bmw 740li report
TRANSCRIPT
TVS Training Academy and Thiagarajar College of Engineering
Assignment 1 & 2 Date: July, 16, 2010
Considered Car: BMW 740li
By
Dhaneesh.V.L (07G20)
P.Mariraja (07G54)
CAR SPECIFICATIONS
ENGINE Displacement 2979ccStroke & bore 89.6 mm & 84.0 mm Compression ratio 10:2Max. Power 240kw @5800rpm Max. Torque 450 Nm @1500‐4500 rpmTRANSMISSION Six speed automatic Gear ratios I Gear 4.17
II Gear 2.34 III Gear 1.52 IV Gear 1.4 V Gear 0.87 VI Gear 0.69
Final drive ratio 3.73CHASSIS Wheel base 3070 mm
Track front & rear 1611/1650 mm
Length 5072mm
Width 1902 mm
Height 1479mm
Ground clearance 144mm
Frontal area 2.41m2
Gross weight limit 2475 kg
Kerb weight 1860 kg
Wheels: Light weight alloy wheels, double spoke, 250/50R18 tyres
Formulas taken for calculation:
Nmin= 800 to 1000 rpm
Nmax= 1.1 Nrated
B.P. = B.P.rated ⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−+
2
1ratedratedrated NN
NN
NN kW
Te= NBP
π26000× Nm
F=rGT Te η××
N
V=65.2×
×G
rN
Air Resistance:
Ra = KaAV2
Rolling Resistance:
Rr = (0.015+0.00016V)W
Total Resistance:
Rt = Ra+Rr
We= (1.04 + 0.0025 G2) W
aP = e
T
WRFg )( −
CALCULATION TABLE
Air Resistance Ra N
Rolling Resistance Rr N
I II III IV V VI I II III IV V VI 5.47 17.44 41.375 49.19 126.82 201.39 71.62 97.63 130.32 138.74 200.3 242.78
21.85 69.82 165.5 196.77 507.26 805.58 104.99 158.2 223.51 240.35 363.43 448.3349.38 157.06 372.38 442.72 1140.42 1812.55 138.94 218.7 314.7 341.96 526.4 653.9387.79 279.27 661.96 787.07 2027.33 3222.32 172.87 279.24 409.88 443.58 689.46 859.54
137.18 436.31 1034.45 1229.8 3167.93 5034.87 206.81 339.75 503.09 545.2 852.57 1065.14197.534 628.36 1489.53 1770.9 4562.67 7250.21 240.75 400.3 596.27 646.81 1015.64 1270.67223.29 710.36 1684.11 2002.3 5157.79 8197.67 253.62 423.26 631.68 685.42 1077.61 1348.87
Engine speed N
rpm
Brake power BP kW
Equivalent torque Te Nm
Tractive force F N
Velocity of the Vehicle V
Km/hr I II III IV V VI I II III IV V VI
1000 47.28 451.59 16880.35 9476.88 6155.08 5644.87 3517.19 2789.89 8.56 15.28 23.533 25.66 41.2 51.92 2000 101.45 484.4 18106.78 10165.41 6602.28 6055 3772.73 2992.57 17.1 30.57 47.07 51.32 82.4 103.84 3000 155.13 493.8 18458.15 10362.68 6730.4 6172.5 3845.94 3050.64 25.71 45.85 70.6 76.98 123.55 155.76 4000 200.94 479.7 17931.09 10066.78 6538.22 5996.2 3731.45 2963.53 34.28 61.14 94.13 102.64 164.73 207.68 5000 231.5 442.1 16525.61 9277.72 6025.74 5526.2 3443.28 2731.2 42.85 76.42 117.67 128.3 205.92 259.6 6000 239.42 381 14241.71 7995.5 5192.95 4762 2967.4 2353.77 51.42 91.17 141.2 153.96 247.1 311.52 6380 234.92 351.7 13146.48 7380.63 4793.6 4392.2 2739.2 2172.76 54.67 97.51 150.14 163.71 262.75 331.25
Total Resistance Rt N
Acceleration of the vehicle
ap m/s2
I II III IV V VI I II III IV V VI 77.09 114.67 171.69 187.93 327.12 444.17 4.12844 3.074414 2.158002 1.990826 1.229358 0.897044
1126.84 228.02 389.01 437.12 870.7 1253.9 4.417941 3.261978 2.240571 2.04893 1.098879 0.664628188.32 375.76 687.08 784.7 1666.8 2466.5 4.488277 3.279307 2.179409 1.965341 0.825688 0.256881260.67 558.51 1071.84 1230.65 2716.79 4081.86 4.341488 3.122324 1.971458 1.738022 0.384302 ‐0.45872343.98 776.06 1537.55 1775 4020.5 6100 3.975535 2.79103 1.617737 1.367992 ‐0.21916 ‐1.28848438.28 1028.66 2085.77 2417.71 5577.3 8520.9 3.391437 2.287462 1.120285 0.856269 ‐0.98879 ‐2.35882476.91 1133.62 2315.78 2681.72 6234.95 8829.35 3.11315 2.050968 0.893986 0.624873 ‐1.32518 ‐2.54536
Overall gear ratio G 15.55 8.73 5.67 5.2 3.24 2.57Equivalent weight We 4070.15 3045.57 2772.62 2741.31 2638.95 2614.87
‐3
‐2.5
‐2
‐1.5
‐1
‐0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 50 100 150 200 250 300 350
ACC
ELER
ATION IN
m/s^2
VEHICLE VELOCITY IN km/hr
ACCELERATION VS VELOCITY
I GEAR
II GEAR
III GEAR
IV GEAR
V GEAR
VI GEAR
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0 50 100 150 200 250 300 350
FORC
E IN NEW
TON
VEHICLE VELOCITY IN km/hr
FORCE VS VELOCITY
I GEAR
II GEAR
III GEAR
IV GEAR
V GEAR
VI GEAR
TOTAL RESISTANCE
0
100
200
300
400
500
600
0
TORQ
UE IN Nm
1000 2000 3000
ENGINE S
T
4000
SPEED IN rpm
TORQUE
5000 6000 7000
TORQUE
0
50
100
150
200
250
300
0 1000 2000 3000 4000 5000 6000 7000
BRAKE
POWER
IN kW
ENGINE SPEED IN rpm
BRAKE POWER
BRAKE POWER
REPORT
For the selected car BMW 740li we can infer from the graphs that the performance of the car will be good under ideal road conditions. The optimum amount of ground clearance and frontal area gives the car its maximum acceleration with low air resistance, rolling resistance is reduced by equal distribution of the load. These factors help the car to reach the speed of 100km/hr in around 6‐8 seconds. Under actual riding condition, the driving method and other external factors the cars performance may vary.
Assignment 2
Instantaneous Piston Velocity (Vp) :
Vp= ⎟⎠⎞
⎜⎝⎛ +
22sinsin θλθωr
Instantaneous Piston Acceleration (ap) :
ap= )2cos(cos2 θλθω +r
Volume of Cylinder at any Crank angle ‘θ’ (Vθ) :
Vθ= )2
sincos1(41
22 θλθπ
+−+−
rBR
V
c
s
SI Engine:
Suction:
θ → 0 to 180
P= 1bar (assumed)
Compression:
θ → 180 to 360
Governing equation PVncom=constant
ncom=1.36 to 1.4
comn
VV
PP
⎟⎟⎠
⎞⎜⎜⎝
⎛=
210
180
180
210
Combustion:
θ → 360
== α2
3P
P 3.2 to 4.2
Expansion:
θ → 360 to 540
exn
VV
PP
⎟⎟⎠
⎞⎜⎜⎝
⎛=
360
390
390
360
nex=1.23 to 1.3
Exhaust:
θ → 540 to 720
P=1bar (assumed)
Fg= 2
4BPg
π×
Fi= 2
480 Bπ
×
Fr=Fg‐Fi
Tangential force at crank pin:
Ft= φφθ
cos)sin( +
rF
Normal component of connecting rod force acting along crank arm:
Fc= φφθ
cos)cos( +
RF
Instantaneous Turning Moment:
Fitm= rFt ×
CALCULATION TABLE
ANGULAR DISPLACEMENT
θ degrees
INSTANTANOUS TURNING MOMENT
Fitm
Nm
INSTANTANEOUS ACCELERATION OF
PISTON ap
m/s2
INSTANTANEOUS ACCELERATION OF
PISTON vp ms
‐1
0 0 20,989 0
30 ‐203 16543 16.78
60 ‐118.16 6032 27.73
90 88.683 ‐4462 27.19
120 155.442 ‐10494 20.37
150 91.662 ‐12081 10.42
180 0 ‐12064 0
210 ‐92.28 ‐12081 ‐10.41
240 ‐161.218 ‐10494 ‐20.4
270 ‐112.63 ‐4462 ‐27.2
300 46.76 6032 ‐27.7
330 49.625 16543 ‐16.778
360 0 20989 0
390 530.494 16543 16.78
420 278.272 6032 27.73
450 285.75 ‐4462 27.19
480 249.69 ‐10494 20.37
510 129.58 ‐12081 10.42
540 0 ‐12064 0
570 ‐91.662 ‐12081 ‐10.41
600 ‐155.44 ‐10494 ‐20.4
630 ‐88.623 ‐4462 ‐27.2
660 118.16 6032 ‐27.7
690 203.05 16543 ‐16.778
720 0 20989 0
ANGULAR DISPLACEMENT
θ degrees
INSTANTANEOUSVOLUME OF CYLINDER
Vθ mm3
INSTANTANEOUS PRESSURE OF CYLINDER
Pθ bars
0 53972 1
30 95613 1
60 203245 1
90 335960 1
120 451516 1
150 525631 1
180 550514 1
210 525631 1.065
240 451516 1.312
270 335960 1.967
300 203245 3.916
330 95613 11
360 53972 24.09
360 53972 96.36
390 95613 45.81
420 203245 17.19
450 335960 8.94
480 451516 6.09
510 525631 4.998
540 550514 4.71
540 550514 1
570 525631 1
600 451516 1
630 335960 1
660 203245 1
690 95613 1
720 53972 1
θ I II III IV V VI 0‐60 P E S P C S
60‐120 P E C E C S 120‐180 P S C E P S
180‐240 E S C E P C 240‐300 E S P S P C
300‐360 E C P S E C 360‐420 S C P S E P
420‐480 S C E C E P 480‐540 S P E C S P
540‐600 C P E C S E 600‐660 C P S P S E
660‐720 C E S P C E
Calculation for combined Turning Moment:
Angular Displacement
(θ)
Instantaneous Turning Moment of each Cylinder Combined
Turning Moment I II III IV V VI
0 0 ‐155.44 155.442 249.69 ‐161.218 0 88.474
30 530.494 ‐88.623 91.662 129.58 ‐112.63 ‐203 347.483 60 278.272 118.16 0 0 46.76 ‐118.16 325.032
90 285.75 203.05 ‐92.28 ‐91.662 49.625 88.683 443.166 120 249.69 0 ‐161.218 ‐155.44 0 155.442 88.474
‐15,000
‐10,000
‐5,000
0
5,000
10,000
15,000
20,000
25,000
0 180 360 540 720
ACC
ELER
ATION IN
mm/s^2
CRANK ANGLE
ACCELERATION VS CRANK ANGLE
instantaneous accelration of the piston
0
100000
200000
300000
400000
500000
600000
0 180 360 540 720
VOLU
ME IN m
m^3
ANGULAR DISPLACEMENT IN DEG
VOLUME VS CRANK ANGLE
Series2
0
20
40
60
80
100
120
0 180 360 540 720
PRESSU
RE IN
bars
ANGULAR DISPLACEMENT IN DEG
PRESSURE VS CRANK ANGLE
PRESSURE
PRESSU
RE IN
bars
0
20
40
60
80
100
120
0 100000 200000
VO
300000
OLUME IN m
pv DIA
400000
mm^3
AGRAM
0 5000000 6000000
PRESSUR
RE
‐300
‐200
‐100
0
100
200
300
400
500
600
0 180 360 540 720
TURN
ING M
OMEN
T IN Nm
ANGULAR DISPLACEMENT IN DEG
TURNING MOMENT
0
50
100
150
200
250
300
350
400
450
500
0
Turning Mom
ent
20 40
C
60
Angular Disp
Combined
80
placement
Turning M
100
Moment
120 1140
Turnin
ng Moment
REPORT
The obtained graphs for angular displacement Vs instantaneous velocity, volume of cylinder, instantaneous acceleration, and instantaneous turning moment and also the p‐v diagram shows the performance of a petrol engine considered. Also the combined turning moment of the engine with six inline cylinders has been calculated.