PSI - Issue 12

T. Novi et al. / Procedia Structural Integrity 12 (2018) 145–164

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Author name / Structural Integrity Procedia 00 (2018) 000–000

M torque M d maximum torque at di ff erential M f frction torque generated by the disc pack M m gears transmitted torque m sr vehicle static mass on rear axle M w torque per wheel p pressure ˙ Q heat transferred r wheel radius R curve radius R m mean radius s e ff ective surface slope T temperature t r rear track

T s wall temperature T ∞ bulk temperature v travel velocity V

vehicle longitudinal speed V M variable dependant on oil level W heat generated by friction w b wheelbase z p

planet equivalent circular gear number of teeth solar equivalent circular gear number of teeth

z s

thermal di ff usivity

α η λ

e ffi ciency

thermal conductivity µ x maximum longitudinal adherence coe ffi cient ν Poisson’s modulus ρ density σ e ff ective surface roughness ∆ τ time lapse ω rotational velocity ∆ ω relative rotational velocity ecu Electronic Control Unit fea Finite Element Analysis fem Finite Element Method fe Finite Element fs - fem Face-based Smoothed Finite Element Method lsd Limited Slip Di ff erential

lvfa Low Velocity Friction Apparatus tcc Thermal Contact Conductance sad Semi-Active Di ff erential

1.1. SAD working principle

The SAD assembly under study can be divided into three parts: a left and a right cartridge with a central housing. The left cartridge derives from a standard open di ff erential and is composed of a solar gear, driveshaft, bushings and a carter which connects the cartridge to the chassis. The central housing is composed of a casing, cross and planet gears. The casing is rigidly connected to the final gear of the transmission, therefore, it receives torque directly from the engine. This torque is transmitted to the cross and planets, as these are obliged to rotate with the di ff erential