Individual Component Fluid Requirements

The individual fluid volumes and, hence, pedal travel losses involve the factors discussed next. The individual fluid volumes associated with the various brake components are computed for a brake line pressure that will produce a deceleration of 0.9 g for the vehicle laden at GVW with a pedal travel of not more than 8.89 cm (3.5 in.).

1. Pad-Rotor Clearance

The fluid volume required to move the pads against the rotor is computed from the axial runout or clearance for the disc brake and the caliper cross-sectional area. During this portion of the pedal application, only negligible brake line pressures are produced. Disc brakes and nearly all drum brakes are self-adjusting, making the clearance a somewhat predictable minimum value.

Excessive axial runout of disc brake rotors will cause increased pad and caliper piston pushback with the brakes are released. The total clearance between the pads and the rotors may be greater than the fluid available from the master cylinder for that circuit. Proper, i.e., quick, pumping of the brakes will normally result in brake pedal rise due to fluid bypass around the primary seals from the reservoir into the brake system, as illustrated in Fig. 5-20. In some cases, excessive front-end shimmy or a severe tight turn and loose or worn suspension components may cause caliper piston pushback sufficient for the brakes to fail from excessive brake pedal travel. When the accident vehicle is examined, no excessive axial rotor runout may be observed, with the true accident causation often remaining unknown to many. See Example 5-2 for an actual case analysis where a loose front bearing caused a partial brake failure.

In the investigation of accidents involving four-wheel disc-brake vehicles with the integrated disc parking brake, using parking brake application to adjust the service brake pads, the parking brake should not be applied during the inspection because critical evidence may be destroyed.

2. Brake Line Expansion

The metal brake line is basically a long cylinder. When the basic equation for a pressurized cylinder is used, the volume increase V_BL of a brake line may be determined by

V_BL = 0.79D³Lp_/tE (5-25)

For a brake line with D = 0.475 cm (0.187 in.), t = 0.0686 cm (0.027 in.), and E

= 20.6 × 10⁶ N/cm² (30 × 10⁶ psi), Eq. (5-25) yields the normalized brake line volume loss coefficient k_BL of

k_BL = V_BL/p_L = 0.060 x 10^-6 , cm³/(N/cm²)cm

(5-26) [k_BL = V_BL/p_L = 0.0064 x 10^-6, in.³/(psi)in.]

For a given vehicle with a specific brake line length L and a certain brake line pressure p_ℓ, the volume loss due to brake line expansion is determined by

V = k Lp_{BL BL } , cm (in.^{3 3})

(5-27) 3. Brake Hose Expansion

Brake hose expansions have been measured. Typical values of brake hose expansion V_H for vehicles in use today are computed by

V = k L p_{H H H } , cm (in.^{3 3})

(5-28) with

where L_H = brake hose length, cm (in.) 4. Master Cylinder Losses

Volume losses for master cylinders in good mechanical condition generally vary with the size of the master cylinder diameter, as indicated here (Ref. 1.3):

where D = outer diameter of pipe, cm (in.)

E = elastic modullus of pipe material, N/cm (psi) L = length of brake line

2

,, cm (in.) p = brake line pressure, N/cm (psi)

t = wall t

2



hhickness of pipe, cm (in.)

k = 4.39 × 10 , cm /(N/cm )cm [k = 0.47 × 10 , in. /(psi)

H -6 3

-6 3

2

H iin.]

Diameter Kmc

19.05 mm 150 × 10^–6 cm³/N/cm²

(3/4 in.) (6 × 10^–6 in.³/psi)

23.8 mm 190 × 10^–6 cm³/N/cm²

(15/16 in.) (8 × 10^–6 in.³/psi)

25.4 mm 220 × 10^–6 cm³/N/cm²

(1 in.) (9 × 10^–6 in.³/psi)

38.1 mm 450 × 10^–6 cm³/N/cm²

(1.5 in.) (19 × 10^–6 in.³/psi)

The volume loss V_mc is determined by

(5-29) where k_mc = specific master cylinder volume loss, cm³/N/cm² (in.³/psi)

5. Caliper Deformation

Caliper deformation is difficult to measure exactly, because residual pocket air and test fluid are compressed and cause an additional small fluid loss of their own. Furthermore, different caliper designs make it impossible to state one coefficient for all applications. However, tests conducted with “steel” pads and corrected for fluid compression show that the caliper volume loss coefficient for fixed caliper designs for one caliper may be approximated by

V_c = k_cp_l + V_r , cm³ (in.³) (5-30) The values for k_c are a function of the caliper piston diameter. For diameters between 38 and 60 mm (1.5 and 2.36 in.), k_c is determined by (Ref 1.3):

k_c = 482 x 10^-6d_wc - 1632 x 10^-6, cm³/(N/cm²)

(5-31) [k_c = 52 x 10^-6d_wc - 69 x 10^-6, in.³/psi]

The residual air volume Vr in the caliper is approximately 0.72 cm³ (0.044 in.³) for a caliper diameter of 60 mm (2.36 in.), or 0.31 cm³ (0.019 in.³) for a 38 mm (1.5 in.) diameter caliper.

6. Brake Pad Compression

For disc brakes, pad compression is an important factor in the selection of a proper material. A certain amount of compressibility or damping is essential for disc brakes to operate without undue noise (Ref. 5.14).

V = k p_{mc mc } , cm (in.^{3 3})

where d = wheel cylinder diameter, cm (in.) V = volume l

wc

c ooss in caliper, cm (in. )^{3 3}

For disc brake pads, the volume loss V_p due to compression is determined by (Ref. 1.3):

(5-32)

For disc brake pads, a relatively well-damped pad material yields a compress-ibility factor C_s = 11 × 10^–6 to 26 × 10^–6 cm/(N/cm²) (3 × 10^–6 to 7 × 10^–6 in./psi) at normal (cold) brake temperature, C_s = 15 × 10^–6 to 33 × 10^–6 cm/(N/cm²) (4 × 10^–6 to 9 × 10^–6 in./psi) for hot brakes with a rotor temperature of approximately 672 K (750°F) with a backing plate temperature of approximately 380 K (225°F).

For example, for a passenger car with a four-wheel disc brake system with 5.71 and 3.81 cm (2.25 and 1.5 in.) wheel cylinder diameters, front and rear, hot brakes, and a brake line pressure of 620 N/cm² (900 psi), Eq. (5-32) yields a maximum volume loss V_p due to pad compression of

With a typical master cylinder size of 2.22 by 2.54 cm (7/8 × 1 in.) for a compact car, the fluid volume is approximately 11.5 cm³ (0.7 in.³). A pad compression loss of 3.02 cm³ (0.186 in.³) may account for nearly 30% of the pedal travel loss alone. In loss of pedal travel cases, the subject brake pads must be compared with original equipment pads, especially when higher brake temperatures are involved.

7. Drum Deformation

The hydraulic brake fluid volume loss V_d due to mechanical drum deformation is computed by (Ref 1.3):

(5-33) with

where A_wc = wheel cylinder area, cm² (in.²)

8. Brake Shoe and Lining Compression in Drum Brakes

The brake fluid volume loss resulting from two brake shoes including the apply mechanism is computed by

V_p=⁴

∑

⁽A C p_{wc s} ^{) ,}_i cm^{3 (in.3)}

where in

C_s

A wheel cylinder area, cm brake shoe comp

(5-34) with

k_s = (100 to 150) x 10^-6 cm³/N [k_s = (27 to 41) x 10^-6 in.³/lb]

9. Thermal Drum Expansion

The brake fluid volume V_T due to the expansion of the drum due to temperature is computed by

V_T = α_TdT_dA_wc , cm³ (in.³) (5-35)

10. Air in Drum Brake Hydraulics

The brake fluid volume loss V_a due to air inclusion is approximately (Ref. 1.3):

(5-36)

11. Brake Shoe/Drum Clearance

The inspection of an accident vehicle generally will reveal any abnormal conditions. Drum and shoe-circle diameter determine the actual lining clearance. It should be noted that some hydraulic drum brakes use a wheel cylinder piston stop, causing the piston to push against a stop in the event of excessive lining wear. When this occurs, the brake shoes are not or are only partially pressed against the drum without producing sufficient brake torque. Although the pedal may feel firm because high brake line pressures are developed, the braking effectiveness may be reduced significantly.

The brake fluid volume V_cℓ due to the clearance between shoes and drum for brakes with good automatic adjustment is

V A cm

where d = drum diameter, cm (in.) w = brake shoe width, cm ((in.)

where A wheel cylinder area, cm (in. ) T drum temperatur

wc 2 2

d

=

= ee, K ( F)

thermal expansion coefficient of cast iron dr

α =T uum material

11 10 cm/cmK [6.55 10 in./in. F]

= ^{−6 −6}

V_a = 0 035. A_wc,cm³ [V_a = 0 014. A_wc, . ]in³

12. Brake Fluid Compression

Volume losses resulting from the compression of brake fluid may have a significant effect on pedal travel as brake fluid temperatures and brake line pressures increase. Measured values of compressibility factor of different dry, gas-free fluids as a function of temperature are shown in Fig. 5-21 for regular brake fluid based on polyglycolether, mineral oil, and silicone. Inspection of Fig.

5-21 reveals that regular brake fluid will double its compressibility factor when the brake fluid temperature increases from 294 to 477 K (70 to 400°F). Silicone-based brake fluids have the highest compressibility.

Figure 5-21. Compressibility factor C_FL for dry brake fluids without gas content.

The volume loss resulting from brake fluid compression is a function of the active volume V_A in the brake system pressurized during the braking process.

The active volume is determined by

V_A=V_o+⁴

∑

^{n (}A w_wc ^{) ,}_i cm in^{3( . )3} (5-38) where A wheel cylinder area cm in

i brake identity V brak

wc

o

=

=

=

, ²( . )²

ee fluid volume with new shoes cm in w wear travel of shoes cm

, ( . )

, (

3 3

= iin.)

The volume loss V_FL due to fluid compression is computed by V_FL =V C_{A FL}p_ , cm in³( . )³

(5-39) where C_FL = brake fluid compressibility factor, cm²/N (1/psi)

For example, for a four-wheel disc brake vehicle with A 25.6 cm (3.976 in. )

the active volume is computed by Eq. (5-38) as V 164 + 4(25.6 + 11.4) 0.635

The volume loss at 620 N/cm² (900 psi) brake line pressure is determined from Eq. (5-39) as

For silicone-based fluids the volume loss would be approximately 3.6 cm³ (0.22 in.³); i.e., a significantly greater loss than that for normal brake fluid.

13. Air or Gas in the Brake System

Air can remain in the brake system when air pockets form which cannot be flushed out during the vacuum bleeding process at the factory. Small air bubbles will adhere to metal surfaces of springs and other parts. Due to surface tension, small-sized air bubbles will remain in the brake fluid, which can be removed only by ultrasound application. Typical residual air volumes in the entire brake system are approximately 3% of the active volume. The 3% includes the residual air in the front disc brake caliper of approximately 0.6%, and 0.4% in the rear disc brake caliper.

If one defines V_G as the volume of the enclosed air at atmospheric pressure, and assumes an isothermal or constant temperature compression based on the valid assumption that the air temperature remains equal to the temperature of the brake fluid during the compression process, then with basic thermodynamics the decrease of air volume is determined by

(5-40) V_GL =V T T_G / [₀1−p_o/ (p_+p_o)] , cm in³( . )³

The absolute temperature T is computed by

(5-41)

At higher pressures, p_ℓ, the square bracket in Eq. (5-40) goes to unity,

indicating that the entire enclosed air volume will be compressed and cause a corresponding drop of the pedal height toward the floor. When the brake fluid is also heated, then the temperature increase will expand the air, thus making the volume loss stemming from the air greater.

For example, for V_G= 4.9 cm³ (0.3 in.³), and ambient and operating temperature of 294 and 394 K (70 and 250°F), respectively, Eqs. (5-40) and (5-41) yield

T = 70 + 460 = 530°R and T = 250 + 460 = 710°R

and

V_GL = 4.9(394 / 294) = 6.57 cm³

[V_GL = 0.3(710 / 530) = 0.40 in.³] 14. Fluid Loss in Hydrovac

The hydraulic control of the hydrovac booster requires a small amount of brake fluid from the driver-operated master cylinder to actuate the vacuum unit.

For most hydrovacs used in medium trucks, the volume loss at zero brake line pressure rise is approximately 0.82 cm³ (0.05 in.³).

15. Volume Loss in Valves

Because the type of valve used in a hydraulic brake system varies with design, no specific loss coefficients can be stated. If a malfunctioning of a particular valve is suspected, special tests must be conducted with the accident and exemplar valves to clearly isolate any contribution to pedal travel loss.

where p = brake line pressure, N/cm (psi) p = atmospheric pre

2 o

l

sssure, N/cm (psi) T = absolute temperature at initial condi

2

0 ttions, K ( R)

T = absolute temperature, K ( R) V = enclosed gaG

ϒ ϒ

ss volume at ambient temperature, cm (in. )^{3 3}

T T K

16. Water Content in Brake Fluid

With time, hydraulic brake fluid will absorb water from the air through the flexible hoses. Brake fluid contaminated by water has a reduced boiling point temperature, which may lead to partial or complete brake failure at elevated brake temperatures due to brake fluid vaporization. Pedal travel will increase significantly. For diagonal split brake circuits, the entire brake system may fail (Refs. 5.15, 5.16).

17. After-market Equipment

After-market valves installed in the brake system hydraulics will have an adverse effect on pedal travel. Depending on how “limited” the master cylinder volume reserves are, they may cause critical pedal travels.

In document Brake Design and Safety, Third Edition (Page 176-184)