Mass properties and automotive lat accel presentation, rev a
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This presentation accompanied the delivery of SAWE Paper #3528 at the 70th International Conference of the SAWE at Houston, TX, USA during May 2011. There are a number of automotive performance aspects which are associated with accelerations in the lateral direction: maneuver (transient and steady state), roll-over, and directional stability. For each of these automotive performance aspects certain mass property parameters play significant roles; it is the intent of this presentation to make explicit exactly how those mass property parameters affect each of those automotive performance aspects.
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Mass properties and automotive lat accel presentation, rev a
- 1. Brian Paul Wiegand, PE 70TH Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011
- 2. PERSONAL INTEREST • SAWE: WROTE PAPERS & JOURNAL ARTICLES • SAE: SEMINAR, PUBLICATIONS, PAPER • 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. 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. TIRE BEHAVIOR COEF OF TRACTION, DRIFT ANGLE WEIGHT TRANSFER SLIDE & ROLLOVER TRANSIENT CONDITION RISE & DECAY, CENTER OF OSCILLATION STEADY STATE CONDITION OVERSTEER & UNDERSTEER DIRECTIONAL STABILITY STATIC & DYNAMIC 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 4
- 5. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 5 COEFFICIENT OF LATERAL TRACTION IS FUNCTION OF NORMAL LOAD: μ = b – m N PARABOLIC NORMAL LOAD – LATERAL FORCE RELATIONSHIP: F = μ N = (b – m N)N = b N – mN2
- 6. LATERAL FORCE – DRIFT ANGLE 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 6
- 7. LATERAL FORCE – DRIFT ANGLE 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 7
- 8. NORMAL LOAD - LATERAL FORCE – DRIFT ANGLE 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 8
- 9. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 9 Faxle= Fi + Fo = (b – m Ni)Ni + (b – m No)No Ni= (Waxle /2) – Waxle ay(hcg /t) No= (Waxle /2) + Waxle ay(hcg /t) AFFECTS THE POTENTIAL LATERAL TRACTION AT AN AXLE:
- 10. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 10 TRACTION POTENTIAL: TRACTION REQUIRED:
- 11. POINTS “A” (SLIDE) & “C” (ROLLOVER): 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 11
- 12. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 12 SLIDE ACCELERATION (POTENTIAL TRACTION = REQUIRED TRACTION, POINT “A”): ROLLOVER ACCELERATION (WEIGHT “TRANSFER” = ½ WEIGHT, POINT “C”):
- 13. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 13
- 14. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 14 + NHTSA NCAP ROLLOVER RESISTANCE RATING (1-5 STARS) BASED (WITH HEAVY “SSF” BIAS) ON: THE “SSF” IS EXACTLY EQUAL TO THE PREVIOUS “ayoverturn” EQUATION
- 15. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 15 SPRUNG MASS ROLLS GEOMETRY CHANGES ROLL ANGLE x ROLL STIFFNESS = LATERAL FORCE x ROLL HEIGHT
- 16. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 16 ROLL ANGLE x ROLL STIFFNESS = LATERAL FORCE x ROLL HEIGHT FRONT AXLE: REAR AXLE: θs kroll = Ws ay hr Cos θs + Ws hr Sin θs + Wusf ay (rrf-hrcf) + Wusr ay (rrr-hrcr)
- 17. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 17
- 18. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 18 THE “OSCILLATION CENTER”, THE INITIAL CENTER OF VEHICLE ROTATION, WHOSE LOCATION DEPENDS ON THE “X FACTOR”, WHICH IN TURN DEPENDS ON YAW RADIUS OF GYRATION & CG.
- 19. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 19 SKIDPAD FOR STEERING CHARACTER & MAXIMUM LATERAL ACCELERATION
- 20. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 20 DISTURBANCE RESPONSE
- 21. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 21 EXPLANATION: TRADITIONAL (pre-1956) STABILITY (STATIC)
- 22. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 22 FROM THE GEOMETRY AND THE 2-D FREE BODY EQUATIONS OF MOTION FOR VEHICLE IN A STEADY STATE CONDITION: SUM LATERAL FORCES = 0, SUM MOMENTS ABOUT CG = 0. THE SOLUTION YIELDS SOME INTERESTING INSIGHTS WHICH CAN BE ADJUSTED SOMEWHAT TO ACCOUNT FOR WEIGHT TRANSFER AND ROLL. “BICYCLE” MODEL, A MORE MODERN ANALYSIS:
- 23. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 23 “BICYCLE” MODEL, SOME ANALYSIS RESULTS:
- 24. 1) MAXIMUM LATERAL (SLIDE) ACCELERATION 2) ROLLOVER ACCELERATION 3) TRANSIENT CONDITION 4) STEADY STATE / STABILITY CONDITION 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 24 FOUR MAJOR AREAS:
- 25. MINIMIZE VEHICLE WEIGHT. LOCATE VEHICLE C.G. SO THERE IS EVEN STATIC WEIGHT/AREA LOAD ON ALL TIRES. MINIMIZE VEHICLE C.G. HEIGHT. MAXIMIZE VEHICLE TRACK. MAXIMIZE TIRE COEFFICIENT “b”, MINIMIZE TIRE COEFFICIENT “m”. MINIMIZE ROLL (MINIMIZE SPRUNG WEIGHT C.G. TO R.C. HEIGHT/MAXIMIZE ROLL STIFFNESS). MINIMIZE DIRECTIONAL STABILITY. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 25
- 26. MINIMIZE VEHICLE C.G. HEIGHT. MAXIMIZE VEHICLE TRACK. MINIMIZE VEHICLE ROLL: MINIMIZE SPRUNG WEIGHT C.G. TO R.C. HEIGHT MAXIMIZE ROLL STIFFNESS. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 26
- 27. MINIMIZE ROLL INERTIA. MINIMIZE YAW INERTIA. MINIMIZE C.G. TO O.C. DISTANCE: MINIMIZE YAW RADIUS OF GYRATION. WEIGHT DISTRIBUTION AS CLOSE TO 50/50 AS POSSIBLE. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 27
- 28. MAXIMIZE WEIGHT (not recommended). MAXIMIXE YAW INERTIA (not recommended). “UNDERSTEER”: FRONT WEIGHT BIAS. REAR CORNERINING STIFFNESS BIAS. FRONT ROLL RESISTANCE BIAS. “NOSE DOWN” ROLL AXIS. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 28
- 29. 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 29
- 30. RESERVE SLIDES IN ANTICIPATION OF QUESTIONS THAT MAY BE ASKED 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 30
- 31. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 31
- 32. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 32
- 33. 70th Annual International Conference of the Society of Allied Weight Engineers, Inc. Houston, TX, 14-19 May 2011 33
Editor's Notes
- MASS PROPERTIES & AUTOMOTIVE LATERAL
- WHY AUTOMOTIVE MASS PROPERTIES? WELL, AS THE VU-GRAPH SAYS, IT’S A MATTER OF PERSONAL INTEREST…………..SAWE PAPER, JOURNAL ARTICLES, SAE MEMBER, SEMINAR, PUBLICATIONS, PERSONAL LIBRARY TECH BOOKS & PAPERS AND, OF COURSE, MASS PROPERTIES HAS GREAT SIGNIFICANCE FOR AUTOMOTIVE PERFORMANCE….FUEL ECONOMY, EMISSIONS, RIDE, SAFETY, ACCELERATION, BRAKING, MANEUVER; A SIGNIFICANCE WHICH IS APPLICABLE (ALTHOUGH NOT EQUALLY) FOR ALL VEHICLES (EVEN ELECTRIC)... AND LAST, BUT NOT LEAST, WRITING A PAPER ON THIS SUBJECT SEEMED TO BE A GOOD WAY TO HELP EXPAND THE SCOPE OF OUR SOCIETY. I UNDERSTAND THAT AS A SOCIETY WE ARE INTERESTED IN BECOMING MORE INCLUSIVE, EXPANDING OUR MEMBERSHIP BASE, AND THIS IS MY SMALL WAY OF CONTRIBUTING TO THAT GOAL. THERE ARE ONLY ABOUT 40 PAPERS IN THE SAWE CATEGORY 31.0; THE VAST MAJORITY OF OUR PAPERS AND JOURNAL TOPICS, ETC., CONCERN AEROSPACE AND MARITIME MATTERS…….
- Airplane behavior is overwhelmingly dictated by aerodynamic forces, while automobile behavior is a matter of tire forces. However, even though the automobile preceded the airplane by nearly two decades the theory of automobile performance and control lagged that of the airplane by about 35 years. The Wright brothers built a wind tunnel to study aerodynamic effects before their first powered, manned flight in 1903. The first tire test machine was probably the rolling drum of Becker, Fromm, and Maruhn in 1930. The war years of WW I and WW II brought most automobile research to a halt, but only accelerated aircraft research. Although the genesis of automotive theory can be traced back to the 1920’s, it was after WW II that there was an explosion of automobile theory development which, to a large degree, was modeled after the airplane example.
- (THIS IS FOR THE STEERING INPUT SCENARIO, THE DIRECTIONAL DISTURBANCE SCENARIO IS SOMEWHAT DIFFERENT…)
- (THIS SHOULD BE REPLACED BY THE REVISED FIGURE!!)
- The roll angle equation is “transcendental” in that it can’t be solved directly but instead must be solved by incremental methods; this equation can be used to determine a vehicle’s “roll gain”. The symbolism for the roll angle equation is: θs = The sprung mass roll angle, degrees. kroll = The total vehicle roll resistance, lb-ft/deg. Ws = The weight of the sprung mass, lb. ay = The lateral acceleration, g’s. hr = The sprung mass roll moment arm, ft. Wusf = The front axle unsprung mass weight, lb. rrf = Front axle unsprung mass vertical c.g. (approx. as roll rad), ft. Wusr = The rear axle unsprung mass weight, lb. rrr = Rear axle unsprung mass vertical c.g. (approx. as roll rad18), ft. hrcf = Front axle roll center height, ft. hrcr = Rear axle roll center height, ft. The symbolism for the normal load equations is: θs = The sprung mass roll angle, degrees. kfroll = The front suspension roll stiffness, lb-ft/deg. krroll = The rear suspension roll stiffness, lb-ft/deg. Wf = The static front axle weight load, lb. Wr = The static rear axle weight load, lb. ay = The lateral acceleration, g’s. hrcf = The height of front roll center above (+) or below ground (-), in. hrcr = The height of rear roll center above (+) or below ground (-), in. tf = The front axle track, in. tr = The rear axle track, in. Ws = The sprung mass weight, lb. lwb = The vehicle wheelbase, in. lrs = The longitudinal distance from the sprung mass CG to the rear axle, in.
- Both “Characteristic Speed” and “Critical Speed” must be determined at lateral acceleration equal to zero (or as close to it as possible); see SAE J670.
- There are literally dozens of “conclusions” of various degree of significance in Chapter 10 of the paper, but this is essentially the conclusion from the 35,000 foot level, so to speak….
- There are literally dozens of “conclusions” of various degree of significance in Chapter 10 of the paper, but this is essentially the conclusion from the 35,000 foot level, so to speak….
- There are literally dozens of “conclusions” of various degree of significance in Chapter 10 of the paper, but this is essentially the conclusion from the 35,000 foot level, so to speak….
- There are literally dozens of “conclusions” of various degree of significance in Chapter 10 of the paper, but this is essentially the conclusion from the 35,000 foot level, so to speak….
- There are literally dozens of “conclusions” of various degree of significance in Chapter 10 of the paper, but this is essentially the conclusion from the 35,000 foot level, so to speak…. WHY THE “NOSE DOWN” ROLL AXIS IMPROVES STABILITY IS EVIDENT WHEN THE CORRECT NORMAL LOAD EQUATIONS ARE SHOWN; THOSR EQUATIONS INCLUDE THE EFFECT OF ROLL CENTER HEIGHTS, WHICH DETERMINE ROLL AXIS INCLINATION.