farm machinery engineering design formulae

8/12/2019 farm machinery engineering design formulae

1/28

Chapter-1Field Efficiency

Field Efficiency

FE= A T T T

nW V nW V overlap AFC K TFC nW V nW V

= = = (1.1)

Notations FE = field efficiencyAFC = actual field capacity, also known as effective field capacityTFC = theoretical field capacityn = number of plow bottomsWT = theoretical width of cut, also known as design width of cut or rated width of cutWA= actual width of cutK= percentage width utilized

Methods to determine Actual field capacity, AFCMethod-1

FE=

haT

T

hae

T

A

T

T

A

T T K

T T

T T T

T

T

T

T

T

TFC AFC

++=

++===

1

1

(1.2)

NoteWhen the T a and T h are negligible equation (1.2) reduces into equation (1.1) as follows

FE =

K

T T

T

T =K

Method-2AFC=

Notations TA= actual time taken per hectorTT= the cortical (ideal) time taken per hector

Te= effective operating time per hectorTa= time lost per hector which is proportional to area ex turning timeTh= time lost per hector which is not proportional to area e.g. time for filling, emptyingUnit draftUnit draft, Lu= L/A (1.3)

NotationsL = draftA = cross sectional area of cut= Width x depth (for rectangular furrow as in tractor drawn MB plough)= x Top width x depth (for triangular furrow as in desi plough)= x (top width+ bottom width) x depth (for trapezoidal furrow as in bullock

drawn country plough)


2/28

Chapter - 2Force Analysis upon Tillage Tools

Case 1When useful and practice forces cant be determined separatelyDraft, L = (Pcos ) cos (2.1)= longitudinal and directional component of RVertical component, V = (P cos ) sin (2.2)

Side force, S= (Psin ) cos (2.3)= lateral component of R= Side force, also known as landside forceR v = (L 2+V 2)0.5 = (Pcos cos )2 + (Pcos sin )2 + (Pcos sin )2 = Pcos (2.4)R h= (L 2+S 2)0.5 = (Pcos cos ) 2 + (psin cos R= (R v2+R h2)

NotationsP = pull force= resultant pull exerted by tractor or by bullock upon implementR = soil reaction force= resultant of useful and parasitic soil force exerted by tractor or by bullock upon

implementR v = vertical component of soil reaction forceR h= horizontal component of soil reaction force

Case 2When useful forces ( P v, P h ) and parasitic forces ( W, F, and f) can be determinedseparately R v = W-P v = W-Psin (2.7)R h = P h-F- f = Pcos -F-f (2.8)R=(R v2+R h2)


3/28

Notations Pv = vertical component of pullPh = horizontal component of pullP = pull force

= resultant pull exerted by tractor or by bullock on the implementF = frictional force = inclination of the pull force with horizontalf = rolling resistance forceW= weight of the implement

NotePv can be determined from V=0 i.e. summation of vertical forces = 0Ph can be determined from H=0 i.e. summation of horizontal forces =0Another useful concept used in solving such type of problem is M =0 i.e.

summation of moments acting at a particular convenient point on tillageimplement = 0


4/28

Chapter-3

Sowing and Planting

Device for metering single seed

Horizontal plate planterVertical plate planterC

(1) Calculation of spacing between seeds along the rowE(A)Horizontal plate planter

N2, T2 N3, T3

d N1, T1 N4, T4 N r

N

FD A

DF

AB = main driveshaftCD = feed shaftEF = plate drive shaft

Speed ratio between plate drive shaft and main drive shaft

=42

314

T T

T T

N

N

N

N r == = Product of tooth on drivers/Product of tooth on driven

Spacing between seeds along row, L is given by

L =r r

DN V nN nN

= (3.1)

Notations N = rpm of ground wheelD = diameter of ground wheel.

N r = rpm of rotord = diameter of rotorV = velocity of ground wheeln = number of cells on rotorProof

In 1 revolution rotor drops n seeds

Number of revolutions to drop 1 seed =1n

Corresponding no. of revolutions of ground wheel = )(1

r N N

n

In 1 revolution distance covered by ground wheel = D


5/28

In )(1

r N N

nRevolution distance covered by ground wheel= D ).(1

r N N

n

= Lr r

DN V nN nN

=

(B) Vertical Plate Planter

L = Vt =

pV V

nd

(3.2)

Notations V= velocity of travelV p= peripheral velocity of plate planter

NoteVelocity of travel otherwise can be referred as velocity of ground wheel orforward travel speed of planter or velocity of plantingPeripheral velocity of plate planter otherwise can be referred as peripheralvelocity of rotor or linear cell speed or linear plate speed

Prooft = time to cover peripheral distance between two consecutive cells of rotor= time gap between falling of seeds from consecutive cells of the rotor= peripheral distance between two consecutive cells of rotor V p

= ( )

p

d n

V

L = Vt =

pV

V

n

d

Correlation between equation (2) and (3) is as follows

L =

==

nd

V V

nd

dN V

nN V

pr r

(3.3)

II. Calculation of velocity of travel, V

(3.4)

==V

31

42

T T

T T

d D

dN DN

V r p

III. Calculation of actual seed rate (Kg/ha):

( DN SZ) m 2 of area is equivalent to dropping of x Kg of seed. So from this conceptseed rate (Kg/ha) i.e. dropping rate of seed in Kg from 10,000 m 2 of area can becalculated.

Notations N= revolution of ground wheel to drop x Kg of seedS = spacing between rowsZ = number of rowsSZ = width of coverage or size of seed drill


6/28

IV. Calculation of number of plants required per hectare

X= 000,10 LS nE

Notations X = number of plants required per hectaren = number of seed per hillE = emergence rateL x S = area required per each hillL = distance between plant to plant or hill to hill in a rowS = distance between row to row

V. Vertical plate planter with rotor mechanism:

Case-I:When rotor turns in same direction as ground wheel

Horizontal distance covered X = VtVertical falling distance, h = gt 2

1

1 = tan -1(x/h)

gh

V X 2=

X = Vt 1 h = gt 2

Notations V = net velocityV=V G-V R (using concept of relative velocity)VG = velocity of ground wheel

VR = velocity of rotor, also known as peripheral velocity of rotor1 = angle with which seed strikes bottom with vertical


7/28

Case-II:When a rotor turns in opposite direction with respect to ground wheel:-

2

h 2 X

Where X = Vt

H = gt2

X = Vgh2

V = V G + V R (using concept of relative velocity)2 = tan -1(X/h)Where 2 = angle with vertical with which seed strikes bottom


8/28

Chapter-4Chaff Cutter

Capacity of a chaff cutter

Note

m = Q = VA = (NLn) (WH) (4.1)

Actual maximum working capacity or rated capacity is 60-70% of theoreticalmaximum capacity

Notations

m = theoretical maximum capacity of chaff cutter, kg/hr = density of feed material, kg/m 3

Q = volumetric flow rate of feed material, m 3/hrV = linear speed of cutterhead, m/s

= linear speed of feed mechanism= rate of advance of material through throat

A = cross sectional area of throat, m 2

N = rotational speed of cutterhead, rpmL = theoretical length of cut, m

= amount of advance of feed mechanism between cuts of two consecutive knives.n = number of knives on cutterheadW = width of throat = minimum width of opening at feed rollsH = height of throat, m

= maximum operating clearance between upper and lower feed rolls

V = DN (4.2)

V=NLn (4.3)

NotationsV = peripheral velocity of feed rolls D = diameter of feed rolls

N = rpm of feed rolls

Also V = V

So NLn = DN

When feed rolls are of different diameter and different rpm

2'''' 2211 N D N D NLn

+= (4.4)

Notations D1 and D 2 = diameter two feed rolls

N1 and N 2 = rpm of two feed rolls


9/28

Vp = D N (4.5)V p = peripheral velocity of cutter head, m/sD = diameter of cutter head or fly wheel, m

Note

There are two types cutter head used in chaff cutter1. Fly wheel type2. cylindrical type

L =n

r i tan2 (4.6)

L = theoretical length of cutr i = distance of inner edge of throat from fly wheel center = clearance angle between knife support assembly and plane of rotation

La = distance travel by fly wheel in one revolution number of knives on flywheel

La =

n

D (4.7)

Analysis for kinetic energy & power of chaff cutter

Kinetic energy of fly wheel in one revolution = MV 2 = M ( r) 2 = M (2 Nr) 2 = M r 2 2 = I 2 (4.8)

Power required (consumed) to drive flywheel, P = V

m p2 (4.9)

Also power consumed to drive flywheel, P = 2 NT

= 2 NT (F.r) = 2 N (A o ) r (4.10)

NotationsT = torque required to drive the flywheel, N.mAo = effective cut area of fodder, m2

= dynamic shear stress of fodder, N/m 2

F = force required to cut per revolution, Nr = effective radius of knife rotation, m


10/28

Chapter 5Sprayer

Flow rate of spray material

Notations

m = Q = (AR v) = (nSVE) Rv = (SVE) R m (5.1)

m = mass flow rate of spray material, kg/hr = density of spray material, kg/m 3

Q = volumetric flow rate, m 3/hrA = area covered by sprayer, ha/hrR v = volumetric application rate, lit/han = number of nozzlesS = spacing between nozzles, mV = velocity of travel of sprayer, m/sE = spraying efficiency of a sprayerR m = mass application rate, kg/ha

Mathematically

q = aV = /4 d 2 x V (5.5)

Q = nq (5.4)

A = n SVE (5.3)

R m = R v (5.2)

Notations n = number nozzlesq = discharge per nozzles (m 2)a = area of each nozzle (m)V = velocity of water through nozzle (m/s)

G = V (5.6)

G = mass flow rate or mass velocity or mass flux per nozzle, kg /m 2s

When coefficient of discharge through orifice, C d is given

m = C dQ (5.7)


11/28

Chapter 6Fuel and combustion

Volumetric efficiency, v Case-1

For a cylinderv =

33 V

m

V

V

A

A A

=

(6.1)

Methods to calculate A

1) RT

PV m

A == (6.2)

2) /1= A specific volume, m 3/kg (6.3) NotationsVA= actual volume of air taken into cylinder, m 3

Vs= swept volume of air inside cylinder, m 3

mA= air compressed during compression, kg = ambient air density, also known as density of air at inlet, kg/m 3

Note m, V, P, T represents mass, volume, Pressure and temperature of ambient airrespectivelyR = 8.31 KJ/ kgmole-K

Case-2For an engine(a) For liquid fuel or fuel of CI engineVolumetric efficiency can be calculated from the following formula

F A

=( )

==F

Q

F

Q

F

A AeV A A (6.4)

Notations

F A

= air to fuel ratio

A = air taken in or mass flow rate of air, kg/min

F = fuel consumed or mass flow rate of fuel, kg/minQA = air taken in or volumetric flow rate of air, m 3/min

A = ambient air densityV = volumetric efficiencyQe = engine displacement(b) For gaseous fuel or fuel of SI engine

(5)(6.5)1=

=== +F

eV

F

F eV

F

F F A

F

A

Q

Q

Q

QQ

Q

QQ

Q

Q

F

A

QF = fuel consumed, m 3/minQA+F = air-fuel mixture taken in, m 3/min


12/28

Thermal Efficiency

Break Thermal Efficiency, BTE is variedly known as engine thermal efficiency or netengine efficiency or thermal efficiency or simply efficiency.

Conceptually

BTE = Heat actually usedHeat input= Actual work outputHeat input= Actual out put / timeHeat input / time

= BHP___ = BHP___

fuel HP x CVF

=

KgKcal

hr Kg

BHP

=

KgKcal

hr BHPKg

hr Kcal

641=

CV SFC hr

Kcal

641

Note 1 HP = 641 Kcal/Kgunit of SFC = Kg / HP-hr (for liquid fuel)

= m 3 / HP-hr (for gaseous fuel)

SFC = specific fuel consumptionCV = calorific value of fuelF = fuel consumed or mass flow rate of fuel

Indicated thermal efficiency, ITE is also known as indicated engine efficiency

Conceptually

ITE = Indicated work (output)Heat input

=CV F

IHPFuelHP

IHP

= (6.9)

In the above expression

IHP = P Q e = P (LAnN) (6.11)

BHP = Q e = p (LAn . N) (6.10)

p = break mean effective pressure (BMEP)P = indicated mean effective pressure (IMEP)


13/28

Using equation (7), (9), (10), (11)

----

IMEP BMEP

IHP BHP

ITE BTE

ME === (6.12)

Also --------------------- (13)BHP = 2 Here, T = engine torque

Relative efficiency

Relative efficiency = Indicated thermal efficiency( ITE)Air standard efficiency( ASE)

= Actual ITE

Ideal ITE (6.14)Where

=in

on BY

Q

W W

=in

out in

Q

QQ (For Otto cycle)

= 1-( )

111

1 ck e

r

k

k (For Diesel cycle)

Note W by , W on refers to work done by the system and work done on the systemrespectively Qout = -ve , Q in = + ve , Won = -ve , W by = + ve

NT = 2 N (Fr) (6.13)

ASE = Net work doneHeat input


14/28

Chapter 7

Traction Theory

Drawbar pull

Drawbar pull, P is variedly known as net pull or net tractive capacity or draft capacity or pull used for useful work or simply as pull

Conceptually P = F- TF (1) PV a=F V t- TF V a drawbar power = axle power towed power net tractive power = gross tractive power rolling resistance power

Notations F = force of traction or soil thrust in direction of motion, also known as gross tractive force

or simply tractive force TF = towed force, also known as motion resistanceVa = actual travel velocity, also known as forward travel velocityV t = theoretical travel velocity

Theoretical travel velocity, V t

V t = r = (2 N)r = 2 N (D/2) = DN (2) Notations r = rolling radius of wheelD = wheel diameter

F = AC + W tan (3) Notations A = area sheared by the equivalent wheel or by the track

= bl (for track/crawler type tractor)= 0.78 bl (for wheel / rubber tyre / pneumatic tyre tractor)

W = weight on the equivalent wheel or on the track.C = cohesion, N/cm 2

= angle of internal friction

Force analysis P = F TF (4)

W TF

W F

W P =

= g - (5) Notations W = dynamic weight on equivalent wheel = coefficient of traction, also known as net coefficient of tractiong = gross traction coefficient = rolling resistance coefficient, also known as motion resistance ratio


15/28

= 0.75 ( 1 e 0.3 CnS) (6)

= 0.75 ( 1 - e - 0.3 CnS)= 0.75 ( 1 - e - 0.3 CnS)

=1.2

0.04nC

+

Cn =( )CI bd

W (8)

Note Equations (6) & (7) applies to single wheel

NotationsW = Dynamic weight on each individual wheel

= Dynamic weight on equivalent wheel 2CI = Cone index, N/cm 2

S = Slip (in decimal)Cn=Wheel numeric per wheel

b = width of tire (rim)d= Diameter of tire (rim) Note

Width of tire is variedly known as sectional width or sectional diameter orsectional thickness

Dynamic weightGenerally dynamic weight refers to dynamic weight on rear wheel. Dynamic weight isalso known as true tire loadConceptually,Dynamic weight = static weight distribution on rear wheel + weight of implement +

weight transfer from front wheelPhysically,Dynamic weight, W, means net load on wheels ( i.e. on the equivalent wheel) during pullcondition. and static weight means load on wheel in rest condition


16/28

Equivalent wheelIn two dimensional analyses the 2 wheels on rear axle of tractor are replaced by a singlewheel having equivalent force properties as that of 2 wheels. Likewise the 2 wheels onfront axle are also replaced by another single wheel. These 2 single wheels, one at rearaxle and another at front axle are known as equivalent wheels at the respective axles.

Net coefficient of traction,

=W T

V P a..

Horizontal drawbar pull ( =Pcos )/Dynamic weight on rear wheel

Tractive efficiency, TE

TE = Drawbar Power/ Axle Power (9)

=W T

V P a..

(10)

=))(.(

.

r

V r F

V P

t

a

=t

a

V F

V P

..

(11)

= )1( S F P (12)

= )1(//

S W F W P

= )1( sg

(13)

= )1( S +

(14)

NotationsT=wheel torqueR = rolling radius

Slip, S

When wheels are rotating but not moving ahead this condition is known as slip Methods to calculate slip Method 1In terms of velocity

Slip=t

a

t

at

V

V

V

V V = 1

Method 2To cover a particular distance


17/28

Slip =0

01

N

N N

Method 2To register a particular rpm

Slip =0

10

L L L

In otherworld slip is the difference between ideal distance a wheel should move and thedistance actually moved by wheel. So slip is also known as travel reduction .

Notations N0, N 1 = rpm without and with slip respectivelyL0, L1 = distance covered without and with slip respectively

Skid

When wheels are sliding i.e. moving ahead along the road but not rotating this conditionis known as skid e.g. sudden application of brakes rotating wheels\. Thus this is justopposite condition to that of slip. Mathematically

Skid= 1=t

a

t

t a

V

V

V

V V (18)


18/28

CHAPTER-8Mechanics of tractor chassis

Weight Transfer

Pcos

YW

X 1

X 2Psin

P = pull force = angle of inclination of pull with horizontalR 1 = Normal reaction force at front wheelR 2 = normal reaction force at rear wheelW = weight of tractor acting through center of gravity of tractorX1 = perpendicular distance between R 2 & WX2 = perpendicular distance between R 1 & R 2

(a) In rest condition

R 1 + R 2 = W (1)W .X1 = R 1.X2 (2)

(b) When implement is attached and pulled

R 1 + R 2 = W + P sin (3)WX 1 = P cos . Y1 + P sin S + R 1 X2 (4)

R 2R 1

R 1 =2 X

1WX

R 2 = W (1 -2

1

X

X )


19/28

+=2

1

2

11

.sin.cos X

S pP

X

WX R

Y

Thus the amount

+

2

1 .sin.cos X

S pP Y by which upward reaction at front wheel decreases due

to pulling of attached implement is called as weight transfer.

=2

1

X

PY (when pull is parallel to ground) &

2

1

X

WX = static weight distribution on front wheel in pull condition

Weight transfer =2

1 .sin.cos X

sP yP +

Conditions:

i. weight transfer =2

1

X

WX R 1 = 0

Front wheel will leave the ground

ii. weight transfer >2

1

X

WX R 1 = negative

Overturning / toppling about rear wheel

iii. weight transfer

farm machinery engineering design formulae

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