STUDY OF ROLL CENTER SAURABH SINGH *, SAGAR SAHU ** *, ** Mechanical engineering, NIT B ABSTRACT As our solar car aims to bring new green technology to cope up with the greatest challenge of modern era i.e. energy demand and ESVC is a racing championship of such innovative technology that bring thrills on speed but in an ecofriendly way. As much it is important to bring speed to car so as equally important to design and fabricate vehicle design so that it can withstand high speeds to let it run and flow smoothly. That is the work of suspension system to keep the optimal tire contact with ground and keep passengers comfortable and one of the most important aspect of which is Roll Center. The vehicle roll center is a key parameter that influences the vehicle roll dynamics. The roll center is considered an important factor in determining overall vehicle ride and handling quality it is important to know how to find roll center for different type of suspension. So it becomes important for vehicle discuss roll center with respect to different suspension parameter and relation between roll center and center of gravity with changing vertical position of roll center for front and rear suspension system. roll center can be an actual pivot point or a virtual point in space and they don t essentially lie along the center line of the vehicle. SAE s definition indicates, if the roll centers of a car are at the same height as the sprung mass Center of Gravity (CG), it will not reveal any body roll during a corner a line connecting the rear suspension roll Centre with that of the front is called the roll axis. Fig. 1: Roll Center I. INTRODUCTION Roll center of a vehicle is the imaginary but accurately defined point on the center-line of the car around which the vehicle rolls, at which the cornering forces in the suspension system are transferred to the vehicle body. The location of the geometric roll center is solely dictated by the suspension geometry. The official definition of roll center are- SAE: a point in the transverse plane through any pair of wheels at which a transverse force may be applied to the sprung mass without causing it to suspension roll. Kinematics: the roll is the point about which the body can roll without any lateral movement at either of the wheel contact areas. The roll Centre can be high off the ground, low, or even below the ground. Depending on the type of suspension, the Fig. 2: Roll Axis Location Reason to find the Roll Center of a car is about predicting how the car reacts while cornering. Knowing where the roll center is in the front of the car gives an idea of what the wheels will be doing as the nose of the car dives under braking or leans in a corner. Without roll center information, one cannot estimate how much the camber angle of the front wheels will change during suspension travel or how much body roll will be present while cornering. Roll center is used to determine the stiffness of spring, ride frequency and various suspension parameters and geometries that will help to keep optimal tire contact in both the conditions of ride( a car s ability to smooth out a bumpy road) and handling ( a car s ability to safely accelerate, brake and corner.) 38
So, the distance between roll center and CoG should be minimum but simultaneously, it is important to keep the minimum distance of roll center from ground in order to minimize jacking forces. To keep our solar car stable in order to negotiate any turn at high speed and keeping above factors in mind, we have performed following iteration on LOTUS SHARK SUSPENSION SOFTWARE and obtained satisfactory value of roll center distance under permissible limit as per our calculations. Fig. 3- Physics Behind Roll Center If N1 and N2 are the normal reaction forces of tires during cornering of vehicle and 2a is the front track width of car, the distance between center of gravity (CoG) and roll center (RC) is L, then to avoid rolling :- N1*a N2a > F*L ------------------ (1) Where F = mv2/r (centrifugal force) N1 = static normal + lateral load Reaction transfer N2= static normal lateral load Reaction transfer Where, lateral load = m*f*(l+x)/ 2a Transfer Here m= mass supported on one wheel f= lateral acceleration of car L+x= height of CoG from ground 2a= track width The value of L as obtained from equation 1 will give the maximum permissible value of distance of roll center from CoG in any dynamic condition. In any condition, if the distance increases from the maximum permissible value, then tire will start losing contact with the ground and vehicle would become unstable. Fig. 5- Results obtained Many of such iterations were performed in order to determine the appropriate height of roll center from ground. Roll-Centre Determination Aronhold Kennedy theorem of three centers: when three bodies move relative to one another they have three instantaneous centers all of which lie on the same straight line. Iwb can be varied by angling the upper and lower wishbones to different positions, thereby altering the load transfer between inner and outer wheels in a cornering maneuver. This gives the suspension designer some control over the handling capabilities of a vehicle. Fig. 4- Iterations performed 39
Instantaneous Center:-Each wheel of an independent suspension has an instantaneous center and it is the point in space that the wheel rotates about as the suspension compresses or rebounds. Point Iwb is sometimes referred to as 'virtual pivot', or as 'instantaneous center'. The instantaneous center dictates scrub radius, camber change and the way forces are transmitted. This pole can give us information about how the suspension moves. The distance from point Iwb to the centerline of the tire is sometimes referred to as 'swing axle length, it's as if the hub/wheel is attached to an imaginary swing axle which hinges around point I. Having that long swing axle would be equivalent to having the double wishbone-type suspension, but the actual construction would be very impractical. Nevertheless it serves as a good simplification. The swing axle length, together with the angle, determine the amount of camber change the wheel will experience during the compression of the suspension. A long swing axle length will cause very little camber change as the suspension is compressed, and a very short one will cause a lot. If the upper link and the A- arm are perfectly parallel to each other the intersection point Iwb is infinitely far removed from the car. This isn't a problem though: just draw line as above.these two lines should always intersect on the side of the center of the car, if they intersect on the outside, camber change will go from negative to positive back to negative, which is not a good thing for the consistency of the traction. Having a suspension that gains negative camber as the body of the car rolls is beneficial. It helps keep the tire perpendicular to the ground during cornering which maximizes tire contact with the track. Roll-Centre determination for different type of suspension:- In the case of the MacPherson strut suspension the upper line defining Iwb is perpendicular to the strut axis In case of double wishbone suspension with Parallel horizontal links:- And with inclined parallel links :> Swing axle roll center is located above the virtual joint of the axle. The roll center for a leaf spring suspension is found by drawing a line between the center of the forward attachment point (A) and the center of the upper shackle attachment point (B). Where that line crosses the vertical center line of the axle is the roll center. The roll center height is the vertical distance from the ground to roll center An important point to note that the roll center will move when the suspension is compressed or lifted, that's why it's actually an instantaneous roll center. How much this roll center moves as the suspension is compressed is determined by the suspension arm length and the angle between the top and bottom suspension arms (or turnbuckles). As the suspension is compressed, the roll center will become higher and the moment arm (distance between roll center and the car's center of gravity (CoG in the picture)) will decrease. This will mean that as the suspension is compressed (when taking a corner, for example), the car will have less tendency to keep rolling (which is good, you do not want to roll over). When using higher grip tires, the suspension arms should be set in such a way that the roll center is raised significantly as the suspension is compressed. Running parallel, equal-length suspension arms will result in a fixed roll center. This means that as the car leans over, the moment arm will be forcing the 40
car to roll more and more. As a general rule of thumb, the higher the center of gravity of your car, the higher the roll center should be to avoid a roll-over. Roll Center Height: - The roll center height is found by projecting a line from the center of the tire-ground contact patch through the front view instant center as shown in Figure. This is repeated for each side of the car. Where these two lines intersect is the roll center of the sprung mass of the car, relative to the ground. It is not necessarily at the centerline of the car, especially with asymmetric suspension geometry or once the car assumes a roll angle in a turn. It is obvious that the roll center location is controlled by the instant center heights above or below ground, the distance away from the tire that the instant center is placed, and whether the instant center is inboard or outboard of the tire contact patch the roll center establishes the force coupling point between the unsprung and sprung masses. roll moment. Note that it is always the vertical distance between the CG and the RC since the forces always work horizontally. Olley s Derivation: - M. Olley s gives his derivation on roll center. He assumes that a SLA suspension mechanism may be approximated in front view by a Planar four-bar linkage as shown in Fig. 1. He also uses a parabolic approximation to the circular arc x=y2/2y shown in Fig.2 (a) to mathematically relate small motions of the outer ball joints to jounce-rebound. When the arm is not initially vertical but has an initial lift a, the expression for x becomes [see Fig.6] (y2/2r) + (ya/r). Fig. 6:- Approximating a Circular arc Referring to Fig. 7, Olley proceeds as follows: When a car corners, the centrifugal force at the center of gravity is reacted by the tires. The lateral force at the CG can be translated to the roll center if the appropriate force and moment (about the roll center) are shown. The higher the roll center the smaller the rolling moment about the roll center (which must be resisted by the springs); the lower the roll center the larger the rolling moment. You will also notice that with higher roll centers the lateral force acting at the roll center is higher off the ground. This lateral force x the distance to the ground can be called the no rolling overturning moment. The forces generated by the tires can be combined to one force, working in the car's roll center. Two equal, but opposite forces, not working in the same point generate a torque equal to the size of the two forces multiplied by the distance between them. So the bigger that distance, the more efficiently a given pair of forces can generate a torque onto the chassis. That distance is called the The equation of the line through the outer joints of the two control arms gives the following expression for the displacement of the tire patch as a function of the control arm displacements. Substituting from Eqs. (1) And (2) into Eq. (3) we get 41
Differentiating Eq. (5) with respect to y we get This is the curvature of the path traversed by the wheel contact point. The radius of curvature, R3, of this path is given by the reciprocal of (d 2 x3 /dy2).therefore This is the rate of tread change. At zero jounce, i.e., when y=0, Eq. (6) becomes Olley s main result is that when R3=, the tire contact patch moves in a straight line. The arc of radius R3 in Fig. 3 becomes a straight line. The rate of tread change becomes a constant for this condition. It follows from Eq. 8 that the height of the roll center above ground becomes a constant. The line from the contact patch to the roll center remains parallel to itself when the wheel moves up and down. The roll center moves up or down by the same amount as the wheel. The geometric condition on the linkage for achieving this is given by Eq. (11),which may be written as follows: Fig. 8- SLA suspension geometric parameters The height of the roll center is related to the rate of tread change by the following expression height of roll center = rate of tread change x (track width/2) (8) Using Eqs. (7) and (8)we may write Olley s choiceof coordinates. The letter t in Eq.(9) represents the track-width.differentiating Eq.(6) with respect to y we get Equation (12) states that when the lengths of the control arms are inversely proportional to the heights of their outer ends above ground, the tire contact patch moves in a straight line, i.e., the height of the roll center remains fixed with respect to ground as the sprung mass moves up and down. II. Application and Conclusion:- Ideally in high performance applications load transfer tends to be minimized as a tire's performance is directly affected by the amount of load that it has to transmit. In a steady state turn the final load transfer, summed across all the axles, is only related to the position of the center of mass above the ground, the track width and the lateral acceleration. SUVs must shift their center of mass lower or decrease their lateral acceleration to avoid tipping. To keep them from tipping many auto manufacturers use tires with lower grip to reduce the vehicles cornering capacity, or the roll stiffness balance front to rear can be altered to encourage understeer or oversteer as necessary to limit the maximum lateral acceleration of the vehicle. III. Author biography SAURABH SINGH, 2 nd year Mechanical engineering, NIT BHOPAL, email-saurabhsinghmanit@gmail.com 42
SAGAR SAHU, 2nd year Mechanical engineering, NIT BHOPAL, email- sagarsahumanit@gmail.com References [1]Gillespie, Fundamentals of Vehicle Dynamics", SAE Publication. Tune To Win - Carroll Smith [2 ]Milliken, W. F., and Milliken, D. L., 1995, "Race Car Vehicle Dynamics", SAE. [3] https://en.wikipedia.org/wiki/suspension_( vehicle) [4]web.iitd.ac.in/...html/../15 Suspension_systems_and_components [5] https://en.wikipedia.org/wiki/roll center [6] http://www.onedirt.com/tech-/suspension/finding-your-centerfinding-yourfront-and-rear-roll-center [7] Suspension Synthesis for N:1 Roll Center Motion [8]http://auto.howstuffworks.com/car-suspension.htm [9]Vehicle Dynamics- theory and application by Reza N. Jazar. [10]Tyre and vehicle dynamics by Hans B. Pacejka. 43