Mass Properties and Automotive Vertical Acceleration

MASS PROPERTIES & AUTOMOTIVE

VERTICAL ACCELERATION

Brian Paul Wiegand, PE70TH Annual International Conference of the Society of Allied Weight Engineers, Inc.

Houston, TX, 14-19 May 2011

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WHY AUTOMOTIVE MASS PROPERTIES?

PERSONAL INTEREST • SAWE: WROTE PAPERS & JOURNAL ARTICLES• SAE MEMBER: SEMINAR, PUBLICATIONS• PERSONAL LIBRARY: BOOKS, TECH PAPERS

SIGNIFICANCE • ACCELERATION / BRAKING, MANEUVER, RIDE• FUEL ECONOMY, EMISSIONS, SAFETY

EXPAND SAWE SCOPE• AEROSPACE MASS PROPERTIES• MARITIME MASS PROPERTIES70th Annual International Conference of the Society of Allied Weight Engineers, Inc.

Houston, TX, 14-19 May 2011

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THE GRAND SCHEME 1. ALL BASIC AUTOMOTIVE PERFORMANCE CAN BE DEVIDED INTO ONE OF THREE

CATEGORIES:1. LONGITUDINAL: ACCELERATION & BRAKING2. LATERAL: TURNING, ROLLOVER, DIRECTIONAL STABILITY3. VERTICAL: SHOCK, VIBRATION, PITCH & ROLL MOTION

2. ALL OTHER AUTOMOTIVE ISSUES CAN BE RELATED TO THE ABOVE: FUEL ECONOMY / EMMISSIONS SAFETY: PASSIVE & ACTIVE NVH: NOISE, VIBRATION, & HARSHNESS

3. THEREFORE, THREE SAWE PAPERS:1. “MASS PROPERTIES & AUTOMOTIVE LONGITUDINAL ACCELERATION”, SAWE

PAPER #1634, ATLANTA, GA, 21-23 MAY 1984.2. “MASS PROPERTIES & AUTOMOTIVE LATERAL ACCELERATION”, SAWE PAPER

#3528, HOUSTON, TX, 14-19 MAY 2011.3. “MASS PROPERTIES & AUTOMOTIVE VERTICAL ACCELERATION”, SAWE PAPER

#3521, HOUSTON, TX, 14-19 MAY 2011.4. AND A FOURTH SUPPORTING PAPER:

4. “AUTOMOTIVE MASS PROPERTIES ESTIMATION”, SAWE PAPER #3490, VIRGINIA BEACH, VA, 22-26 MAY 2010.

70th Annual International Conference of the Society of Allied Weight Engineers, Inc.Houston, TX, 14-19 May 2011

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MASS PROPERTIES & AUTOMOTIVE VERTICAL

ACCELERATION SHOCK

SHOCK TRANSFER: SPRING RATE, SPRUNG MASS, UNSPRUNG MASS, ROLLING RADIUS ROAD CONTACT

ROAD CONTACT PARAMETERS: SPRING RATE, MASS RATIO VIBRATION

RESPONSE GAIN: SPRING RATE, DAMPING, MASS RATIO GYROSCOPIC REACTION

GYROSCOPIC REACTION: ROLLING MASS, ANGULAR VELOCITY RIDE MOTIONS

BEAT FREQUENCY PRINCIPAL MODES: BOUNCE & PITCH CONJUGATE CENTERS “FLAT RIDE”: FRONT-REAR SUSPENSION INTERACTION


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SHOCK


A VERY SIMPLE MODEL IS ALL THAT IS NEEDED TO INVESTIGATE SHOCK TRANSMISSION TO SPRUNG MASS:

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SHOCK


TO INVESTIGATE THE EFFECT OF THE UNSPRUNG MASS A SOMEWHAT MORE COMPLICATED MODEL IS NEEDED:

EARLY AUTOMOTIVE DESIGNERS WERE WARY OFREDUCING THE UNSPRUNG MASS “TOO MUCH”:

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SHOCK


PROBABLY THE OLDEST KNOWN TECHNIQUE FOR REDUCING ROAD SHOCK TRANSMISSION IS TO INCREASE THE WHEEL RADIUS:

http://upload.wikimedia.org/wikipedia/en/2/2b/HansomCab.gif

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ROAD CONTACT


FROM THE SPRING-MASS SYSTEM EQUATIONS THE FOLLOWING CAN BE DERIVED:

NOTE THE APPEARANCE OF THE UNSPRUNG-TO-SPRUNG MASS RATIO: “mus/ms”. THIS RATIO CAN BE REDUCED BY INCREASING THE SPRUNG MASS, BUT AS THAT ADVERSELY EFFECTS SO MANY PERFORMANCE CRITERIA (ACCELERATION, FUEL ECONOMY, ETC.) THAT IS NOT A GOOD IDEA. SO…….

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ROAD CONTACT


WE’LL INVESTIGATE WHAT HAPPENS AS THE UNSPRUNG MASS IS VARIED:

Road Contact Parameters as Unsprung Weight Varies Range RangeQuarter Model, General SHM Equations, at 30 mph: 4.3 1.13

1 2 4 3 5 6 7 8

Ws Wus chg k ds fn T min l max dlb lb %Wus lb/in in cpm sec (ft) (in)

920 73 -50% 193.3 4.8 86.04 0.697 4.3 5.13920 80 -45% 193.3 4.8 86.04 0.697 4.5 5.17920 93 -36% 193.3 4.8 86.04 0.697 4.9 5.24920 106 -27% 193.3 4.8 86.04 0.697 5.2 5.31920 117 -19% 193.3 4.8 86.04 0.697 5.5 5.37920 145 0% 193.3 4.8 86.04 0.697 6.1 5.51920 173 19% 193.3 4.8 86.04 0.697 6.6 5.65920 184 27% 193.3 4.8 86.04 0.697 6.9 5.71920 197 36% 193.3 4.8 86.04 0.697 7.1 5.78920 210 45% 193.3 4.8 86.04 0.697 7.3 5.85920 290 100% 193.3 4.8 86.04 0.697 8.6 6.26

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ROAD CONTACT


WHAT’S HAPPENING MAY BE BETTER UNDERSTOOD GRAPHICALLY:

Road Contact Parameters vs Unsprung Weight

0.0

2.0

4.0

6.0

8.0

10.0

0 100 200 300 400

Unsprung Weight (lb)

Min

Len

gth

(ft),

Max

D

epth

(in)

min l (ft)

max d (in)

CONCLUSION: FOR PAVED ROADS MINIMUM “l” MORE IMPORTANT (TEND TOWARD DECREASING “mus”)

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ROAD CONTACT


NOW WE’LL INVESTIGATE WHAT HAPPENS AS THE SPRING CONSTANT IS VARIED:

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ROAD CONTACT


AGAIN, WHAT’S HAPPENING MAY BE BETTER UNDERSTOOD GRAPHICALLY:

CONCLUSION: AS DECREASING “mus” TENDS TO WORK AGAINST MAX “d” THE SPRINGS MAY BE SOFTENED TO COMPENSATE.

Road Contact Parameters vs Spring Stiffness

0.02.04.06.08.0

10.012.0

0.0 100.0 200.0 300.0 400.0

Spring Stiffness @ Wheel (lb/in)

Und

ulat

ion

Min

L (f

t),

Max

d (i

n)

min l (ft)

max d (in)

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VIBRATION


ROAD SURFACE INPUT TO A VEHICLE SUSPENSION SYSTEM IS CHARACTERIZED BY ROAD’S “PSD” (POWER SPECTRAL DENSITY). PSD’s FOR VARIOUS ROAD TYPES ARE EMPIRICALLY DETERMINED, BUT MAY BE REDUCED TO TYPE REPRESENTATIVE MATHEMATICAL MODELS.

ROAD PSD’s ARE IN THE SPATIAL DOMAIN, BUT FOR STUDY OF AN AUTOMOBILE MOVING OVER THE ROAD AT SOME VELOCITY “V” (ft/sec) THE CONVERSION TO TIME DOMAIN IS:

FREQUENCY:ft/sec x cycles/ft = cycles/secPOWER:ft/sec x in2/cycles/ft = in2/cycles/sec

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VIBRATION


THE RESULTING TIME DOMAIN PSD’s FOR VARIOUSVELOCITIES THROUGHOUT THE VEHICLE OPERATIONAL ENVELOPE MAY BE DOUBLE DIFFERENTIATED (d2/dt2) TO OBTAIN PLOTS OF ROAD VERTICAL ACCELERATION / FREQUENCY vs. FREQUENCY.

FOR EACH VEHICLE WEIGHT CONDITION FROM “1-UP” TO GVWR THERE IS A TRANSMISSIBILITY FACTOR BY WHICH THE ROAD ACCELERATION INPUT PLOTS MAY BE MULTIPLIED TO OBTAIN VEHICLE RESPONSE ACCELERATION PLOTS.

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VIBRATION


TRANSMISSIBILITY FACTORSSPRUNG MASS FREE BODY: UNSPRUNG MASS FREE BODY:

SPRUNG MASS DYNAMIC EQUILIBRIUM: UNSPRUNG MASS DYNAMIC

EQUILIBRIUM:

THE RESULTING SET OF SECOND ORDER DIFFERENTIAL EQUATIONS……

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VIBRATION


…SOLVED FOR THE TRANSMISSIBILITY FACTORS:SPRUNG MASS ACCELERATION RESPONSE TO ROAD ACCELERATION INPUT:

SPRUNG MASS ACCELERATION RESPONSE TO AXLE FORCE INPUT:

SPRUNG MASS ACCELERATION RESPONSE TO BODY FORCE INPUT:

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VIBRATION


THE TRANSMISSIBILITY FACTORS PLOTTED:

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VIBRATION


UNSPRUNG MASS EFFECT ON ROAD INPUT-TO- SPRUNG MASS TRANSMISSIBILITY FACTOR:

DECREASING UNSPRUNG MASS REDUCES TRANSMISSION FOR FREQUENCIES GREATER THAN SPRUNG MASS RESONANCE.

ALTHOUGH MASS RATIO IS SHOWNONLY UNSPRUNG MASS WAS VARIED >

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VIBRATION


UNSPRUNG MASS EFFECT ON SPRUNG MASS RESPONSE -TO-SPRUNG MASS INPUT TRANSMISSIBILITY FACTOR:

AGAIN, SINCE THE SPRUNG MASS RESONANCE FREQUENCY DOESN’T CHANGE, ONLY THE UNSPRUNG MASS IS BEING VARIED. SINCE SPRUNG MASS (“BODY”) INPUT CONSISTS OF SUCH THINGS AS ENGINE VIBRATION, EXHAUST PULSATIONS, ETC., THEUNSPRUNG MASS VARIATION HAS VIRTUALLY NO EFFECT.

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VIBRATION


SPRUNG MASS RESPONSE-TO-UNSPRUNG MASS INPUT:

“AXLE” (UNSPRUNG MASS) LEVEL INPUT FORCE DUE TO IMBALANCE, MISALIGNMENT, OUT-OF-ROUND, & STIFFNESS VARIATIONS.

FORCE / SPRUNG MASS x GAIN = RESPONSE

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GYROSCOPIC REACTION


NOTE THAT HALVING THE WHEEL RADIUS RESULTS IN 1/16th THE INERTIA BUT ONLY 1/8th THE GYRO REACTIONTORQUE

TORQUE REACTION DIRECTION – FLEMMING’S RIGHT HAND RULE:

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RIDE MOTIONS: “BEAT”

70TH Annual International Conference of the Society of Allied Weight Engineers, Inc.Houston, TX, 14-19 May 2011

WHEN BOUNCE & PITCH INTERACT:

“BEAT” FREQUENCY (BARF!)

BOUNCE & PITCH CAN’T INTERACT WHEN EQUAL:

WHICH REDUCES TO WHEN THE “DYNAMIC INDEX” IS ONE:

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RIDE MOTIONS: PITCH & BOUNCE


NODE 1 WOULD BE REGARDED AS A “PITCH” NODE AND NODE 2 WOULD BE REGARDED AS A “BOUNCE” NODE.

THE EQUATIONS OF DYNAMIC EQUILIBRIUM ARE WRITTEN FOR SPRUNG MASS FREE BODY AND SOLVED. NOTE THESE TWO EQUATIONS HAVE ONE TERM IN COMMON:

“(krlr-kflf)/Ms”

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RIDE MOTIONS: PITCH & BOUNCE


GENERAL EQUATIONS OF MOTION >>>>>>>>

UNCOUPLED PURE BOUNCE & PURE SPRING MOTIONS >>

BECOME:WHEN:

I.E.,

LOCATION OF NODES >>

COEFFICIENTS >>>>

FWD FROM C.G. IS POS., AFT FROM C.G. IS NEG.

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RIDE MOTIONS: SPRING CENTER


THE S.C. IS A SPECIAL POINT AS A FORCE PRESSING DOWN AT THE S.C. WILL CAUSE ONLY VERTICAL MOVEMENT, NO ROTATION.

HOWEVER, WHEN RELEASED A BOUNCE AND A ROTATION MOVEMENT WILL RESULT. THIS IS CALLED “STATICALLY UNCOUPLED” AND/OR “DYNAMICALLY COUPLED” MOTION.

TO LOCATE THE SPRING CENTER >>>>>>>

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RIDE MOTIONS: CONJUGATE POINTS


FIND COEFFICIENTS:

FIND NODE POINT LOCATIONS:

FIND FREQUENCIES @ NODES:

A FORCE AT “J” WILL ONLY CAUSE A ROTATION AT “H”, AND VICE VERSA.

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RIDE MOTIONS: “FLAT RIDE”


TIME DIFFERENTIAL BETWEEN FRONT AND REAR WHEELS ON BUMP:MOTION PER TIME (“t”) EQUATION:PITCH ANGLE RESULTING FROM FRONT & REAR HEIGHTS:

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RIDE MOTIONS: NODE LOCATION


JUST AS IT IS IMPORTANT TO GET RIDE MOTIONS AS SIMPLE AS POSSIBLE AND AS CLOSE TO TOLERABLE FREQUENCY AS POSSIBLE, IT IS ALSO IMPORTANT HOW THE NODE POINTS ARE LOCATED WITH RESPECT TO THE PASSENGERS.

1931 CADILLAC V12 LIMOUSINE

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CONCLUSIONS


THE ESSENCE OF AUTOMOTIVE DESIGN WITH REGARD TO VERTICAL ACCELERATIONS IS TO MINIMIZE SHOCK, VIBRATION, & ADVERSE GYROSCOPIC REACTIONS; AND TO GET AUTOMOTIVE RIDE MOTIONS AS SIMPLE AND SMOOTH AND COMFORTABLE FOR HUMAN SENSITIVITY AS POSSIBLE.

TO THIS END CERTAIN MASS PROPERTIES PLAY DETERMINING ROLES: SPRUNG MASS, UNSPRUNG MASS, SPRUNG MASS C.G. LOCATION, SPRUNG MASS MOMENT OF INERTIA IN PITCH, SPRUNG MASS PITCH RADIUS OF GYRATION, UNSPRUNG MASS (ROLLING) MOMENT OF INERTIA; ALL AS DEMONSTRATED.

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Q&A

FIVE MINUTES ARE ALLOCATED FOR ASKING QUESTIONS OF THE AUTHOR


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BACKUP


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BACKUP


1958 JAGUAR XK150S

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BACKUP


1980 FORD FIESTA S

Mass Properties and Automotive Vertical Acceleration

Automotive

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