Method for simulating the temporal evolution of a physical system in real time

A method for simulating physical behavior of a tire with which a vehicle is equipped, tread of the tire having contact with the ground, the method comprising:

• executing, via at least one processor of a computer system, a driving simulator;
• while the driving simulator is executing:
• defining, via the processor, a maximum number of iterations per period of time based on a moment during simulation;
• executing a plurality of iterations over a plurality of periods of time;
• while the driving simulator is executing, after defining the maximum number of iterations per period of time:
• repeatedly determining, via the at least one processor, if the maximum number of iterations per period of time have been executed, wherein when a maximum number of predefined periods of time have been executed the driving simulator terminates;
• and
• executing via the at least one processor, an iterative algorithm as part of the driving simulator to determine if a convergence criterion has been met, the iterative algorithm comprising:
• repeating, until either (A) a convergence criterion has been met or (B) the maximum number of predefined periods of time have been executed:
• capturing, via a sensor at a sampling rate of 0.001 ms, an input variable, the input variable identifying physical conditions of a vehicle tire in contact with ground;
• estimating, via the at least one processor of the computer system based at least in part on the input variable, a current value of at least one estimated variable,
• the estimated variable being:
• a magnitude of longitudinal forces (Fx) transmitted by the vehicle tire between the ground and a vehicle comprising the vehicle tire,
• a magnitude of transverse forces (Fy) transmitted by the vehicle tire between the ground and the vehicle,
• a moment of self-alignment torque (Mx) acting on the vehicle tire at a center of contact with the ground about a vertical axis, or
• an abscissa (b) of border between regions of sliding and gripping contact;
• and
• comparing, via the at least one processor, the current value of the at least one estimated variable to a stored value of the at least one estimated variable, the stored value of the at least one estimated variable having been calculated on an immediately preceding iteration, resulting in a comparison,
• wherein:
• the plurality of iterations are performed per period of time;
• the convergence criterion is met when the comparison is smaller than a predetermined threshold, wherein determining if the convergence criterion is met occurs in less than 0.001 ms;
• and
• upon meeting the convergence criterion the driving simulator terminates;
• and
• outputting the at least one estimated variable to identify physical behavior of the vehicle tire, such that the computer system identifies and outputs the at least one estimated variable using less computational power than if the plurality of iterations occurred under a single period of time.