Characterization of Engine Variable Cam Phaser Fluid Dynamics and Phaser's Ability to Reject System Disturbances

Vane type cam phasers have been widely used in internal combustion engines to vary valve timing to achieve purposes such as low emissions, greater torque, and higher horsepower. One of the primary concerns in using a vane phaser is its position holding ability when disturbances are present. Disturbances include cam torque oscillation, cam pulley speed fluctuation, oil pressure fluctuation, and engine acceleration or deceleration. Cam torque disturbance is the biggest contributor to phaser position error. This paper will first present the generic schematic of a variable cam phasing system and its challenges, followed by the characterization of the fluid dynamics of the vane phaser, with an emphasis on the effects of pressure, leakage, and oil aeration on the vane phaser fluid dynamics and its ability to reject cam torque disturbance. Finally, numerical evaluations of the vane phaser's ability to reject cam torque disturbance and sensitivity to various system parameters will be presented.

NOTATIONS

ϕ

Fractional air content by volume

χ

Fractional air by volume that is undissolved

γ

Polytropic index

β

Effective oil bulk modulus

β₀

A reference oil bulk modulus

θ

Rotor angular displacement relative to its equilibrium position

θ₀

Bias spring pre-compressed angle

θ_d

Desired cam position relative to cam pulley

θ_S

Phaser moving authority or stroke

ω_h

Hydraulic natural frequency

ζ

Damping ratio

A

Effective pressure area

I

Cam load inertia

L

Leakage coefficient

L₁

Flow coefficient in flow path from advancing chamber to vent via OCV

L₂

Flow coefficient in flow path from supply to advancing chamber via OCV

L₃

Flow coefficient in flow path from supply to retarding chamber via OCV

L₄

Flow coefficient in flow path from retarding chamber to vent via OCV

L₅

Leakage coefficient in leak path from supply to advancing chamber

L₆

Leakage coefficient in leak path from supply to retarding chamber

L₇

Leakage coefficient in leak path from advancing chamber to vent

L₈

Leakage coefficient in leak path from advancing chamber to retarding chamber

L₉

Leakage coefficient in leak path from retarding chamber to vent

K

Phaser bias spring rate

N

Number of oil chambers of same type

P

Oil pressure

P_a0

Static oil pressure in advancing chamber

P_a

Oil pressure change from P_a0 in advancing chamber

P_abs

Absolute oil pressure

P_atmos

Absolute atmosphere pressure

P_m0

Differential oil pressure across the load at equilibrium condition

P_m

Oil pressure change from P_m0

P_r0

Static oil pressure in retarding chamber

P_r

Oil pressure change from P_r0 in retarding chamber

P_s

Supply oil pressure

P_sat

Air saturate pressure

q_l

Oil leakage

r₀

Force to torque gain, or distance from force centroid to centerline

s

Laplace transform operator

t

Time

T

Temperature

T_abs

Absolute temperature

T_f

Friction torque

V_t

Total volume of oil chambers

x

Oil control valve spool displacement

x_S

Oil Control Valve (OCV) spool stroke

x₁

OCV spool displacement to shut off flow from retarding chamber to vent

x₂

OCV spool displacement to shut off flow from supply to advancing chamber

x₃

OCV spool displacement to open flow from supply to retarding chamber

x₄

OCV spool displacement to open flow from advancing chamber to vent

dB

Decibel

FTP

Federal test procedure

lpm

Liter per minute

OCV

Oil control valve

PCM

Powertrain control module

PD

Proportional and derivative

PI

Proportional and integral

PID

Proportional, integral and derivative

PWM

Pulse width modulated

VCP

Variable cam phasing