DYNATUNE-XL RIDE & HANDLING MODELING APPROACH
The DYNATUNE-XL RIDE & HANDLING MODULE started its life as a simple Lotus 123 sheet, designed to calculate the Yaw Frequency Response Function with the Equations of a Bicycle Model. In order to do so the Tire model did exist solely out of a Front & Rear Axle Cornering Stiffness and gradually evolved into the BASE TIRE MODEL. Then in RELEASE 7.0 a 7-DOF-Model was added to calculate more Specific Vehicle Data which also required a more sophisticated Tire Model, the ENHANCED TIRE. To make it all complete a basic Ride Model was incorporated which allowed to create a "One for All" Tool for the basic Vehicle Dynamics "Ride & Handling" Setup of a Vehicle.
These 3 Key-Features and 2 Tire Models have governed the Architecture of the Tool until now:
These 3 Key-Features and 2 Tire Models have governed the Architecture of the Tool until now:
BASE Vehicle Modelling Approach BiCYCLE MODEL
DYNATUNE-XL R&H has originally been developed around the standard equations of a linear bicycle model, which are very well described in automotive engineering literature and do not need additional explaining here. The capabilities of a bicycle model are demonstrated nowadays in every ESP system, where it is being used to estimate accurately even extreme vehicle conditions.
The classic limitations of a Bicycle Model - being a Single-Track Model and not permitting calculation effects of Vehicle Roll - can be largely overcome by adding some additional detailed chassis calculations and including all Elasto-Kinematic Suspension & Tire Characteristics into one resulting Front and Rear AXLE cornering stiffness (ref. BUNDORF). This approach does permit the Bicycle model to be used accurately to calculate Understeer Budget, Step Steer Response & Frequency Steer Response in various load conditions, even up to then Non-Linear Range of the Tire. |
ADVANCED VEHICLE MODELING APPROACH
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In the DYNATUNE-XL R&H 7-DOF model all instantaneous Contact Patch Loads in X-Y-Z directions, caused by Aerodynamic Loads, Traction / Braking and Lateral Acceleration are calculated for the desired vehicle condition.
Based on these Contact Patch Loads, data like Wheel Deflections, Kinematic & Elasto-Kinematic Wheel Movements, Ride-Height changes and instantaneous Center of Gravity Height are all being calculated and displayed.
All relevant parameters and calculation results from the 7-DOF Vehicle Model are being used - if necessary - for updating the boundary conditions of the Linear Bicycle Model. Out of the 7-DOF Vehicle Model can - for any Condition of Lateral Acceleration - the Resulting Axle Cornering Stiffness be extracted. Transplanting this information into the Bicycle Model does permit to evaluate also Understeer Budget & Transient Stability at that given Operating Condition. In fact by doing so, it is possible to use the Bicycle Model also outside of the Linear Range of the Tire.
In RELEASE 8.1 one can find on the Car-Center-line all the results for the Additionally introduced new Power-Train Features. The new Steering System Parameters can be found on the Left 7 Right Front Wheel Section.
Based on these Contact Patch Loads, data like Wheel Deflections, Kinematic & Elasto-Kinematic Wheel Movements, Ride-Height changes and instantaneous Center of Gravity Height are all being calculated and displayed.
All relevant parameters and calculation results from the 7-DOF Vehicle Model are being used - if necessary - for updating the boundary conditions of the Linear Bicycle Model. Out of the 7-DOF Vehicle Model can - for any Condition of Lateral Acceleration - the Resulting Axle Cornering Stiffness be extracted. Transplanting this information into the Bicycle Model does permit to evaluate also Understeer Budget & Transient Stability at that given Operating Condition. In fact by doing so, it is possible to use the Bicycle Model also outside of the Linear Range of the Tire.
In RELEASE 8.1 one can find on the Car-Center-line all the results for the Additionally introduced new Power-Train Features. The new Steering System Parameters can be found on the Left 7 Right Front Wheel Section.
VEHICLE MODELING APPROACH - TIRE MODELS
1 - BASE TIRE MODEL
Correct tire data is of fundamental importance for any simulation of vehicle behavior. However Tire Data can be very complex and are unfortunately many times not accurately available. In DYNATUNE-XL R&H all LINEAR vehicle behavior is calculated with a bicycle model based on front and rear cornering stiffness. This "BASE TIRE MODEL" approach permits to keep tire data management simple, efficient and focused only the most important principal tire-parameter-identifiers (which if needed can also be easily extracted from more complex tire models):
- Grip Level (Friction Coefficient µ) [-]
- Cornering Stiffness [N/°]
- Camber Thrust [N/°]
- Aligning Torque Stiffness [Nm/°]
As can be seen in the 2 left graphs, the tire characteristics "Lateral Force" and "Aligning Moment" show the commonly well known non-linear behavior (quadratic/parabolic function) over slip angle. However, looking at their derivatives "Cornering Stiffness" and "Aligning Torque Stiffness" at the right, one can see that these parameters show almost linear behavior in the operating range (in fact, the derivative of a quadratic/parabolic function is a linear function). The DYNATUNE-XL R&H "BASE TIRE MODEL" assumes for these parameters (partially) linear behavior, making in this way a robust approach to high g-Levels possible.
In effect, as shown by the red arrows in the 2 right graphs Cornering Stiffness (or Aligning Torque Stiffness) will increase with increasing vertical load (arrow-up) and decrease with increasing slip angle (=increasing lateral load) close to 0 at the maximum grip level (arrow-down). The operating range is identified with the diagonal line. Following this ideology for each AXLE a resulting AXLE Cornering Stiffness will be calculated and based on the load transfer data from the 7-DOF Model for any given lateral G-Level the data to be used in the Bicycle Model will be updated with resulting in correct Front and Rear Axle Cornering Stiffness for that particular G-Level.
The Front and Rear main Tire Parameters are defined at a Reference Load Condition which are to some extend scalable with a parameter that governs tire-sensitivity to vertical load changes. By using a Reference Load and a Load Sensitivity Parameter the DYNATUNE-XL R&H "BASE TIRE MODEL" can be easily adjusted to reflect correct tire behavior for any specific load condition of the vehicle.
- Grip Level (Friction Coefficient µ) [-]
- Cornering Stiffness [N/°]
- Camber Thrust [N/°]
- Aligning Torque Stiffness [Nm/°]
As can be seen in the 2 left graphs, the tire characteristics "Lateral Force" and "Aligning Moment" show the commonly well known non-linear behavior (quadratic/parabolic function) over slip angle. However, looking at their derivatives "Cornering Stiffness" and "Aligning Torque Stiffness" at the right, one can see that these parameters show almost linear behavior in the operating range (in fact, the derivative of a quadratic/parabolic function is a linear function). The DYNATUNE-XL R&H "BASE TIRE MODEL" assumes for these parameters (partially) linear behavior, making in this way a robust approach to high g-Levels possible.
In effect, as shown by the red arrows in the 2 right graphs Cornering Stiffness (or Aligning Torque Stiffness) will increase with increasing vertical load (arrow-up) and decrease with increasing slip angle (=increasing lateral load) close to 0 at the maximum grip level (arrow-down). The operating range is identified with the diagonal line. Following this ideology for each AXLE a resulting AXLE Cornering Stiffness will be calculated and based on the load transfer data from the 7-DOF Model for any given lateral G-Level the data to be used in the Bicycle Model will be updated with resulting in correct Front and Rear Axle Cornering Stiffness for that particular G-Level.
The Front and Rear main Tire Parameters are defined at a Reference Load Condition which are to some extend scalable with a parameter that governs tire-sensitivity to vertical load changes. By using a Reference Load and a Load Sensitivity Parameter the DYNATUNE-XL R&H "BASE TIRE MODEL" can be easily adjusted to reflect correct tire behavior for any specific load condition of the vehicle.
Combined Slip Conditions (Lateral and Longitudinal Tire Loads) are simulated according to the Friction Circle Equations for Tire Friction Coefficient µ. At "zero" Longitudinal Force, Tire Cornering Stiffness will be maximal and at full longitudinal µ saturation, Tire Cornering Stiffness will be minimal. Equally the lateral friction coefficient µ will be maximal at "zero" longitudinal load and minimal at maximum traction/braking force
2 - ENHANCED TIRE MODEL
In DYNATUNE-XL R&H from RELEASE 7.0 onwards is the "ENHANCED TIRE MODEL" available as an extension to the "BASE TIRE MODEL". The "ENHANCED TIRE MODEL" will transform the 6 parameters (Cornering & Aligning Torque Stiffness, Camber Thrust, Reference Load, Mue and Load Sensitivity Factor) from the "BASE TIRE MODEL" into a conventional NON-LINEAR TIRE MAP in which Lateral Tire Force is represented as a function of Tire Slip Angle and Tire Vertical Load. A specific TIRE DATA USER TOOL - as shown in the picture above - has been developed to visualize the Tire Data from the Enhanced Tire Model.
With the "ENHANCED TIRE MODEL" all NON-LINEAR Calculations based on the 7-DOF Vehicle Model can be calculated correctly to the very highest lateral accelerations by balancing inside and outside tire slip angles more accurately with inside and outside tire lateral loads (a matter, which is approximated by the partially linearized axle cornering stiffness approach in the "BASE TIRE MODEL").
All other "LINEAR" Calculations/Procedures based on the Bicycle Model do remain with the "BASE TIRE MODEL".
In DYNATUNE-XL R&H from RELEASE 7.0 onwards is the "ENHANCED TIRE MODEL" available as an extension to the "BASE TIRE MODEL". The "ENHANCED TIRE MODEL" will transform the 6 parameters (Cornering & Aligning Torque Stiffness, Camber Thrust, Reference Load, Mue and Load Sensitivity Factor) from the "BASE TIRE MODEL" into a conventional NON-LINEAR TIRE MAP in which Lateral Tire Force is represented as a function of Tire Slip Angle and Tire Vertical Load. A specific TIRE DATA USER TOOL - as shown in the picture above - has been developed to visualize the Tire Data from the Enhanced Tire Model.
With the "ENHANCED TIRE MODEL" all NON-LINEAR Calculations based on the 7-DOF Vehicle Model can be calculated correctly to the very highest lateral accelerations by balancing inside and outside tire slip angles more accurately with inside and outside tire lateral loads (a matter, which is approximated by the partially linearized axle cornering stiffness approach in the "BASE TIRE MODEL").
All other "LINEAR" Calculations/Procedures based on the Bicycle Model do remain with the "BASE TIRE MODEL".
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In RELEASE 8.0 Tire Grip / Friction Coefficient has become Load Dependent in the ENHANCED TIRE Model. With this Upgrade the ENHANCED TIRE Model has made the last and final step to ultimate flexibility within the constraints of not becoming as complex as a Pacejka Magic Formula Model.
In RELEASE 8.0 Camber Thrust Force is also being considered in the Final Lateral Grip / Friction Coefficient Calculation. Forces caused by Tire Slip Angle and Forces created due to Camber/Inclination Angle are added up into the Final Grip Value Calculation. |
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NOTE:
- DYNATUNE DOES NOT USE TIRE RELAXATION-LENGTH PARAMETERS.
- DYNATUNE DOES NOT USE TIRE RELAXATION-LENGTH PARAMETERS.
VEHICLE MODELING APPROACH - POWER-TRAIN & BRAKE-SYSTEM
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The Power-Train is modeled very very elementary by providing only a User Defined Power to the Wheels.
In RELEASE 8.1 one can provide additionally a "Braking" power to the Wheels in order to simulate either Regenerative Braking or the Effects of ICE Overrun in combination with Limited Slip Differentials. |
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The Power-Train does provide "at all times" the necessary Power to the Wheels and does not consider any Gear Ratio's or Differential Gear Reductions. Detailed Drive-Line Analysis can be executed in the DYNATUNE-XL DRIVE-LINE DESIGN MODULE
This of course will mean that vehicles with enough Power will be Traction Limited during acceleration from Standstill and Power Limited at higher velocities due to Aerodynamic Drag etc. This Approach does permit to simulate correctly both ICE as EV power units. |
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IN RELEASE 8.1 the User can opt for Limited Slip Differentials. The are typically characterized by a Preload - which is causing some initial locking and a Locking Percentage which does indicate the amount of Traction Torque Difference between outside wheel and inside wheel. The same is applicable for Overrun or Regen Scenario's.
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In Real-Life conditions, when running straight (i.e at G-Lat = 0) the Differential Preload will cause an extra Understeering Component to the Linear Understeer Gradient. This Effect is also considered in the DYNATUNE-XL R&H Module (See Bundorf Table). The Differential Preload however is considered to be an "Internal Moment" and does - for reasons of numeric simplification - not show up explicitly transformed into any additional Longitudinal Forces.
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For simulation conditions with G-Lat <>0 AND G-Long <> 0 the LSD differential (if activated of course) will become immediately active and distribute the Drive Torque across the Axle as per it's setting to the higher loaded (outside) Wheel. This will continue to happen up to the instantaneous grip level at which the inside wheel will saturate the instaneous Grip Level at which the Simulation will stop.
The such induced difference between Left and Right Longitudinal Forces will create an additional Yaw Moment around the CoG of the Vehicle which in case of Traction will support the Turning of the Vehicle (Oversteer) and in case of Overrun / Regen will reduce the Turning of the Vehicle (Understeer). |
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If no LSD has been activated the simulation will stop as soon one wheel loses grip and would start spinning freely. The same principle would be applicable to hydraulic braking. Also here the simulation would stop when one of the wheels would lock up. If one would be interested to investigate Full Torque Vectoring in Braking & Traction Conditions (as nowadays on 4 Motor EV High Performance Vehicles) one can turn on these Features as shown below and the Longitudinal Forces will be distributed according to the Grip Levels at all Wheels, logically resulting in higher overall Vehicle Performance.
VEHICLE MODELING APPROACH - DYNAMIC RIDE Model
The DYNATUNE-XL R&H Dynamic Linear Ride Model, which is being used for calculating Ride Step Input & Ride Frequency Response, exists basically out of two independent vertical half vehicle models with front and rear body, springs and (linearized) dampers. Front and Rear Unsprung Masses are connected to both Front and Rear Body by suspension spring and damper, as to ground via the tire vertical spring combined with a generic tire damping (which is derived from typical numbers for % critical tire damping). All equations are solved via Laplace Transformations.
Generic calculations for natural bounce & pitch frequencies with/o bounce and pitch centers are classically calculated by solving the differential equations of a simplified reduced order model.
Generic calculations for natural bounce & pitch frequencies with/o bounce and pitch centers are classically calculated by solving the differential equations of a simplified reduced order model.