Advanced Computer Aided Design in Conceptual Automotive ...

Institute of Automotive Engineering Graz University of Technology

Advanced Computer Aided Design in Conceptual Automotive Development

Habilitation Thesis

submitted to the Faculty of Mechanical Engineering at Graz University of Technology to receive the Venia Docendi for Virtual Product Development (Virtuelle Produktentwicklung)

Mario Hirz

Graz, 2011

4. Conceptual full vehicle development

Figure 4.63 provides an overview of the calculation procedure for concept studies. Depending on the applied hybrid concept, the implemented control unit defines the operation strategy, the energy management and the interaction of transmission systems. A combination of the stationary driving resistance maps of both power systems provides the basis for the calculation of climbing rate, maximum vehicle speed, acceleration behavior and driving elasticity at each operation point. In addition, the predefinition of load distribution in given driving cycles enables an estimation of fuel and energy consumption in order to calculate the combined power efficiency of the system. A separate consideration of the energy spending can be used for the calculation of CO2 emission output taking into account fuel consumption and electric energy expenditure. In the case of a plug-in hybrid system, the well to tank emissions of the electric power generation process have to be considered separately.

4.6.3. Lateral dynamics pre-calculation

Geometrical data

Geometry module

Basis geometries Exterior Interior Geometry check Import geometries Traffic sight

Vehicle dynamics Product structure Product structure key data

Weight data

Weight calculation • Weight • Centers of gravity • Moments of inertia

Lateralcalculation vehicle Weight dynamics Single-track model asdfasds -

Steering angle Steering tendency Yaw & slip behavior Critical vehicle speed

2D-sectioning Geometry & dimension data

Vehicle & component masses & moments of inertia

Figure 4.64: Process of lateral vehicle dynamics analysis

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Calculation module

Data pool

Besides longitudinal characteristics, a car’s driving behavior when cornering is an important factor with respect to safety, comfort and controllability. The integration of lateral vehicle dynamics simulation into the virtual concept car is based on a single-track model, which is connected to the geometry module, the weight calculation procedure and of course the general data pool structure. Figure 4.64 shows the process of lateral vehicle dynamics simulation and the data flow within the computation procedure. The information about geometry and dimensions, as well as masses and moments of inertia, are delivered from the corresponding modules, and specific key data are imported from the relevant data sheet. The computation of lateral dynamic characteristics is accomplished in the calculation module and results in specific figures for the assessment of the steering angle as a function of vehicle speed and cornering radius, the general steering tendency (under-steering, neutral, over-steering), the yaw and slip behavior as a function of the cornering velocity and the critical vehicle speed. In addition, different standardized driving maneuvers are investigated in the course of conceptual lateral dynamics vehicle pre-calculation.

4. Conceptual full vehicle development

In the present full-vehicle-related approach for virtual pre-development, the lateral dynamics of a car are simulated based on a steady-state, single-track model. This linear model with two degrees of freedom (yaw and slip) was introduced by Riekert and Schunck in the year 1940 [122]. Figure 4.65 includes the schemata of a single-track model at cornering and shows the geometrical relations, as well as the acting lateral forces. In comparison with a real car, several assumptions enable a simplified analysis. Thus, there are no longitudinal forces considered, the z -coordinate of the center of gravity is set to the road level, and the four wheels of the car are centralized in two wheels at the vehicle middle plane. No influences from side wind are considered, and the vehicle speed v of the balance point CG is assumed to be in a normal direction to the vehicle track curve, which means that the centrifugal force of the vehicle is directed from the instantaneous center of rotation CR. The equations are related to low vehicle speed and low magnitudes of slip angles, so that the trigonometric relations can be simplified as: sin x x, cos x 1 and tan x x. At very low vehicle speed (static consideration), the theoretical steering angle δA is defined according to the requirements of the Ackermann’s law (London, 1817) [108]. Ackermann obtained a patent for a kingpin steering system, which refined an advantageous arrangement of the front wheels in relation to the rear wheels such that the elongations of the front wheel axes intersect the rear wheel axis at the same point. The inside front wheel follows a smaller cornering radius than the outside one, which avoids the disadvantages of lateral buckling or high restoring forces on the steering mechanism. In Figure 4.65, the instantaneous center of rotation at Ackermann steering angle CRA represents the theoretical cornering center of the car at low speed. Besides its influence on the vehicle driving dynamics, the Ackermann center of rotation is used to calculate the minimum turning cycle radius of the treated vehicle concept.

δ A Ψ. l F v F SF vF αF

β

v

Ψ

R δ-(αF-αR) CR

lF

FC

CG Ψ. l R v

α R+β CRA

wb vR

lR

αR

FSR

Figure 4.65: Single-track model when cornering, according to [122]

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4. Conceptual full vehicle development

The Ackermann steering angle reads (4.13) where it holds for small angles: .

(4.14)

As vehicle speed increases, the wheels are moved with slippage, which leads to the tire slip angels. As a function of the steering angle δ, the side slip angle β, the yaw speed and the vehicle speed v, the front tire slip angle αF and the rear tire slip angle αR read and .

(4.15)

The instantaneous center of rotation CR travels along a curve, which is influenced by the general steering behavior of the car. In the case of a neutral steering axis, the cornering radius R remains the same for different values of vehicle speed. The front and rear tire slip angles are calculated as a function of the steering angle and the side slip angle, as well as of the vehicle speed and its yaw speed according to the geometrical relations in Figure 4.66. The difference of αF – αR can be understood as a correction angle for keeping the car on track at rising cornering speeds [160]. Lateral tire characteristics show a non-linear behavior and are strongly dependent on the type and material of the applied tires. Assuming that slip angles αF and αR are sufficiently small, the lateral force characteristics can be linearized (Figure 4.66).

Figure 4.66: Lateral tire characteristics [71]

As a simplification, the following calculations consider a linear tire slip characteristic. The lateral forces at the front and rear wheel (FSF and FSR) are calculated as a function of the tire-side stiffness factors (cSF and cSR) and the corresponding slip angles αF and αR. The lateral tire forces in the single-track model are in balance with the centrifugal vehicle force FC according to , and .

(4.16)

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4. Conceptual full vehicle development

The position of the vehicle in the corner at low speed is described by the base side slip angle β0 which reads .

(4.17)

The differential side slip angle Δβ describes approximately the required lateral tire slip angle on the rear (not steered) axle at a given vehicle speed. It is evident that the differential slip angle increases with rising vehicle speed (or rising lateral acceleration ay). In the case of an under-steering vehicle, Δβ has a negative prefix, which leads to an increasing side slip angel with rising speed. In the case of an over-steering vehicle, the differential side slip angle becomes positive, which leads to a reduction of the side slip angle as a function of the cornering vehicle speed. The differential side slip angle is calculated by .

(4.18)

Finally, the side slip angle is calculated as .

(4.19)

Increasing vehicle speed during cornering procedures leads to increased front and rear tire slip angles and consequently to an enlarged differential side slip of the car. This behavior is based on the balance of lateral forces in the vehicle, which increase with a growing lateral vehicle acceleration ay, which reads .

(4.20)

The correction steering angle Δδ is an additional angle to the Ackermann steering angle δA, which has to be applied for keeping the car on a constant driving radius. The correction steering angle of a car depends on the vehicle mass, the wheel load distribution, the lateral tire characteristics, the vehicle speed and the cornering radius and represents the driverindependent steering characteristic of a car and is calculated from .

(4.21)

Δδ = 0 … neutral Δδ > 0 … under-steering Δδ < 0 … over-steering The driver-independent steering tendency of a car can be defined as a function of the correction steering angle. A neutral vehicle behavior is achieved at Δδ = 0, which requires a balanced relation of the center of gravity position and the tire side stiffness factors at the front and rear wheels. An under-steering driving tendency is characterized by a positive correction steering angle (Δδ > 0), which is at the case with most conventional cars on the market. In the case of equivalent tire side stiffness at the front and rear axles, the center of gravity lies in the front half of the car (lR > lF). An over-steering driving tendency is accomplished at negative correction steering angles (Δδ < 0), which require an unbalanced

204

4. Conceptual full vehicle development

tire side stiffness characteristic (cSR < cSF) and/or a tail-heavy load distribution layout of the car (lR < lF). With the exception of some runabouts, most cars on the market are equipped with the same tire types and dimensions at the front and rear axles, so that the tire side stiffness behavior is equivalent. In the case of spinning or blocking wheels under specific driving conditions, the loss of lateral driving force can lead to uncontrollable driving behavior.

Figure 4.67: Steering tendency at cornering [71]

A balanced vehicle layout is able to reduce abrupt vehicle reactions and supports driver countermeasures. An under-steering tendency will occur in the case of a loss of lateral tire force by front drive spinning wheels, or blocking front wheels at braking maneuvers. An over-steering tendency will occur in the case of loss of lateral tire force by rear drive spinning wheels, or blocking rear wheels at braking maneuvers. Figure 4.67 shows the steering tendency at cornering as a function of the correction steering angle. The yaw amplification factor indicates the relation between yaw speed and steering angle at stationary operation and represents a key figure for the description of the driving stability of a car. This relation is characterized by differing progressions for under-steering, neutral and over-steering tendencies as a function of the vehicle speed. In the case of under-steering cars, the driving stability has a maximum at the so-called characteristic vehicle speed vchar , which is positioned exactly at the 50% point from the curve to the line for neutral vehicles [160]. The characteristic vehicle speed reads .

(4.22)

At higher speeds, the yaw reaction decreases. The characteristic vehicle speed is an indicator of the steering sensibility. Modern cars have a characteristic speed between about 65 and 100 km/h, whereas smaller vchar values lead to increasing under-steering tendencies. Cars with over-steering tendencies have an asymptotic driving stability curve, which convergences to the critical vehicle speed vcrit , which is calculated according to [160] by .

(4.23)

In this way, under-steering vehicles are always stable, while over-steering vehicles become unstable above the critical vehicle speed. The moment of inertia does not influence the

205

4. Conceptual full vehicle development

critical vehicle speed, but rather the damping of an initial perturbation. Figure 4.68 shows yaw reactions as a function of vehicle speed for different car types.

Ψ δ

= =

horizontal tangent in the maximum (vchar)

under-steering

vchar vcrit

v

Figure 4.68: Yaw reactions as a function of vehicle speed

In early concept development, the general vehicle layout concerning weight, center of gravity and wheel dimensions has a significant influence on the lateral dynamics behavior is an important challenge for the definition of well-balanced cars with safe driving characteristics. The implementation of specific equations and key-figures related to driving dynamics within an integrated approach for conceptual full-vehicle development supports an efficient vehicle layout and allows a consideration of multifarious influencing factors.

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Kraftfahrzeugtechnik Kraftfahrzeugtechnik I, LV-Nr.: 331.190 Wintersemester 2011/12 Kraftfahrzeugtechnik II, LV-Nr.: 331.192 Sommersemester 2012

Univ.-Prof. Dr.techn. Wolfgang Hirschberg Dr.techn. Helmut M. Waser

Institut fu ¨ r Fahrzeugtechnik Member of Frank Stronach Institute

FTG Stand: 14. September 2011

105

6. Fahrzeuglenkungen 6.1. Fahrzeuglenkungen 6.1.1. Allgemeines Die Lenkung ist jener Teil des Fahrzeugf¨ uhrungssystems, welcher der Quersteuerung des Fahrzeugs dient. Die Steuerung erfolgt u ¨ber die gelenkten R¨ader des Fahrzeugs, welche um ihre jeweilige Lenkdrehachse ( Spreizachse“) innerhalb ihres Lenkbereiches ¨ ¨ ” verdreht werden. Uber die Anderung der Schr¨aglaufwinkel erfolgt damit eine Steuerung der Reifenseitenkr¨afte. Die gelenkten R¨ader befinden sich • an der (den) Vorderachse(n) des Fahrzeugs (Standardlenkung ) • oder zus¨atzlich an der (den) Hinterachse(n) (Allradlenkung ). • Bei Nutzfahrzeugen baut man selbstlenkende Hinterachsen als gelenkte Vorlauf- oder Nachlaufachsen. Bei Fahrzeugen f¨ ur extremen Gel¨andeeinsatz wird die Lenkungswirkung durch gesteuerte(n) Bremsung / Antrieb einzelner R¨ader unterst¨ utzt oder ganz u ¨bernommen z.B. Traktore, Kettenfahrzeuge: Torque Vectoring. Entwicklungsstufen von Lenkungen: • Mechanische Lenkung , Steuerung durch den Fahrer (Lenkrad): weitentwickelter Standard ¨ • Uberlagerungslenkung: Fahreraktion δ wird durch kleinen elektronisch geregelten Zusatzlenkwinkel φ u ¨berlagert • Steer-by-Wire: Ersatz des mechanischen Lenkungs¨ ubertragens durch Aktoren, Sensoren und leitungsgebundenen Datenfluss (Zukunftskonzept).

6.1 Fahrzeuglenkungen

106

 'R

R

*R

ECU

ECU

 L



Mechanische PKWStandardlenkung

 

'L

ÜberlagerungsLenkung

  *L

Steer by WireSystem

Abbildung 6.1.: Entwicklungsstufen von Fahrzeuglenkungen

6.1.2. Geometrie der Radlenkung Die Lenkdrehung eines gelenkten Rades erfolgt um seine durch die Radaufh¨angung vorgegebene Lenkdrehachse S, welche zum Zweck einer guten LenkungsR¨ uckstellung zur Vertikalen schief angeordnet wird. Die Kinematik der Radlenkdrehung ist in Abb. 6.2 dargestellt, unter Verwendung der folgenden Bezeichnungen: • Lenkungsdrehachse S, mit dem Durchstoßpunkt P durch die Fahrbahnebene • Radmittelpunkt C • Radaufstandspunkt W auf der Fahrbahnebene.

6.1 Fahrzeuglenkungen

Einflu ¨ sse von:

107

auf:  

Nachlauf Nachlaufwinkel →  Spreizung Lenkrollradius → Sturz →

Lenkungs- R¨ uckstellung: ◦ 4 . . . 10 PKW, 2 . . . 5◦ LKW 6 . . . 12◦ PKW, 3 . . . 10◦ LKW Lenkmoment beim Bremsen und Lenkungs-R¨ uckstellung Reifenseitenkraft-Charakteristik zC

ε

zW zC B xC

zW

zC

σ

S

δ

γ

Lenkdrehachse S

γ

S B

yC

C

C

C yC

A

rS

A

P

zW

xC P

W P

n

r0

W

W yW

xW Fahrbahnebene

Abbildung 6.2.: Geometrie der Radlenkung

Longitudinale Projektion

Laterale Projektion

Vertikale Projektion

r0 σ γ

n ε rs

δ

Lenkrollradius Spreizung Radsturz

Nachlauf (strecke) Nachlaufwinkel stat. Radius

Radlenkwinkel

Beachte: Der Radlenkwinkel δ wird um die zW -Achse gemessen (normal auf die Fahrbahnebene).

6.1 Fahrzeuglenkungen

108

Momente um die Lenkachse S: zC zW

Näherung für Nachlaufwinkel ε