Transcript Document

Vehicle Axle Loads depend on






Hitch loads
Aerodynamic drag
Inertia Force ( ax W/g)
Slope/grade (θ )
Rolling resistance
Vehicle geometry (towing/towed)
L, c, b, h, hh, hb, ha
Fundamental rule of vehicle dynamics
Control forces act on the tires’ contact patches
(i.e. accelerate, brake, turn)
Find Axle Loads Wr and Wf
DA
x
Wsinθ
W/g ax
h
Rhx
hh
A
Rhz
 Fx  max
Wr
 Fz  maz
 M A  W f L  DAhA 
z
B
Rxf
Fxf
θ
b
c
dh
Wcosθ
W
Rxr
Fxr
ha
L
Wf
 M y  I z
W
a x h  Rhx hh  Rhz d h  Wh sin   Wc cos  I y  0
g
Solving for Axle Load Wf
W
W  (Wc cos  R h  R d  a h  D h  Wh sin  ) / L
f
hx h
hz h g x
A A
Taking moments about point B, we can similarly find Wr
W
W  (Wb cos  R h  R ( d  L )  a h  D h  Wh sin  ) / L
r
hx h
hz h
A A
g x
What happens to axle loads for changes in:
1. Grade?
2. Hitchloads?
3. Acceleration?
4. Drag?
Trailer (with boat/ATV/payload) FBD
DAb
x
Wbsinθ
Wb/g ax
Wbcosθ
Rhz
Wb
hb
hab
hh
z
Rxtr
A
Rhx
e
θ
f
Wt
 M A  Wb hb sin   Rhz (e  f )  Wb f cos  Rhx hh 
 Fx : 
Wb
a x  Rxtr  Wb sin   Rhx  D A  0
g
Wb
a x hb  D Ab h Ab  0
g
Solving the system of eqn’s
Let’s rearrange the equations…
W
 M A  Wb hb sin  R hz ( e  f )  Wb f cos  R hx hh  g ax hb  D Ab hAb  0
 Fx : 
Wb
ax  R xtr  W sin   R hx  D A  0
g
To obtain:
R hx 
Wb
ax  R xtr  W sin   D A
g
R hz  (Wb hb sin   Wb f cos  R hx hh 
Solve this eqn
first
W
ax hb  D Ab hAb ) /(e  f )
g
Two steps:
1. Calculate Rhx and Rhz , then
2. Substitute Rhx and Rhz into axle load formulas for Wr , Wf
Gradeability… ability to climb grades
Ability to climb is a function of:
 Need friction between towing tires and surface
 Traction forces = f(μ, axle weights)
 Traction force ≥ downhill weight = Wtotal sinө
Forces in x-direction
W
 Fx  traction  rolling  hitch  drag  grade  a x
g
 Fx  { Fxr  Fxf }  { Rxf  Rxr }  Rhx
W
 D A  W sin   a x
g
Assume no hitch and drag forces, constant velocity, then
 Fx  { Fxr  Fxf }  W sin  x
But remember maximum traction is limited by friction available at surface!
Fxf   W f
Fxr   Wr
Vehicle towing trailer uphill at constant velocity
Let drag, rolling, & inertia forces = 0
traction force( s)  (vehicle trailer weights) in x  direction
Ftraction  W sin  Wb sin  (W  Wb ) sin
4WD
F4WD  Fxf  Fxr   Wf   Wr  (Wf  Wr )
FWD
FFWD  Fxf   Wf
RWD
FRWD  Fxr   Wr
Let’s do some examples…
What grade can a vehicle climb?
Friction limited
Power limited
Anything else?
http://www.youtube.com/watch?v=OS5b_cuDVhs
First, what is “slope and grade?”
Slope: Angle θ
Slope: Grade (%)
Slope, θ
Grade
radians degrees
%
1.15
0.0200
2
2.29
0.0400
4
3.43
0.0599
6
4.57
0.0798
8
5.71
0.0997
10
8.53
0.1489
15
11.31
0.1974
20
21.80
0.3805
40
30.96
0.5404
60
38.66
0.6747
80
45.00
0.7854
100
Cos()
0.9998
0.9992
0.9982
0.9968
0.9950
0.9889
0.9806
0.9285
0.8575
0.7809
0.7071
Sin()
0.0200
0.0400
0.0599
0.0797
0.0995
0.1483
0.1961
0.3714
0.5145
0.6247
0.7071
rise
100
run
Grade Angle ,   tan 1 ( grade / 100)
Grade (%) 
rise
θ
run
for sam ll angles....
sin    ( radians)
Vehicle towing trailer uphill at constant velocity
Van/Trailer Axle Loads and Traction Analysis
Van sym
mag units
front axle weight Wfs
1520 lbs
rear axle weight Wrs
1150 lbs
total weight W
2670 lbs
Boat/trailer sym
axle weight Wta
hitch load Fxbs
total weight Wt
road friction coef.
slope

θ
mag
1200
250
1450
units
lbs
lbs
lbs
0.3
20 %
11.31 degrees
Ftotal  (W  Wb ) sin 
Ftotal  (2670 1450)(.2)
Ftotal  (4120)(0.2)
Ftotal  824 lbs
assum e:
Wr  1495 lbs
W f  1320 lbs
Will a 4WD, FWD or RWD have enough
traction to climb grade?
Which drive will be “grade-able?”
(4WD, FWD or RWD)
Recall…force to overcome…. 824 lbs.
F4WD  Fxf  Fxr  ( W f  Wr )
F4WD  0.3 ( 2815) lbs  845 lbs
FFWD  Fxf   W f  0.3( 1320)  396 lbs
FRWD  Fxr   Wr  0.3( 1495)  449 lbs
FWD and RWD will slip!
Automate calculations with a spreadsheet….
Connect ot course website at:
http://coen.boisestate.edu/reggert/ME485/ME485.htm
Click on… GradeabilityS09 (*.xls)
Gradeability (Ford E150 plus ATV and trailer)
ME485/585 Vehicle Design
Van and ATV Trailer
Van/Trailer Axle Loads and Traction Analysis
Van sym
mag units
Grade
front axle weight Wfs
3200 lbs
deg rads sin()
rear axle weight Wrs
2800 lbs
0
0.000 0.000
total weight W
6000 lbs
1
0.017 0.017
CG height h1
28 inches
2
0.035 0.035
hitch height h2
14 inches
3
0.052 0.052
hitch rear overhang d
23 inches
4
0.070 0.070
wheelbase L
60 inches
5
0.087 0.087
fr axle to CG b
28.0 inches
6
0.105 0.105
rear axle to CG c
32.0 inches
7
0.122 0.122
c/L 0.5333
8
0.140 0.139
d/L 0.3833
9
0.157 0.156
10 0.175 0.174
Boat/trailer sym
mag units
11 0.192 0.191
axle weight Wta
1100 lbs
12 0.209 0.208
hitch/tongue load Fxbs
100 lbs
13 0.227 0.225
total weight Wt
1200 lbs
14 0.244 0.242
wheelbase Lt
110 inches
15 0.262 0.259
CG height h3
35 inches
20 0.349 0.342
f/Lt 0.0833
25 0.436 0.423
30 0.524 0.500
road friction coef. 
0.3
-51.4 -0.896 -0.781
RJE
Hitch loads
err% Fxb Fzb
0
0 100
0.0
21
96
0.0
42
92
0.0
63
88
0.1
84
84
0.1
105
80
0.2
125
76
0.2
146
71
0.3
167
67
0.4
188
63
0.5
208
59
0.6
229
54
0.7
249
50
0.9
270
46
1.0
290
42
1.2
311
37
2.1
410
16
3.2
507
-6
4.7
600 -28
-937
Axle loads
Wr
Wf
2938 3162
2986 3109
3033 3055
3079 3001
3124 2945
3168 2889
3211 2832
3253 2773
3294 2714
3334 2655
3373 2594
3412 2533
3449 2470
3485 2408
3520 2344
3553 2280
3706 1948
3831 1601
3926 1242
01/26/09
Traction Forces
Total FWD RWD 4WD
Wx Fxf
Fxr Fxtot
0 949 882 1830
126 933 896 1829
251 917 910 1826
377 900 924 1824
502 884 937 1821
628 867 950 1817
753 849 963 1813
877 832 976 1808
1002 814 988 1803
1126 796 1000 1797
1250 778 1012 1790
1374 760 1023 1783
1497 741 1035 1776
1620 722 1045 1768
1742 703 1056 1759
1863 684 1066 1750
2463 584 1112 1696
3043 480 1149 1629
3600 373 1178 1550
241 -301 4311 -5624 1293 -90 1203
Excess traction force 6918 5534 6827