2001-01-0595 A Model-Based Brake Pressure Estimation ... - Delphi

orifice with flow area a 1 , and enters the caliper’s chamber
to build up pressure P c so as to move the brake pad. At
the same time, the release valve is closed. When the
control command is in “RELEASE” mode, the fluid from
the caliper chamber flows through the release valve’s
orifice with flow area a 2 , and goes back to the tank. In
this mode, the apply valve is closed. A third state is the
“HOLD” mode, which is when both apply and release
valves are closed. The brake pad is modeled by a mass,
spring and damper system.
Pressure Relief Valve
M
P s
a 1
Apply
command
Q 1
Release
command
Q 2
a 2
V 0
P c
Caliper
Piston x p
Figure 1 Model schematic of one simplified channel
hydraulic-mechanical schematic of the brake pressure
control system
To summarize, the symbols used in Figure 1 are defined
as follows:
P s hydraulic line pressure
P c caliper chamber pressure
x p caliper piston displacement
V o initial chamber volume
Q 1 flow rate from apply valve
Q 2 flow rate from release valve
a 1 orifice area for apply valve
a 2 orifice area for release valve
K p
B p
a p caliper piston area
M p mass of the piston
B p damping coefficient
K p effective spring constant
MATHAMATICAL MODEL
From Figure 1, the mathematical model of TCS brake
pressure control system is described by the following
equations [3][4].
M ⋅ x + B ⋅ x + K ⋅ x = P ⋅ a − F
(1)
p
⋅⋅
p
Q −Q
p
⋅
p
V
+
p
p
+ V
β
c
dPc
⋅
dt
⋅
c o
1 2 = a p ⋅ xp
(2)
V a ⋅ x
c
Q
Q
1
= (3)
p
p
2 ⋅(
Ps
− Pc
)
= Cd
⋅ a1
⋅
(4)
ρ
= C
⋅ a
⋅
2⋅
Pc
ρ
2 d 2
(5)
where ρ is the fluid density, C d is the orifice flow
discharge coefficient, β is fluid bulk modulus, V c is the
feeding chamber volume, and F ko is the spring preload.
MODEL SIMPIFICATION
Assuming that the brake pressure is calculated only when
the brake pad is in full contact with the brake disc. Then,
⋅⋅
x ≈ 0 , ≈ 0
p
⋅
x . The fluid compliance effect is also
p
assumed negligible for the small volume V c , that is,
V
c
+
β
V
o
≈ 0
simplified to
K x = P ⋅ a − F
p
p
c
. Equations (1) and (2) are therefore,
⋅ (6)
p
ko
p
ko