i:e: FT Fe Ft where FT trailing shoe tip resultant force The magnitude of the self-energizing action is greatly influenced by the rubbing surface tempera-ture, dampness, wetness, coeff
Trang 1and the road surface The relationship between the
decelerating force and the vertical load on a wheel
is known as the adhesion factor (a) This is very
similar to the coefficient of friction () which
occurs when one surface slides over the other, but
in the case of a correctly braked wheel, it should
always rotate right up to the point of stopping to
obtain the greatest retarding resistance
Typical adhesion factors for various road
sur-faces are given in Table 11.2
11.2 Brake shoe and pad fundamentals
11.2.1 Brake shoe self-energization (Fig 11.2)
The drum type brake has two internal semicircular
shoes lined with friction material which matches up
to the internal rubbing face of the drum The shoes
are mounted on a back plate, sometimes known as
a torque plate, between a pivot anchor or wedge type abutment at the lower shoe ends, and at the upper shoe top end by either a cam or hydraulic piston type expander For simplicity the expander
in Fig 11.2 is represented by two opposing arrows and the shoe linings by two small segmental blocks
in the mid-region of the shoes
When the drum is rotating clockwise, and the upper tips of the shoes are pushed apart by the expander force Fe, a normal inward reaction force
N will be provided by the drum which resists any shoe expansion
As a result of the drum sliding over the shoe linings, a tangential frictional force Ft N will
be generated between each pair of rubbing surfaces The friction force or drag on the right hand shoe (Fig 11.2) tends to move in the same direction as its shoe tip force Feproducing it and accordingly helps to drag the shoe onto the drum, thereby effectively raising the shoe tip force above that of the original expander force The increase in shoe tip force above that of the input expander force is described as positive servo, and shoes which provide this self-energizing or servo action are known as leading shoes
i:e: FL Fe Ft where FL leading shoe tip resultant force Likewise considering the left hand shoe (Fig 11.2) the frictional force or drag Ft tends to oppose and cancel out some of the shoe tip force Fe produ-cing it This causes the effective shoe tip force to be less than the expander input force The resultant reduction in shoe tip force below that of the initial
Table 11.2 Adhesion factors for various road surfaces
factor
1 Concrete, coarse asphalt dry 0.8
2 Tarmac, gritted bitumen dry 0.6
3 Concrete, coarse asphalt wet 0.5
6 Gritted bitumen tarmac greasy 0.25
7 Gritted bitumen, snow
8 Gritted bitumen, snow
Fig 11.2 Drum and shoe layout
Trang 2input tip force is described as negative servo, and
shoe arrangements which have this de-energizing
property are known as trailing shoes
i:e: FT Fe Ft
where FT trailing shoe tip resultant force
The magnitude of the self-energizing action is
greatly influenced by the rubbing surface
tempera-ture, dampness, wetness, coefficient of friction and
speed of drum rotation
Changing the direction of rotation of the drum
causes the original leading and trailing shoes to
reverse their energizing properties, so that the
lead-ing and traillead-ing shoes now become traillead-ing and
leading shoes respectively
The shoe arrangement shown in Fig 11.2 is
described as a leading-trailing shoe drum brake
Slightly more self-energizing is obtained if the
shoe lining is heavily loaded at the outer ends as
opposed to heavy mid-shoe loading
11.2.2 Retarding wheel and brake drum torques
(Fig 11.2)
The maximum retarding wheel torque is limited by
wheel slip and is given by
Tw a WR (Nm) where Tw wheel retarding torque (Nm)
a adhesion factor
W vertical load on wheel (N)
R wheel rolling radius (m)
Likewise the torque produced at this brake drum
caused by the frictional force between the lining
and drum necessary to bring the wheel to a
stand-still is given by
TB Nr (Nm) where TB brake drum torque (Nm)
coefficient of friction between
lining and drum
N radial force between lining and
drum (N)
r drum radius (m)
Both wheel and drum torques must be equal up
to the point of wheel slip but they act in the
oppos-ite direction to each other Therefore they may be
equated
i:e: TB Tw
Nr aWR
; Force between
lining and drum N arWR(N)
Example A road wheel has a rolling radius of 0.2 m and supports a load of 5000 N and has an adhesion factor of 0.8 on a particular road surface
If the drum radius is 0.1 m and the coefficient of friction between the lining and drum is 0.4, deter-mine the radial force between the lining and drum
N arWR
0:8 5000 0:2 0:4 0:1
20 000 N or 20 kN
11.2.3 Shoe and brake factors (Fig 11.2)
If the brake is designed so that a low operating force generates a high braking effort, it is said to have a high self-energizing or servo action This desirable property is obtained at the expense of stability because any frictional changes dispropor-tionately affect torque output A brake with little self-energization, while requiring a higher operat-ing force in relation to brake effort, is more stable
in operation and is less affected by frictional changes
The multiplication of effort or self-energizing property for each shoe is known as the shoe factor The shoe factor S is defined as the ratio of the tangential drum drag at the shoe periphery Ftto the force applied by the expander at the shoe tip Fe i:e: Shoe factor Tangential drum forceShoe tip force
S FFt e The combination of different shoe arrangements such as leading and trailing shoes, two leading shoes, two trailing shoes etc produces a brake factor
B which is the sum of the individual shoe factors Brake factor Sum of shoe factors i:e: B (SL ST), 2SL, 2STand
(Sp Ss) 11.2.4 Drum shoe arrangements (Fig 11.3(a±c)) Leading and trailing shoe brakes (Fig 11.3(a)) If
a single cylinder twin piston expander (double acting) is mounted between two shoe tips and the opposite shoe tips react against a fixed abutment, then the leading shoe is forced against the drum
in the forward rotation direction, whilst the trailing shoe works against the rotation direction producing
Trang 3Fig 11.3 (a±d) Various brake shoe arrangements
Trang 4much less frictional drag Such an arrangement
provides a braking effect which is equal in both
forward and reverse motion Rear wheel brakes
incorporating some sort of hand brake mechanism
are generally of the lead and trailing shoe type
Two leading shoe brakes (Fig 11.3(b)) By
arran-ging a pair of single piston cylinders (single acting)
diametrically opposite each other with their pistons
pointing in the direction of drum rotation, then
when hydraulic pressure is applied, the drum to
lining frictional drag force pulls the shoes in the
same direction as the shoe tip piston forces, thus
causing both shoes to become self-energizing Such
a layout is known as a two leading shoe drum type
brake In reverse, the braking force is reduced due
to the drag force opposing the piston tip forces;
both shoes in effect then have a trailing action
Two leading shoe brakes are possibly still the most
popular light commercial type front wheel brake
Two trailing shoe brakes (Fig 11.3(c)) If now two
separate single acting cylinders are mounted
between the upper and lower shoe tips so that
both pistons counteract the rotational forward
direction of the drum, then the resultant lining
drag force will be far less for each shoe, that is,
there is a negative servo condition
Brakes with this layout are therefore referred to
as two trailing shoe brakes This arrangement is
suitable for application where lining stability is
important and a servo assisted booster is able to
compensate for the low resultant drag force relative
to a given input shoe tip force A disadvantage of a
two trailing shoe brake is for the same brake effect
as a two leading shoe brake; much higher hydraulic
line pressures have to be applied
Duo-servo shoe brakes (Fig 11.3(d)) A double
acting cylinder expander is bolted to the back plate
and the pistons transmit thrust to each adjacent
shoe, whereas the opposite shoe tip ends are joined
together by a floating adjustment link On
applica-tion of the brake pedal with the vehicle being
driven forward, the pistons move both shoes into
contact with the revolving drum The shoe
sub-jected to the piston thrust which acts in the same
direction as the drum rotation is called the primary
shoe and this shoe, when pulled around with the
drum, transfers a considerable force to the adjacent
shoe tip via the floating adjustment link This
sec-ond shoe is known as the secsec-ondary shoe and its
initial movement with the drum pushes it hard against the anchor pin, this being permitted by the pistons themselves floating within the cylinder
to accommodate any centralization which might become necessary Under these conditions a com-pounding of both the primary circumferential drag force and that produced by the secondary shoe itself takes place so that a tremendous wedge or self-wrapping effect takes place far in excess of that produced by the two expander pistons alone These brakes operate equally in the forward or reverse direction Duo-servo shoe brakes give exception-ally good performance but are very sensitive to changes in shoe lining properties caused by heat and wetness
Because the secondary shoe performs more work and therefore wears quicker than the primary shoe, lining life is equalized as far as possible by fitting a thick secondary shoe and a relatively thin primary shoe
11.2.5 The principle of the disc brake (Fig 11.4(a, b and c))
The disc brake basically consists of a rotating cir-cular plate disc attached to and rotated by the wheel hub and a bridge member, known as the caliper, which straddles the disc and is mounted
on the suspension carrier, stub axle or axle casing (Fig 11.4(b)) The caliper contains a pair of pistons and friction pads which, when the brakes are applied, clamp the rotating disc, causing it to reduce speed in accordance to the hydraulic pressure behind each piston generated by the pedal effort The normal clamping thrust N on each side of the disc (Fig 11.4(b and c)) acting through the pistons multiplied by the coefficient of friction generated between the disc and pad interfaces pro-duces a frictional force F N on both sides of the disc If the resultant frictional force acts through the centre of the friction pad then the mean dis-tance between the centre of pad pressure and the centre of the disc will be
R2 R1
2 R:
Accordingly, the frictional braking torque (Fig 11.4(a)) will be dependent upon twice the frictional force (both sides) and the distance the pad is located from the disc centre of rotation That is,
Braking torque 2N R2 2 R1
(Nm) i:e: TB 2NR (Nm)
Trang 5Example If the distance between the pad's centre of pressure and the centre of disc rotation
is 0.12 m and the coefficient of friction between the rubbing faces is 0.35, determine the clamping force required to produce a braking torque of
84 Nm
TB 2NR
; Clamping force N 2RTB
2 0:35 0:1284
1000 N
11.2.6 Disc brake pad alignment (Fig 11.4) When the pads are initially applied they are loaded against the disc with uniform pressure, but a small tilt tendency between the leading and trailing pad edges caused by frictional pad drag occurs In add-ition the rate of wear from the inner to the outer pad edges is not uniform The bedding-in conditions of the pads will therefore be examined in the two parts
as follows:
1 Due to the thickness of the pad there is a small offset between the pad/disc interface and the pad's back plate reaction abutment within the caliper (Fig 11.4(c)) Consequently, a couple is Fig 11.4 (a±c) Disc and pad layout
Trang 6produced which tends to tilt the pad into contact
with the disc at its leading edge harder compared
to the trailing edge This in effect provides a very
small self-energizing servo action, with the result
that the wear rate at the leading edge is higher
than that at the trailing edge
2 The circular distance covered by the disc in one
revolution as it sweeps across the pad face
increases proportionately from the inner to the
outer pad's edges (Fig 11.4(a)) Accordingly the
rubbing speed, and therefore the work done,
increases from the inner to the outer pad edges,
with the result that the pad temperature and
wear per unit area rises as the radial distance
from the disc centre becomes greater
11.2.7 Disc brake cooling (Fig 11.4)
The cooling of the brake disc and its pads is
achieved mostly by air convection, although some
of the heat is conducted away by the wheel hub
The rubbing surface between the rotating disc and
the stationary pads is exposed to the vehicle's
frontal airstream and directed air circulation in
excess of that obtained between the drum and shoe
linings Therefore the disc brake is considerably
more stable than the drum brake under continued
brake application The high conformity of the pad
and disc and the uniform pressure enable the disc
to withstand higher temperatures compared to the
drum brake before thermal stress and distortion
become pronounced Because there is far less
dis-tortion with discs compared to drums, the disc can
operate at higher temperatures A further feature
of the disc is it expands towards the pads, unlike
the drum which expands away from the shoe
lin-ings Therefore, when hot, the disc brake reduces
its pedal movement whereas the drum brake
increases its pedal movement
Cast ventilated discs considerably improve the
cooling capacity of the rotating disc (Fig 11.4(b))
These cast iron discs are in the form of two annular
plates ribbed together by radial vanes which also
act as heat sinks Cooling is effected by centrifugal
force pushing air through the radial passages
formed by the vanes from the inner entrance to
the outer exit The ventilated disc provides
consid-erably more exposed surface area, producing
some-thing like a 70% increase in convection heat
dissipation compared to a solid disc of similar
weight Ventilated discs reduce the friction pad
temperature to about two-thirds that of a solid
disc under normal operating conditions Pad life
is considerably increased with lower operating
tem-peratures, but there is very little effect on the
fric-tional properties of the pad material Ventilated wheels have very little influence on the disc cooling rate at low speeds At very high speeds a pressure difference is set up between the inside and outside
of the wheel which forces air to flow through the vents towards the disc and pads which can amount
to a 10% improvement in the disc's cooling rate The exposure of the disc and pads to water and dirt considerably increases pad wear
The removal of dust shields will increase the cooling rate of the disc and pad assembly but it also exposes the disc and pads to particles of mud, dust and grit which adhere to the disc This will cause a reduction in the frictional properties of the rubbing pairs If there has to be a choice of a lower working temperature at the expense of contaminat-ing the disc and pads or a higher workcontaminat-ing tempera-ture, the priority would normally be in favour of protecting the rubbing surfaces from the atmo-spheric dust and from the road surface spray 11.2.8 A comparison of shoe factors and shoe stability (Fig 11.5)
A comparison of different brake shoe arrange-ments and the disc brake can be made on a basis
of shoe factor, S, or output torque compared against the variation of rubbing coefficient of fric-tions (Fig 11.5) The coefficient of friction for most linings and pads ranges between 0.35 and 0.45, and
it can be seen that within the normal coefficient
of friction working range the order of smallest to greatest shoe factor is roughly as follows in Table 11.3
This comparison shows that the torque output (shoe factor) for a single or two trailing shoes is only approximately one-third of the single or two leading shoe brake, and that the combination of a leading and trailing shoe is about twice that of the two trailing shoe, or roughly two-thirds of the two leading shoe arrangement (Fig 11.5) The disc and pad's performance is very similar to the two trailing shoe layout, but with higher coefficients of friction the disc brake shoe factor rises at a faster rate than that of the two trailing shoe brake Overall, the duo-servo shoe layout has a superior shoe factor relative
to all other arrangements, amounting to roughly five times that of the two trailing shoes and just under twice that of the two leading shoe brake Conversely, the lining or pad stability, that is, the ability of the shoes or pads to maintain approxi-mately the same shoe factor if there is a small change in the coefficient, due possibly to wetness
or an increase in the friction material temperature, alters in the reverse order as shown in Table 11.3
Trang 7Generally, brakes with very high shoe factors are
unstable and produce a relatively large change in
shoe factor (output torque) for a small increase or
decrease in the coefficient of friction between the
rubbing surfaces Layouts which have low shoe
factors tend to produce a consistent output torque
for a considerable shift in the coefficient of friction
Because of the instability of shoe layouts with high
shoe factors, most vehicle designers opt for the
front brakes to be either two leading shoes or disc
and pads, and at the rear a leading and trailing shoe
system They then rely on vacuum or hydraulic
servo assistance or full power air operation Thus
having, for example, a combined leading and
trail-ing shoe brake provides a relatively high leadtrail-ing
shoe factor but with only a moderate degree of
stability, as opposed to a very stable trailing shoe
which produces a very low shoe factor The
proper-ties of each shoe arrangement complement the
other to produce an effective and a reliable
founda-tion brake Leadings and trailing shoe brakes are
still favoured on the rear wheels since they easily
accommodate the hand brake mechanism and
pro-duce an extra self-energizing effect when the hand
brake is applied, which in the case of the disc and
pad brake is not obtainable and therefore requires
a considerable greater clamping force for wheel
lock condition
11.2.9 Properties of friction lining and pad materials
Friction level (Fig 11.6) The average coefficient
of friction with modern friction materials is between 0.3 and 0.5 The coefficient of friction should be sufficiently high to limit brake pedal effort and to reduce the expander leverage on com-mercial vehicles, but not so high as to produce grab, and in the extreme case cause lock or sprag
so that rotation of the drum becomes impossible The most suitable grade of friction material must
be used to match the degree of self-energization created by the shoe and pad configuration and applications
Resistance to heat fade (Fig 11.6) This is the ability of a lining or pad material to retain its coefficient of friction with an increase in rubbing temperature The maximum brake torque the lin-ing or pad is to absorb depends on the size and type
of brake, gross vehicle weight, axle loading, the front to rear braking ratio and the maximum attainable speed A good quality material should retain its friction level throughout the working temperature range of the drum and shoes or disc and pads A reduction in the frictional level in the Fig 11.5 Relationship of shoe or brake factors and the coefficient of friction for different shoe layouts and the disc brake
Trang 8higher temperature range may be tolerated,
pro-vided that it progressively decreases, because a
rapid decline in the coefficient of friction could
severely reduce the braking power capability
when the vehicle is being driven on long descents
or subjected to continuous stop-start journey
work The consequences of a fall in the friction
level will be greater brake pedal effort with a
very poor retardation response It has been
established that changes in the frictional level
which occur with rising working temperatures
are caused partly by the additional curing of
the pad material when it heats up in service and
partly because chemical changes take place in the
binder resin
Recovery from fade (Fig 11.6) This is a measure
of the ability of a friction material to revert to its
original friction level upon cooling after brake
lin-ing or pad temperature fade has taken place The
frictional characteristics of a good quality material
will return on cooling, even after being subjected to
repeatedly severe heating, but an inferior material
may have poor recovery and the friction level may
be permanently altered Poor recovery is caused
principally by a chemical breakdown in the
ingre-dients This may cause hardening, cracking,
flak-ing, charring or even burning of the linings or pads
If the linings or pads are using thermoplastic binder
resins a deposit may form on the rubbing surfaces
which may distort the friction properties of the
material
Resistance to wear (Fig 11.6) The life of a friction material, be it a lining or pad, will depend to a great extent upon the rubbing speed and pressure The wear is greatly influenced by the working tempera-ture At the upper limits of the temperature range, the lining or pad material structure is weakened, so that there is an increase in the shear and tear action
at the friction interface resulting in a higher wear rate
Resistance to rubbing speed (Fig 11.7) The coeffi-cient of friction between two rubbing surfaces should in theory be independent of speed, but it has been found that the intensity of speed does tend
to slightly reduce the friction level, particularly at the higher operating temperature range Poor fric-tion material may show a high fricfric-tion level at low rubbing speeds, which may cause judder and grab when the vehicle is about to stop, but suffers from
a relatively rapid decline in the friction lever as the rubbing speed increases
Resistance to the intensity of pressure (Fig 11.8)
By the laws of friction, the coefficient of friction should not be influenced by the pressure holding the rubbing surfaces together, but with developed friction materials which are generally compounds held together with resin binders, pressure between the rubbing surfaces does reduce the level of fric-tion It has been found that small pressure increases
at relative low pressures produce a marked reduc-tion in the fricreduc-tion level, but as the intensity of
Fig 11.6 Effects of temperature on the coefficient of
friction
Fig 11.7 Effects of rubbing speed on the level of friction over the temperature range
Trang 9pressure becomes high the decrease in friction level
is much smaller A pressure-stable lining will
pro-duce deceleration proportional to the pedal effort,
but pressure-sensitive materials will require a
rela-tively greater pedal force for a given braking
perfor-mance Disc brakes tend to operate better when
subjected to high rubbing pressures, whereas shoe
linings show a deterioration in performance when
operating with similar pressures
Resistance to water contamination (Fig 11.9) All
friction materials are affected by water
contamina-tion to some extent Therefore, a safe margin of
friction level should be available for wet
condi-tions, and good quality friction materials should
have the ability to recover their original friction
level quickly and progressively (and not behave
erratically during the drying out process) A poor
quality material may either recover very slowly or
may develop over-recovery tendency (the friction level which is initially low due to the wetness rises excessively during the drying out period, falling again as the lining or pad dries out completely) Over-recovery could cause brake-grab and even wheel-lock, under certain driving conditions
Resistance to moisture sensitivity The effects of atmospheric dampness, humidity or dew may increase the friction level for the first few applica-tions, with the result that the brakes may become noisy and develop a tendency to grab for a short time Moisture-sensitive friction materials should not be used on brakes which have high self-energizing characteristics
Friction materials Materials which may be used for linings or pads generally have their merits and limitations Sintered metals tend to have a long life but have a relatively low coefficient of friction Ceramics mixed with metals have much higher coefficient of friction but are very rigid and there-fore must be made in sections They tend to be very harsh on the drums and disc, causing them to suffer from much higher wear rates than the asbestos-based materials There has been a tendency to produce friction materials which contain much less asbestos and much more soft metal, such
as brass zinc inserts or aluminium granules Non-asbestos materials are now available which contain DuPont's Kevlar, a high strength aramid fibre One manufacturer uses this high strength fibre in pulp form as the main body for the friction material,
Fig 11.8 Effects of rubbing pressure on the coefficient
of friction
Table 11.3 Shoe factor, relative braking power and
stability for various brake types
factor Relativebraking
power
Stability
Single trailing shoe 0.55 Very low Very high
Two trailing shoes 1.15 Very low Very high
Leading and trailing
Duo-servo shoes 5.0 Very high Very low
Fig 11.9 Effects of water contamination on the material's friction recovery over a period of vehicle stops
Trang 10whereas another manufacturer uses a synthetically
created body fibre derived from molten
blast-furnace slag reinforced with Kevlar for the main
body Some non-asbestos materials do suffer from
a drastic reduction in the coefficient of friction
when operating in winter temperatures which, if
not catered for in the brake design, may not be
adequate for overnight parking brake hold
11.3 Brake shoe expanders and adjusters
11.3.1 Self-adjusting sector and pawl brake shoe
mechanism (Fig 11.10(a, b and c))
With this leading and trailing shoe rear wheel brake
layout the two shoes are actuated by opposing twin
hydraulic plungers
A downward hanging hand brake lever pivots from the top of the trailing shoe A toothed sector lever pivots similarly from the top of the leading shoe, but its lower toothed sector end is supported and held in position with a spring loaded toothed pawl Both shoes are interlinked with a strut bar
Hand brake operation When the hand brake lever
is applied the cable pulls the hand lever inwards, causing it to react against the strut As it tilts it forces the trailing shoe outwards to the drum At the same time the strut is forced in the opposite direction against the sector lever This also pushes the leading shoe via the upper pivot and the lower toothed pawl towards the drum The hand brake shoe expander linkage between the two shoes
Fig 11.10 (a±c) Self-adjusting sector and pawl shoes with forward full hand brake