Screw thread measurements and Gear measurement


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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.

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Screw thread measurements and Gear measurement

  1. 1. 8/20/2014 1Hareesha N Gowda, DSCE, Blore-78
  2. 2. Terminology of screw threads
  3. 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. 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. 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. 6. Screw Thread terminology Pitch Crest Root Flank Thread Angle Pitch line Axis of thread Axial thickness Addendum Dedendum Flank angle Major dia Pitch dia Minor dia EXTERNAL THREAD TERMINOLOGY
  7. 7. Screw Thread terminology  Pitch: The distance from a point on a screw thread to a corresponding point on the next thread measured parallel to the axis.  Lead The distance a screw thread advances in one turn. For a single start threads, lead=pitch, For double start, lead=2xpitch, & so on.  Thread Form: The cross section of thread cut by a plane containing the axis.  Major Diameter: This is the diameter of an imaginary cylinder, co- axial with the screw, which just touches the crests of an external thread or roots of an internal threads. It is also called as ‘Nominal diameter’
  8. 8. Screw Thread terminology  Minor diameter: This is the diameter of an imaginary cylinder, co-axial with the screw which just touches the roots of an external thread or the crest of an internal thread. This is also referred to as ‘root’ or ‘core diameter’.  Effective diameter or Pitch diameter: It is the diameter of an imaginary cylinder coaxial with the axis of the thread and intersects the flanks of the thread such that width of the threads & width of spaces between threads are equal.  Flank: It is the Thread surface that connects crest with root. • Depth of thread: It is the distance between crest and root measured perpendicular to axis of screw.
  9. 9. Screw Thread terminology  Angle of thread: Included angle between sides of thread measured in axial plane.  Helix angle: Angle that the thread makes with plane perpendicular to thread axis.  Flank angle: It is half the included angle of the thread.  Addendum: It is the distance between the crest and the pitch line measured perpendicular to axis of the screw.  Dedendum: It is the distance between the pitch line & the root measured perpendicular to axis of the screw.
  10. 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. 11. Measurement of major diameter The instruments which are used to find the major diameter are by  Bench micrometer Bench micrometer
  12. 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. 13. Measurement by Bench micrometer: Clamp Fiducial Indicator Measuring Anvils Holding centres Micrometer head Supports BENCH MICROMETER
  14. 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 fiducial indicator is used to ensure all the measurements are made at same pressure. The instrument has a micrometer head with a vernier scale 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. 15. Measurement by Bench micrometer: Then the cylinder is replaced by the threaded work piece and the new reading is taken
  16. 16. Measurement by Bench micrometer:
  17. 17. Measurement by Bench micrometer: Holding centre Measuring anvil Holding centre Measuring anvil StandardCylinder ScrewThread Measurement of Major diameter
  18. 18. Measurement of the major diameter of an Internal thread: An indirect approach of measuring internal dia is obtained by obtaining the cast of the Thread. The main art thus lies in obtaining a perfect cast.
  19. 19. Measurement of the major diameter of an Internal thread:
  20. 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. 21. Measurement of Minor diameter
  22. 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. 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. 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. 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. 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. 27. Tool makers microscope:
  28. 28. Tool makers microscope: Lamp Hollow base Collimator lens Base Column Eye piece Optical head Mirror work table with carriage
  29. 29. Tool makers microscope:
  30. 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. 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. 32. Screw pitch gauge
  33. 33. Measurement of screw thread angle (Flank angle)
  34. 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. 35. Two wire method:  The effective diameter can not be measured directly but can be calculated from the measurements made.  Wires of exactly known diameters are chosen such that they contact the flanks at their straight portions.  If the size of the wire is such it contacts the flanks at the pitch line, it is called the ‘best size’ of wire which can be determined by geometry of screw thread.  The screw thread is mounted between the centers & wires are placed in the grooves and reading M is taken.  Then the effective diameter E =T+P where T =M-2d, & P is a value which depends on diameter of wire, pitch & angle of the screw thread.
  36. 36. Two wire method: M M-Dimension over the wire
  37. 37. Two wire method:
  38. 38. Two wire method:
  39. 39. Two wire method:
  40. 40. Two wire method: P AP=OP-OA
  41. 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. 42. Three Wire method
  43. 43. Three Wire method  This method is more accurate than two wire method as it ensures alignment of micrometer faces parallel to the thread axis.  Here, three wires of exactly known diameters are used, one on one side & the two on the other side. The wires may be held in hand or hung from a stand.  From the fig, M=diameter over the wires E= effective diameter (to be found) d= diameter of wires, h=height of wire center above the pitch line, r=radius of wire, H=depth of thread, D=major diameter of the thread.
  44. 44. Three Wire method E M H A B C D  P h E M Dia 'd'  E
  45. 45. Three Wire method 2 cot 22 cosec1dEMOr 2 cot 22 cosec122 2 cot 42 rcosec2EMi.e. 2r2hEMwires,over theDistance 2 cot 42 cosec 2 )( 2 cot 42 H CDand 2 cot 22 cot 2 cosec 22 cosecABAD,ABDetriangl      P P rEr P Pd CDADhFurther PP DEH d theFrom                                       
  46. 46. Three Wire method out.foundbecanEknown,isdasM,ofluecorrect vathefindingAfter above.derivedformulaeusingvaluesaltheoreticwith thecompare then&ypracticallMofvaluethemeasurecanWe P5155.1d3DM 732.1 2 cot,2 2 eccos,60,P6495.0DE 0.6495PthreadofDepththreads,MetricFor thread.theofdiametermajortheisDwhereP605.1d1657.3DM 921.1 2 cotand,1657.2 2 cosec0.64P,-DE 0.64Pthreadofdepth,55thread,WhitworthFor o o              
  47. 47. BEST WIRE SIZE P    A P/2 P/4 Pitch line BEST SIZE OF WIRE B
  48. 48. BEST WIRE SIZE sec P sec P 2D thread.theofpitchtheisPwhere 4 P ABline,pitchon theliesABsinceAlso. 2 secAB2OB2Di.e. )(Dwiresizebestofdia 2 1 wireofradiusOBBut . 2 secAB 2 cos AB 2 -90sin AB OB OB AB 2 -90sinor, OB AB AOBSinOAB,triangleIn the line.pitchat thethreadtheofportionflanklar toperpendicuis OBfiginshownaswords,otherInthread.screwtheofdiametereffectiveor linepitchat thecontactmakeswhichonetheiswiresizebestThe b b b                                  
  49. 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. 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. 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. 52. External and Internal spur Gear…
  53. 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. 54. Helical Gear…
  55. 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. 56. Straight and Spiral Bevel Gears
  58. 58. Forms of Teeth • In actual practice following are the two types of teeth commonly used 1. Cycloidal teeth ; and 2. Involute teeth. Cycloidal Teeth • A cycloid is the curve traced by a point on the circumference of a circle which rolls without slipping on a fixed straight line. • When a circle rolls without slipping on the outside of a fixed circle, the curve traced by a point on the circumference of a circle is known as epi-cycloid. • On the other hand, if a circle rolls without slipping on the inside of a fixed circle, then the curve traced by a point on the circumference of a circle is called hypo-cycloid.
  59. 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. 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.
  62. 62. • 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°.
  63. 63. • 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. • Dedendum circle. It is the circle drawn through the bottom of the teeth. It is also called root circle. Note : Root circle diameter = Pitch circle diameter × cos φ , where φ is the pressure angle.
  64. 64. 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 Pc ,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,
  65. 65. Diametral pitch. It is the ratio of number of teeth to the pitch circle diameter in millimetres. It is denoted by pd. 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 dedendum circles of a gear. It is equal to the sum of the addendum and dedendum.
  66. 66. 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.
  67. 67. Comparison Between Involute and Cycloidal Gears • In actual practice, the involute gears are more commonly used as compared to cycloidal gears, due to the following advantages : Advantages of involute gears • The most important advantage of the involute gears is that the centre distance for a pair of involute gears can be varied within limits without changing the velocity ratio. This is not true for cycloidal gears which requires exact centre distance to be maintained. • In involute gears, the pressure angle, from the start of the engagement of teeth to the end of the engagement, remains constant. It is necessary for smooth running and less wear of gears. But in cycloidal gears, the pressure angle is maximum at the beginning of engagement, reduces to zero at pitch point, starts decreasing and again becomes maximum at the end of engagement. This results in less smooth running of gears. • The face and flank of involute teeth are generated by a single curve where as in cycloidal gears, double curves (i.e. epi-cycloid and hypo-cycloid) are required for the face and flank respectively. Thus the involute teeth are easy to manufacture than cycloidal teeth. In involute system, the basic rack has straight teeth and the same can be cut with simple tools. • Note : The only disadvantage of the involute teeth is that the interference occurs with pinions having smaller number of teeth. This may be avoided by altering the heights of addendum and dedendum of the mating teeth or the angle of obliquity of the teeth.
  68. 68. 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.
  69. 69. 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. • The tip of tooth on the pinion will then undercut the tooth on the wheel at the root and remove part of the involute profile of tooth on the wheel. This effect is known as interference, and occurs when the teeth are being cut. • In brief, the phenomenon when the tip of tooth undercuts the root on its mating gear is known as interference. •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.
  70. 70. • 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.
  71. 71. • 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 vernier caliper. • The gear tooth thickness can be conveniently measured by a gear tooth vernier as 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 vernier has two vernier scales. The vertical vernier scale 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 vernier scale is used to measure the width (w) of the teeth.
  72. 72. • 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 chordal thickness and d is called the chordal addendum. W=AB=2AD WKT, θ=360/4N, Where N= number of teeth.