Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Mass Properties and Automotive Vertical Acceleration

276 views

Published on

The mass properties of a vehicle affect its motion in all directions, translational and rotational. Previously this author has dealt with how mass properties affect automotive longitudinal acceleration and automotive lateral acceleration . Now a consideration is in order of how mass properties affect automotive vertical acceleration. Of course, lateral or longitudinal inputs can lead to vertical responses; every aspect of a vehicle’s dynamics is interconnected with every other aspect, but it is convenient to divide up automotive dynamics as if the subject were truly a matter of independent motions in the longitudinal, lateral, and vertical directions.

Initially, this paper will investigate the significance of mass properties with regard to automotive ride (transmission of road shock & vibration) and road-holding (maintaining contact at the tire/road interface) through the use of simple, undamped, 1-DOF models. Later, the full story of how mass properties influence the bounce and pitch motions of the sprung mass will necessitate recourse to more complex 2-DOF models. The mass properties of greatest relevance to this investigation will prove to be the “sprung mass”, the “unsprung masses”, the “sprung mass distribution” (longitudinal, lateral, and vertical c.g.), the rotational inertias of the rotating portions of the “unsprung masses”, and the “sprung mass” longitudinal and lateral mass moments of inertia.

Published in: Automotive
  • Be the first to comment

  • Be the first to like this

Mass Properties and Automotive Vertical Acceleration

  1. 1. Brian Paul Wiegand, PE 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011
  2. 2.  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 PROPERTIES 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 2
  3. 3. 1. ALL BASIC AUTOMOTIVE PERFORMANCE CAN BE DEVIDED INTO ONE OF THREE CATEGORIES: 1. LONGITUDINAL: ACCELERATION & BRAKING 2. LATERAL: TURNING, ROLLOVER, DIRECTIONAL STABILITY 3. 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 3
  4. 4.  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 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 4
  5. 5. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 5 A VERY SIMPLE MODEL IS ALL THAT IS NEEDED TO INVESTIGATE SHOCK TRANSMISSION TO SPRUNG MASS:
  6. 6. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 6 TO INVESTIGATE THE EFFECT OF THE UNSPRUNG MASS A SOMEWHAT MORE COMPLICATED MODEL IS NEEDED: EARLY AUTOMOTIVE DESIGNERS WERE WARY OF REDUCING THE UNSPRUNG MASS “TOO MUCH”:
  7. 7. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 7 PROBABLY THE OLDEST KNOWN TECHNIQUE FOR REDUCING ROAD SHOCK TRANSMISSION IS TO INCREASE THE WHEEL RADIUS:
  8. 8. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 8 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…….
  9. 9. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 9 WE’LL INVESTIGATE WHAT HAPPENS AS THE UNSPRUNG MASS IS VARIED: Road Contact Parameters as Unsprung Weight Varies Range Range Quarter 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 d lb lb %Wus lb/in in cpm sec (ft) (in) 920 73 -50% 193.3 4.8 86.04 0.697 4.3 5.13 920 80 -45% 193.3 4.8 86.04 0.697 4.5 5.17 920 93 -36% 193.3 4.8 86.04 0.697 4.9 5.24 920 106 -27% 193.3 4.8 86.04 0.697 5.2 5.31 920 117 -19% 193.3 4.8 86.04 0.697 5.5 5.37 920 145 0% 193.3 4.8 86.04 0.697 6.1 5.51 920 173 19% 193.3 4.8 86.04 0.697 6.6 5.65 920 184 27% 193.3 4.8 86.04 0.697 6.9 5.71 920 197 36% 193.3 4.8 86.04 0.697 7.1 5.78 920 210 45% 193.3 4.8 86.04 0.697 7.3 5.85 920 290 100% 193.3 4.8 86.04 0.697 8.6 6.26
  10. 10. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 10 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) MinLength(ft),Max Depth(in) min l (ft) max d (in) CONCLUSION: FOR PAVED ROADS MINIMUM “l” MORE IMPORTANT (TEND TOWARD DECREASING “mus”)
  11. 11. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 11 NOW WE’LL INVESTIGATE WHAT HAPPENS AS THE SPRING CONSTANT IS VARIED:
  12. 12. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 12 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 0.0 2.0 4.0 6.0 8.0 10.0 12.0 0.0 100.0 200.0 300.0 400.0 Spring Stiffness @ Wheel (lb/in) UndulationMinL(ft), Maxd(in) min l (ft) max d (in)
  13. 13. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 13 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/sec POWER: ft/sec x in2/cycles/ft = in2/cycles/sec
  14. 14. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 14 THE RESULTING TIME DOMAIN PSD’s FOR VARIOUS VELOCITIES 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.
  15. 15. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 15 TRANSMISSIBILITY FACTORS SPRUNG MASS FREE BODY: UNSPRUNG MASS FREE BODY: SPRUNG MASS DYNAMIC EQUILIBRIUM: UNSPRUNG MASS DYNAMIC EQUILIBRIUM: THE RESULTING SET OF SECOND ORDER DIFFERENTIAL EQUATIONS……
  16. 16. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 16 …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:
  17. 17. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 17 THE TRANSMISSIBILITY FACTORS PLOTTED:
  18. 18. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 18 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 SHOWN ONLY UNSPRUNG MASS WAS VARIED >
  19. 19. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 19 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., THE UNSPRUNG MASS VARIATION HAS VIRTUALLY NO EFFECT.
  20. 20. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 20 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
  21. 21. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 21 NOTE THAT HALVING THE WHEEL RADIUS RESULTS IN 1/16th THE INERTIA BUT ONLY 1/8th THE GYRO REACTION TORQUE TORQUE REACTION DIRECTION – FLEMMING’S RIGHT HAND RULE:
  22. 22. 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 22 WHEN BOUNCE & PITCH INTERACT: “BEAT” FREQUENCY (BARF!) BOUNCE & PITCH CAN’T INTERACT WHEN EQUAL: WHICH REDUCES TO WHEN THE “DYNAMIC INDEX” IS ONE:
  23. 23. 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 23 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”
  24. 24. 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 24 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.
  25. 25. 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 25 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 >>>>>>>
  26. 26. 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 26 FIND COEFFICIENTS: FIND NODE POINT LOCATIONS: FIND FREQUENCIES @ NODES: A FORCE AT “J” WILL ONLY CAUSE A ROTATION AT “H”, AND VICE VERSA.
  27. 27. 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 27 TIME DIFFERENTIAL BETWEEN FRONT AND REAR WHEELS ON BUMP: MOTION PER TIME (“t”) EQUATION: PITCH ANGLE RESULTING FROM FRONT & REAR HEIGHTS:
  28. 28. 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 28 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
  29. 29. 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 29 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.
  30. 30. FIVE MINUTES ARE ALLOCATED FOR ASKING QUESTIONS OF THE AUTHOR 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 30
  31. 31. 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 31
  32. 32. 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 32 1958 JAGUAR XK150S
  33. 33. 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 33 1980 FORD FIESTA S

×