The University of Western Ontario Department of Mechanical and Materials Engineering MME419 Mechanical Engineering Project MME499 Mechanical Engineering Design (Industrial) Racing Tires in Formula SAE Suspension Development by Ryan Alexander 250 332 546 Faculty Advisor: Prof. Singh Date Submitted: Nov. 9, 2009 SOTA REPORT I
Executive Summary The importance of tires is often understated in motorsports, but the reality is that all vehicle performance is ultimately determined by how effectively the tire contact patches are used. This paper focuses on the key factors and measures of tire performance, an introduction to tire modeling, as well as an overview of the current tire technology available. Recommendations are also provided for use in the design and tuning phases of the 2010 Suspension Development project. II
Table of Contents Executive Summary... ii Table of Contents... iii List of figures... iv Introduction... 5 Current Tire Technology... 5 Tire Constructions... 5 Tire Characteristics... 7 How Tire Adhesion Works... 7 Inflation Pressure... 8 Tire Temperature... 8 Camber Thrust... 9 Vertical Load... 10 Friction Circle Concept... 11 Tire Modeling... 12 Conclusion... 14 Works Cited... 15 III
List of figures Figure 1: Bias-ply versus Radial-ply Tire Constructions (Gillespie, 1992, p. 337)... 5 Figure 2: Mechanisms of tire-road friction(gillespie, 1992, p. 341)... 7 Figure 3: Carpet plot of lateral force due to camber angle and normal force for a given tire (Gillespie, 1992, p. 356)... 9 Figure 4: Tire load sensitivity for various camber angles (Milliken & Milliken, 1995, p. 54)... 10 Figure 5: Tire friction coefficient vs normal load on dry roads (Gillespie, 1992, p. 345)... 11 Figure 6: Example G-G Diagram (Milliken & Milliken, 1995, p. 54)... 12 Figure 7: Comparison between the possible approaches to tire modeling (Pacejka, 2006, p. 85)... 13 IV
Introduction This report provides an overview of the relevance of tires in suspension system design and tuning for a high performance Formula SAE vehicle. An overview of current tire technology is provided and important tire characteristics are summarized to gain an understanding of tire interaction between the road, the tire, and the suspension system. Recommendations are also provided based on the research for implementation in the design project during the development and tuning phases. Current Tire Technology Tire Constructions There are two main types of tire constructions available for use in automotive applications, bias-ply and radial-ply (Clark, 1971, p. 5). Figure 1 illustrates the difference in construction. Figure 1: Bias-ply versus Radial-ply Tire Constructions (Gillespie, 1992, p. 337) 5
Bias-ply tires originated in North America and Radial-ply tires originated in Europe. Eventually the benefits of Radial-ply tires became well-understood and since have been adopted for the vast majority of automotive applications (Gillespie, 1992, p. 336). The tires available for the 2010 Formula SAE vehicle are all of the Radial-ply construction and the main differences are in tire compound, size, and minor variations in construction. Therefore, all discussion within this report will be about Radial-ply constructed tires. 6
Tire Characteristics How Tire Friction Works The forces on a tire are not applied at a single point or line, but are the resultant of shear and normal stresses distributed on the contact patch (Gillespie, 1992, p. 341). There are two main mechanisms responsible for the friction between tire and road illustrated in Figure 2. Figure 2: Mechanisms of tire-road friction (Gillespie, 1992, p. 341) Adhesion is the result of intermolecular bonds between the rubber and the surface of the road and hysteresis represents energy loss in the rubber as it deforms when sliding over the bumps in the road surface. In road tires, most of the friction generated is due to adhesion. Since adhesion is mostly responsible for tire grip, it can be easily seen how foreign and movable material between the road and the tire can have an adverse impact on grip. Real examples of this that might affect the Formula SAE vehicle are sand or water on the racing surface (Gillespie, 1992, p. 341). 7
Inflation Pressure It appears that there is some disagreement between authorities with respect to the importance of tire pressure in automotive application with respect to generated tire friction. Milliken states that peak tire performance is dependent on tire pressure and tire pressure should be generally adjusted to maintain as even a contact pressure on the ground as possible (Milliken & Milliken, 1995, p. 55). Gillespie states that inflation pressure does not appear to substantially affect tire/road coefficients on dry roads. However, on wet roads, a higher inflation pressure is known to significantly improve tractive coefficients (Gillespie, 1992, p. 345). Based on experience with Formula SAE tires, it seems that both experts are correct. Dry tire pressure does certainly affect grip and that has been proven during vehicle tuning but there is a larger effect with rain tires and a tire company representative from Hoosier, a popular racing tire, recommends running rain tires at 2 psi higher than dry tires would be run. Tire Temperature Van Valkenburgh states that the most significant consideration with respect to racing tires is the temperature of the rubber under operating conditions (Van Valkenburgh, 2000). It is clear that when driving a racing vehicle, there is substantially more grip when a tire is at peak operating temperature than when a tire is cold. In accordance with Milliken s statement regarding setting inflation pressure to even the contact pressure of the tire, tire temperature across the width of the tire can be used as an indicator to determine how evenly the tire contact patch is being used. For example, if the centre of the contact patch is colder than the outside, a higher tire pressure may be used. 8
The same holds true with camber angle where the inside versus outside temperatures could be compared to assess if the selected camber angle is evenly using the contact patch. Camber Thrust Camber thrust is the force that is generated by a tire due to its vertical inclination angle, or camber angle (Gillespie, 1992, p. 355). Camber thrust is a key aspect to consider when designing the suspension system of a performance vehicle because it indicates at what camber the tires should be operating in order to develop the maximum possible lateral force and subsequent vehicle performance. The mechanism of camber thrust is not well-understood in available literature, but it is posited by Milliken that on a Radial-ply tire that the camber thrust may be generated due to the distortion in the tread pattern when the tire is angled. Figure 3: Carpet plot of lateral force due to camber angle and normal force for a given tire (Gillespie, 1992, p. 356) Figure 3 illustrates the camber thrust developed, in pounds, for different camber angles at various normal loads for a given tire at zero slip angle (I.E. tire is pointed straight ahead) and is still generating lateral force. 9
First hand study of Formula SAE tire data indicates that when generating lateral force using a combination of camber thrust and slip angle (steering angle), the trend does not follow what Figure 3 might suggest. Instead, a peak lateral force versus slip angle is found to be at around 3 degrees camber (for the 2009 chosen tire) and when going beyond this camber, the maximum lateral tire force decreases. Figure 4: Tire load sensitivity for various camber angles (Milliken & Milliken, 1995, p. 54) Milliken provides Figure 4 that better illustrates tire sensitivity to camber angle with respect to lateral friction coefficient and introduces a new concept which is the effect of camber on normal load sensitivity. Vertical Load Variations in normal load on the tires disturb the contact patch and change the lateral force potential of the tire which is unfavourable if peak vehicle performance is desired (Rajamani, 2006, p. 313). Figure 5 illustrates the tire coefficient of friction decreasing with increased vertical load on the tire. First-hand Formula SAE tire data analysis indicates the same trend, although the coefficients of friction are higher on a racing tire. 10
It can be seen in Figure 4 that with camber angles that provide higher peaks in lateral force versus slip angle also creates increased normal load sensitivity. Figure 5: Tire friction coefficient vs normal load on dry roads (Gillespie, 1992, p. 345) µp and µs in Figure 5 correspond to peak friction coefficient and sliding friction coefficient, respectively. Friction Circle Concept Regardless of the combination of vehicle steering, braking, or driving forces applied to a wheel, the amount of lateral force that the tire can produce is determined by the tire/road friction coefficient multiplied by the normal load on the tire (Milliken & Milliken, 1995, p. 344). The maximum friction force at a given normal load can therefore be illustrated by a friction circle with longitudinal friction force on the vertical axis and lateral friction force on the horizontal axis. The friction circle can provide insight into how well a driver is using the contact patches made available by the vehicle by translating this concept into a lateral acceleration circle called a g-g diagram by Milliken. 11
Figure 6: Example G-G Diagram (Milliken & Milliken, 1995, p. 54) An example g-g diagram is provided in Figure 6 with longitudinal acceleration on the vertical axis and lateral acceleration on the horizontal axis. The line that appears scribbled on this plot represents how the instantaneous vehicle acceleration changed during a lap on a racing track. At any given point on the race track, it s possible to see if the driver is maximizing the potential of the vehicle by looking at how close he is to the circle that bounds the driver s accelerations. Tire Modeling As computers are used with increasing frequency to simulate full vehicle dynamics, the demand for accurate tire models has increased substantially and new technologies and modeling techniques are being developed and introduced on a continual basis. There are two fundamental ways of approaching tire simulation; empirical and theoretical. Empirical modeling is generally accomplished by physically testing tires and developing numerical coefficient matrices that represent the tires when solved for given inputs. Theoretical modeling uses complex mathematical equations in an 12
attempt to model each physical characteristic of the tire. Figure 7 illustrates some differences in the modeling techniques with respect to accuracy and effort. Figure 7: Comparison between the possible approaches to tire modeling (Pacejka, 2006, p. 85) Some models are built for simplicity while sacrificing some accuracy and some strive to fully represent the tire in all its operating conditions. Both types of which are useful in analysis. The fairly simple and mostly empirical MRA Tire Model which does not include important factors such as tire temperature, but is very simple to use in Matlab, has been used in the development of UWO Formula Racing vehicles because of its simplicity and ease of use. Other models exist such as the Pacejka Magic Formula and are much more in depth and accurate using complex mathematical equations combined with coefficients to represent each tire, but this model requires a powerful solver such as ADAMS /CAR or OptimumT to be useful in suspension development. 13
Conclusion Based on the above findings, it is clear that tires play a crucial role in vehicle performance. It is therefore a top priority in this project to choose the most appropriate suspension geometry and tire combination through careful analysis. A 1-year license to OptimumT, a cutting-edge tire data analysis software was recently awarded for testing to the 2010 UWO Formula SAE suspension development project for use in suspension design. It is recommended to make extensive use of this software, and for the team to purchase the software for future use once the license has expired. Once the vehicle is built and tested, tires remain an important priority for vehicle tuning. It is recommended that the team acquire tire temperature gauges so that it is possible to justify the choice of tire pressure and camber angle by checking for even use of the tire contact patch through temperature measurement. 14
Works Cited Clark, S. K. (1971). Mechanics of Pneumatic Tires. Washington: National Highway Traffic Safety Administration. Gillespie, T. D. (1992). Fundamentals of Vehicle Dynamics. Warrendale, Pennsylvania: Society of Automotive Engineers. Milliken, D. L., & Milliken, W. F. (1995). Race Car Vehicle Dynamics. Warrendale, Pennsylvania: Society of Automotive Engineers. Pacejka, H. B. (2006). Tire and Vehicle Dynamics, 2nd edition. Warrendale, Pennsylvania: Society of Automotive Engineers. Rajamani, R. (2006). Vehicle Dynamics and Control. Troy, New York: Springer. Van Valkenburgh, P. (2000). Race Car Engineering & Mechanics. Seal Beach, California: Paul Van Valkenburgh. 15