Vehicle Longitudinal Load Transfer parts I_II_MAR13
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Vehicle Longitudinal Load Transfer parts I_II_MAR13

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Vehicle Longitudinal Load Transfer parts I_II_MAR13

Vehicle Longitudinal Load Transfer parts I_II_MAR13

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Vehicle Longitudinal Load Transfer parts I_II_MAR13 Vehicle Longitudinal Load Transfer parts I_II_MAR13 Presentation Transcript

  • 1 Wm Harbin Technical Director BND TechSource Vehicle Load Transfer
  • 2 Vehicle Load Transfer Part I General Load Transfer
  • 3  Within any modern vehicle suspension there are many factors to consider during design and development.  Factors in vehicle dynamics: • Vehicle Configuration • Vehicle Type (i.e. 2 dr Coupe, 4dr Sedan, Minivan, Truck, etc.) • Vehicle Architecture (i.e. FWD vs. RWD, 2WD vs.4WD, etc.) • Chassis Architecture (i.e. type: tubular, monocoque, etc. ; material: steel, aluminum, carbon fiber, etc. ; fabrication: welding, stamping, forming, etc.) • Front Suspension System Type (i.e. MacPherson strut, SLA Double Wishbone, etc.) • Type of Steering Actuator (i.e. Rack and Pinion vs. Recirculating Ball) • Type of Braking System (i.e. Disc (front & rear) vs. Disc (front) & Drum (rear)) • Rear Suspension System Type (i.e. Beam Axle, Multi-link, Solid Axle, etc.) • Suspension/Braking Control Systems (i.e. ABS, Electronic Stability Control, Electronic Damping Control, etc.) Factors in Vehicle Dynamics View slide
  • 4  Factors in vehicle dynamics (continued): • Vehicle Suspension Geometry • Vehicle Wheelbase • Vehicle Track Width Front and Rear • Wheels and Tires • Vehicle Weight and Distribution • Vehicle Center of Gravity • Sprung and Unsprung Weight • Springs Motion Ratio • Chassis Ride Height and Static Deflection • Turning Circle or Turning Radius (Ackermann Steering Geometry) • Suspension Jounce and Rebound • Vehicle Suspension Hard Points: • Front Suspension • Scrub (Pivot) Radius • Steering (Kingpin) Inclination Angle (SAI) • Caster Angle • Mechanical (or caster) trail • Toe Angle • Camber Angle • Ball Joint Pivot Points • Control Arm Chassis Attachment Points • Knuckle/Brakes/Steering • Springs/Shock Absorbers/Struts • ARB (anti-roll bar) Factors in Vehicle Dynamics View slide
  • 5  Factors in vehicle dynamics (continued): • Vehicle Suspension Geometry (continued) •Vehicle Suspension Hard Points (continued): • Rear Suspension • Scrub (Pivot) Radius • Steering (Kingpin) Inclination Angle (SAI) • Caster Angle (if applicable) • Mechanical (or caster) trail (if applicable) • Toe Angle • Camber Angle • Knuckle and Chassis Attachment Points • Various links and arms depend upon the Rear Suspension configuration. (i.e. Dependent vs. Semi-Independent vs. Independent Suspension) • Knuckle/Brakes • Springs/Shock Absorbers • ARB (anti-roll bar) •Vehicle Dynamic Considerations • Suspension Dynamic Targets • Wheel Frequency • Bushing Compliance • Lateral Load Transfer with and w/o ARB • Roll moment • Roll Stiffness (degrees per g of lateral acceleration) • Maximum Steady State lateral acceleration (in understeer mode) • Rollover Threshold (lateral g load) • Linear Range Understeer (typically between 0g and 0.4g) Factors in Vehicle Dynamics
  • 6  Factors in vehicle dynamics (continued): • Vehicle Dynamic Considerations (continued) • Suspension Dynamic Analysis • Bundorf Analysis • Slip angles (degrees per lateral force) • Tire Cornering Coefficient (lateral force as a percent of rated vertical load per degree slip angle) • Tire Cornering Forces (lateral cornering force as a function of slip angle) • Linear Range Understeer • Steering Analysis • Bump Steer Analysis • Roll Steer Analysis • Tractive Force Steer Analysis • Brake Force Steer Analysis • Ackerman change with steering angle • Roll Analysis • Camber gain in roll (front & rear) • Caster gain in roll (front & rear – if applicable) • Roll Axis Analysis • Roll Center Height Analysis • Instantaneous Center Analysis • Track Analysis • Load Transfer Analysis • Unsprung and Sprung weight transfer • Jacking Forces • Roll Couple Percentage Analysis • Total Lateral Load Transfer Distribution (TLLTD) Factors in Vehicle Dynamics
  • 7  While the total amount of factors may seem a bit overwhelming, it may be easier to digest if we break it down into certain aspects of the total.  The intent of this document is to give the reader a better understanding of vehicle dynamic longitudinal and lateral load transfer as a vehicle accelerates/decelerates in a particular direction.  The discussion will include: Part I – General Load Transfer Information • Load vs. Weight Transfer • Rotational Moments of Inertia • Sprung and Unsprung Weight Part II – Longitudinal Load Transfer • Vehicle Center of Gravity • Longitudinal Load Transfer • Suspension Geometry • Instant Centers • Side View Swing Arm • Anti-squat, Anti-dive, and Anti-lift Vehicle Load Transfer Part III – Lateral Load Transfer • Cornering Forces • Suspension Geometry • Front View Swing Arm • Roll Center Heights • Roll Axis • Roll Stiffness • Anti-roll bars • Tire Rates • Roll Gradient • Lateral Load Transfer
  • 8 Load vs. Weight Transfer
  • 9  In automobiles, load transfer is the imaginary "shifting" of weight around a motor vehicle during acceleration (both longitudinal and lateral). This includes braking, or deceleration (which can be viewed as acceleration at a negative rate). Load transfer is a crucial concept in understanding vehicle dynamics.  Often load transfer is misguidedly referred to as weight transfer due to their close relationship. The difference being load transfer is an imaginary shift in weight due to an imbalance of forces, while weight transfer involves the actual movement of the vehicles center of gravity (Cg). Both result in a redistribution of the total vehicle load between the individual tires. Load vs. Weight Transfer
  • 10  Weight transfer involves the actual (small) movement of the vehicle Cg relative to the wheel axes due to displacement of liquids within the vehicle, which results in a redistribution of the total vehicle load between the individual tires.  Liquids, such as fuel, readily flow within their containers, causing changes in the vehicle's Cg. As fuel is consumed, not only does the position of the Cg change, but the total weight of the vehicle is also reduced.  Another factor that changes the vehicle’s Cg is the expansion of the tires during rotation. This is called “dynamic rolling radius” and is effected by wheel-speed, temperature, inflation pressure, tire compound, and tire construction. It raises the vehicle’s Cg slightly as the wheel-speed increases. Load vs. Weight Transfer
  • 11  The major forces that accelerate a vehicle occur at the tires contact patch. Since these forces are not directed through the vehicle's Cg, one or more moments are generated. It is these moments that cause variation in the load distributed between the tires.  Lowering the Cg towards the ground is one method of reducing load transfer. As a result load transfer is reduced in both the longitudinal and lateral directions. Another method of reducing load transfer is by increasing the wheel spacings. Increasing the vehicles wheel base (length) reduces longitudinal load transfer. While increasing the vehicles track (width) reduces lateral load transfer. Load vs. Weight Transfer
  • Rotational Moments of Inertia 12 y x z Vertical Lateral Longitudinal Roll (p) Yaw (r) Pitch (q) Cg
  • Moment of Inertia  Polar moment of inertia • A simple demonstration of polar moment of inertia is to compare a dumbbell vs. a barbell both at the same weight. Hold each in the middle and twist to feel the force reacting at the center. Notice the dumbbell (which has a lower polar moment) reacts quickly and the barbell (which has a higher polar moment) reacts slowly. 13 Wdo 2  d1 d1 CL d2 d2 CL W W Example: W = 50 lb (25 lb at each end) d1 = 8 in d2 = 30 in 22 1 3200)8(*25*2 inlb 22 2 000,45)30(*25*2 inlb
  • Moment of Inertia  Sum the polar moments of inertia • The total polar moment of inertia for a vehicle can be determined by multiplying the weight of each component by the distance from the component Cg to the Cg of the vehicle. The sum of the component polar moments of inertia would establish the total vehicle polar moment of inertia. • A vehicle with most of its weight near the vehicle Cg has a lower total polar moment of inertia is quicker to respond to steering inputs. • A vehicle with a high polar moment is slower to react to steering inputs and is therefore more stable at high speed straight line driving. 14
  • Moment of Inertia  Effects of polar moments of inertia • Here is an example of a V8 engine with a typical transmission packaged into a sports car. 15 Example: WEng = 600 lb WTran = 240 lb dEng = 40 in dTran = 10 in dEng dTran dWdWM TranTranEngEngo 22 )()()(  222 000,984)10(240)40(600)( inlbinlbinlbM o 
  • Moment of Inertia 16 Example: WEng = 600 lb WTran = 240 lb dEng = 70 in dTran = 40 in dEng dTran  Effects of polar moments of inertia • Here is an example of a V8 engine with a typical transmission packaged into a sedan. dWdWM TranTranEngEngo 22 )()()(  222 000,324,3)40(240)70(600)( inlbinlbinlbM o 
  • 17 Load Transfer
  • 18 Load Transfer  Load Transfer • The forces that enable a road vehicle to accelerate and stop all act at the road surface. • The center of gravity, which is located considerably above the road surface, and which is acted upon by the accelerations resulting from the longitudinal forces at the tire patches, generates a moment which transfers load. • As asymmetric load results in differing traction limits, a vehicles handling is affected by the “dynamic load distribution”.
  • 19 Load Transfer equations & terms Load Transfer g onAcceleratiVehicleWeightVehicle ForceInertial *  Wheelbase CGForceInertial TransferLoad height*  am=FLawSecondsNewton :' F = force m = mass a = acceleration g = ag = acceleration due to gravity = 32.2ft/sec2 = 9.8m/sec2 ax = acceleration in the x direction ay = acceleration in the y direction az = acceleration in the z direction Weight = mass * ag
  • 20 Load Transfer  Load transfers between the Center of Gravity and the road surface through a variety of paths. • Suspension Geometry • Front: Location of instant centers (Side View Swing Arm) • Rear: Instant centers, Lift Bars (Side View Swing Arm) • Suspension Springs • Front: Coils, Air Springs, leafs or Torsion bars and Anti- roll bars • Rear: Coils, Air Springs, leafs or Torsion bars and Anti- roll bars
  • 21 Load transfer (continued) • Dampers (Shock Absorbers) • During transient conditions • Tires • During all conditions (where the rubber meets the road) Where and how you balance the load transfer between the Springs, Geometry, Dampers and Tires are key determinates as to how well the car will accelerate and brake and the stability associated with each condition. Load Transfer
  • 22 Load Transfer Control Devices  Dampers (Shock Absorbers) • Along with the springs, dampers transfer the load of the rolling (pitching) component of the vehicle. They determine how the load is transferred to and from the individual wheels while the chassis is rolling and/or pitching. • Within 65-70% critically damped is said to be the ideal damper setting for both handling and comfort simultaneously. Most modern dampers show some digression to them as well, meaning they may be 70% critically damped at low piston speeds but move lower to allow the absorption of large bumps. Damping is most important below 4 in/second as this is where car control tuning takes place.
  • 23 Load Transfer Control Devices  Springs • Along with the dampers (shock absorbers), springs transfer the load of the sprung mass of the car to the road surface. During maneuvers, depending on instant center locations, the springs and dampers transfer some portion of the (m x a), mass x acceleration, forces to the ground. • Spring Rate is force per unit displacement for a suspension spring alone . • For coil springs this is measured axially along the centerline. • For torsion bar springs it is measured at the attachment arm. • For leaf springs it is measured at the axle seat. • The spring rate may be linear (force increases proportionally with displacement) or nonlinear (increasing or decreasing rate with increasing displacement). • Units are typically lb/in.
  • 24 Load Transfer Control Devices  Anti-roll bars • [Drawing 1] shows how an anti-roll bar (ARB) is twisted when the body rolls in a turn. This creates forces at the four points where the bar is attached to the vehicle. The forces are shown in [Drawing 2]. Forces A on the suspension increase [load] transfer to the outside tire. Forces B on the frame resist body roll. The effect is a reduction of body roll and an increase in [load] transfer at the end of the chassis which has the anti-roll bar. Because the total [load] transfer due to centripetal force is not changed, the opposite end of the chassis has reduced [load] transfer. [6] Drawing 2 Drawing 1Direction of Turn A A B B
  • 25  Bushing Deflection (suspension compliance) • All of the calculations shown in this presentation do not include bushing deflection. There are many rubber bushings within a vehicle suspension to consider when analyzing suspension compliance. Load Transfer Control Devices
  • 26 Load Transfer Control Devices  Frame/Chassis Deflection • All of the calculations shown in this presentation are made under the assumption that the frame or chassis is completely rigid (both in torsion and bending). Of course any flexing within the frame/chassis will adversely effect the performance of the suspension which is attached to it.
  • Sprung and Unsprung Weight  100% Unsprung weight includes the mass of the tires, rims, brake rotors, brake calipers, knuckle assemblies, and ball joints which move in unison with the wheels.  50% unsprung and 50% sprung weight would be comprised of the linkages of the wheel assembly to the chassis.  The % unsprung weight of the shocks, springs and anti-roll bar ends would be a function of their motion ratio/2 with the remainder as % sprung weight.  The rest of the mass is on the vehicle side of the springs is suspended and is 100% sprung weight. 27
  • Sprung and Unsprung Weight 28
  • Springs Motion Ratio  The shocks, springs, struts and anti-roll bars are normally mounted at some angle from the suspension to the chassis.  Motion Ratio: If you were to move the wheel 1 inch and the spring were to deflect 0.75 inches then the motion ratio would be 0.75 in/in. 29 Motion Ratio = (B/A) * sin(spring angle)
  • Springs Motion Ratio 30  The shocks, springs, struts and anti-roll bars are normally mounted at some angle from the suspension to the chassis.  Motion Ratio: If you were to move the wheel 1 inch and the spring were to deflect 0.75 inches then the motion ratio would be 0.75 in/in. Motion Ratio = (B/A) * sin(spring angle)
  • Wheel Rates 31  Wheel Rates are calculated by taking the square of the motion ratio times the spring rate. Squaring the ratio is because the ratio has two effects on the wheel rate. The ratio applies to both the force and distance traveled.  Because it's a force, and the lever arm is multiplied twice. • The motion ratio is factored once to account for the distance-traveled differential of the two points (A and B in the example below). • Then the motion ratio is factored again to account for the lever-arm force differential. Example: K | A----B------------P • P is the pivot point, B is the spring mount, and A is the wheel. Here the motion ration (MR) is 0.75... imagine a spring K that is rated at 100 lb/in placed at B perpendicular to the line AP. If you want to move A 1 in vertically upward, B would only move (1in)(MR) = 0.75 in. Since K is 100 lb/in, and B has only moved 0.75 in, there's a force at B of 75 lb. If you balance the moments about P, you get 75(B)=X(A), and we know B = 0.75A, so you get 75(0.75A) = X(A). A's cancel and you get X=75(0.75)=56.25. Which is [100(MR)](MR) or 100(MR)2. Wheel Rate (lb/in) = (Motion Ratio)2* (Spring Rate)
  • 0 50 100 150 200 250 300 -2.49 -2.22 -1.95 -1.68 -1.42 -1.15 -0.89 -0.63 -0.36 -0.10 0.16 0.41 0.67 0.93 1.18 1.44 1.69 1.94 2.19 2.44 WheelRate(lb/in) Reboundto Jounce (in) Wheel Rate vs. Wheel Position Coil-over Shock ARB Wheel Rates 32  Since the linkages pivot, the spring angles change as the components swing along an arc path. This causes the motion ratio to be calculated through a range. The graph below shows an example of these results for both coil-over shock and anti-roll bar for an independent front suspension from rebound to jounce positions. KW = Wheel Rate (lb/in) = (Motion Ratio - range)2* (Spring Rate - linear) KW = MR2 * KS Example: Coil-over KS = 400 lb/in (linear) Coil-over MR= 0.72-.079 in/in ARB KS = 451.8 lb/in (body roll) ARB MR= 0.56-0.61 in/in Ride height
  • 0 50 100 150 200 250 300 -2.49 -2.22 -1.95 -1.68 -1.42 -1.15 -0.89 -0.63 -0.36 -0.10 0.16 0.41 0.67 0.93 1.18 1.44 1.69 1.94 2.19 2.44 WheelRate(lb/in) Reboundto Jounce (in) Wheel Rate vs. Wheel Position Coil-over Shock ARB Wheel Rates 33  In longitudinal pitch, the anti-roll bar (ARB) rotates evenly as the chassis moves relative to the suspension. Therefore, the ARB only comes into play during lateral pitch (body roll) of the vehicle (it also comes into play during one wheel bump, but that rate is not shown here). KW = Wheel Rate (lb/in) = (Motion Ratio - range)2* (Spring Rate - linear) KW = MR2 * KS Example: Coil-over KS = 400 lb/in (linear) Coil-over MR= 0.72-.079 in/in ARB KS = 451.8 lb/in (body roll) ARB MR= 0.56-0.61 in/in Ride height
  • Spring Rates/Ride Frequency 34  The static deflection of the suspension determines its natural frequency.  Static deflection is the rate at which the suspension compresses in response to weight. 0 20 40 60 80 100 120 140 160 180 200 0 10 20 30 40 50 60 70 80 90 100 w=Frequency(cycles/min) x = Static Deflection (in) Ride Natural Frequency vs. Static Wheel Deflection x 188 
  • Spring Rates/Ride Frequency 35  Ride frequency is the undamped natural frequency of the body in ride. The higher the frequency, the stiffer the ride.  Based on the application, there are ballpark numbers to consider. • 30 - 70 CPM for passenger cars • 70 - 120 CPM for high-performance sports cars • 120 - 300+ CPM for high downforce race cars  It is common to run a spring frequency higher in the rear than the front. The idea is to have the oscillation of the front suspension finish at the same time as the rear.  Since the delay between when the front suspension hits a bump and the rear suspension hits that bump varies according to vehicle speed, the spring frequency increase in the rear also varies according to the particular speed one wants to optimize for.
  • Spring Rates/Ride Frequency 36  Once the motion ratios has been established, the front and rear spring rates can be optimized for a “flat” ride at a particular speed.
  • 37 Vehicle Load Transfer Part II Longitudinal Load Transfer
  • 38 Center of Gravity
  • 39  Locating the center of gravity in the X-Y (horizontal) plane is performed by placing the vehicle on scales and identifying the corresponding loads. • X, Y, positions are noted • % Front, % Rear, % Left, % Right, % Diagonal (RF,LR)  Locating the center of gravity height (hcg) can be achieved by raising one end of the vehicle and identifying the load change on the un-raised end which is a result of the height change on the raised end. Center of Gravity Location
  • 40 Center of Gravity Location WR lRl F L Cg WF SCALE SCALE Center of Gravity Horizontal Plane Location
  • 41 Center of Gravity Location 100%         tot LFRF front W WW W 100%         tot RRLR rear W WW W 100%         tot LRLF left W WW W 100%         tot RRRF right W WW W 100%         tot LRRF diag W WW W
  • 42 Center of Gravity Location 100 3542 880880 %7.49         frontW 100 3542 891891 %3.50         rearW 100 3542 891880 %50         leftW 100 3542 891880 %50         rightW 100 3542 891880 %50         diagW Example: C3 Corvette Upgrade Weight total = 3542 lb W RF = 880 lb W LF = 880 lb W RR = 891 lb W LR = 891 lb
  • 43 Center of Gravity Location L W W L W W tot r tot f f        1 L W W L W W tot f tot r r        1
  • 44 Center of Gravity Location 98 3542 1782 98 3542 1760 1in3.49        f 98 3542 1760 98 3542 1782 1in7.48        r Example: C3 Corvette Upgrade W tot = 3542 lb W F = 1760 lb W R = 1782 lb L = 98.0 in
  • 45 Center of Gravity Height Location   LWWLMHorizontal fRR 0:     coscoscossin0 coscossin0: LWLWLWhWor LWWLWhWMRaised ffRcg ffRcgR  
  • 46 Center of Gravity Height Location The center of gravity height above the spindle centerline is: hW LW W LW aboveh tot f tot f cg      * * sin* cos** 2      cos sin tan    L h hCGtotal on level ground is: (where rt = tire radius) t tot f cg r hW LW totalh     * * 2
  • 47 Center of Gravity Height Location The center of gravity height above the spindle centerline is: 12*3542 9604*62.22 98.6sin*3542 98.6cos*98*62.22 11.5  98.6cos 98.6sin 98 12 98.6tan  hCGtotal on level ground is: (where rt = tire radius) 89.11 12*3542 9604*62.22 in17  Example: C3 Corvette W tot = 3542 lb W F = 1760 lb W R = 1782 lb L = 98.0 in rt = 11.89 in h = 12 in WF= 22.62 lb
  • 48 Longitudinal Load Transfer
  • 49 Longitudinal Load Transfer  Longitudinal (vehicle fore-aft direction) load transfer occurs due to either positive (acceleration) or negative (braking) acceleration.  Load transfer is associated with each of these accelerations. This is due to the acceleration forces acting between the tire contact patches at the road surface and the vehicle center of gravity height which is above the road surface.
  • 50 Longitudinal Load Transfer The vehicle load distribution on level ground is shown in the following equations. A B WF WR lRl F L Cg WT        L W=WW=LWAxleFront R FRF          L W=WW=LWAxleRear F RFR  
  • 51 Longitudinal Load Transfer The vehicle load distribution on level ground is shown in the following equations. A B WF WR lRl F L Cg WT lb=WW=LWAxleFront FRF 1760 98 7.48 3542         lb=WW=LWAxleRear RFR 1782 98 3.49 3542         Example: C3 Corvette W T = 3542 lb W F = 1760 lb W R = 1782 lb L = 98.0 in lF = 49.3 in lR = 48.7 in
  • 52 Longitudinal Load Transfer The load transfer can be most easily determined on level ground, at a speed low enough such that aerodynamic resistance force would be negligible (zero). The equations are then solved for the static load at each axle and any load transferred due to acceleration or deceleration. A B WF +/- W WR +/- W lRl F L acceleration force Cgaccel Fa WT hcg L h a a W L h am= L h F=W cg g x T cgcg aT **
  • 53 Longitudinal Load Transfer The load transfer can be most easily determined on level ground, at a speed low enough such that aerodynamic resistance force would be negligible (zero). The equations are then solved for the static load at each axle and any load transferred due to acceleration or deceleration. A B WF +/- W WR +/- W lRl F L acceleration force Cgaccel Fa WT hcg lb= L h F=W cg aT 2.286 98 17 *)2.32/15(*3542  Example: C3 Corvette W T = 3542 lb L = 98.0 in hcg = 17 in ax = 15 ft/sec2 ag = 32.2 ft/sec2
  • 54        L h a a L W=WW=0=M(B) cg g xR TF *  Longitudinal Load Transfer In forward acceleration the load on the front axle can be found by solving the moment about point B of the figure. A B WF - W WR + W lRl F L acceleration force Cg accel Fa WT hcg
  • 55 Longitudinal Load Transfer In forward acceleration the load on the front axle can be found by solving the moment about point B of the figure. Example: C3 Corvette W T = 3542 lb W F = 1760 lb W = 286.2 lb l R = 48.7 in L = 98.0 in hcg = 17 in ax = 15 ft/sec2 ag = 32.2 ft/sec2 A B WF - W WR + W lRl F L acceleration force Cgaccel Fa WT hcg lb=WW=0=M(B) F 8.1473 98 17 * 2.32 15 98 7.48 3542        Check: 1473.8 lbs + 286.2 lbs = 1760 lb
  • 56 Longitudinal Load Transfer In forward acceleration the load on the rear axle can be found by solving the moment about point A of the figure. A B WF + W WR - W lRl F L acceleration force Cg accel Fa WT hcg        L h a a L W=WW=0=M(A) cg g xF TR * 
  • 57 Longitudinal Load Transfer In forward acceleration the load on the rear axle can be found by solving the moment about point A of the figure. A B WF + W WR - W lRl F L acceleration force Cgaccel Fa WT hcg Example: C3 Corvette W T = 3542 lb W R = 1782 lb W = 286.2 lb l F = 49.3 in L = 98.0 in hcg = 17 in ax = 15 ft/sec2 ag = 32.2 ft/sec2 lbs=WW=0=M(A) R 2.2068 98 17 * 2.32 15 98 3.49 3542        Check: 2068.2 lbs - 286.2 lbs = 1782 lbs
  • 58 Longitudinal Acceleration Pitch  The vehicle pitch angle , if no suspension forces oppose it (no anti-dive, anti-lift, or anti-squat), is a function of the load transfer (W) and the wheel rate (KW). • If the front wheel rate is KWf and the rear is KWr then the load transfer (W) would be divided between the left and right wheels. Therefore vertical displacements (Z) of the sprung (body) mass at the wheel locations are as shown. ZR ZF   Cg Cg JOUNCE JOUNCE REBOUND REBOUND (Jounce and Rebound are also known as Bump and Droop)
  • 59 Longitudinal Acceleration Pitch K W =Z K W =Z Wf F Wr R 2/2/    180 L K W + K W = L Z+Z = L K W + K W = WrWf deg FRWrWf rad * 2/2/2/2/  ZR ZF   Cg Cg (no anti-dive, anti-lift, or anti-squat)
  • 60 Longitudinal Acceleration Pitch in=Zin=Z FR 62. 26.230 2/2.286 455. 35.314 2/2.286  deg63.* 98 26.230 2/2.286 35.314 2/2.286 01097. 98 62.455. 98 26.230 2/2.286 35.314 2/2.286      180 + = + = + = deg radrad Example: C3 Corvette Upgrade KSf = 400 lb/in MRf = 0.759 in/in KWf = 230.26 lb/in KSr = 600 lb/in MRr = 0.724 in/in KWr = 314.35 lb/in W = 286.2 lb L = 98.0 in ZR ZF   Cg Cg (no anti-dive, anti-lift, or anti-squat) KW = MR2 * KS
  • 61 Suspension Geometry
  • Instant Centers  Instant Center (IC) • Simply put, an instant center is a point in space (either real or extrapolated) around which the suspension's links rotate. • “Instant" means at that particular position of the linkage. • "Center" refers to an extrapolated point that is the effective pivot point of the linkage at that instant. • The IC is used in both side view swing arm (SVSA) and a front view swing arm (FVSA) geometry for suspension travel. 62 Front View GeometrySide View Geometry
  • Swing Arms  Swing Arms • There are many different types of vehicle suspension designs. All of which have instant centers (reaction points) developed by running lines through their pivots to an intersection point. • A swing arm by definition has an minimum of two pivot points attaching a suspension component to the vehicle chassis or underbody. To simplify the concept, imagine a line running from the IC directly to the suspension component. This line is referred to as the swing arm. 63FVSA Swing Arm SVSA Swing Arm
  • Swing Arms  Swing Arms • The side view swing arm controls force and motion factors predominantly related to longitudinal accelerations, while the front view swing arm controls force and motion factors due to lateral accelerations. 64 FVSA Swing Arm SVSA Swing Arm
  • 65  Shown is a schematic of a solid rear drive axle with the linkages replaced with a swing arm. In a solid drive axle the axle and differential move together and are suspended from the chassis using springs and/or trailing arms. Side View Swing Arm Cg e d L Fza Fxa Fx Fz IC hb
  • 66  Shown is a schematic of an independent rear suspension (IRS) with the linkages replaced with a swing arm. In an IRS the differential is mounted to the chassis as the half shafts move independently and are suspended from the chassis using springs, control arms and trailing arms. Side View Swing Arm Cg e d L Fza Fxa Fx Fz IC h b r
  • 67 Anti- Geometry
  • 68 Anti- Geometry  Anti-squat Anti-squat in rear suspensions reduces the jounce (upward) travel during forward acceleration on rear wheel drive cars only.  Anti-dive Anti-dive geometry in front suspensions reduces the jounce (upward) deflection under forward braking.  Anti-lift Anti-lift in rear suspensions reduces rebound (downward) travel during forward braking.
  • 69 Anti-Squat Geometry
  • 70 Anti-squat geometry  Anti-squat During forward (longitudinal) acceleration the vehicle load transfer tends to compress the rear springs (suspension jounce) and allow the front springs to extend (suspension rebound). Anti-squat characteristics can be designed into the rear suspension geometry. Anti-squat geometry produces a side view swing arm (SVSA) that predicts suspension component behavior.  Cg JOUNCE REBOUND
  • 71 Anti-squat geometry  Anti-squat Geometry that produces an instant center (IC) through which acceleration forces (Fza and Fxa) can act to reduce or eliminate drive wheel spring deflection during acceleration. Cg e d L Fza Fxa Fx Fz IC h b r WT 100% Anti-squat Line
  • 72  Instant center locations are projected onto the longitudinal axis of the vehicle. This provides the location where the forces transmitted during acceleration effectively act.  The resultant horizontal and vertical components of the tractive force transmitted through these instant centers determine the load percentage transfer that acts through the suspension linkages, with the remaining load acting through the suspension springs. Anti-squat geometry
  • 73 Anti-squat geometry The percentage of anti-squat is now determined relative to the 100% (h/L) angle. If a suspension has 100% anti-squat, all the longitudinal load transfer is carried by the suspension linkages and not by the springs (h/L line would be parallel to the swing arm line). L h = d re =  btan Cg e d L Fza Fxa Fx Fz IC h b r WT 100% Anti-squat Line b
  • 74  The magnitude of the vertical (Fza) components determines, in part, the ability for the driver to accelerate without spinning the tires.  The magnitude of the vertical (Fza) components also dictates the load % transfer that is transmitted through the springs and dampers to the road surface and the load % that transfers directly through the suspension linkages. Anti-squat geometry
  • 75  The load transfer during acceleration is as shown:  The tractive effort (Fx) at the drive wheels is calculated as: L h a a W = L h am=F x g T za x g T xxa a a W =F=F Anti-squat geometry (1) (2)
  • 76  By examining the free body of the rear suspension and summing moments about the contact patch, the equation below is derived.  Since Fxa is the Tractive Force. d re F=F 0=reF-dF0=M xaza xazaR   d re a a W =F x g T za  Anti-squat geometry (3) (4) Cg e d L Fza Fxa Fx Fz IC h b r WT 100% Anti-squat Line b
  • 77  Equating equations (1) and (4) results in an equation which indicates the relationships for 100% anti-squat.  The angle the instant center (IC) must lie on for 100% anti- squat is: d re = L h d re a a W = L h a a W =F x g T x g T za    L h = d re =  btan Anti-squat geometry (5) (6)
  • 78  If the tan β < h/L then squat will occur. L h = d re =  btan Anti-squat geometry Cg e d L Fza Fxa Fx Fz IC h b r WT 100% Anti-squat Line b
  • 79  Anti-squat rear solid axle • Shown is a SVSA of a solid rear drive axle. The torque reaction is taken by the suspension components. Anti-squat geometry Cg e d L Fza Fxa Fx Fz IC hb L h d e =squatAnti %100 100* / / / tan % Lh de Lh =squatAnti  b
  • 80  Anti-squat rear solid axle • Shown is a SVSA of a solid rear drive axle. The torque reaction is taken by the suspension components. Anti-squat geometry Cg e d L Fza Fxa Fx Fz IC hb %125100* 100/20 45/25.11 / tan %  Lh =squatAnti b L h d e =squatAnti %100 Example: Solid Axle e= 11.25 in d = 45 in L = 100 in h = 20 in
  • 81  Anti-squat independent rear suspension • Shown is a SVSA of an independent rear suspension (IRS). The torque reaction is taken by the chassis. Anti-squat geometry L h d re =squatAnti   %100 100* / / / tan % Lh dre Lh =squatAnti   b Cg e d L Fza Fxa Fx Fz IC h b r WT 100% Anti-squat Line b
  • 82  Anti-squat independent rear suspension • Shown is a SVSA of an independent rear suspension (IRS). The torque reaction is taken by the chassis. Anti-squat geometry L h d re =squatAnti   %100 Example: C3 Upgrade e= 15.62 in d = 32.84 in L = 98 in h = 17 in r = 11.89 in %5.65100* 98/17 84.32/89.1162.15 / tan %    Lh =squatAnti b Cg e d L Fza Fxa Fx Fz IC h b r WT 100% Anti-squat Line b
  • 83 Anti-squat geometry  Anti-squat effects on longitudinal pitch angle 100*% * =oncompensatipitch Wf Wr K K L h L h d re                                       L h Kd re KL h K WfWrWr x g T a a W L =(rad)anglePitch * 2* 1* 2* 1* 2* 1** 1 
  • 84 Anti-squat geometry  Anti-squat effects on longitudinal pitch angle Example: C3 Corvette Upgrade e – r = 3.73 in WT = 3542 lb d = 32.84 in KWr = 314.35 lb/in L = 98 in KWf = 230.26 lb/in h = 17 in ax = 180 in/sec2 r = 11.89 in ag = 386.4 in/sec2                       98 17 * )2*26.230( 1 84.32 73.3 * )2*35.314( 1 98 17 * )2*35.314( 1 180* 4.386 3542 * 98 1 =(rad)anglePitch  squatAntidegrad=(deg)anglePitch %5.65@45.0 180 *0079.0    %28100* 4103. 1136. % =oncompensatipitch Check: (1-.28)*.63deg = .45deg
  • 85 Anti-squat geometry  Anti-squat effects on longitudinal pitch angle Example: C3 Corvette Upgrade e – r = 3.73 in WT = 3542 lb d = 32.84 in KWr = 314.35 lb/in L = 98 in KWf = 230.26 lb/in h = 17 in ax = 180 in/sec2 r = 11.89 in ag = 386.4 in/sec2                       98 17 * )2*26.230( 1 0* )2*35.314( 1 98 17 * )2*35.314( 1 180* 4.386 3542 * 98 1 =(rad)anglePitch  squatAntidegrad=(deg)anglePitch %0@63.0 180 *011.0    If e-r/d = 0, then Anti-squat = 0
  • 86 Longitudinal Acceleration Pitch in=Zin=Z FR 62. 26.230 2/2.286 455. 35.314 2/2.286  deg63.* 98 26.230 2/2.286 35.314 2/2.286 01097. 98 62.455. 98 26.230 2/2.286 35.314 2/2.286      180 + = + = + = deg radrad Example: C3 Corvette Upgrade KSf = 400 lb/in MRf = 0.759 in/in KWf = 230.26 lb/in KSr = 600 lb/in MRr = 0.724 in/in KWr = 314.35 lb/in DW = 286.2 lb L = 98.0 in ZR ZF   Cg Cg (no anti-dive, anti-lift, or anti-squat) KW = MR2 * KS Check: if e-r/d = 0, then anti-squat = 0 0.63˚ @ 0% Anti-squat Previous Slide No. 60
  • 87 Anti-dive Geometry
  • 88 Anti-dive geometry  Anti-dive During braking (longitudinal deceleration) the vehicle load transfer tends to compress the front springs (suspension jounce) and allow the rear springs to extend (suspension rebound). Anti-dive is usually designed into both front and rear suspensions (Anti-dive at the front and Anti-lift in the rear). Anti-dive geometry produces a side view swing arm (SVSA) that predicts suspension component behavior. Cg JOUNCE REBOUND
  • 89 Anti-dive geometry  Anti-dive The total longitudinal load transfer under steady acceleration or braking is a function of the wheelbase (L), CG height (h), and braking force (WT)*(ax /ag). Cg L h WT WT (ax/ag) = braking force +  load -  load L h a a W = L h am=load x g T 
  • 90 Anti-dive geometry  Anti-dive The total longitudinal load transfer under steady acceleration or braking is a function of the wheelbase (L), CG height (h), and braking force (WT)*(ax /ag). lb= L h am=load 2.286 98 17 *180* 4.386 3542  Example: C3 Corvette Upgrade WT = 3542 lb L = 98 in h = 17 in ax = 180 in/sec2 (.46 g) ag = 386.4 in/sec2
  • 91 Anti-dive geometry Example: C3 Corvette Upgrade WT = 3542 lb L = 98 in h = 17 in 0 500 1000 1500 2000 2500 3000 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 AxleLoad(lbf) Deceleration (g's) Load Transfer vs. Deceleration Front Load (lbf) Rear Load (lbf) L h a a W = L h am=load x g T 
  • 92 Anti-dive geometry  Brake Bias (brake force distribution) • The following factors will affect the load on an axle for any given moment in time: • Weight distribution of the vehicle (static). • CG height – the higher it is, the more load transference during braking. • Wheelbase – the shorter it is, the more load transference during braking. • The following factors will affect how much brake torque is developed at each corner of the vehicle, and how much of that torque is transferred to the tire contact patch and reacted against the ground: • Rotor effective diameter • Caliper piston diameter • Lining friction coefficients • Tire traction coefficient properties  Cg JOUNCE REBOUND
  • 93 Anti-dive geometry  Brake Bias (brake force distribution) • Braking force at the tire contact patch vs. the total load on that tire will determine the braking bias. • Changing the CG height, wheelbase, or deceleration level will dictate a different force distribution, or bias, requirement for a braking system. • Conversely, changing the effectiveness of the front brake components without changing the rear brake effectiveness can also cause our brake bias to change.  Cg JOUNCE REBOUND
  • 94 Anti-dive geometry  Brake Bias (brake force distribution)  Cg JOUNCE REBOUND 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 %ofVehicleLoadTransfer %ofTotalBrakingForce Deceleration (g's) Typical Brake System Bias % Front Load % Front Braking % Rear Load % Rear Braking
  • 95 Anti-dive geometry 100*)(%*)/(*tan% brakingfronthL=diveAnti fb  Anti-dive (front) and Anti-lift (rear) suspension • Shown is an SVSA with lines (100% Anti-dive/lift) representing the load transfer during braking. If the IC’s are below these lines, the percentage of anti will be below 100%. If the IC’s are above these lines, the percentage of anti will be above 100%. Cg L ICr h br WT ax bfICf %FB x L 100% Anti-dive Line 100% Anti-lift Line 1 - %FB x L 100*)%1(*)/(*tan% brakingfronthL=liftAnti r b
  •  Anti-dive (front) and Anti-lift (rear) suspension • Shown is an SVSA with lines (100% Anti-dive/lift) representing the load transfer during braking. If the IC’s are below these lines, the percentage of anti will be below 100%. If the IC’s are above these lines, the percentage of anti will be above 100%. 96 Anti-dive geometry Example: C3 Corvette Upgrade tan bf = .1124 tan br = .4894 L = 98 in h = 17 in % front braking @ .46g = .71 %46100*)71(.*)765.5(*1124.% =diveAnti %82100*)29(.*)765.5(*4894.% =liftAnti
  •  Anti-dive (front) and Anti-lift (rear) suspension • Since Anti-dive and Anti-lift are a resultant of braking force, and the braking force changes due to brake bias, the % Anti changes as the rate of deceleration changes. 97 Anti-dive geometry 0% 20% 40% 60% 80% 100% 120% 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 %Anti-dive&Anti-lift %ofTotalBrakingForce Deceleration (g's) Anti-dive & Anti-lift vs. Brake Bias % Anti-dive % Front Braking % Anti-lift % Rear Braking
  • 98 Design factors in Anti-dive and Anti-Squat Since load transfer is a function of deceleration rate, and the brake forces are shared, anti-dive geometry on the drive axle may need to be more aggressive than anti-squat geometry. Swing arm length and angle dictates the rate of change of geometry forces.
  • 99 Design factors in Anti-dive and Anti-Squat For an independent suspension a percentage of 100% would indicate the suspension is taking 100% of the load transfer under acceleration/braking instead of the springs which effectively binds the suspension. However, in the case of leaf spring rear suspension the anti-squat can often exceed 100% (meaning the rear may actually raise under acceleration) and because there isn't a second arm to bind against, the suspension can move freely. Traction bars are often added to drag racing cars with rear leaf springs to increase the anti-squat to its maximum. This has the effect of forcing the rear of the car upwards and the tires down onto the ground for better traction.
  • 100 References: 1. Ziech, J., “Weight Distribution and Longitudinal Weight Transfer - Session 8,” Mechanical and Aeronautical Engineering, Western Michigan University. 2. Hathaway, R. Ph.D, “Spring Rates, Wheel Rates, Motion Ratios and Roll Stiffness,” Mechanical and Aeronautical Engineering, Western Michigan University. 3. Gillespie, T. Ph.D, Fundamentals of Vehicle Dynamics, Society of Automotive Engineers International, Warrendale, PA, February, 1992, (ISBN: 978-1-56091- 199-9). 4. Reimpell, J., Stoll, H., Betzler, J. Ph.D, The Automotive Chassis: Engineering Principles, 2nd Ed., Butterworth-Heinemann, Woburn, MA, 2001, (ISBN 0 7506 5054 0). 5. Milliken, W., Milliken, D., Race Car Vehicle Dynamics, Society of Automotive Engineers International, Warrendale, PA, February, 1994, (ISBN: 978-1-56091- 526-3). 6. Puhn, F., How to Make Your Car Handle, H.P. Books, Tucson, AZ, 1976 (ISBN 0- 912656-46-8).
  • 101 Next… Part III - Lateral Load Transfer Thank You! For additional information please visit our free website at: http://bndtechsource.ucoz.com/