Instantaneous IRI John B Ferris Associate Professor Mechanical

Instantaneous IRI John B. Ferris Associate Professor, Mechanical Engineering Director, Vehicle Terrain Performance Lab March 21

Instantaneous IRI Motivation Background Golden Qcar is Linear Time-Invariant (LTI) LTI → Impulse Response and Superposition • • Proposed Definition of Instantaneous IRI (IRIi) § • • Contribution of Input to Response, fij Problem: IRI is nonlinear integrator Desired Properties: average IRIi = IRI Definition of IRIi Validate Properties Comments and Discussion Dr. John B. Ferris Associate Professor Slide 2 brabantio. me. vt. edu/sites/VTPL 2

Golden Qcar is Linear Time-Invariant Qcar model comprises • Masses – mass does not change • Linear Springs – rate doesn’t change • Linear Dampers – doesn’t change Linear Time Invariant (LTI) Equations of Motion are Dr. John B. Ferris Associate Professor Slide 3 brabantio. me. vt. edu/sites/VTPL 3

LTI → Impulse Response Dr. John B. Ferris Associate Professor Slide 4 brabantio. me. vt. edu/sites/VTPL 4

LTI → Superposition Why do we care: LTI Systems Superposition § Break up complicated forces into sums of simpler forces, compute the response and add to get the total solution § If x 1 and x 2 are solutions to an LTI system then Dr. John B. Ferris Associate Professor Slide 5 brabantio. me. vt. edu/sites/VTPL 5

LTI → Superposition Why do we care: LTI Systems Superposition Dr. John B. Ferris Associate Professor Slide 6 brabantio. me. vt. edu/sites/VTPL 6

Qcar is LTI Linear Time Invariant (LTI) Completely defined by Impulse Response Dr. John B. Ferris Associate Professor Slide 7 brabantio. me. vt. edu/sites/VTPL X 1: sprung mass X 2: unsprung mass 7

Qcar is LTI Dr. John B. Ferris Associate Professor Slide 8 brabantio. me. vt. edu/sites/VTPL 8

Contribution of Input to Response fij : fraction of response at j due to excitation at i Properties of fij Dr. John B. Ferris Associate Professor Slide 9 brabantio. me. vt. edu/sites/VTPL 9

Contribution of Input to Response Skipping some math… define fij as Which is just a function of the impulse response, the road heights, and the times Dr. John B. Ferris Associate Professor Slide 10 brabantio. me. vt. edu/sites/VTPL 10

Golden Qcar is LTI So… what’s the problem? ? • IRI is nonlinear (abs values) • We can rewrite IRI for sampled data as Dr. John B. Ferris Associate Professor Slide 11 brabantio. me. vt. edu/sites/VTPL 11

Desired Properties of IRIi Average IRIi = IRI Dr. John B. Ferris Associate Professor Slide 12 brabantio. me. vt. edu/sites/VTPL 12

Definition of IRIi Substitute into Gives Define Dr. John B. Ferris Associate Professor Slide 13 brabantio. me. vt. edu/sites/VTPL 13

Validate Properties of IRIi Define Okay…is this valid? Average IRIi = IRI? ? =1 =L Dr. John B. Ferris Associate Professor Slide 14 brabantio. me. vt. edu/sites/VTPL 14

Comments and Discussion Definition of Instantaneous IRI, IRIi Can have varying speeds and is purely a function of the Qcar parameters, the measurement times and the road heights! Thank you! Questions? ? Dr. John B. Ferris Associate Professor Slide 15 brabantio. me. vt. edu/sites/VTPL 15