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Power Transmission: Belts, Chains, Clutches, and Brakes

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Power Transmission: Belts, Chains, Clutches, and Brakes Tightening Torque For dry, unlubricated, or average threads, K = 0.2. For lubricated threads, K = 0.15. – PowerPoint PPT presentation

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Title: Power Transmission: Belts, Chains, Clutches, and Brakes


1
Power Transmission Belts, Chains, Clutches, and
Brakes
2
Power Transmission
  • In many machine designs, power must be
    transmitted from a driving source to the rest of
    the machine. The driving source may be an
    electric motor, engine, windmill, whatever
    often, the energy must be transmitted to the rest
    of the machine to accomplish useful work.
  • We will talk about flexible elements used to
    transmit power, and the control of that power.

3
Belts and Chains
  • Flexible elements, which are economical
    alternatives to gears for transmitting rotary
    motion between shafts. Can be lighter, smaller,
    and as efficient as gears.
  • However, usually the life is more limited.
  • Bicycle gears (chain drive) versus automotive
    gears efficient, lightweight, compact, vastly
    greater range of ratios.

4
Types of Belts
  • Common belts include flat, round, V, and
    timing belts. Flat belts can be very efficient,
    but require high tension levels, which require
    beefier parts. Round belts are similar,
    outstanding for non-parallel shafts. V belts are
    most common, as we will discuss. These belts all
    depend on friction between the belt and the
    pulley (or sheave). Most slip a few .

5
Timing Belts
  • Toothed or synchronous belts dont slip, and
    therefore transmit torque at a constant ratio
    great for applications requiring precise timing,
    such as driving an automotive camshaft from the
    crankshaft.
  • Very efficient. More than other types of belts.

6
Timing Belt Nomenclature
7
Flat, Round, and V Belts
  • Flat and round belts work very well. Flat belts
    must work under higher tension than V belts to
    transmit the same torque as V belts. Therefore
    they require more rigid shafts, larger bearings,
    and so on.
  • V belts create greater friction by wedging into
    the groove on the pulley or sheave. This greater
    friction great torque capacity.

8
V Belt Sheave Cross Section
Wedging action along sides high torque cap.
The included angle 2? ranges between 34o and 40o.
9
V Belt Cross Sections (U.S.)
10
Flat Belts vs. V Belts
  • Flat belt drives can have an efficiency close to
    98, about the same as a gear drive.
  • V belt drive efficiency varies between 70 and
    96, but they can transmit more power for a
    similar size. (Think of the wedged belt having
    to come un-wedged.)
  • In low power applications (most industrial uses),
    the cheaper installed cost wins vs. their greater
    efficiency V belts are very common.

11
Flat Belt Drive Nomenclature
12
Force Profile in Belt Drive
13
Flat Belt Drive Equations
  • T (F1 F2)r
  • hp (F1 F2)V/33,000 Tn/63,000
  • speed ratio n1/n2 r2/r1
  • sin? (r2 r1)/c
  • contact angle (small) ? ? 2 ?
  • cent. force in belt Fc (w/g)V2
  • F1 Fc ? /(?-1)(T1/r1)
  • ? ef?/sin?
  • (Where ? 90o for a
    flat belt)

14
Chains
  • Compared to belts, chains can transmit more power
    for a given size, and can maintain more precise
    speed ratios.
  • Like belts, chains may suffer from a shorter life
    than a gear drive. Flexibility is limited by the
    link-length, which can cause a non-uniform output
    at high speeds.

15
Chains
  • Chain drives can be very efficient. Bicycle
    example there are very few belt-drive bicycles.
  • The fact that the user controls the length (with
    master links) is a plus. However, the sprockets
    wear out much more frequently than does a belt
    sheave. Take your pick!

16
Chain Nomenclature
17
View with side plates omitted
18
Chain Sizes (U.S.)
  • The chain number is nominally the
    roller-to-roller pitch in 1/80 inch increments.
  • Size 40 chain ½ pitch bike chain.
  • Size 80 chain 1 pitch.
  • Size 120 chain 1 ½ pitch.

19
Clutches Brakes
  • Both use friction to control rotational power.
  • Clutches are used to couple decouple rotating
    members typically a power source from the rest
    of a machine. Auto example.
  • Brakes are used to dissipate rotational energy.

20
Friction Materials
  • Clutches and brakes depend on friction to
    operate. Typically one surface is metal, either
    steel or cast iron. The other surface is usually
    of a composite nature, for example soft metal
    particles embedded with reinforcing fibers in a
    bonding matrix.
  • Conflicting requirements of minimal wear, but
    acceptable f.

21
Single Plate Disc Clutch
(for yoke shifter)
22
Hydraulically Actuated Multiple Plate Clutch,
Wet or Dry
Whats wrong with this picture?
23
Wet Clutches
  • Why on earth would an engineer design a clutch
    where the plates operate in an oil bath? Isnt
    friction the idea?
  • Cooling, smooth operation (no grabbing, and
    reduced wear, thats why.
  • True that f is reduced and so sizes must be
    increased but a worthwhile tradeoff.

24
Cone Clutches Brakes
25
Simple Band Brake
Very similar to a belt drive torque capacity is
T (F1 F2)r
26
Differential Band Brake
The friction force helps to apply the band
therefore it is self-energizing. Can become
self-locking Fa (1/a)(cF2 sF1)
27
Short-Shoe Drum Brakes
If the shoe is short (less than 45o contact
angle), a uniform pressure distribution may be
assumed which simplifies the analysis in
comparison to long-shoe brakes.
28
Self-Energizing Self-Locking Brakes
If the rotation is as shown, then Fa (Fn/a)(b
fc). If b lt fc, then the brake is
self-locking. Think of a door stop, that is a
self-locking short shoe brake.
29
Long-Shoe Drum Brakes
Cannot assume uniform pressure distribution, so
the analysis is more involved.
30
Internal Long-Shoe Drum Brakes
Formerly in wide automotive use being replaced
by caliper disc brakes, which offer better
cooling capacity (and many other
advantages). Brakes can dissipate enormous
amounts of power.
31
  The band brake shown has a power capacity of
40 kW at 600 rpm. Determine the belt
tensions.   Given ? 250?, r 250 mm, a 500
mm, and f 0.4.
32
  • Torque T (9549 x kW)/n
  • (9549 x 40)/600 636.6 N-m
  • F1 F2e f?,
  • where ? is in radians, so
  • F1 F2e (.4)(4.363) 5.727F2
  • T (F1 F2)r
  • Or, T (.25)(5.727F2 F2) 1.182F2

33
  • Therefore, F2 538.6 N, and,
  • F1 3,085 N

34
Power Screws, Fasteners, and Connections
35
Threads and Connections
  • We will start off discussing the mechanics of
    screw threads. Next, power screws threaded
    fasteners will be examined. Since threaded
    fasteners are often used to make connections, we
    will end with that topic.

36
The Inclined Plane
  • Wrapped into a helix, this becomes one of the
    worlds great inventions.
  • By inspection, a steeper angle gains you
    elevation more quickly, but the applied force
    must increase.

W
fN
Q
?
N
37
Helically-Inclined Planes
Differential element of one thread transferring
force to the mating thread. The helix or lead
angle ? the slope of the ramp, and is a
critical design parameter. ? is the thread angle,
and is another important parameter.
38
?, ?, and f
  • On a screw thread, the helix angle ? controls the
    distance traveled per revolution and the force
    exerted.
  • ?, the thread angle, effects the friction force
    resisting motion. Sometimes friction is
    desirable (e.g., so that threads wont loosen),
    and sometimes it is not.
  • f is the coefficient of friction, and plays an
    important role in all threads.

39
? and ?
  • ?, the helix angle, is given by
  • tan ? L/(?dm)
  • where,
  • L the lead or pitch (threads per unit length)
  • dm the mean dia. of the thread contact surface.
    As dm increases, ? decreases.
  • ?, the thread angle, is determined by the design
    of the threads not a function of L or dm.

40
Thread Friction Examples
  • Acme Threads
  • Bolt Threads
  • Pipe Threads

41
Power Screws
Force F acts on moment arm a to produce a torque
T. Tables show standard sizes of power screw
threads. In this drawing, only the nut rotates.
42
Power Screw Thread Types
Acme in wide use, but less efficient.
Square most efficient, but hard to make.
Modified Square compromise.
43
Self-Locking of Power Screws
  • Self locking is an important design feature
    for jacks. Occurs when the coefficient of
    thread friction is gt the tangent of the helix
    angle the cosine of the thread angle
  • f gt cos?ntan ?

44
Power Screw Efficiency
Note the wide range as a function of both f and ?.
45
Threaded Fasteners Nomenclature
46
Threaded Fasteners Thread Forms
Note that the crests roots may be either flat
or rounded
47
Threaded Fasteners UNS ISO
  • UNS Unified National Standard. Threads are
    specified by the bolt or screw diameter (also
    called the major diameter)in inches, and the
    number of threads per inch.
  • ISO International Standards Organization.
    Threads are specified by the major diameter in
    mm, and the pitch, or, number of mm per thread.
  • Generally UNS and ISO threads are NOT
    interchangeable. (3mm is close to 1/8.)

48
Threaded Fasteners UNS
  • The specification is written in the format
  • Dia threads/in UNC or UNF class and
    internal or external RH or LH.
  • UNC Unified National Coarse
  • UNF Unified National Fine
  • Class ranges from 1 (cheap inaccurate) to 3
    (expensive precise). Class 2 is common.
  • A external, B internal

49
Threaded Fasteners UNS
  • RH right hand threads, LH left hand
  • Example thus would be
  • ½ 13 UNC 2A RH
  • Notes
  • UNF and UNC are redundant information.
  • For diameters less than ¼, a numeric size is
    specified instead of the diameter. (000 14)

50
Threaded Fasteners ISO
  • Metric designations are a little simpler.
    Preceded by an M, then the diameter in mm, then
    the pitch (mm per thread, not threads per mm).
    There are also coarse and fine threads in the ISO
    system.
  • Examples M10 x 1.5
  • M10 x 1.25

51
Coarse Versus Fine Threads
  • Coarse threads are fine ? for normal
    applications. They are easier to assemble, a
    little more forgiving of dings, possibly cheaper
    to make, and for a given size of bolt, they exert
    less force than do fine threads good for softer
    materials bolted together.
  • Fine threads develop greater force per applied
    torque, and are more effective at resisting
    vibration-induced loosening.

52
Bolts, Screws, and Studs
The same fastener could be a bolt or a screw,
depending on if a nut is used. Studs are
threaded at both ends.
53
Bolt Grades
  • Bolts (and nuts) are made from a variety of
    materials. The SAE Grade is an indication of the
    strength of the material, based on the proof
    stress, Sp (slightly less than the yield stress).
    Sp ranges from 33 ksi for a grade1 bolt, up to
    120 ksi for a grade 8 bolt. The proof load of a
    bolt is the load at which permanent deformation
    commences.

54
SAE Bolt Head Markings
Hexagonal bolt heads are stamped with radial
lines to indicate the grade. The grade the
number of lines 2.
http//raskcycle.com/techtip/webdoc14.html
55
Thread Manufacture
  • Threads are generally produced by either
    rolling (forming with a specialized die) or by
    cutting, as on a lathe. Rolled threads are
    stronger and have better fatigue properties due
    to the cold work put into the material.
  • Power screw threads may be ground to achieve a
    very smooth surface to reduce f. Threads may
    also be cast into a part.

56
Stresses in Threaded Fasteners
  • Due to imperfect thread spacing, most of the
    load between a bolt and a nut is taken by the
    first pair of threads. This is partially
    relieved by bending and localized yielding,
    however most thread failures occur in that
    region. The stress concentration ranges from 2
    to 4.

57
Major-Diameter Stresses
  • Axial stress is given by the familiar
  • ? P/A
  • For A, use either the root diameter for power
    screws, or tabulated values for fasteners.
  • Torsional stress is given by the familiar
  • ? T/J 16T/ ?d3
  • for interpretation of T and d. T is the
    applied torque for power screws, or ½ the wrench
    torque, for fasteners.

58
Bearing Stress
  • Bearing stress, the compressive stress between
    the surfaces of the threads, is given by ?b
    P/(?dmhne)
  • P load,
  • dm pitch or mean screw thread diameter,
  • h depth of thread, and
  • ne number of threads in engagement.
  • ?b is usually not a limiting design factor.

59
Nomenclature for Thread Stress Analysis
60
Direct Shear Stress on Threads
  • In addition to the torsional shear stress we
    just discussed, the threads also experience
    direct shear stress. The threads are considered
    to be loaded as a cantilever beam (wrapped around
    a cylinder), with the load evenly distributed
    over the mean screw diameter. Because the nut
    threads are wrapped inside of a larger cylinder
    than the bolt threads, they experience less
    stress.

61
Direct Shear Stress on Threads
  • Then we have,
  • ? 3P/(2 ?dbne), where,
  • d root dia. for the screw or major dia. for the
    nut,
  • b the thread thickness at the root, and
  • ne the number of threads in engagement.
  • Note that ? can be a limiting factor.

62
Bolt Tightening Preload
  • Bolted joints commonly hold parts together in
    opposition to both normal and shear forces.
  • In certain applications it is desirable to
    tighten a bolted joint to a specified preload Fi,
    which is some fraction of the bolts proof load,
    Fp.

63
Bolt Tightening Preload
  • An engineer would specify a preload in the
    case of fatigue applications, in order to
    minimize the relative magnitude of the
    alternating load Pa compared to the average load
    Pmean.
  • Preloading is also important in sealing
    applications, as in a gasketed joint. Both
    reasons are important for auto cylinder heads.

64
Preload Values
  • The optimum preload is often given by eq. 15.20
  • Fi 0.75 Fp for connections to be reused, or
  • Fi 0.90 Fp for permanent connections.
  • The proof load Fp is, Fp SpAt, where the proof
    stress Sp is an SAE
  • specification, and tension area At is found in
    Tables.

65
Tightening Torque
  • To develop the specified preload, the tightening
    torque is given by
  • T KdFi, where
  • T the tightening torque,
  • d the nominal bolt diameter (e.g., ½),
  • Fi the desired preload, and
  • K a torque coefficient

66
Tightening Torque
  • For dry, unlubricated, or average threads,
  • K 0.2. For lubricated threads, K 0.15.
  • Rewrite eq. as,
  • Fi T/(Kd) to see that, for a given torque, Fi
    increases with lubricated threads.

67
Relaxation and Exactness
  • Most joints lose on the order of 5 of the
    original preload over time, due to relaxation
    effects (usually over the course of 100s or 1000s
    of hours).
  • By now it should be clear that threaded fasteners
    are extremely complex. Often extensive testing
    is done for critical applications.

68
Tension Joints
  • Bolted joints are frequently used to clamp
    together parts that themselves carry additional
    loads these additional loads increase the bolt
    tension. The engineer often must determine
    acceptable loads for such joints.
  • We consider both the joints and the parts as
    springs, with spring constants kb and kp.

69
Tension Joints
After assembly with preload Fi, applied load P
will change the force in the bolt and the parts.
70
Tension Joints
  • P ?Fb ?Fp, where
  • ?Fb the increased tension in the bolt, and
  • ?Fp the decreased compression force in the
    parts. The deformations are given by
  • ?b ?Fb/kb, and ?p ?Fp/kp
  • Then compatibility requires that
  • ?Fb/kb ?Fp/kp

71
Joint Constant C
  • The joint stiffness factor, or joint constant, is
    defined in eq. 15.22 as C kb/(kb kp).
    Then the preceding equations yield
  • ?Fb CP and ?Fp (1 C)P
  • kb is usually small compared to kp, and so C is a
    small fraction.

72
Forces in Bolted Joints
  • When a load P is applied to a bolted joint, the
    tensile force Fb in the bolt increases, and the
    compressive force Fp in the parts decreases. As
    long as Fp gt 0, the forces are
  • Fb CP Fi
  • and,
  • Fp (1 C)P Fi

73
Determination of C
  • Deflection ? is given by ? PL/AE, and the
    spring rate k is given by k P/ ?. Combining
    these we obtain
  • kb AbEb/L
  • and
  • kp ApEp/L

74
Determination of kb
In determining kb, the threaded and the
unthreaded parts of the bolt are considered as
separate springs in series. 1/kb Lt/AtEb
Ls/AbEb
75
Determination of kp
kp is more complex the stress distribution in
the parts is clearly non-uniform, and depends on
factors like washers, etc. It is approximated by
the double-cone illustrated.
76
Determination of kp
  • Estimate of kp for standard hex-head bolts and
    washers is given by
  • kp (.5 ?Epd)/2 ln 5(.58L.5d)/(.58L2.5d)
  • d bolt diameter and
  • L grip (thickness of bolted assembly).
  • Alternatively, just use kp 3kb !

77
Some Rules of Thumb for Threaded Fasteners
  • Threaded depth for a bolt diameter d, the length
    of full thread engagement should be 1.0d in
    steel, 1.5d in cast iron, and 2.0d in aluminum.
  • In gasketed joints, bolts are arrayed in a bolt
    circle or other pattern. The bolt-to-bolt
    spacing should not exceed about 6d to maintain
    uniform pressure.

78
Rivets
Rivets often find application in larger
structures such as bridges and towers. They are
also used extensively in aircraft construction.
A rivet starts off as a cylinder with one head
(usually rounded). The protruding cylinder is
deformed to create a second head, which locks the
joint in compression.
79
Joints Primarily in Shear
  • Both bolts and rivets are used in connections
    that primarily experience shear loading (separate
    from the case of axial or normal loading which we
    just examined).
  • Such connections may experience any of several
    failure modes, and the engineer must analyze for
    each mode.

80
Shear Joint Failure Modes
Shearing Failure of Fastener ? 4P/ ?d2 d
diameter of fastener
81
Shear Joint Failure Modes
Tensile Failure of Plate ?t P/(w de)t,
where de effective hole dia., w width, and t
thickness of thinnest plate
82
Effective Hole Diameter
  • In analyzing potential tensile failure of the
    plate, the effective hole diameter is used rather
    than the diameter of the fastener.
  • de the fastener diameter 1/16 for drilled
    holes, or,
  • de the fastener diameter 1/8 for punched
    holes (this is usually used).

83
Shear Joint Failure Modes
Bearing Failure of Plate or Fastener ?b P/dt,
where d diameter of fastener and t thickness
of the thinnest plate.
84
Shear Joint Failure Modes
a gt 1.5d
Shearing Failure of Plate ? t P/2at, where t
thickness of thinnest plate and a closest
distance from fastener to edge.
85
Joint Efficiency
  • The efficiency of a joint is defined as
  • e Pall/Pt,
  • where
  • Pall is the smallest of the allowable loads in
    the preceding failure mode examples, and
  • Pt is the static tensile strength of the plate
    with no holes. e is always less than 100.

86
Welded Joints
  • Welded joints are produced by localized melting
    of the parts to be joined, in the region of the
    joint. Often a filler metal (or plastic, in the
    case of plastics) is added, creating a chemical
    bond in the parts that may be stronger than the
    base material.
  • There are many, many welding processes an
    entire engineering major.

87
Strength of Butt Welds
The height h does not include the crowned region
generally it is just the plate thickness.
88
Strength of Fillet Welds
Specified size is based on h, but stress is
calculated with t, the region of minimum cross
sectional area.
89
Factor of Safety for Welds in Shear
  • Just as many riveted or bolted joints are in
    shear, so too are many welded joints. The factor
    of safety for a welded joint is given by
  • n Sys/ ? 0.5Sy/ ? (eq.
    15.44)

90
Purchased vs. Designed Components
  • We went into shafts in some detail because shafts
    tend to be custom-designed for each application.
  • Often the components that the engineer puts onto
    the shaft, however, are purchased. These
    components can be analyzed as much as one likes,
    but its usually best to work with the
    manufacturers application data.

91
Polar Moment of Inertia
  • The polar moment of inertia is the sum of Ix
    and Iy for each weld about the centroid of the
    weld group. Knowing J, apply
  • ?t Tr/J
  • to find ?t at a given point, and then use
  • ? (?t2 ?d2)½
  • to find the max ? , which is used to find the
    required weld size.

92
Eccentric Loading of Welded Joints (P.E.
Question!)
Determination of the exact stress distribution is
very complicated. With some simplifying
assumptions, the following procedure gives
reasonably accurate results. Direct shear stress
is given by ?d P/A, where A the throat area
of all the welds.
93
Eccentric Loading of Welded Joints
  • ?d is taken to be uniformly distributed over
    the length of all the welds.
  • Due to the eccentricity e, a torque T is
    developed about the centroid C of the weld group
    T Pe. The torque causes an additional shear
    stress in the welds
  • ?t Tr/J
  • J polar moment of inertia of the weld group
    about C, based on the throat area.

94
Eccentric Loading of Welded Joints
  • ?t Tr/J
  • In this equation, r is the distance from C to
    the point in the weld of interest. ?t is not
    uniform across the weld group, and one point will
    experience the greatest stress resultant
  • ? (?t2 ?d2)½

95
Location of the Centroid (Review)
C is located at coordinates x-bar and y-bar,
where x-bar (?Aixi)/ ?Ai, and y-bar (?Aiyi)/
?Ai, where i denotes a given weld segment, and
the coordinate origin is conveniently chosen. A
key is that the weld throat t is assumed to be
very small, sometimes 0.
96
Moment of Inertia of a Weld and the Parallel Axis
Theorem.
Use the familiar bh3/12, substituting t and L for
b and h as appropriate. However, assume t3 0
to simplify. Remember the parallel axis theorem,
Ix Ix Ay12, to find the moment of inertia
about the centroid of the weld group. (So even
if Ix 0, you still have A.)
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