Vehicle Axle Loads depend on
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Vehicle Axle Loads depend on Hitch loads Aerodynamic drag Inertia Force ( a x W/g) Slope/grade (θ ) Rolling resistance Vehicle geometry (towing/towed) L, c, b, h, h h, h b, h a
description
Vehicle Axle Loads depend on. Hitch loads Aerodynamic drag Inertia Force ( a x W/g ) Slope/grade ( θ ) Rolling resistance Vehicle geometry (towing/towed) L, c, b, h, h h, h b, h a. Fundamental rule of vehicle dynamics. - PowerPoint PPT Presentation
Transcript of Vehicle Axle Loads depend on
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
0cossin yhhzhhxxAAfA IWcWhdRhRhag
WhDLWM
θ
c Wf
Fxf
Rxf
Wr
Fxr
Rxr
x
z
ha
DA
W/g axWcosθ
Wsinθ
W
hh
Rh
x Rhz
h
L
dh
bA
B
zyzzxx IMmaFmaF
Solving for Axle Load Wf
LWhA
hA
Dhx
agW
Lh
dhz
Rh
hhx
RWbr
W /)sin)(cos(
LWhA
hA
Dhx
agW
hd
hzR
hh
hxRWc
fW /)sincos(
Taking moments about point B, we can similarly find Wr
What happens to axle loads for changes in:1. Grade?2. Hitchloads?3. Acceleration?4. Drag?
Trailer (with boat/ATV/payload) FBD
0cos)(sin AbAbbxb
hhxbhzbbA hDhag
WhRfWfeRhWM
θ
f
x
z
hab
DAb
Wb/g ax Wbcosθ
Wbsinθ
Wbhb
Rxtr
Wt
e
0sin: Ahxbxtrxb
x DRWRag
WF
Rhx
hhRhz
A
Solving the system of eqn’s
0cos)(sin AbAbbxhhxbhzbbAhDha
gW
hRfWfeRhWM
0sin: Ahxxtrxb
xDRWRa
gW
F
)/()cossin( fehDhagW
hRfWhWRAbAbbxhhxbbbhz
Axtrx
b
hxDWRa
gW
R sin
Let’s rearrange the equations…
To obtain:
Two steps:1. Calculate Rhx and Rhz , then2. Substitute Rhx and Rhz into axle load formulas for Wr , Wf
Solve this eqn first
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
rxr
fxf
WF
WF
xx ag
WgradedraghitchrollingtractionF
xAhxxrxfxfxrx ag
WsinWDR}RR{}FF{F
Assume no hitch and drag forces, constant velocity, then
xxfxrx sinW}FF{F
But remember maximum traction is limited by friction available at surface!
Vehicle towing trailer uphill at constant velocity
)(4 rfrfxrxfWD
WWWWFFF
FWD
RWD
4WD
sin)(sinsinbbtraction
WWWWF
Let drag, rolling, & inertia forces = 0
directionxinweightstrailervehiclesforcetraction )()(
Let’s do some examples…
fxfFWDWFF
rxrRWDWFF
What grade can a vehicle climb?
Friction limitedPower limitedAnything else?
http://www.youtube.com/watch?v=OS5b_cuDVhs
First, what is “slope and grade?”
Grade% radians degrees Cos() Sin()2 0.0200 1.15 0.9998 0.02004 0.0400 2.29 0.9992 0.04006 0.0599 3.43 0.9982 0.05998 0.0798 4.57 0.9968 0.0797
10 0.0997 5.71 0.9950 0.099515 0.1489 8.53 0.9889 0.148320 0.1974 11.31 0.9806 0.196140 0.3805 21.80 0.9285 0.371460 0.5404 30.96 0.8575 0.514580 0.6747 38.66 0.7809 0.6247
100 0.7854 45.00 0.7071 0.7071
Slope, θ
θ
rise
run
)100/(tan,
100(%)
1 gradeAngleGrade
run
riseGrade
)(sin
....
radians
anglessamllfor
Slope: Angle θ
Slope: Grade (%)
Vehicle towing trailer uphill at constant velocity
Van/Trailer Axle Loads and Traction AnalysisVan sym mag units
front axle weight Wfs 1520 lbsrear axle weight Wrs 1150 lbs
total weight W 2670 lbs
Boat/trailer sym mag unitsaxle weight Wta 1200 lbshitch load Fxbs 250 lbs
total weight Wt 1450 lbs
road friction coef. 0.3slope θ 20 %
11.31 degrees
sin)( btotal WWF
lbsF
F
F
total
total
total
824
)2.0)(4120(
)2)(.14502670(
lbs1320W
lbs1495W
:assume
f
r
Will a 4WD, FWD or RWD have enough traction to climb grade?
Which drive will be “grade-able?” (4WD, FWD or RWD)
lbs449)1495(3.0WFF
lbs396)1320(3.0WFF
lbs845lbs)2815(3.0F
)WW(FFF
rxrRWD
fxfFWD
WD4
rfxrxfWD4
Recall…force to overcome…. 824 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 RJEVan/Trailer Axle Loads and Traction Analysis
Van sym mag units Total FWD RWD 4WDfront axle weight Wfs 3200 lbs deg rads sin() err% Fxb Fzb Wr Wf Wx Fxf Fxr Fxtotrear axle weight Wrs 2800 lbs 0 0.000 0.000 0 0 100 2938 3162 0 949 882 1830
total weight W 6000 lbs 1 0.017 0.017 0.0 21 96 2986 3109 126 933 896 1829CG height h1 28 inches 2 0.035 0.035 0.0 42 92 3033 3055 251 917 910 1826
hitch height h2 14 inches 3 0.052 0.052 0.0 63 88 3079 3001 377 900 924 1824hitch rear overhang d 23 inches 4 0.070 0.070 0.1 84 84 3124 2945 502 884 937 1821
wheelbase L 60 inches 5 0.087 0.087 0.1 105 80 3168 2889 628 867 950 1817fr axle to CG b 28.0 inches 6 0.105 0.105 0.2 125 76 3211 2832 753 849 963 1813
rear axle to CG c 32.0 inches 7 0.122 0.122 0.2 146 71 3253 2773 877 832 976 1808c/L 0.5333 8 0.140 0.139 0.3 167 67 3294 2714 1002 814 988 1803d/L 0.3833 9 0.157 0.156 0.4 188 63 3334 2655 1126 796 1000 1797
10 0.175 0.174 0.5 208 59 3373 2594 1250 778 1012 1790Boat/trailer sym mag units 11 0.192 0.191 0.6 229 54 3412 2533 1374 760 1023 1783
axle weight Wta 1100 lbs 12 0.209 0.208 0.7 249 50 3449 2470 1497 741 1035 1776hitch/tongue load Fxbs 100 lbs 13 0.227 0.225 0.9 270 46 3485 2408 1620 722 1045 1768
total weight Wt 1200 lbs 14 0.244 0.242 1.0 290 42 3520 2344 1742 703 1056 1759wheelbase Lt 110 inches 15 0.262 0.259 1.2 311 37 3553 2280 1863 684 1066 1750CG height h3 35 inches 20 0.349 0.342 2.1 410 16 3706 1948 2463 584 1112 1696
f/Lt 0.0833 25 0.436 0.423 3.2 507 -6 3831 1601 3043 480 1149 162930 0.524 0.500 4.7 600 -28 3926 1242 3600 373 1178 1550
road friction coef. 0.3-51.4 -0.896 -0.781 -937 241 -301 4311 -5624 1293 -90 1203
Excess traction force 6918 5534 6827
01/26/09
Grade Hitch loads Axle loads Traction Forces
