Transcript Slide 1

Designs with moving parts
BADI 1
John Errington MSc
Axes and degrees of freedom
A rigid object in free
space can move in six
different ways:
Rotation about x, y, z
axes
Translation about x, y z
axes
We say it has six degrees
of freedom.
Joints: movable and fixed
• Joints are ways of fastening
pieces together
• Fixed joints prevent any
movement between the parts:
This picture shows a dovetail joint
used in woodwork
• Movable joints allow some
movement but restrict the degrees
of freedom: this picture shows a
rose joint used in the suspension
of racing cars.
1 degree of freedom: rotation
Finger joints also
elbow and knee joints
allow only one degree
of freedom
This kind of joint is
like a hinge as used
on cupboards and
doors
2 degrees of freedom
The hip joint allows two
degrees of freedom:
• Forwards-backwards
• Inwards-outwards
4 degrees of freedom
• The spine is made up of bones
(vertebrae) separated by pads
(disks)
• The joints of the spine allow
movement but only within a very
restricted range at each joint
–
–
–
–
Stretching
Bending sideways
Bending forwards
Turning
• Lateral translation (sideways and
forward/back) are not allowed.
Sliding mechanisms
Door bolts are good examples of the case where
one part slides inside another. 1DOF
The toolpost on a lathe must have its position
very closely controlled. A wedge shaped slide
arrangement provides this control and can be
adjusted to take up wear.
Designs with moving parts
• Many designs such as these electric
drills feature moving parts.
• A shaft can move in any of three
different directions (up-down, frontback, left-right) and can rotate in three
different directions. It has six degrees
of freedom.
• Practical applications usually require
the removal of some of these
alternatives, so that in the drill we
leave only the freedom to rotate about
the chuck axis.
y
Rigid body (motor)
has six degrees of
freedom
z
x
Drill must have
only 1 degree of
freedom: axial
rotation forward or
reverse about the
x axis
In use pressing the drill
bit against the workpiece
causes a reaction
pressing the moving parts
to the back of the casing.
y
y
Front view
Controlling the shaft as
shown here will prevent:
Rear view
Translation up/down,
sideways or front/back
z
z
Rotation about y and z axes
How to restrict movement
• Controlling these movements requires us
to hold the shaft in some way. However
• When two surfaces rub together the
friction between them causes heat and
wear.
• So we need devices that will constrain the
motion and yet minimise friction to give a
reliable product.
Friction
Friction is a force that tends to
oppose the relative motion of two
surfaces in contact with each
other
The work done in overcoming friction
results in noise, heat and wear of
moving parts
What causes friction?
1. Friction occurs in part because rough surfaces tend to
catch on one another as they slide past each other.
Even surfaces that are apparently smooth can be rough
at the microscopic level. They have many ridges and
grooves. The ridges of each surface can get stuck in the
grooves of the other, effectively creating a type of
mechanical bond, or glue, between the surfaces.
2. Smooth surfaces in contact also tend to attract one
another at the molecular level, forming chemical bonds.
These bonds can prevent an object from moving, even
when it is pushed. If an object is in motion, these bonds
form and release. Making and breaking the bonds takes
energy away from the motion of the object.
Examples of coefficients of friction
MATERIAL 1
MATERIAL 2
DRY
Static
LUBRICATED
Sliding
Static
Sliding
0.04
Teflon (PTFE)
Steel
0.04
0.04
Diamond
Diamond
0.10
0.05 - 0.1
Graphite
Steel
0.10
0.10
Brake Material
Cast Iron
0.40
0.20
Steel
Copper Lead Alloy
0.22
0.16
Tungsten Carbide
Tungsten Carbide
0.22
0.12
Cadmium
Cadmium
0.50
0.05
Copper
Mild Steel
0.53
0.36
0.18
Steel (Mild)
Steel (Mild)
0.74
0.57
0.09-0.19
Iron
Iron
1.00
Cast Iron
Cast Iron
1.10
0.15
Aluminum
Aluminum
1.35
1.40
Phos. Bronze
Mild Steel
0.34
Cadmium
Mild Steel
0.46
Rubber
Asphalt (Dry)
0.80
0.25 - 0.75
Rubber
Concrete (Dry)
0.85
0.45 - 0.75
0.15
0.15 - 0.2
0.07
0.30
0.17
Factors affecting the friction
between surfaces
•
•
•
•
Are the surfaces smooth
Clean
Wet or dry
Lubricated or dry
– Lubricants provide a protective film that separates the
two rubbing surfaces and reduces the level of friction
in the two rubbing surfaces.
• Surface temperatures
Dry surfaces
• For low surface pressures the friction is directly
proportional to the pressure between the
surfaces. As the pressure rises the friction
factor rises slightly. At very high pressure the
friction factor then quickly increases to seizing
• For low surface pressures the coefficient of
friction is independent of surface area.
• At low velocities the friction is independent of the
relative surface velocity. At higher velocities the
coefficient of friction decreases.
Well lubricated surfaces
• The friction resistance is almost independent of the
specific pressure between the surfaces.
• At low pressures the friction varies directly as the relative
surface speed.
• At high pressures the friction is high at low velocities
falling as the velocity increases to a minimum at about
0.6m/s. The friction then rises in proportion to the
square of the velocity.
• The friction is not so dependent of the surface materials.
• The friction is related to the temperature as this affects
the viscosity of the lubricant
How Lubricants Work
Any surface contains irregularities, even when polished to a mirror
finish. These irregularities may not be visible, except under a
microscope. When two surfaces are brought gently together, only some
points on the surfaces will make contact. These contacts will be
brought closer together when a force is applied at right angles to the
surfaces (this force is referred to as a ‘normal load’), and the number of
contact points will increase.
Lubricated surfaces
If a protective film were present on each of the surfaces,
the surfaces would be separated. The protective film must
adhere to each surface in order not to be sheared off or
pushed aside by the movement of the surfaces, particularly
under a load.
Bearings
Bearings provide either a sliding or a rolling contact
whenever relative motion exists between parts of a
machine. Sliding contact bearings are referred to as plain
bearings and rolling contact bearings are often called
antifriction bearings.
Bearings that provide sliding contact fall into three general
classes:
– radial bearings that support rotating shafts;
– thrust bearings that support axial loads on rotating shafts; and
– linear bearings that guide moving parts in a straight line.
Bearings keep shafts in place
• Here tapered
roller bearings
keep the car
wheel in place
while allowing it
to rotate.
• The bearings are
subject to both
axial (thrust) load
and radial load
Plain bearings
A common plain bearing design is to use a
hardened and polished steel shaft and a soft
bronze bushing. In such designs the softer
bronze portion can be allowed to wear away, to
be periodically renewed.
Plain 'self-lubricating' bearings utilize porous
journals within which a lubricant is held. As the
bearing operates and lubricant is displaced from
the bearing surface, more is carried in from nonwear parts of the bearing.
Dry plain bearings
Dry plain bearings can be made of a variety of
materials including PTFE (Teflon) or ceramic. The
ceramic is very hard, and sand and other grit
which enter the bearing are simply ground to a fine
powder which does not inhibit the operation of the
bearing.
PTFE has a very low coefficient of friction and acts
as a lubricant – but it isn’t very hard so is often just
used as a coating on the inside surfaces
Plain Bearings
•
•
•
•
A steel insert with babbitt (lead alloy) bonded to the bearing surface
Plain bearings are keyed to keep them in place
A lip or flange allows the plain bearing to accept thrust loads
Commonly used as crankshaft and rod bearings in car engines
Lubrication of plain bearings
The relative motions between the mating surfaces of a plain
bearing may take place in the following ways:
1. Pure sliding without any lubricating medium between
the moving surfaces.
2. Hydrodynamic lubrication where a film buildup of
lubricating medium is produced by the relative motion of
the components.
3. Hydrostatic lubrication where a lubricating medium is
introduced under pressure between the moving surfaces.
4. A combination of hydrodynamic and hydrostatic
lubrication.
Anti friction bearings
Ball
Thrust
roller
tapered roller
Antifriction bearings
Antifriction bearings minimize friction by removing
any possible sliding between bearing surfaces and
replacing all contacts with rolling interfaces. They
substitute balls or rollers for a hydrodynamic or
hydrostatic fluid film to carry loads with reduced
friction. They utilize a separator to space the
hardened rolling elements apart.
The Anti-Friction Bearing Manufacturers
Association Standards (AFBMA) provides
standardized dimensions, tolerances and fits of
ball and roller bearings so replacement is easy.
advantages and disadvantages of
plain bearings vs antifriction bearings.
Advantage
Plain bearings
Disadvantage
Plain bearings
Quieter in operation
High friction between mating surfaces
result in high power consumption.
Lower cost
More susceptible to damage from
impurities in lubrication system.
Require less space
More susceptible to damage from
impurities in lubrication system.
Bearing life is not limited by fatigue
Have more stringent lubrication
requirements.
Rolling Friction
When a cylinder rolls on a surface the force resisting
motion is termed rolling friction. Rolling friction is generally
considerably less than sliding friction.
If W is the force between the rolling cylinder and the
stationary surface, R is the radius of the cylinder and F is
the force required to overcome the rolling friction, then
F = fr x W / R
fr is the coefficient of rolling friction and has the same unit
of length as the radius R.
Typical values for rolling friction
Material
Rolling friction
Steel on Steel
0.0005m
Wood on Steel
0.0012m
Wood on Wood
0.0015m
Iron on Iron
0.00051m
Iron on Granite
0.0021m
Iron on Wood
0.0056m
Polymer on Steel
0.002m
Hard rubber on Steel
0.0077m
Hard rubber on Concrete
0.01 - 0.02m
Rubber on Concrete
0.015 - 0.035m
Note: Values for rolling friction from various sources are not consistent and these values should
only be used for approximate calculations. Remember also the coefficient of rolling friction is
dependent on the cylinder radius and therefore has units of length (metres).
Types of antifriction bearing
The types of antifriction
bearing are grouped by
the shape of the rolling
element and they are:
• ball bearings.
• cylindrical roller bearings.
• tapered roller bearings.
and
• needle roller bearings.
Single-Row Ball Bearing. Non-Filling Slot
This type of ball bearing is also known as the Conrad or
Deep-groove type. It is a symmetrical unit capable of taking
combined radial and thrust loads. These bearings are not
self-aligning therefore accurate alignment between shaft
and housing bore is required.
Parts of a Ball Bearing
BALL
CAGE
INNER RACE
OUTER RACE
• Mostly used for radial loads
• Thrust loads need deep grooves in races
• Excessive thrust load causes wear and
deformation of races and balls
Roller Bearings (antifriction)
• Hard steel rollers held between an inner and
outer “race” and held in alignment by a “cage”
• May be tapered to absorb radial and thrust loads
or straight to absorb radial loads only
Cylindrical Roller
These bearings have solid or helically wound hollow
cylindrical rollers. The free ring may have a restraining
flange to provide some restraint to endwise movement in
one direction or maybe without a flange so that the bearing
rings may be displaced axially with respect to each other.
Tapered Roller
Tapered roller bearings are
a variation on the cylindrical
rollers. They are held in
accurate alignment by a
guide flange on the inner
ring. The shape of the roller
is tapered rather than
straight right cylindrical. This
allows thrust loads to be
withstood in addition to the
radial loads.
Needle Roller
Needle bearings are characterized by
their relatively small size rollers. The
diameter of needle roller is usually
less than ¼" in diameter. The length of
needle roller can range from 3 to 10
times its diameter. The loose-roller is
the most widely used needle roller and
it has no integral races. The needle
rollers are located directly between
the shaft and the outer bearing bore.
This type of bearing is capable of high
radial load capacity.
Thrust bearings
• Used to provide
lateral stabilisation to
a rotating shaft
• Susceptible to
damage if axial load
is exceeded
• Often used in
conjunction with a ball
or roller bearing to
control the axial load
PTFE
• PTFE is widely used as an additive in lubricating
oils and greases. Due to the low surface energy
of PTFE, stable unflocculated dispersions of
PTFE in oil or water can be produced. Contrary
to the other solid lubricants discussed, PTFE
does not have a layered structure. The macro
molecules of PTFE slip easily along each other,
similar to lamellar structures. PTFE shows one
of the smallest coefficients of static and dynamic
friction, down to 0.04. Operating temperatures
are limited to about 260ºC.
More about plain bearings
Plain lubricated bearings
Plain bearings can be classified into two types: hydrodynamic bearings
and hydrostatic bearings.
• Hydrodynamic bearings create lift between the mating surfaces by
wedging lubricant into the contact area with a relatively high
rotational speed. The disadvantage of this design is the lack of
lubricant on the surfaces when the shaft begins to rotate. Thus
machineries that utilize this type of bearings should not be subjected
to a high load during startup.
• Hydrostatic bearings utilize an external source to force lubricant into
the contact. They are used in heavily loaded and slow moving
machines where the rotation speed is not great enough to form full
film lubrication.
Tin-Lead & Tin-Copper Alloys
(white metal bearings)
• Tin-Lead & Tin-Copper alloys have good characteristics
for bearings. Most importantly for bearings, the material
should be hard and wear resistant and have a low
coefficient of friction. It must also be shock resistant.
tough and sufficiently ductile to allow for slight
misalignment prior to running in.
• These alloys consist of small particles of a hard
compound embedded in the tough ductile background of
a solid solution. In service the latter can wear away
slightly leaving the hard compound to carry the load.
This wear also provides channels to allow in lubricant
(oils). All bearing metals contain Antimony (Sb) which
creates hard cubic crystals.
Circumferential Groove Bearings
This type of bearing has an oil
groove extending circumferentially
around the bearing. The oil is
maintained under pressure in the
groove. The groove divides the
bearing into two shorter bearings
that tend to run at a slightly
greater eccentricity. This design is
most commonly used in
reciprocating load main and
connecting rod bearings because
of the uniformity of oil distribution.
Pressure Bearings
Pressure bearings employ a groove over the top half of the bearing. The
groove terminates at a sharp dam about 45° beyond the vertical in the direction
of shaft rotation. Oil is pumped into this groove by shear action from the
rotation of the shaft and is then stopped by the dam. In high speed operating.
this situation creates a high oil pressure over the upper half of the bearing. The
pressure created in the oil groove and surrounding upper half of the bearing
increases the load on the lower half of the bearing. This self-generated load
increases the shaft eccentricity. Stability under high speed and low-load
condition can be attained if the eccentricity is increased to 0.6 or greater. The
primary disadvantage of this design is dirt in the oil will tend to smooth out the
sharp edge of the dam and impair the effectiveness to create high pressures.
Multiple Groove Bearings
Multiple groove bearings are sometimes used to provide
increased oil flow. The interruptions in oil flow film also
appear to give this bearing some merit as a stable design.
Hydrostatic Bearings
Hydrostatic bearings are used when operating conditions require full
film lubrication that cannot be developed hydro-dynamically. The
hydrostatically lubricated bearing is supplied with lubricant under
pressure from an external source. Advantages of the hydrostatic
bearing over bearings of other type are lower friction, higher load
capacity, higher reliability, and longer life.
Antifriction Bearings
Antifriction bearings include ball and roller
bearings. They are more desirable than plain
bearings due to their lower friction and
reduced lubrication requirement. However
the life of an antifriction bearing is limited by
the fatigue life of the material they are made
of and the type of lubricant being used.