Tire Transient Response Modeling With First-Order Lag Dynamics
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Solution Overview
Problem
Current tire dynamic models are unable to accurately simulate transient responses of lateral and longitudinal forces during time-varying conditions, such as changing slip ratios and applied loads, which are crucial for evaluating vehicle behavior and designing efficient tires for advanced vehicle control systems.
Innovation Solution
A tire model determining method using a first-order lag model that simulates transient responses by performing regression calculations on measured data, adjusting time constants to minimize square residuals, and incorporating functions that change with slip ratio or applied load to accurately predict tire behavior.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a tire dynamic model is used to calculate cornering characteristic in steady state, then the cornering characteristic can be provided by supplying slip angle, but the model is not capable of simulating transient response of longitudinal force which changes with time by supplying temporally varying slip ratio
Solution Approach 1:
The patent transforms the static tire dynamic model into a dynamic model by introducing a first-order lag element with time constant. This allows the model to simulate transient responses of longitudinal force when temporally varying slip ratio is supplied, while maintaining steady-state cornering characteristic accuracy. The dynamic model structure enables the system to adapt from steady-state to transient-state simulations.
Solution Approach 2:
The patent changes the model parameters by introducing a time constant parameter that characterizes the transient response behavior. By adjusting this time constant parameter, the model can accurately represent different transient response characteristics of the tire, enabling simulation of both steady-state and transient-state behaviors without sacrificing cornering characteristic precision.
2Measurement precision
If the longitudinal force in steady state is calculated with the use of the tire dynamic model, then the cornering characteristic can be obtained, but the characteristic of a vehicle that has an ABS cannot be evaluated because the braking force is based on transient state characteristic
Solution Approach 1:
The patent introduces a first-order lag dynamic model that can simulate transient response characteristics. This enables the evaluation of vehicle behavior with ABS systems by accurately representing the transient-state braking force characteristics, which differ from steady-state characteristics. The dynamic model structure allows simultaneous representation of both steady-state and transient-state behaviors.
3Measurement precision
If the tire dynamic model supplies constant slip angle, then the cornering characteristic in steady state can be provided, but the transient response of lateral force cannot be simulated by making the applied load fluctuate in time-series manner
Solution Approach 1:
The patent introduces a first-order lag element with time constant into the tire dynamic model, transforming it from a static to a dynamic model. This enables the simulation of transient response of lateral force when applied load fluctuates in time-series manner, while maintaining accurate steady-state cornering characteristic predictions. The dynamic model structure allows the system to respond to time-varying inputs appropriately.
4Ease of manufacture
If a simple regression calculation is performed on measured data, then the calculation process is simple, but the simulation precision of transient response is insufficient
Solution Approach 1:
The patent employs an iterative optimization process where the time constant parameter is adjusted based on the sum of square residuals between measured transient response data and simulated data. This feedback mechanism allows the model to automatically refine its parameters to achieve high simulation precision while maintaining a relatively simple calculation framework. The iterative process continues until convergence criteria are met.
Solution Approach 2:
The patent optimizes the time constant parameter through iterative adjustment to minimize the sum of square residuals. By changing this critical parameter based on measured data, the model achieves high precision in transient response simulation without requiring complex computational algorithms, thus maintaining calculation simplicity while improving accuracy.
Data Source
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AI summary
A transient response of a tire is simulated by using a effective data of a physical amount. The physical amount is set as a rolling condition of the tire and varies in time. The effective data of the physical amount is calculated by a convolution integral of a response function of an introduced first-order lag response and a time gradient of time-series data of the physical amount. In a tire model determining method, a time constant of a response function of the first-order lag response is determined from measured transient response data. In a tire transient response data calculating method, a transient response data is calculated by using the effective data of the physical amount which is calculated by using a desired physical amount and the first-order lag response.