Formula Student Germany Tires Creating a Future for

Formula Student Germany Tires Creating a Future for Engineers

Tires – Content § Forces § Properties § Tires / Vehicle § Testing Creating a Future for Engineers

Forces § Longitudinal and lateral acceleration of an FS car ax g-g Diagramm of the LR 07 +0. 8 g ay -1. 3 g -1. 5 g +1. 5 g Creating a Future for Engineers

Forces § Longitudinal and lateral acceleration of an FS car ax +0. 8 g ay -1. 3 g Cornering -1. 5 g +1. 5 g Creating a Future for Engineers

Forces § Longitudinal and lateral acceleration of an FS car ax +0. 8 g ay -1. 3 g Braking -1. 5 g +1. 5 g Creating a Future for Engineers

Forces § Longitudinal and lateral acceleration of an FS car ax +0. 8 g ay -1. 3 g After the apex -1. 5 g +1. 5 g Creating a Future for Engineers

Forces § Equilibrum ax+ay m az Fz Fx Fy Creating a Future for Engineers

Forces x z x Law of friction Fz Fz µ y Friction „Circle“ Fx Fz FT Fy FT Creating a Future for Engineers

Forces Front right Front left Fz az Fz Fx ax Fx Fy ay *m= Fz Fy Fz Fx Fx Fy Acceleration of the car Rear left Fy Rear right Creating a Future for Engineers

Tires – Content § Forces § Properties § Tires / Vehicle § Testing Creating a Future for Engineers

Properties Important for Formula Student § Tire Data § Construction § Dimensions § Weight § Reliability / Temperature Creating a Future for Engineers

Properties – Tire Data Slip angle v Direction of movement Orientation of the tire x y Fy Creating a Future for Engineers

Properties – Tire Data Lateral Force and Slip Angle for certain Fz 4000 Front left 3500 Lateral Force [N] 3000 Fz Fy, max 2500 2000 Fx Fy 1500 1000 cα 500 0 -500 -1000 -1500 -2000 -2500 -3000 -3500 -4000 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Slip Angle [deg] Creating a Future for Engineers

Properties – Tire Data Load Sensitivity 4000 3500 Fz = 1000 N Fz = 2000 N Fz = 3000 N 3000 Lateral Force [N] 2500 2000 1500 1000 The coefficient of friction changes with the load of the tire. 500 0 -500 The slip angle for the maximum lateral force changes with the load. -1000 -1500 -2000 -2500 -3000 -3500 -4000 -12 -10 -8 -6 -4 -2 0 2 4 Slip Angle [deg] 6 8 10 12 Load sensitivity is the basic prerequisite for anti-roll bars. Creating a Future for Engineers

Properties – Tire Data Camber Angle Fx 4000 γ = 0 deg γ = -3 deg 3500 3000 Lateral Force [N] 2500 2000 Fy 1500 1000 500 0 -500 -1000 -1500 -2000 -2500 -3000 -3500 -4000 -12 -10 -8 -6 -4 -2 0 2 Slip Angle [deg] 4 6 8 10 12 More camber results in higher lateral forces but reduces the capability of a tire to produce longitudinal forces. Creating a Future for Engineers

Properties – Tire Data Influence on the Coefficient of Friction Approximation Co. F changes with surface pressure in contact patch : § Camber § Load sensitivity: § Construction Camber: § Tire Dimension Size of Area of highest surface pressure § Inflation Pressure § Rim Width Creating a Future for Engineers

Properties – Tire Data Pneumatic Trail v Direction of Tire Velocity of Tire x y Pneumatic Trail nr Fy Creating a Future for Engineers

Properties – Tire Data Pneumatic Trail 100 80 γ = 0 deg 60 MZ [Nm] 40 20 0 -20 The pneumatic trail results in an self aligning torque along the vertical axis of the tire. -40 -60 -80 -100 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Slip Angle [deg] Creating a Future for Engineers

Properties - Construction Radial 90 º Cross Ply º-60º 30 Creating a Future for Engineers

Properties - Construction Cross Ply Properties Higher vertical and sidewall stiffness Lateral force and wear sensitive to camber Longitudinal force not really sensitive to camber Self aligning torque same as radial tire Lower weight than radial tire º-60º 30 Lower slip angle sensitivity No distinct maximum in lateral force over slip angle Slip ratio better to control under braking Creating a Future for Engineers

Properties - Construction Properties Radial Lower vertical and sidewall stiffness 90 º Used at higher cambers than cross ply tires Wear almost not sensitive to camber Lateral and longitudinal force very sensitive to camber Self aligning torque same as cross ply tire Higher weight than cross ply tire High slip angle sensitivity little slip angles Distinct maximum in lateral force over slip angle Creating a Future for Engineers

Properties - Construction 4000 Radial 3500 3000 Cross Ply Lateral Force [N] 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500 -3000 -3500 -4000 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Slip Angle [deg] Creating a Future for Engineers

Properties – Dimensions and Weight Dimensions: Diameter / Width / Diameter of Rim - Influence on: Rotation, size of contact patch, package space, weight, lateral stiffness, center of gravity of wheel, temperature Weight: Weight of tire: Tires in Formula Student weight between 4, 2 kg und 6, 0 kg Overall weight difference for one car: up to 7, 2 kg Creating a Future for Engineers

Properties – Reliability and Temperature § Optimal working temperature Is it possible to reach this temperature with my car? § Range of working temperature Differences in ambient temperature between Detroit / FSG § Time to reach the working temperature Important for the first dynamics day (Sprint, Figure 8, …. ) § Influence of heat cycles on the tire Creating a Future for Engineers

Tires – Content § Forces § Properties § Tire / Vehicle § Testing Creating a Future for Engineers

Tire / Vehicle Example LR 07: Starting Basis LR 06: Weight: Wheelbase: Average Track: Weight Distribution: Height of Co. G: Tires: VA: HA: 220 kg 1600 mm 1220 mm 51% HA 273 mm Hoosier 20. 5 x 6. 0 -13 Hoosier 20. 5 x 7. 0 -13 Creating a Future for Engineers

Tire / Vehicle Requirements LR 07: § More feedback to the driver § Lower steering forces § Faster than the LR 06 Track – Tires – Vehicle – Driver Creating a Future for Engineers

Tire / Vehicle More feedback to the driver § Transmission of the tires status to the steering wheel: § Radial tires Lower steering forces: § Wheel load lever arm and caster trail are important. Wheel load lever arm: Creating a Future for Engineers

Tire / Vehicle - Faster than the LR 06 Wheel base / Track for LR 07: Depends on load sensitivity of the tire Short Wheelbase: § High dynamic wheel loads under acceleration and braking better acceleration, braking performance is reduced marginally Wide Track: § Lower dynamic wheel loads while cornering higher lateral acceleration Height of Co. G: Effects the performance like track and wheelbase Creating a Future for Engineers

Tire / Vehicle - Faster than the LR 06 Weight Distribution LR 07: Depends on load sensitivity of the tire Rear heavy car: § Higher load on driven wheels higher acceleration Performance § For equal temperatures: Tire dimensions changed to wider tires at the rear § With these tire dimensions the lateral performance equals to a 50% / 50% car § With these tire dimensions the braking performance will be lower Creating a Future for Engineers

Tire / Vehicle - Faster than the LR 06 Tire Temperatures LR 07: Widest tires possible, but reaching working temperature Equal temperatures at front and rear tires: § Ratio of tire widths = Ratio of weight distribution § Driven tires more slip higher temperatures 6“ Front, 8“ Rear: Weight Distribution Rear tires are driven: Weight Distribution Influence of longitudinal slip and absolute temperatures depends on the tire. Temperatures are influenced mainly by the weight of the car. Creating a Future for Engineers

Tire / Vehicle - Faster than the LR 06 Kinematic LR 07: Consequences of low spring rates and demands of the radial tire (high negative camber while cornering, no camber during braking) 1. Conventional Kinematic: The roll angle is transmitted to the tire as positive camber. For compensation static camber can be adjusted Result: Car uses the tire in contrast to its demands (no camber while cornering, high camber while braking) Creating a Future for Engineers

Tire / Vehicle - Faster than the LR 06 Kinematic LR 07: Consequences of low spring rates and demands of the radial tire (high negative camber while cornering, no camber during braking) 2. Kinematic with aggressive camber gain: Camber is not influenced by roll angle. Camber gain over vertical wheel travel results in camber under longitudinal accelerations. Advantage: Usually vertical wheel travel is lower under longitudinal accelerations than under lateral accelerations Result: The tire is used better than with a conventional kinematic no camber while cornering, low camber while braking Creating a Future for Engineers

Tire / Vehicle - Faster than the LR 06 Kinematic LR 07: Consequences of low spring rates and demands of the radial tire (high negative camber while cornering, no camber during braking) 3. Kinematic with aggressive camber gain and 100% Anti-X (LR 07): Camber is not influenced by roll angle. 100% Anti-X prevents camber gain under longitudinal accelerations. Result: Best use of tire no camber while cornering, no camber while braking Optimal use of tire only possible with active suspension adjustments high negative camber while cornering, no camber while braking Creating a Future for Engineers

Tire / Vehicle - Faster than the LR 06 Kinematic LR 07: Consequences of low spring rates and demands of the radial tire Concept 3: Aggressive Kinematic low spring rates, radial tires Concept 1: Conventional Kinematic high spring rates, cross ply tires Creating a Future for Engineers

Tire / Vehicle Slip Angle: The slip angle for the maximal lateral force changes with vertical load: Solution: § Geometry of steering linkage results in different toe-angles (Effect depends on steering angle, sometimes package difficult) § Active toe control Little influence on performance (inner tire has almost no vertical load) Creating a Future for Engineers

Tire / Vehicle Slip Ratio: Tuning the drive train for the slip properties of the tire (Example LR 07) a = 1. 02 g Creating a Future for Engineers

Tire / Vehicle Rim Width: Tires with low lateral sidewall stiffness increase performance on wider rims § Higher sidewall stiffness. § Kinematic Effect of inclined sidewalls: Same result like negative camber Fy Fy Creating a Future for Engineers

Tires – Content § Forces § Properties § Tires / Vehicle § Testing (this section is shortened) Creating a Future for Engineers

Testing Rim Width: Radial tire 195/500 R 13 on inner tire 8“ rim outer tire Creating a Future for Engineers

Testing Temperature: Absolute temperature influenced by: Local Temperatures influenced by: Slip, load, inflation pressure Camber, rim width, inflation pressure § Every section of the contact patch should operate at an reasonable temperature § Camber is not only a compromise between lateral and longitudinal performance High negative camber can lead to unequal temperatures in the contact patch Some section may be to cold or to hot § Toe and hard springs / dampers result in additional slip, temperature rises Creating a Future for Engineers

See you at Hockenheim 06. – 10. August 2008 Creating a Future for Engineers