal flow threshing cylinder for the threshing teeth of a knife bar,trapezoidal tooth,spike tooth,rasp bar and rectangular bar. The main structure of the rice crawler combine harvester used is as shown in Figure 3玩1.



Figure 3玩1Rice crawler combine harvester


1玨reel cutting table˙  2玨control panel˙  3玨feeder conveyor˙  4玨tangential flow threshing cylinder (TFC unit)˙  
5玨vibrating and cleaning sieve˙  6玨longitudinal axial flow threshing cylinder (LFC unit)˙  7玨transmission˙  8玨engine˙  
9玨crawler chassis



There are two main categories of threshing and separation modelsㄩ  regression models,which do not describe the threshing and separation process but instead summarize and build statistics of test results˙  and theoretical models,which create assumptions and simplifications of the threshing and separation process,based on a theoretical basis of the threshing and separation mechanism. Regression models are more easily determined,as they are only applicable to specific test apparatus. Theoretical models,conversely,can be used to design several threshing and separation units,but these theoretical models are very rare. Also,though widely accepted,some theoretical models are not completely correct. 





Rice crawler combine harvester was typical in structure,consisting primarily of a reel cutting table,control panel,feeder conveyor,tangential flow threshing cylinder,vibrating and cleaning sieve,longitudinal axial flow threshing cylinder,transmission,engine,and crawler chassis. The TFC unit was laid out horizontally,perpendicular to the longitudinal axial forward direction of the combine harvester. The LFC unit had a longitudinal axial layout,parallel to the longitudinal axial forward direction of the combine harvester. The axis of the LFC unit corresponded to the cross玨section centerline of the TFC unit. The main structure of the TLFC unit is as shown in Figure 3玩2.



Figure 3玩2Combined transverse and axial flow threshing unit


1玨TFC unit˙  2玨tangential flow threshing tooth˙  3玨spiral feed head˙  4玨longitudinal axial flow threshing tooth˙  5玨LFC unit



The diameter of the TFC unit was 490 mm and its length was 1125 mm. The threshing teeth were arranged in a four head spiral,and bar spacing between any two adjacent threshing bars was 55 mm. The height of the threshing tooth was 70 mm. The concave clearance at the entrance was 40 mm and 30 mm at the output concave clearance. The speed of the TFC unit was set to 24玩47 
m﹞s-1. There were four kinds of tangential threshing toothㄩ  the knife bar,rectangular bar,spike tooth,and rasp bar. The four threshing teeth on the TFC unit are as shown in Figure 3玩3.



Figure 3玩3Structural diagram of four threshing tooth TFC unit


(a) Spike tooth˙ (b) Knife bar˙ (c) Rectangular bar˙ (d) Rasp bar



There were four kinds of LFC unit threshing toothㄩ  the trapezoidal tooth,rectangular bar,spike tooth,and rasp bar. The spike tooth on the LFC unit is as shown in Figure 3玩4.



Figure 3玩4Schematic diagram of LFC unit and threshing and separation cell


(a) Spike tooth LFC unit˙ (b) Threshing and separation cell


The diameter of the LFC unit was 500 mm,and its total length was 3390 mm. There were helical blades of 170 mm in length in front of the LFC unit,2740 mm trapezoidal teeth within its center,and a discharge plate of 480 mm in length at the rear of the unit. The coordinate origin (the starting point of grain separation) was a point of 960 mm from the top of the unit. The concave clearance of the LFC unit was 30 mm,and the concave wrap angle was 180～. Six lines of threshing bars were evenly arranged on the circumference of the LFC unit,and the space between any two adjacent threshing bars was 150 mm. The LFC unit speed was 21玩95 m/s.

3玩1玩1Grain threshing and separation model


The threshing and separation method described in this chapter was validated through a series of experiments,for the TFC unit and LFC unit both. In the threshing unit that consisted of threshing cylinder,grid concave and cylinder cover,the grains were removed from the ears and separated,for the most part,through the grid concave and into the grain box. To model the grain threshing and separation process as Peter I. Miu␛9玨13␝,the following general assumptions were taken into considerationㄩ  (a)the material throughput is constant,where material moves through the threshing space as a continuous stream˙  (b)the material to be processed is homogeneous,i.e.,the ears are uniformly distributed within the straw mass˙  (c)in the TFC unit,the material is homogeneous in any cross玨section (perpendicular to the longitudinal axis direction) of the threshing space˙  (d)in the LFC unit,the material is homogeneous in any cross section of the threshing space˙  (e)the mass of the material is continuously distributed throughout the threshing space and its volumetric density is a continuous function of position and time.

(1) Tangential flow threshing cylinder

Based on these assumptions,the grain threshing and separation of the TFC unit was as



dydl=k(1-y)                            (3玩1)

dzdl=u(y-z)                            (3玩2)


where y is the rate of accumulative threshed grain˙  z is the rate of accumulative separated grain˙  l is the arc length of the grid concave. Coefficients k (primary threshing coefficient) and u (primary separation coefficient) were affected by the material properties,structural variables,and operating variables of the threshing unit.


When the rice is at the entrance of the TFC unit,l=0. Assuming the threshed grain=0,the y is also zero. Thus,Equation (3玩1) can be solved as



y=1-e-kl
(3玩3)


When the rice is at the entrance of the TFC unit,l=0. Assuming the separated grain=0,the z is also zero. Thus,according to Equation (3玩3),Equation (3玩2) can be solved as



dzdl+uz=
u(1-e-kl)
(3玩4)


Equation (3玩4) is a non玨homogeneous linear equation. In order to obtain the general solution of Equation (3玩4),both a general answer of a homogeneous version of Equation (3玩4) and a particular answer of a non玨homogenous version must be solved. The homogeneous equation of Equation (3玩4) is as



dzdl+uz=0
(3玩5)


The solution to the homogeneous equation of Equation (3玩4) is obtained by



z=C(l)e-ul
(3玩6)


where C(l) is the function of the arc length of grid concave  l. In order to express C(l),Equation (3玩6) must be solved firstㄩ  



dzdl=C∩(l)
e-ul-uC(l)
e-ul
(3玩7)


By substituting Equation (3玩7) and Equation (3玩6) for Equation (3玩4),Equation (3玩4) can then be solved.



C∩(l)=
ueul-
ue(u-k)l
(3玩8)


Equation (3玩8) is as followsㄩ  



C(l)=eul-uu-ke(u-k)l+C0(3玩9)


where C0 is a coefficient. Both the general and particular versions of Equation (3玩4) combined can be written as



z=e-uleul-uu-ke(u-k)l+C0(3玩10)


When the rice is at the entrance of the TFC unit,l=0. Assuming that the separated grain was zero,z=0. So,Equation (3玩10) could be solved as



z=1+uk-ue-kl-kk-ue-ul(3玩11)


According to Equation (3玩1) and Equation (3玩2),Equation (3玩4) can be expressed as



dzdl=u(1-e-kl-z)(3玩12)


Equation (3玩12) is then written as



dzdl(1-z)=u1-e-kl1-z=米-u1-ze-kl
(3玩13)


Because the rate of accumulative threshed grain y is greater than the rate of accumulative separated grain z,k 
is far greater than l. When the arc length of the grid concave l is over 300 mm,e-kl＞0 and could be ignored. According to Equation (3玩11) and Equation (3玩12),the separated experimental coefficients u can be written as



u=-ln(1-z)l
(3玩14)


The threshed experimental coefficients k is provided by Equation (3玩15).



k=1+uzz+e-ul
(3玩15)


If ddl
dzdl=0
,then dzdl
 is the maximum. Based on Equation (3玩12),the minimum arc length of grid concave lm is expressed. 



lm=lnkuk-u
(3玩16)



When the difference between the rate of threshed grain y and the rate of separated grain z was at its maximum,the differential result of dz/dl was maximum,and lm was the minimum arc length. When l<lm,the threshed rate capacity was much greater than the separated rate capacity,and the result of (y-z) grew larger. The threshing and separating capability of the TFC unit was then unstable and unreliable. When l>lm,the threshed rate capacity was much lower than the separated rate capacity,and the result of (y-z) shrank. The threshing and separating capability of the TFC unit was then stable and reliable␛14␝.

(2) Longitudinal flow threshing cylinder

The straw was threshed and separated preliminarily by the TFC unit. Next,the straw was transported to the LFC unit  so as to be threshed and separated again. The mixture in the LFC unit contained both un玨threshed grain (sj) and un玨separated grain (si). The total grain rate in the LFC unit is then qj,described asㄩ  



qj=si+sj
(3玩17)


Assuming that 汛x is an arbitrary infinitely small distance,which is one point of the LFC,竹 is the re玨threshed coefficient,and 汕 is the re玨separated coefficient˙  i and j are natural numbers (i=0,1,2,3ㄛ＃˙  j=1,2,3,＃). Threshed grain probability density f(x) is  described as



f(x)␛1-F(x)␝=竹
(3玩18)


where x is one point of the LFC,and F(x) is the cumulative total rate of threshed grain through the concave grid.

Equation (3玩18) is then written as



F(x)=÷x0f(汎)d汎(3玩19)


where 汎 is a variable. Equation (3玩18) and Equation (3玩19) can be merged intoㄩ 



dF(x)1-F(x)=竹dx(3玩20)


The cumulative total rate of threshed grain from the concave grid of the LFC is



F(x)=1-e-竹x(3玩21)


Threshed grain probability density is expressed as



f(x)=sj竹e-竹x(3玩22)


Similarly,the separated grain probability density is expressed as



g(x)=汕e-汕x(3玩23)


The total rate of un玨threshed grain can be described



sn(x)=sj1-÷x0竹e-竹汎d汎=sje-竹x
(3玩24)


where x=L
,and L is the effective threshing and separation length of the LFC unit. Thus,the un玨threshed grain discharged from the tail hole of the LFC unit is considered as lost grain. The un玨threshed grain rate Sn(L) is expressed as



sn(L)=sje-竹L(3玩25)


According to probability theory,independent constant random variables with the densities f(x) and sn(x) for sum variables convolute Equation (3玩26) with these density functions h∩(x)ㄩ 



h∩(x)=f(缶)g(x-缶)=÷x0f(x)g(x-缶)d缶(3玩26)


where 缶 is a variable. Based on Equation (3玩26),Equation (3玩27) is written as



h∩(x)=竹汕竹-汕(e-汕x-e-竹x)(3玩27)


The grain separation probability density h(x) is expressed as



h(x)=sjh∩(x)+sig(x)=sj竹汕竹-汕(e-汕x-e-竹x)+si汕e-汕x
(3玩28)


The rate of cumulative separated grain through the LFC unit突s concave grid is writtenas



H(x)=sj汕e-竹x-竹e-汕x竹-汕+sj+si(1-e-汕x)
(3玩29)


In every cross玨section of the LFC unit at a current position x of the threshing length,the mass balance for grain can be obtainedㄩ 



H(x)+sn(x)+sf(x)=qj(3玩30)


To this effect,the total rate of un玨separated grain in the LFC unit is obtainedㄩ 



sf(x)=qj-Hj(x)-sn(x)(3玩31)


where x=L
,and the un玨separated grain discharged from the tail hole of the LFC unit is lost grain. The un玨separated grain rate of the LFC unit is expressed as



sf(L)=sie-汕L-sje-竹L+汕e-竹L-竹e-汕L竹-汕
(3玩32)


3玩1玩2Threshing and separation test of model

The separated grain z measured using the four different types of tangential flow threshing teeth (knife bar,rectangular bar,spike tooth and rasp bar) are shown in Table 3玩1玩


Table 3玩1Coefficients and parameters of primary threshing and separation using different threshing teeth



Serial

numberCoefficients and parameters

Threshing teeth of TFC unit

Spike toothKnife barRectangular barRasp bar

1Arc length of grid concave l/mm676玩67676玩67676玩67676玩67
2Rate of accumulative separation grain z/%44玩7647玩7141玩4146玩32
3Rate of accumulative threshing grain y/%85玩0487玩0482玩3386玩14
4Primary separation coefficient u/m-11玩831玩921玩741玩88
5Primary threshing coefficient k/m-12玩813玩022玩562玩92
6Minimum arc length lm/mm437玩74411玩94470玩34423玩78


Based on the rate of cumulative threshed grain y and separated grain z,primary separated coefficient u,and primary threshing coefficient k can be calculated by Equation (3玩14) and Equation (3玩15),respectively. The rate of cumulative threshed grain y can also be obtained by Equation (3玩3). The minimum arc length of grid concave lm can be determined 
by Equation (3玩16). All the calculation results are shown in Table 3玩1. In the TFC unit,y and z were a function of l. Assuming that k=2,2玩5,3,3玩5,and 4 m-1 (these scopes represent the test values),u=1,1玩5,2,2玩5,and 3 m-1 (again,because these scopes were test values),y and z were calculated. The results are shown in Table 3玩2. 


Table 3玩2The primary threshed coefficient k,primary separated coefficient u,cumulative threshed grain

rate y,and cumulative separated grain rate z 



No.k/m-1y/%u/m-1z/%

1274玩16124玩18
22玩581玩581玩537玩03
3386玩87248玩75
43玩590玩642玩558玩94
5493玩32367玩49
6386玩87130玩32
7386玩871玩540玩65
8386玩87248玩75
9386玩872玩555玩14
10386玩873玩161玩09
11274玩16240玩35
122玩581玩58244玩50
13386玩87248玩75
143玩590玩64252玩20
15493玩32255玩00


The rate of accumulative threshed grain y and the rate of accumulative separated grain z were then drawn using MATLAB software. The results are shown in Figure 3玩5.



Figure 3玩5Cumulative threshing and separating rates of the TFC unit with different threshing bars


(a) Cumulative threshing rate˙ (b) Cumulative separating rates


The rice straw was first threshed and separated preliminarily by the TFC unit. Next,the straw with grain was moved to the LFC unit so as to be threshed and separated again. The un玨threshed grains needed to be re玨threshed,and the un玨separated grain and threshed grain needed to be re玨separated. The knife bar was used in the TFC unit. The trapezoidal tooth,rectangular bar,spike tooth,and rasp bar were installed,respectively,in the LFC unit to perform the threshing and separation tests. The separated grains from the LFC unit were divided into 13 parts,perpendicular to the axial direction. The percentage of the total grain in every part,the un玨threshed grain rate,and the un玨separated grain rate were measured for the four longitudinal axial flow threshing teeth. All the test results are shown in Table 3玩3. 


Table 3玩3Accumulative separation grain percentages. means㊣standard errors under LFC unit



Packet sequence numberRectangular barRasp barSpike toothTrapezoidal tooth

16玩19㊣0玩384玩81㊣0玩324玩67㊣0玩295玩40㊣0玩28
29玩91㊣0玩8713玩21㊣0玩6714玩55㊣0玩6210玩66㊣0玩74
311玩42㊣1玩4511玩29㊣1玩2312玩75㊣1玩0614玩01㊣1玩36
46玩59㊣0玩325玩51㊣0玩325玩81㊣0玩296玩56㊣0玩27
55玩51㊣0玩274玩67㊣0玩235玩13㊣0玩225玩46㊣0玩28
63玩40㊣0玩242玩87㊣0玩263玩10㊣0玩233玩22㊣0玩19
72玩40㊣0玩232玩04㊣0玩171玩90㊣0玩132玩34㊣0玩26
81玩94㊣0玩212玩28㊣0玩231玩33㊣0玩221玩34㊣0玩22
91玩50㊣0玩171玩57㊣0玩160玩86㊣0玩181玩10㊣0玩23
101玩13㊣0玩161玩14㊣0玩160玩72㊣0玩120玩63㊣0玩18
110玩91㊣0玩090玩77㊣0玩090玩58㊣0玩070玩43㊣0玩12
120玩66㊣0玩040玩62㊣0玩030玩28㊣0玩040玩32㊣0玩02
130玩19㊣0玩010玩47㊣0玩040玩16㊣0玩040玩22㊣0玩02
Un玨separated rate/%0玩46㊣0玩040玩91㊣0玩050玩44㊣0玩040玩58㊣0玩03
Un玨threshed rate/%0玩08㊣0玩010玩14㊣0玩010玩02㊣0玩010玩04㊣0玩01


The re玨threshing coefficient 竹 was then  obtained by Equation (3玩22),and the reseparation coefficient 汕 could be obtained by Equation (3玩23). The results are as shown in Table 3玩4. 


Table 3玩4Threshing and separation coefficient of LFC unit



ParametersRectangular barRasp barSpike toothTrapezoidal tooth

Un玨threshed grain rate/%0玩080玩140玩020玩04
Un玨separated grain rate/%0玩460玩910玩440玩58
Rethreshing coefficient 竹/m-12玩592玩313玩312玩95
Reseparation coefficient 汕/m-12玩872玩432玩712玩60


The threshing probability density equation f(x) of the LFC unit and separation probability density equation h(x) of the LFC unit were drawn using MATLAB. The results are shown in Figure 3玩6.



Figure 3玩6Grain threshing and separation probabilities density curves of the LFC unit


(a) Cumulative threshing rate˙ (b) Cumulative separating rates


The accumulative threshed grain rate (y) and the accumulative separated grain rate (z) increased 
with increasing the arc length of the grid concave. The threshing and separation capacity of the knife bar in the TFC unit was stronger than other threshing teeth. The maximum primary threshing rate of the knife bar is 87玩04%ㄛand the maximum primary separation rate is 47玩71%. In order to ensure that the separation capacity is stronger than the threshing capacity of the knife bar,the minimum arc length of the grid concave screen was set to 411玩90 mm. After being primarily threshed and separated by the TFC unit,the un玨threshed rate was 12玩60%,and the un玨separated grain rate was 39玩33% at the entrance of the TFC unit. At a length of 0玩96玨1玩31 m,the grain threshing probability density of the spike tooth used in the LFC unit was stronger than other threshing teeth. At a length of 1玩48玨2玩91 m,the grain separation probability density of the trapezoidal tooth used in the LFC unit was stronger than other threshing teeth.

3玩2Rice Stalk Movement during Rice Threshing
3玩2玩1Numerical model of threshing unit

In order to present the movement parameters of the rice straw which was threshed by combine harvesterㄛthe threshing unit model was modeled by Pro/E software with the scale of 1￣1,and then the process of threshing was simulated on EDEM software. The relationship of movement velocity and trajectory with the simulation time can be obtained by EDEM,which also can be verified by the experimental result. Straw movement condition in threshing unit is very complicated␛15␝. 

The threshing device of tangential and axial threshing unit in a combine harvester mainly includes the tangential threshing unit,the auxiliary feeding unit and the axial threshing unit. The tangential and axial threshing unit solid modeling of a combine