Screw thread measurements and Gear measurement

This presentation gives the information about Screw thread measurements and Gear measurement of the subject: Mechanical measurement and Metrology (10ME32/42) of VTU Syllabus covering unit-4.

1. 8/20/2014 1Hareesha N Gowda, DSCE, Blore-78

2. Terminology of screw threads

3. Screw thread-definition
a screw thread is the helical ridge produced by forming a
continuous helical groove of uniform section on the
external or internal surface of a cylinder or a cone.
A screw thread formed on a cylinder is known as straight or
parallel screw thread, while the one formed on a cone is
known as tapered threads.

4. Types of thread
External thread: a thread formed on outside of a
work piece is known as external thread. Example:
on bolts or studs etc.
Internal thread: a thread formed on inside of a
work piece is known as internal thread. Example:
on a nut or female screw gauge.

5. Screw thread -use
Screw threads are used:
•To hold parts together-act as fastners(ex: V-threads)
•To transmit motion & power (Square, Acme threads)

6. Screw Thread terminologyPitch
Crest
Root
Flank
Thread
Angle
Pitch line
Axis of thread
Axial thickness
Addendum
Dedendum
Flank
angle
Major diaPitch diaMinor dia
EXTERNAL THREAD TERMINOLOGY

7. Screw Thread terminology
Pitch:Thedistancefromapointonascrewthreadtoa
correspondingpointonthenextthreadmeasuredparalleltothe
axis.
LeadThedistanceascrewthreadadvancesinoneturn.Fora
singlestartthreads,lead=pitch,
Fordoublestart,lead=2xpitch,&soon.
ThreadForm:Thecrosssectionofthreadcutbyaplane
containingtheaxis.
MajorDiameter:Thisisthediameterofanimaginarycylinder,co-
axialwiththescrew,whichjusttouchesthecrestsofanexternal
threadorrootsofaninternalthreads.Itisalsocalledas‘Nominal
diameter’

8. Screw Thread terminology
Minordiameter:Thisisthediameterofanimaginary
cylinder,co-axialwiththescrewwhichjusttouchestheroots
ofanexternalthreadorthecrestofaninternalthread.This
isalsoreferredtoas‘root’or‘corediameter’.
EffectivediameterorPitchdiameter:Itisthediameterof
animaginarycylindercoaxialwiththeaxisofthethreadand
intersectstheflanksofthethreadsuchthatwidthofthe
threads&widthofspacesbetweenthreadsareequal.
Flank:ItistheThreadsurfacethatconnectscrestwithroot.
•Depthofthread:Itisthedistancebetweencrestandroot
measuredperpendiculartoaxisofscrew.

9. Screw Thread terminology
Angleofthread:Includedanglebetweensidesofthread
measuredinaxialplane.
Helixangle:Anglethatthethreadmakeswithplane
perpendiculartothreadaxis.
Flankangle:Itishalftheincludedangleofthethread.
Addendum:Itisthedistancebetweenthecrestandthe
pitchlinemeasuredperpendiculartoaxisofthescrew.
Dedendum:Itisthedistancebetweenthepitchline&
therootmeasuredperpendiculartoaxisofthescrew.

10. MEASUREMENT OF VARIOUS ELEMENTS OF
THREAD
To find out the accuracy of a screw thread it will
be necessary to measure the following:
1) Major diameter.
2) Minor diameter.
3) Effective or Pitch diameter.
4) Pitch
5) Thread angle and form

11. Measurement of major diameter
The instruments which are used to find the major
diameter are by
Bench micrometer
Bench micrometer

12. Ordinary micrometer:
The ordinary micrometer is quite suitable for measuring the
external major diameter.
It is first adjusted for appropriate cylindrical size (S) having
the same diameter (approximately).This process is known as ‘
gauge setting’ .
After taking this reading ‘ R the micrometer is set on the
major diameter of the thread, and the new reading is ‘R2

13. Measurement by Bench micrometer:Clamp
Fiducial
Indicator
Measuring
Anvils
Holding centres
Micrometer head
Supports
BENCH MICROMETER

14. Measurement by Bench micrometer:
For getting the greater accuracy the bench micrometer is used for
measuring the major diameter.
In this process the variation in measuring Pressure, pitch errors are being
neglected.
The fiducialindicator is used to ensure all the measurements are made at
same pressure.
The instrument has a micrometer head with a vernierscale to read the
accuracy of 0.002mm. Calibrated setting cylinder having the same diameter
as the major diameter of the thread to be measured is used as setting
standard.
After setting the standard, the setting cylinder is held between the anvils
and the reading is taken

15. Measurement by Bench micrometer:
Then the cylinder is replaced by the threaded work piece and the new
reading is taken

16. Measurement by Bench micrometer:

17. Measurement by Bench micrometer:Holding centre
Measuring anvil
Holding centre
Measuring anvil
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Measurement of Major diameter

18. Measurement of the major diameter of an
Internal thread:
An indirect approach of measuring internal diais obtained by
obtaining the cast of the Thread. The main art thus lies in
obtaining a perfect cast.

19. Measurement of the major diameter of an
Internal thread:

20. Measurement of Minor diameter
The minor diameter is measured by a comparative
method by using floating carriage diameter measuring
machine and small ‘ V pieces which make contact with
the root of the thread.
These V pieces are made in several sizes, having
suitable radii at the edges.
V pieces are made of hardened steel.
The floating carriage diameter-measuring machine is
a bench micrometer mounted on a carriage.

21. Measurement of Minor diameter

22. The threaded work piece is mounted between the centres of the
instrument and the V pieces are placed on each side of the work
piece and then the reading is noted.
After taking this reading the work piece is then replaced by a
standard reference cylindrical setting gauge.
Measurement of Minor diameter

23. Measurement of Minor diameter of
Internal threads:
The Minor diameter of Internal threads are
measured by
1. Using taper parallels
2. Using Rollers.

24. Measurement of Minor diameter of
Internal threads:
1.Using taper parallels:
For diameters less than 200mm the use of Taper parallels and
micrometer is very common.
The taper parallels are pairs of wedges having reduced and
parallel outer edges.
The diameter across their outer edges can be changed by sliding
them over each other.

25. Measurement of Minor diameter of
Internal threads:
Using rollers:
For more than 200mm diameter this method is used.
Precision rollers are inserted inside the thread and proper
slip gauge is inserted between the rollers.
The minor diameter is then the length of slip gauges plus
twice the diameter of roller.

26. Pitch measurement
The most commonly used methods for
measuring the pitch are
1. Pitch measuring machine
2. Tool makers microscope
3. Screw pitch gauge

27. Tool makers microscope:

28. Tool makers microscope:Lamp
Hollow base
Collimator lens
Base
Column
Eye piece
Optical head
Mirror
work table
with carriage

29. Tool makers microscope:

30. Tool makers microscope:
1. Worktable is placed on the base of the instrument.
2. The optical head is mounted on a vertical column it can be moved up
and down.
3. Work piece is mounted on a glass plate.
4. A light source provides horizontal beam of light which is reflected
from a mirror by 90 degree upwards towards the table.
5. Image of the outline of contour of the work piece passes through the
objective of the optical head.
6. The image is projected by a system of three prisms to a ground glass
screen.
7. The measurements are made by means of cross lines engraved on the
ground glass screen.
8. The screen can be rotated through 3 60°.
9. Different types of graduated screens and eyepieces are used

31. Pitch measuring machine
When the pointer is accurately placed in position, the micrometer reading is
noted. The stylus is then moved along into the next thread space, by rotation of
the micrometer, and a second reading taken.
The difference between the two readings is the pitch of the thread. Readings are
taken in this manner until the whole length of the screw thread has been
covered.
Spring loaded head permits the
stylus to move up the flank of the
thread and down into the next space
as it is moved along.
Accurate positioning of the stylus
between the two flanks is obtained
by ensuring that the pointer T is
always opposite to its index mark
when readings are taken.

32. Screw pitch gauge

33. Measurement of screw thread angle
(Flank angle)

34. Measurement of effective diameter
Effective diameter measurement is carried
out by following methods.
1 two wires method
3. three wires method.
4. Micrometer method.

35. Two wire method:
Theeffectivediametercannotbemeasureddirectlybut
canbecalculatedfromthemeasurementsmade.
Wiresofexactlyknowndiametersarechosensuchthat
theycontacttheflanksattheirstraightportions.
Ifthesizeofthewireissuchitcontactstheflanksatthe
pitchline,itiscalledthe‘bestsize’ofwirewhichcanbe
determinedbygeometryofscrewthread.
Thescrewthreadismountedbetweenthecenters&
wiresareplacedinthegroovesandreadingMistaken.
ThentheeffectivediameterE=T+P
whereT=M-2d,&Pisavaluewhichdependsondiameter
ofwire,pitch&angleofthescrewthread.

36. Two wire method:
M
M-Dimension over the wire

37. Two wire method:

38. Two wire method:

39. Two wire method:

40. Two wire method:
P
AP=OP-OA

41. Three Wire method
The three-wire method is the accurate method.
In this method three wires of equal and precise
diameter are placed in the groves at opposite sides of
the screw.
In this one wire on one side and two on the other side
are used. The wires either may held in hand or hung
from a stand.
This method ensures the alignment of micrometer
anvil faces parallel to the thread axis.

42. Three Wire method

43. Three Wire method
Thismethodismoreaccuratethantwowiremethod
asitensuresalignmentofmicrometerfacesparallel
tothethreadaxis.
Here,threewiresofexactlyknowndiametersare
used,oneononeside&thetwoontheotherside.
Thewiresmaybeheldinhandorhungfromastand.
Fromthefig,M=diameteroverthewires
E=effectivediameter(tobefound)
d=diameterofwires,h=heightofwirecenterabove
thepitchline,r=radiusofwire,H=depthofthread,
D=majordiameterofthethread.

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49. GEAR…..
•Power transmission is the movement of energy
from its place of generation to a location where
it is applied to performing useful work
•A gear is a component within a transmission
device that transmits rotational force to another
gear or device

50. TYPES OF GEARS
1. According to the position of axes of the
shafts.
a.Parallel
1.Spur Gear
2.Helical Gear
3.Rack and Pinion
b. Intersecting
Bevel Gear
c. Non-intersecting and Non-parallel
worm and worm gears

51. SPUR GEAR
•Teeth is parallel to axis
of rotation
•Transmit power from
one shaft to another
parallel shaft
•Used in Electric
screwdriver, oscillating
sprinkler, windup alarm
clock, washing machine
and clothes dryer

52. External and Internal spur Gear…

53. Helical Gear
•The teeth on helical gears are cut at an angle
to the face of the gear
•This gradual engagement makes helical gears
operate much more smoothly and quietly than
spur gears
•One interesting thing about helical gears is
that if the angles of the gear teeth are correct,
they can be mounted on perpendicular shafts,
adjusting the rotation angle by 90 degrees

54. Helical Gear…

55. Rack and pinion
•Rack and pinion gears
are used to convert
rotation (From the
pinion) into linear
motion (of the rack)
•A perfect example of this
is the steering system on
many cars

56. Straight and Spiral Bevel Gears

57. WORM AND WORM GEAR

58. FormsofTeeth
•Inactualpracticefollowingarethetwotypesofteethcommonly
used
1.Cycloidalteeth;and2.Involuteteeth.
CycloidalTeeth
•Acycloidisthecurvetracedbyapointonthecircumferenceofa
circlewhichrollswithoutslippingonafixedstraightline.
•Whenacirclerollswithoutslippingontheoutsideofafixedcircle,
thecurvetracedbyapointonthecircumferenceofacircleisknown
asepi-cycloid.
•Ontheotherhand,ifacirclerollswithoutslippingontheinsideofa
fixedcircle,thenthecurvetracedbyapointonthecircumferenceof
acircleiscalledhypo-cycloid.

59. Construction of cycloidal teeth for gear
•The cycloidal teeth of a gear may be constructed as shown in Fig. (b).
•The circle C is rolled without slipping on the outside of the pitch circle
and the point P on the circle C traces epi-cycloid PA, which represents
the face of the cycloidal tooth.
•The circle D is rolled on the inside of pitch circle and the point P on
the circle D traces hypo-cycloid PB, which represents the flank of the
tooth profile.
The profile BPA is one side of the
cycloidal tooth. The opposite side
of the tooth is traced as explained
above.

60. Involute Teeth
•An involute of a circle is a plane curve generated by a point on a tangent,
which rolls on the circle without slipping or by a point on a taut string which
in unwrapped from a reel as shown in Fig.
•In connection with toothed wheels, the circle is known as base circle. The
involute is traced as follows :
•A3, the tangent A3T to the involute is
perpendicular to P3A3 and P3A3 is the
normal to the involute.
•In other words, normal at any point of an
involute is a tangent to the circle.

61. NOMENCLATURE OF SPUR GEARS

63. •Pitch circle. It is an imaginary circle which by pure rolling action would give
the same motion as the actual gear.
•Pitch circle diameter. It is the diameter of the pitch circle. The size of the
gear is usually specified by the pitch circle diameter. It is also known as pitch
diameter.
•Pitch point. It is a common point of contact between two pitch circles.
•Pitch surface. It is the surface of the rolling discs which the meshing gears
have replaced at the pitch circle.
•Pressure angle or angle of obliquity. It is the angle between the common
normal to two gear teeth at the point of contact and the common tangent
at the pitch point. It is usually denoted by φ. The standard pressure angles
are 14 1/2 °and 20°.

64. •Addendum. It is the radial distance of a tooth from the pitch circle to
the top of the tooth.
•Dedendum.It is the radial distance of a tooth from the pitch circle to
the bottom of the tooth.
•Addendum circle. It is the circle drawn through the top of the teeth
and is concentric with the pitch circle.
•Dedendumcircle. It is the circle drawn through the bottom of the
teeth. It is also called root circle.
Note : Root circle diameter = Pitch
circle diameter ×cosφ, where φis
the pressure angle.

65. Circular pitch. It is the distance measured on the circumference of the
pitch circle from a point of one tooth to the corresponding point on
the next tooth. It is usually denoted by P
c,Mathematically,
•A little consideration will show that the two gears will mesh together
correctly, if the two wheels have the same circular pitch.
Note : If D1 and D2 are the diameters of the two meshing gears having
the teeth T1 and T2 respectively, then for them to mesh correctly,

66. Diametralpitch. It is the ratio of number of teeth to the pitch circle
diameter in millimetres. It is denoted by p
d. Mathematically,
Module. It is the ratio of the pitch circle diameter in millimeters to the
number of teeth. It is usually denoted by m. Mathematically,
Clearance. It is the radial distance from the top of the tooth to the
bottom of the tooth, in a meshing gear. A circle passing through the
top of the meshing gear is known as clearance circle.
Total depth. It is the radial distance between the addendum and the
dedendumcircles of a gear. It is equal to the sum of the addendum
and dedendum.

67. Face of tooth. It is the surface of the gear tooth above the pitch surface.
Flank of tooth. It is the surface of the gear tooth below the pitch surface.
Top land. It is the surface of the top of the tooth.
Face width. It is the width of the gear tooth measured parallel to its axis.
Profile. It is the curve formed by the face and flank of the tooth.

69. ComparisonBetweenInvoluteandCycloidalGears
•Inactualpractice,theinvolutegearsaremorecommonlyusedascomparedtocycloidal
gears,duetothefollowingadvantages:
Advantagesofinvolutegears
•Themostimportantadvantageoftheinvolutegearsisthatthecentredistancefora
pairofinvolutegearscanbevariedwithinlimitswithoutchangingthevelocityratio.
Thisisnottrueforcycloidalgearswhichrequiresexactcentredistancetobe
maintained.
•Ininvolutegears,thepressureangle,fromthestartoftheengagementofteethtothe
endoftheengagement,remainsconstant.Itisnecessaryforsmoothrunningandless
wearofgears.Butincycloidalgears,thepressureangleismaximumatthebeginningof
engagement,reducestozeroatpitchpoint,startsdecreasingandagainbecomes
maximumattheendofengagement.Thisresultsinlesssmoothrunningofgears.
•Thefaceandflankofinvoluteteetharegeneratedbyasinglecurvewhereasin
cycloidalgears,doublecurves(i.e.epi-cycloidandhypo-cycloid)arerequiredfortheface
andflankrespectively.Thustheinvoluteteethareeasytomanufacturethancycloidal
teeth.Ininvolutesystem,thebasicrackhasstraightteethandthesamecanbecutwith
simpletools.
•Note:Theonlydisadvantageoftheinvoluteteethisthattheinterferenceoccurswith
pinionshavingsmallernumberofteeth.Thismaybeavoidedbyalteringtheheightsof
addendumanddedendumofthematingteethortheangleofobliquityoftheteeth.

70. Advantages of cycloidal gears
Following are the advantages of cycloidal gears :
•Since the cycloidal teeth have wider flanks, therefore the cycloidal gears are
stronger than the involute gears, for the same pitch. Due to this reason, the
cycloidal teeth are preferred specially for cast teeth.
•In cycloidal gears, the contact takes place between a convex flank and concave
surface, whereas in involute gears, the convex surfaces are in contact. This
condition results in less wear in cycloidal gears as compared to involute gears.
However the difference in wear is negligible.
•In cycloidal gears, the interference does not occur at all. Though there are
advantages of cycloidal gears but they are outweighed by the greater simplicity and
flexibility of the involute gears.

71. Interference in Involute Gears
•Fig. shows a pinion with centre O1, in mesh with wheel or gear with centre O2.
•MN is the common tangent to the base circles and KL is the path of contact
between the two mating teeth.
•Thetipoftoothonthepinionwillthenundercutthetoothonthewheelattheroot
andremovepartoftheinvoluteprofileoftoothonthewheel.Thiseffectisknown
asinterference,andoccurswhentheteetharebeingcut.
•Inbrief,thephenomenonwhenthetipoftoothundercutstherootonitsmating
gearisknownasinterference.
•A little consideration will show,
that if the radius of the addendum
circle of pinion is increased to O 1
N, the point of contact L will move
from L to N.
•When this radius is further
increased, the point of contact L
will be on the inside of base circle of
wheel and not on the involute
profile of tooth on wheel.

72. •Similarly, if the radius of the addendum circle of the wheel increases beyond O2M,
then the tip of tooth on wheel will cause interference with the tooth on pinion. The
points M and N are called interference points.
•From the above discussion, we conclude that the interference may only be avoided,
if the point of contact between the two teeth is always on the involute profiles of
both the teeth. In other words, interference may only be prevented, if the
addendum circles of the two mating gears cut the common tangent to the base
circles between the points of tangency.
•When interference is just avoided, the maximum length of path of contact is MN
when the maximum addendum circles for pinion and wheel pass through the points
of tangency N and M respectively as shown in Fig.
Obviously, interference may be
avoided if the path of contact does
not extend beyond interference
points. The limiting value of the
radius of the addendum circle of the
pinion is O1N and of the wheel is
O2M.

73. •Measurement of tooth thickness
•The tooth thickness is generally measured at pitch
circle and is therefore, the pitch line thickness of
the tooth. Following method is used for
measuring the gear tooth thickness :
•Measurement of tooth thickness by gear tooth
verniercaliper.
•The gear tooth thickness can be conveniently
measured by a gear tooth vernieras shown in the
fig.
•Since the gear tooth thickness varies from the tip
to the base circle of the tooth, the instrument
must be capable of measuring the tooth thickness
at a specified position on the tooth.
•The gear tooth vernierhas two vernierscales. The
vertical vernierscale is used to set the depth (d)
along the pitch circle from the top surface of the
tooth at which the width (w) has to be measured.
While the horizontal vernierscale is used to
measure the width (w) of the teeth.

74. •Considering one gear tooth, the theoretical
values of w and d can be found out which may
be verified by the instrument.
•As shown in the figure , w is a chord ADB, but
tooth thickness is specified as an arc distance
AEB. Also the depth d adjusted on the
instrument is slightly greater than the
addendum CE", width w is therefore called
chordalthickness and d is called the chordal
addendum.
W=AB=2AD
WKT, θ=360/4N,
Where N= number of teeth.