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Two-Mass Suspension Model Differential-equations
Two-Mass Suspension Model Differential-equations
Click <a href="https://www.euromotor.org/pluginfile.php/2871/mod_resource/content/0/pres3/slides-9.html" >slides-9.html</a> link to view the file.
Two-Mass Suspension Model Differential-equations
◄ Two-Mass Suspension Model
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Title
Demands on a Vehicle Suspension
Sinusoidal Pattern of Unevenness
Periodic Pattern of Unevenness
Spectrum of a Periodic Pattern of Unevenness
Irregular Pattern of Unevenness
Power Spectral Density of Unevenness
Power Spectral Density of Unevenness dependent on Angular Frequency
Power Spectral Density dependent onAngular Frequency
Setup for Measuring Unevenness (ika)
Working Principle of Contactless Distance Measurement
Sensing of a Spectrum of Unevenness
Constitution of the Spring Rate of a Pneumatic Tire
Spring Rate of a Utility Vehicle Tire dependent on Inner Pressure
Linearisation of the Spring Rate of a Tire
Radial Spring Rate of a Utility Vehicle Tire dependent on Velocity and Slip Angle
Damping Factor of a Tire Dependent onRolling Velocity and Excitation Frequency
Title
Front Axle of a Utility Vehicle suspended by Leaf Springs
Leaf Springs - Simple Leaf Spring
Leaf Springs - Trapezoidal Spring
Spring Leafs - Parabolic Spring
Spring Leafs with Additional Springs
Spring Rate of a Leaf Spring with Additional Springs
Spring Rate of a Leaf Spring with Dry Friction
Development Stages of Leaf Springs
Single Leaf Spring with Torque Rod
Torsion Bar - Theory
Torsion Bar Spring
Coil Springs - Theory
Relative Spring Rates
Gas Springs - Basics
Gas Springs - Hydropneumatic
Gas- Filled Springs - Hydro-Pneumatic Spring
Supporting Spring Cylinder with hydraulic level control system and adjustable damping
Air-spring bellows
Characteristic of the Load Capacity of an Air-spring Bellow
Characteristic of Load Capacity of Air-Spring U-bellows
Gas-Filled Springs - Pneumatic Spring
Air-spring and Damper Unit with Bearing U-bellows
Eigenfrequency of Different Suspension Systems
Differences Between Steel Springs and Air Springs
Title
Tasks of a Damper
Damper Design
General Assembly of HydraulicShock Absorbers
Monotube Damper
Twintube Damper
Typical Damper Concepts
Damper Work Chart for the Determination of Damper Characteristics
Damper Force depending on the Relative Velocity due to Damping Coefficient
Influence of Damper Layout on Wheel Load Variation
Dual Piston Damper (F&S, ADC-1)
AdjustableDampers (F&S, ADC-1)
Adjustable Dampers (F&S, ADC 2.2)
Amplification Factors of Different Vehicle Seats
Suspended seat
Model of a Seated Person
Amplification Function of Head Acceleration
Lines of Equal Perception Intensity KZ
Rated Vibration Intensity
Lines of Equal Perception Intensity
Title
Tire models - Vertical Dynamics
Tire models Laplace-Transformation
Frequency Progression of the Tire Models
Single-Mass Suspension Model
Single-MassSuspension Model Differential-equations
Amplification Function of the Single-Mass Suspension System
Two-Mass Suspension Model
Determination of the Amplification Function
Determination of the Amplification Function
Synthetically Generated Road Signal
Vertical Displacement, Velocity and Acceleration of Road, Wheel and Body
Parametric Variation with Different Wheel-Mass
Parametric Variation with Different Spring Rates of Tires
Parametric Variation with Different Body Spring Rates
Parametric Variation with Different Shock Absorbers
Influence of Constructive Changes on the Suspension
Classification of ControlledSuspension Systems
Electronic Damper Control (EDC)
Characteristic Map for Damping Force
Active Suspension
Comparison between Trucks and Cars
Influence of Frictional Forces within Springs
Structure of a Three-Mass Suspension Model
Amplification Function and Seat-Acceleration
Title
Single-Track Suspension Model
Single-track Suspension Model - Equationsof Motion
Single-Track Suspension Model - Natural Circular Frequencies and Damping Factors
Single-track Suspension Model - Influence of Velocity
Single-Track Suspension Model - Influence of Body-Eigen frequencies
Single-track Suspension Model - Influence of Location of Measuring Point
Configuration of Single-track Suspension Model with Coupling Mass
Single-Track Suspension Model - Impulse Excitation
"Hydrolastic" Compound Suspension
Two-Axle Vehicle with Spring Coupling
Platform Truck Model
Semitrailer Truck Model
Swing Tandem Axle with Hydraulic Damping (MB)
Title
Cybernetic Tasks of the Driver while Handling a Vehicle
Control Loop Driver - Vehicle
Demands on the Vehicle Characteristicsfor good ?Vehicle Behaviour?
Demands on Tires of Road Vehicles
Section of a Tubeless Passenger Car Tire
Definitionof the Cord Angle
Influence of the Carcass Cord Angle
Bias Tire
Radial Tire (Belted Tire)
Pressure Distribution in Contact Area of straight running Tires
Force Transmission in Longitudinal Direction
Relationship between Rotational Slipand Friction Coefficient
Friction Coefficient dependant on Velocity and Tread Depth on Dry Road
Expulsion of Water Film out of Contact Area between Tire and Road
Friction Coefficient for Braking Forces dependent on the Velocity and Water Film Height on the Road
Friction Coefficient for Braking Forces dependent on the Tread Depth and Water Film Height on the Road
Height-to-Width Ratio
Definition of "Slip Angle"
Deformation of the rolling Tire by a Lateral Force Fy
Cornering Force dependent on Slip Angle - Wheel Load as Parameter
Cornering Force dependent on Wheel Load - Slip Angle as Parameter
Cornering Force dependent on Tire Pressure - Slip Angle as Parameter
Aligning Torque M? dependent on Slip Angle Wheel Load as Parameter
GOUGH Tire Performance Map
Definition of the Camber Angle
Camber Force F and Camber Torque M
Cornering Force F dependent on Camber for different Wheel Load
Lateral ?Longitudinal Force Characteristic Map
Superposition of Tire-, Lateral-,and Longitudinal Forces
Lateral ? Longitudinal Force Characteristic Map dependent on Brake Slip
Quasistatic Loss of Lateral Force and Change in Aligning Torque due to Harmonic Variation of Wheel Load
Lateral Forces as a Function of Tire Slip
Amplitude, Frequency and Vehicle Velocity
Phase Angle, Frequency and Vehicle Velocity
Transient Tire Models
Tire Behaviour of Transient Tire Models
Transient Tire Behaviour
Transient Tire Behaviour
Title
Single Track Vehicle Model
Linearized Tire Slip Stiffness c for Different Tires
Single Track Vehicle Model Motion Parameters
Single Track Vehicle Model - Equations of Motion
Steady State Cornering
Steady State Cornering - Difference in Tire Slip Angle
Driving Conditions with the Definition by Olley (1940)
Steering Angle Characteristics on the Single Track Vehicle Model
Steering Angle Characteristics on the Single Track Vehicle Model
Different Definitions of Steering Behaviour
Definition of Steering Bahaviour by BERGMANN (1965)
Non-Stationary Behaviour
Yaw Eigenfrequency and Yaw Damping as Dependent on Velocity
Vehicle Characteristics dependent on Yaw Damping and Yaw Eigen frequency
Yaw Amplification Factor as a Function of Vehicle Velocity
Dynamic Behaviour of Control Element - Vehicle
Time Functions of Vehicle Motion Variables after Stepped Steering Input
Transfer Functions - Sinusoidal Steering
Frequency Amplification Function
Frequency Amplification Functions
Frequency Amplification Functions
Title
ADAMS-Model of a Complete Vehicle forDriving Dynamics Simulation (Audi A8)
Lateral force due to Tire Slip dependent on Tire Slip Angle and Wheel Load
Longitudinal Force as a Function of Longitudinal Slip
Testing Procedures for Driving Behaviour of Automobiles
Sudden Steering Input
Four Wheel Vehicle Model
Simulation Results for Steady State Cornering - Left-Hand Bend
Yaw Amplification Factor as a Function Of the Vehicle Velocity
Overall View of Parametric Variations
Simulation Results Parametric Version Nr.1
Forces on a Double-Track Springing Model During Cornering
Wheel Load of the Double Track Springing Model
Cornering Force dependent on Wheel Load Difference
Simulation Results Parametric Variation Nr. 2
Simulation Results Parametric Variation Nr.3
Cornering Force with/without Stabilizer Bar
Simulation Results Parametric Variation Nr. 4
Title
Change in Wheel Position during Springing
Absolute and Relative Camber
Superposition of Cornering Forces by Tire Slip and Camber
Simulation Results of Parametric Variation Nr.5
Definition of Toe Angle
Characteristic Curves for Toe Angle and Camber Angle
Simulation Results of Parametric Variation Nr. 6
Simulation Results of Parametric Variation Nr. 7
Additional Steering on Rear Axle
Build-Up of Lateral Force immediately after Sudden Steering-Angle Change
Simulation Results of Par. Variation Nr. 8
Characteristic Map of Additional Rear Axle Steering System for Sideslip Angle (Steady-State)
Frequency Curve of a Vehicle with/without Sideslip Angle Compensation
Dynamic Axle-Load Shift during Braking
Difference in Yaw Velocity while Acceleratingout of Curve on Adherent Road Surface
Difference in Yaw Velocity while Acceleratingout of Curve on Slippery Road Surface
Causes for Load Alteration Effect
Change of Lateral Force during Load-Alteration Effect
Deviation of Center of Gravity CourseDuring Load-Alteration Effect
Deviation of yaw Velocity 1s after Load-Alteration Effect (Front-Wheel Drive)
Parameters which Characterize Vehicle Motions during Braking in Curves
Yaw Moment while Braking under Split-Circumstances
Elastokinematic Design of the Front Wheel Suspension
Title
Relationship between Steering Input and Change in Direction
Demands on the Steering System
Steering torque depending on vehicle velocity
Steering Systems
Position of the Steering Axis
Front axle of a Mercedes Benz truck
Position of the Steering Axis
Virtual Steering Travel Axis - Audi A4
Castor angle,Castor trail in wheel centre,Castor offset, Wheel castor offset and Lateral force
Castor angle and Castor offset depending on Steering angle
Steering Return due to Lateral Force
Disturbing force lever arm for longitudinal tire forces
Weight-self-alignment due to spread angle
Disturbing Force Lever Arm and Steering Offset depending on Steering Angle
Definition of Toe
Change in Camber during Steering
Steering linkage concepts
Ackermann
Relationship between steering angle, slipangle and position of center of curve
Toe Difference Angle as a Function of the mean Steering Angle
Relationship between steering-wheel angleand steering wheel torque
Steering Gear Ration under influence of Steering Torque
Steering Components
Rack-and-Pinion Steering System
Worm-and-RollerSteering System
Ball-and-Nut Steering System
Operating-scheme of aBall-and-Nut Power Steering System, ZF
Rack-and Pinion Power Steering System, ZF
Operating scheme of the Servotronic
Valve Characteristic of the Servotronic
Characteristic of Steering Wheel Torque depending on Lateral Acceleration
Title
Independent Wheel Suspension, Schematic
Rigid Axle, Schematic
Twist Beam Axle, Schematic
Multilink Wheel Suspension
Spherical Wheel Suspension
Plane Wheel Suspension
Change of Wheel Base and Track Width
Intantaneous Center of Axle in Longitudinal Plane
Force Transmission between Contact Areaof Tires and Body during Cornering
Intantaneous Center of Reciprocal Spring Travel
Change of Position of Roll Pole during Cornering
Forces on the Wheel Carrier during Braking and Accelerating
Force Transmission between Contact Area and Body during Braking
Force Transmission between Contact Area and Body during Acceleration
Anti-Dive and Anti-Squat
Transverse Link made out of Rubber with Vulcanized Inner Bushing
Elastokinematics of a Wheel Carrier guided by Five Links with elastic Steering Rod
Assessment Criteria of Wheel Suspensions
Inclined Springing Angle and Brake Supporting Angle
Title
Rear Axle of Car Guided by Spring Leafs
Statically Determinate Suspension on the Rear Axle of a Car, Ford Taunus
Statically Indeterminate Suspension on the Rear Axle of a Car - Opel Rekord
Lateral Guidance of a Rigid Axle by a Watt Linkage - Mazda RX 7
Change in Toe Angle of a Rigid Axle due to Reciprocal Spring Travel
A-Bracket Rigid Rear Axle, Lancia Y 10
DeDion-Rigid Axle Opel Diplomat
Torsion Crank Axle - Audi 80, 1972
Twist Beam Rear Axle - VW-Scirocco, 1974
Twist Beam Rear Axle - Audi A4, 1994
Twist Beam Rear Axle - Ford Fiesta,1995
Geometry of the Twist Beam Rear Axle during Roll Springing
Function of Track Correcting Bearingsof Twist Beam Rear Axle
Geometry of the Double Joint Swing Axle
Double Joint Swing Axle, VW Beatle
Single Joint Swing Axle with Compensating Spring, MB 220 (1959)
Geometry of the Trailing-Arm Wheel Suspension
Trailing-Arm Wheel Suspension with Torsion-Bar Spring - Renault 9, 11
Semi-Trailing-Arm Wheel Suspension ofa Driven Axle, Opel Omega (1994)
Geometry of the Semi-Trailing-Arm Wheel Suspension
Screw-Linkage Rear Axle BMW 5-series, 7-series respectively until 1996 and 1994
Non-Driven Semi-Trailing-Arm Rear Axle - VW Sharan, 1996
Geomety of the Plain Double-Wishbone Suspension
Geometry of the Spherical Double-Wishbone Suspension
Three Dimensional Double Wishbone Suspension of a Driven Front Axle - Honda Prelude
Double Wishbone Front Axle - Mercedes-Benz E-Class, 1996
" Central Point Guided " Spherical Double Wishbone Rear Axle, BMW Z1
McPherson Front Axle Audi 100, 1991
Suspension-Strut-Type Wheel Suspension VW Golf IV, 1997
Reduction of the Clamping Forces within Piston Rod Guidance
Reduction of the Clamping Forces within Piston Rod Guidance
Elastokinema-tically Tuned Suspension-Strut-Type Front Axle
Double Joint Suspension-Strut-Type Front Axle with ideal Steering Axis - BMW 5-series (1996 )
Shock-Absorber Strut Front Axle - MB 190
Four-Link Wheel Suspension- Audi A4, 1994
Five-Link Wheel Suspension - Chevrolet Corvette, 1983
Multilink Wheel Suspension - MB 190
Multilink Wheel Suspension - BMW 5-series, 1996
Automotive Engineering Lecture 2: Vertical Dynamics
Automotive Engineering Lecture 2: Lateral Dynamics
Determination of the Amplification Function ►