Profile Measurement of Gears

-Definition of involute gear profile
-Form and quality requirement of gears
-Contact & noncontact methods for gear profile measurement

1. PROFILE MEASUREMENTS OF GEARS EFE BERKAY GÜVEN BSc . Mechanical Engineer [email protected]

2. SECTIONS Definition of involute gear profile Form and quality requirement of gears Contact & noncontact methods for gear profile measurement EFE BERKAY GÜVEN [email protected] 2

3. 1. DEFINITION OF INVOLUTE GEAR PROFILE Fig . - 1.1 Definition of Involute Profile [1] EFE BERKAY GÜVEN [email protected] 3

4. 1.1 INVOLUTE DEFINITION AND GEOMETRIC PROPERTIES The involute curve is a spiral begin n ing at the base circle and having an infinite n umber of equidistant coils . (Fig. 2 . ) On l y a smaIl portion of the innermost coil has been utilized in practicaI applications . The easiest way to visualize this is by describing the way it can be generated . Fig . - 1.2 The Basic Involute Curve [2] EFE BERKAY GÜVEN [email protected] 4

5. 1.1 INVOLUTE DEFINITION AND GEOMETRIC PROPERTIES The involute curve can be generated by a point on a tightIy held , inextensible and extremely thin thread that is unwound from a fixed circle, called the base circle (Fig. 1.3 a). This method is called the string method . Fig . - 1.3 Methods for generating an involute curve : a) the string method ; b) a beam rolling around a fixed base circle ; c) beam and base circle rolling with each other without slip. [3] EFE BERKAY GÜVEN [email protected] 5

6. 1.1 INVOLUTE DEFINITION AND GEOMETRIC PROPERTIES An involute can also be generated by a beam ro lling ar o und a fixed base circle (Fig. 1.3 b ) or by a beam and base cir cl e Rolling with each other without slip (Fig. 1.3c ). All these principles are used in gear generating and inspection machines . EFE BERKAY GÜVEN [email protected] 6

7. 1.1 INVOLUTE DEFINITION AND GEOMETRIC PROPERTIES Important geometric properties of the involute curve can be derived from its generation. Some of the s e properties are used either for the inspection machine movements or referenced in the inspection re s ults . The line tangent to the base circle , drawn from any point of th e involute, i s alway s perpendicular to the involute curve ( s ee Fig. 1.4 ). The s egment of the tangent line, Q B , is the radiu s of curvature of the involute for the point Q. Points wher e the string separate from the ba s e circle are instantaneous centers of the involu t e curvature. For any point on the involute , arc length AB, contained by the beginning of the involute and the point of tangency , is equal to the length of the line segment QB tangent to the base circle . Fig . - 1.4 Geometric properties of Involute [3] EFE BERKAY GÜVEN [email protected] 7

8. 1.1 INVOLUTE DEFINITION AND GEOMETRIC PROPERTIES Fig . - 1.5 a) Generation of Involute b) involute action [4] EFE BERKAY GÜVEN [email protected] 8

9. 1.2 INVOLUTE FUNCTION Let the involute or polar angle be Ɵ , the pressure angle be Φ , and the roll angle be ε . Then let us assume for simplicity t hat the base radius equals 1 unit of linear measurement. In this case, the length of an arc equals the ang ular measurement using radians as measuring units . Fig . - 1.6 Geometric properties of Involute [3] EFE BERKAY GÜVEN [email protected] 9

10. 1.2 INVOLUTE FUNCTION Therefore, = ε - Φ , where ε = arcAB = Segment BQ = OB.tan ( Φ ) = 1.tan( Φ ) = tan( Φ ). The involute function can be derived by replacing ε with its function of Φ : = tan( Φ )- Φ   Fig . - 1.6 Geometric properties of Involute [3] EFE BERKAY GÜVEN [email protected] 10

11. 1.2 INVOLUTE FUNCTION M ost analytical gear inspection machines use these involute geometry properties: • Length of roll QB equals t h e length of ar c of ro ll AB. • The line tangent to the base circle is always perpendicular to the involute curve. EFE BERKAY GÜVEN [email protected] 11

12. 2. FORM AND QUALITY REQUIREMENTS OF GEAR SURFACES EFE BERKAY GÜVEN [email protected] 12

13. 2.1 QUALITY CLASSIFICATION Commercial Gears : This is the least precise gear group. Applications are broad and varied, largely in competitive consumer products industrial equipment. These gears are produced by methods favoring high Production and low cost. Sizes range from small to very large and encompass both coarse and fine pitches. Precision Gears : Closer control of gear function and performance is provided by this gearing. Application and demand is more limited than for the commercial class. The instrument field is largest user of these gears, but many precision power gears are components in machine tools, aircraft engine drives, and turbines. Fabrication requires quality machines, good procedures, and sometimes secondary refining processes such as grinding or shaving. Ultraprecision Gears : This classification is an extension of the precision class and represents gears which have the best quality. Applications are limited to high-quality instruments, special control systems and computers, and military navigation and fire control systems. Fig . - 2.1 Tolerance chart for gearing [5] EFE BERKAY GÜVEN [email protected] 13

14. 2.1 MEASUREMENT OF GEAR ACCURACY Gear metrology refers to a special branch of metrology as relevant to gear accuracy, gear measurement techniques, and instruments. It usually requires specialized training and expertise to perform adequately. The main objectives of gear accuracy measurement are as follows: Check the compatibility/level of gear accuracy with the specified tolerances before actual use, i.e., to assure required accuracy and quality. Provide an insight into the performance of the gear manufacturing process including the setup of the gear making machine tools, condition of the gear cutting tools, machine tool control, and basic machining practices. Determine the distortions caused by possible heat treatment to facilitate corrective action. Minimize overall cost of manufacture by controlling rejection and scrapping. The gear accuracy or quality may then be described by a single number that indicates how closely it complies with an appropriate acceptance standard. EFE BERKAY GÜVEN [email protected] 14

15. 2.1 MEASUREMENT OF GEAR ACCURACY Gear accuracy refers to how closely its main geometric features resemble the theoretical design. Significant gear metrology parameters that are used to quantify gear accuracy may be divided into two major classes. Dimensional or macro geometry parameters. Micro geometry parameters. Inaccuracy or errors in the micro- and macro geometry of a gear causes deviation from the ideal motion transmission conditions. In other words, the level and amount of deviations/errors in these parameters govern the functional performance of gears. EFE BERKAY GÜVEN [email protected] 15

16. 2.1.1 MACRO GEOMETRY PARAMETERS It could be argued that the most significant macro geometry parameter of a gear is the tooth thickness . The tooth thickness is generally defined as the length of arc of the pitch circle between opposite faces of the same tooth, i.e., the thickness of a gear tooth along the pitch circle. Fig . - 2.2 Macro Geometry [5] EFE BERKAY GÜVEN [email protected] 16

17. The various measurement methods can lead to slightly different tooth thickness results on any given gear. Variations in profile, pitch, helix, runout, and measurement location will have different effects depending on the measuring method employed, see Table. A precise prediction of how these variations impact the measurement result cannot be made. These variations cannot be separated from the measurement of tooth thickness. Therefore, a precise prediction of a measurement result from one method in relation to another method cannot be accurately made, although the different measuring methods will usually be reasonably consistent. Table – 2.1 Affect of Tooth Thickness [5] EFE BERKAY GÜVEN [email protected] 17

18. 2.1.2 MICRO GEOMETRY PARAMETERS The two major classes of microgeometry parameters are form parameters and location parameters . The former involves the shape of the teeth while the latter is associated with the actual teeth positioning. Significant form parameters are profile and lead , whereas pitch and runout are significant as far as location parameters are concerned. The number and magnitude of errors in these microgeometry parameters quantifies the quality of gears and may significantly affect their functional performance. Deformation and inaccurate clamping of the workpiece and tool, form defects of the cutter, vibration in the machine tool, errors in the machine tool axis, etc. are notable causes of errors in microgeometry parameters. In general, the assignment of gear quality grades are a function of the severity of the form and location errors. EFE BERKAY GÜVEN [email protected] 18

19. 3 Fig . – 2.3 Micro Geometry of Gears [5] EFE BERKAY GÜVEN [email protected] 19

20. 2.1.3 QUALITY PARAMETERS OF GEARS Fig . – 2.4 Quality Parameters of Gears [5] EFE BERKAY GÜVEN [email protected] 20

21. Fig . – 2.5 Quality Parameters of Gears [5] EFE BERKAY GÜVEN [email protected] 21

22. Fig . – 2.6 Quality Parameters of Gears [5] EFE BERKAY GÜVEN [email protected] 22

23. 2.1.4 THE K-CHART METHOD OF PROFILE EVALUATION The K-chart is probably the most widely used technique for qualifying or disqualifying a gear, T h e K-chart is a simple appraisal for deciding whether or not the gear profile is within the spec ification . Fig . – 2.7 Quality Parameters of Gears [3] EFE BERKAY GÜVEN [email protected] 23

24. 2.1.4 THE K-CHART METHOD OF PROFILE EVALUATION However, it is important to note that the K-chart is no t a good tool for analyzing the source of a proble m . It is only a go/no-go gage which tells whether the profile is good or bad . W hen a gear does not fit the K-chart, a more detailed analysis must be conducted in order to find and eliminate the s ource of the problem; e.g., total error must be broken down into the slope and form components. EFE BERKAY GÜVEN [email protected] 24

25. 2.1.4 THE K-CHART METHOD OF PROFILE EVALUATION Despite its seeming simplicity, the K chart can become a matter of controversy. Many companies-and s ometimes different people within the same company differ about how to interpret a K-chart. For example, is the tracing in Fig . 2.7 inside or outside the K-chart tolerance? EFE BERKAY GÜVEN [email protected] 25

26. 2.1.4 THE K-CHART METHOD OF PROFILE EVALUATION The answer depends on which interpretation method is used.An inspection tracing could be justified to a `` plus `` material condition as shown on the left of the figure or a `` minus `` as shown on the right.Sometimes , K- chart bands are defined with more than three points.This opens up a further proliferation of evaluations . Fig . – 2.8 A - K cha rt with more than, three points. [3] EFE BERKAY GÜVEN [email protected] 26

27. 2.1.4 THE K-CHART METHOD OF PROFILE EVALUATION Some people may justify the high point located anywhere between SAP and EAP, as shown on the right of Fig . 2.8.But some may use a specific range of roll angle for justifying the high point.An example shown in Fig . 2.8, where a middle portion of the tracing is used for justifying a high point of the involute.As a result , the same tracing could be considered as outside ( left ) or inside ( right ) a K- chart . Fig . – 2.8 A - K cha rt with more than, three points. [3] EFE BERKAY GÜVEN [email protected] 27

28. 2.1.5 GEAR TOLERANCES AND STANDARDS In order to achieve a closer tolerance thereby ensuring high functional performance of the gears, gear fabrication should be more precise. This inevitably results in increased manufacturing cost. To achieve acceptable quality with tight tolerances, the gears have to be sent for post-finishing treatments, especially when fabricated by conventional processes. EFE BERKAY GÜVEN [email protected] 28

29. 2.1.5 GEAR TOLERANCES AND STANDARDS Various international standards exists that provide different quality level/grades for all types of gears by comparing their deviations from the tolerance specified as for each quality level. The quality grade is selected based upon the functional requirement of the gear. The manufacturing techniques and process is then chosen to achieve the tolerance specified for that grade. EFE BERKAY GÜVEN [email protected] 29

30. 2.1.5 GEAR TOLERANCES AND STANDARDS The American Gear Manufacturers Association (AGMA) standard is an example of such an international standard. They are developed by the AGMA and approved by the American National Standards Institute (ANSI). The current AGMA standards are as follows: EFE BERKAY GÜVEN [email protected] 30

31. 2.1.5 GEAR TOLERANCES AND STANDARDS These standards cover tolerances and measuring methods. These are the current new standards that replaced the older standards ANSI/AGMA 2000- A88 (for spur and helical gears), and AGMA 390.3a (for bevel and worm gears). Other important international standards are also widely used. These include the German standards DIN 3962 and 3963 for spur and helical gears and DIN 3965 for bevel gears ; Japanese standards JIS B 1702 for spur and helical gears; and JIS 1704 for bevel gears ; International Standards Organization ISO 1328 , British standards BS 436. EFE BERKAY GÜVEN [email protected] 31

32. 2.1.5 GEAR TOLERANCES AND STANDARDS Quality is the characteristic properties of a gear distinguishing the nature of its manufacturing tolerances , Gear quality For a description of the application of gear tooth quality, Variation is the measured plus or minus change from the specified value, see below figure. Fig . – 2.9 Variation . [5] Fig . – 2.10 Variation . [5] EFE BERKAY GÜVEN [email protected] 32

33. 2.1.5 GEAR TOLERANCES AND STANDARDS Allowable variation is the permissible plus or minus deviation from the specified value, see side figure. Tolerance is the amount by which a specific dimensions is permitted to vary. The tolerance is the difference between the maximum and minimum limits and is an absolute value without sign, see below figure. Fig . – 2.11 Variation . [5] EFE BERKAY GÜVEN [email protected] 33

34. 2.1.5 GEAR TOLERANCES AND STANDARDS The manufacturer or the purchaser may wish to measure one or more of the geometric features of a gear to verify its accuracy grade. A gear which is specified to an AGMA accuracy grade must meet all the individual tolerance requirements applicable to the particular accuracy grade and size as noted in tables. EFE BERKAY GÜVEN [email protected] 34

35. 2.1.5 GEAR TOLERANCES AND STANDARDS EFE BERKAY GÜVEN [email protected] 35

36. 2.1.6 EVALUATION TO PROFILE ERRORS EFE BERKAY GÜVEN [email protected] 36

37. 2.1.7 FACTORS INFLUENCING GEAR QUALITY Common variables that influence all processes Hob , shave , roll , broach , tool sharpening and measurement Workpiece spindle tooling Axial runout or wobble Radial runout or eccentricity Repeability of mounting accuracy Tool spindle and bearings Radial and Axial Runout Backlash - Tool maintenance and tool mounting EFE BERKAY GÜVEN [email protected] 37

38. 3. CONTACT & NONCONTACT METHODS FOR GEAR PROFILE MEASUREMENT EFE BERKAY GÜVEN [email protected] 38

39. 3.1 BASIC INSPECTION TERMS Runout (Radial) - The total variation of the radial distance of a gea r’ s teeth from its center (or bore). Runourerrors contribute to gear noise, binding. and additional stress in mating gears. Runout (Sectional) - A condition of radial runout where much of the error occurs in dew teeth and is not evenly distributed over the entire gear. This is a more severe error than evenly distributed run o u t. Runout (Axial) - Also called wobhie or face runout, The total variation ofa gear's teeth along its axis, measured from a reference plane perpendicular to its axis. While in itself not detrimental, it is almost always accompanied by lead variation, which causes excessive stress, noise. and possible binding in mating gears. EFE BERKAY GÜVEN [email protected] 39

40. 3.1 BASIC INSPECTION TERMS Lead - The axial advance of a screw thread (or gear tooth) in one turn (revolution, 360°). Lead Error - The difference between the theoretical lead trace and the actual lead trace. U sually measured from one end of the tooth to the other, normal to the theoretical lead trace. Contributes t o end-of-tooth contact with the mating gear, causing possible noise, surface crushing , binding, and early failure. EFE BERKAY GÜVEN [email protected] 40

41. 3.1 BASIC INSPECTION TERMS Lead Average- The ave r a g e of the lead error of the gears teeth. Usually based on four lead traces taken around the gear at 90 º intervals . Lead Variation - The condition in a gear where some teeth vary in lead. plus and minus, from the average lead. Total Lead Variation - The total amount of lead variation, plus to minus. Usually based on four lead traces taken around the gear at 90 º intervals. Plus Lead, Minus Lead - Plus lead is minus helix angle. Minus lead is plus helix angle . (See Fig. 3. 3 ) EFE BERKAY GÜVEN [email protected] 41

42. 3.1 BASIC INSPECTION TERMS Fig . – 3.1 Uniform , radial , and axial runout [6] EFE BERKAY GÜVEN [email protected] 42

43. 3.1 BASIC INSPECTION TERMS Fig . – 3.2 Types of lead errors [6] EFE BERKAY GÜVEN [email protected] 43

44. 3.1 BASIC INSPECTION TERMS Fig . – 3.3 Charting lead variation caused by face runout - wobble [6] EFE BERKAY GÜVEN [email protected] 44

45. 3.1 BASIC INSPECTION TERMS Involute (Profile) - The curved shape of the gear teeth, usually from the S.A.P. or T.I.F. to the end of the tooth. Involute (P rof ile ) Error - The difference between the theoretical profile and the measured profile.Ca n cause noise, stresses, and early failure in mating gears. Involute (Profile) Average - The average of the profile error the gear's teeth, Usually of four profile traces taken around the gear at 90° intervals . EFE BERKAY GÜVEN [email protected] 45

46. 3.1 BASIC INSPECTION TERMS Involute (Profile) Variation - The total amount of profile variation, plus to minus. Usua ll y of four profile traces taken around the gear at 90° intervals. Total Involute (Profile) Variation - The total amount of profile variati o n, plus to minus. Usually of four profile traces taken around the gear at 90° intervals Plus Involute, Minus Involute - Plus involute is plus material a t tip of gear. Minus involute is minus material at tip of gear.(See Fig. 3. 4) Spacing - The measured distance between corresponding points on adjacent gear teeth. EFE BERKAY GÜVEN [email protected] 46

47. 3.1 BASIC INSPECTION TERMS Spacing Variation (Tooth to Tooth) - The difference between any two adjacent measurements of spacing. Can contribute to noise, stress, and early failure. Pitch - The theoretical distance between corresponding points on adjacent teeth, Pitch Variation (Error) - The difference between the theoretical pitch and the measured spacing EFE BERKAY GÜVEN [email protected] 47

48. 3.1 BASIC INSPECTION TERMS Index - The theoretical angular position of teeth about an axis. Index Variation (Error) - The displacement of any tooth from its theoretical position relative to a datum tooth. Fig . – 3.4 Charting involute variation on consecutive teeth [6] EFE BERKAY GÜVEN [email protected] 48

49. 3.1 BASIC INSPECTION TERMS Angular Velocity Error (Variable Velocity)- A tooth positioning error in a gear which was cut with runout. Subsequent operations (shaving, rolling) are unable to remove this runout, as teeth are not diametrically opposite, through the correct center ..These subsequent operations tend to mask this runout, making this error difficult to find. It can be detected with a specially designed "high P. A." master gear if the gear is helical. It can also be detected with equipment that can check index error or with a "single flank" type gear roller. This type of'error causes the driven gear of a gear set to speed up and slow down in one revolution, causing noise. EFE BERKAY GÜVEN [email protected] 49

50. 3.1 BASIC INSPECTION TERMS Fig . – 3.6 Tooth-to-tooth spacing [6] Fig . – 3.5 Angular Position of the teeth [6] EFE BERKAY GÜVEN [email protected] 50

51. 3.2 Universal gear measuring instruments (GMI) Gears are measured using CMMs or special mechanically or CNC-controlled gear measuring instruments (GMI). The devices differ with respect to the methods of measurement applied, the measurement strategy and the software used for the evaluation of the measured data. Fig . – 3.6 GMI Gear Measuring Instruments [7] EFE BERKAY GÜVEN [email protected] 51

52. 3.2 UNIVERSAL GEAR MEASURING INSTRUMENTS (GMI) Mechanically controlled GMI, which are partially still in use today, generate the movements of the probe system with respect to the gear by mechanical elements according to the generation principle of involute or helix. The basic involute motion originates from a rolling of a straight bar on a base circle disc. For helix measurements the motion consists of a linear axial displacement of the probe, superimposed to a rotation around the gears axis (i.e. A screw motion). EFE BERKAY GÜVEN [email protected] 52

53. 3.2 UNIVERSAL GEAR MEASURING INSTRUMENTS (GMI) On CNC-controlled GM I s, which are exclusively offered today, numerically controlled drives and an appropriate control software presets the superimposed travels of the measuring axes, registered and controlled by linear and angular scales within the axes. The devices usually have two or three linear axes and one rotation axis. The alignment of the gear to be inspected and the determination of its positions can be performed both mechanically or by calculation . Fig . – 3.7 CNC Gear Inspection [8] EFE BERKAY GÜVEN [email protected] 53

54. 3.3 CMMS FOR GEAR MEASUREMENTS Very soon after introducing CMMs to industrial production it was realized that they were versatile enough to inspect such complicated objects as involute and bevel gears, screws, worms and even gear cutting tools like hobs. In fact, one of the major reasons to provide rotary tables as an additional equipment for CMMs was the measurement of gears, as a gear inspection according to international standards without a rotary table required complex multiple probing styluses EFE BERKAY GÜVEN [email protected] 54

55. 3.3 CMMS FOR GEAR MEASUREMENTS Until the beginning of the 90% conventional CMM probes limited the velocity on gear measurements, even though scanning probe systems were available since the beginning of the 80s. Additionally, due to their serial design principle, these probing heads had to be mounted vertically on the CMM. This reduced the accessibility of helical tooth spaces, because of the preferred vertical clamping of the measuring object , which avoids any bending of the gear shaft. Thus, gear measurements on CMMs required specifically designed probing stylus configurations (as long as an automatic stylus change was not available), leading to a reduced measuring velocity and, sometimes, a reduced accuracy. Fig . – 3.8 Comparison of probing systems a) typical CMM probing system, b) direct coupling of three parallel sensors EFE BERKAY GÜVEN [email protected] 55

56. 3.3 CMMS FOR GEAR MEASUREMENTS Contrasting to this, GMls were equipped with specially designed probing systems oriented perpendicularly to the gear axis ( i . e. in the horizontal direction). Moreover, some of these probing systems offered a swiveling into the normal direction of the gear flank. Together with a specialized numerical control and optimized clamping between centers, GMls instead of CMMs were preferably used in mass gear production. EFE BERKAY GÜVEN [email protected] 56

57. 3.3 CMMS FOR GEAR MEASUREMENTS Since about ten years, completely new and very fast probing systems are available for CMMs, which, due to new design principles, can be mounted on the CMM in any direction . Moreover, some of them offer a swiveling axis , an electronically defined deflection direction or even the ability to measure along electronically prescribed tracks. The latter might be of major advantage for the measurement of complicated flanks, tools, small gaps etc. Fig . – 3.9 Multi-Sensor CMM Gear Measurement EFE BERKAY GÜVEN [email protected] 57

58. 3.3 CMMS FOR GEAR MEASUREMENTS As the special advantages of GM I s compared to CMMs more and more vanish, a clear tendency can be observed, where the two "worlds" of gear and CMM metrology merge, just like the merging of CMM and form testers. Today, devices are available that are equally convenient for gear, form and conventional CMM measurements . On the other hand, modern GM I s are able to take over conventional form and CMM measuring tasks, as they occur on complex measuring objects like layshafts , tools, etc. EFE BERKAY GÜVEN [email protected] 58

59. 3.4 LASER IN MEASUREMENT (NONCONTACT) To use laser in measurement with the integrated camera, we need to arrange the laser pen exactly below the web camera so that it is parallel to the optical axis of the camera’s lens as shown in Fig. 3. Practically, it’s not possible even a minor error would give a huge error at greater distances, but this technique works well at short distances (∼2 m). Fig . – 3.10 Laser and camera-based measurement [10] EFE BERKAY GÜVEN [email protected] 59

60. 3.4 LASER IN MEASUREMENT (NONCONTACT) The reason for this arrangement in this way is to check out the ray diagram. When the laser beam is projected at some surface, it makes a laser dot on it and then image of that laser dot is formed at focal plane of web camera. Assuming that angle of view of camera is parallel, then by applying laws of similar triangles, we get the distance . EFE BERKAY GÜVEN [email protected] 60

61. 3.5 CAMERA IN MEASUREMENT An on-machine vision-based measurement method that can measure 2D contouring/tracking errors of a micro-machining process had been previously developed. An on-machine depth-error measurement method was proposed in this study to fulfill the complete 3D machining error measurement. The method adopts image re-constructive technology and camera pixel correction to provide non-contact measurement capability. To improve the measurement limits due to the pixel resolution and the filler of view of a CCD, a 2-step measurement method with use of a depth model was developed . EFE BERKAY GÜVEN [email protected] 61

62. 3.6 LASER AND CAMERA BASED MEASUREMENT (NONCONTACT) Fig. 3.1 1 shows a distance measurement system for underground unmanned vehicle. It is designed in order to measure the distance between the obstacle and the vehicle itself by acquiring the values in centimeter. As we see in Fig. 3.1 1, the data is calibrated to its actual values in order to reduce the error in measurement. The symbols and arrows are used to explain the measurement procedure. Fig . – 3.11 Geometric analysis of laser beam [11] EFE BERKAY GÜVEN [email protected] 62

63. 3.6 LASER AND CAMERA BASED MEASUREMENT (NONCONTACT) A camera based gear tooth measurement system is proposed in Fig. 3.1 2. There are two cameras integrated to the projector and both are controlled through computer. This system has some limitations as well. Camera needs to have reasonable frame per second (fps) to process the require data. Turn table should move accordingly during measurement in order to measure whole gear teeth. Fig . – 3.12 Geometric analysis of laser beam [11] EFE BERKAY GÜVEN [email protected] 63

64. 3.7 PRINCIPLES OF TRADITIONAL MECHAN I CAL OR CNC INVO LU TE INSPECTION Traditional involute inspection concepts are based on combining the linear motion of the probe carrier and the rotational motion of the gear. T his combined movement generates an involute path for the probe relative to the gear profile. While the probe moves along the path that is tangent to the base circle , the distance equal the length of roll a, and t he gear rotates the angle A (Fig 3.13 ). Fig . – 3.13 Basic me cha nics of an involute inspe c tion process using a probe. [3] EFE BERKAY GÜVEN [email protected] 64

65. 3.7 PRINCIPLES OF TRADITIONAL MECHAN I CAL OR CNC INVO LU TE INSPECTION One important beneficial distinction of the traditional involute inspection method is the unchanging probe contact point throughout the entire probe travel . (Fig. 3.13 ). Thi s unchanging contact point simplifies the inspection process by reduc in g the number of variables their need to be monitored. The probe deflection represents a deviation of the gear profile from the involute curve. If the gear profile is a perfect involute, the probe deflection would stay constant th roughout the entire movement, and the resulting inspection cha rt would be a straight horizontal line. A deviation from this straight line would constitute the profile error. EFE BERKAY GÜVEN [email protected] 65

66. 3.7.1 NON-TRADITIONAL INVOLUTE INSPECTION With the proliferation of coordinate measuring machines, other involute inspection methods have come into being, S ome CMMs use the traditional method, but some don't. Nevertheless, the inspection results are presented in the old fa s hioned way-profile tracing i s scaled proportionately to the length of angle of roll, as shown in the upper section of Fig. 3 . 13. EFE BERKAY GÜVEN [email protected] 66

67. 3.7.1 NON-TRADITIONAL INVOLUTE INSPECTION Machines that do not use t raditional method include . • CMMs without rotary tables. The probe contours a fixed gear . • CMMs with rotary tables, but williout tangential slides. The principle difference between non-traditional and traditional machine is the fact that n on-traditional machine have three axes instead of four. A fewer number of axes makes one part of the machine less expensive; however. İ t also creates an additional burden in another area of the machine . In both non- traditio n al case ,in addition to two moving machine axes, the system has to keep track of one extra variable-the co ntac t point of the probe. Thu s t he machine cannot take full advantage of involute properties for reducing the number of variable to monitor during involute in sp ection . EFE BERKAY GÜVEN [email protected] 67

68. 3.7.1 NON-TRADITIONAL INVOLUTE INSPECTION Fig. 3.14 depicts the involute inspection principle for the machine without a tangential slide. X & Y coordinates of the probe contact are continuously changing as the probe moves from root to tip (See Fig. 3.14 ). To make matters worse, in the case of helical gears. X, Y and Z coordinate of the probe contact are continuously changing. The advantages of non-traditional machines are that they have fewer axes, and their 3-d i mensional probe give them the potential for adding non-gearing inspection capabi li ties to the machine . The di s advantages of us ing these nontraditional machines include the need to, monitor the extra variables during involute inspection, which can make the systems either les accurate or more expensive to develop, and the requirement for 3-dimensional probe s which add a si gnificant co st to the apparatu s . Fig . – 3.14 Basic me cha nics of an involute inspe c tion process using a probe. [3] EFE BERKAY GÜVEN [email protected] 68

69. REFERENCES [1] https://www.tec-science.com/mechanical-power-transmission/involute-gear/calculation-of-involute-gears/ , [2] https://mathimages.swarthmore.edu/index.php/Involute , [3] Involute Inspection Methods and Interpretation of Inspection Results , Yefim Kotlyar , July / August 1997 , [4] Shigley’s Mechanical Engineering Design , Richard Budynas - Keith Nisbett , 2014, [5] Gear Quality Parameters , Bahadır Karba , https://www.slideshare.net/BAHADIRKARBA/gear-quality-parameters , [6] Gear Inspection and Measurement , Robert Moderow , July / August 1992, [7] https://www.youtube.com/watch?v=zOdCG4UQnNM [8] http://hopwoodgears.com/index.php/gear-inspection/ [9] Gear Metrology , G.Goch [10] https://metrology.news/multi-sensor-cmm-gear-measurement-software/ [11] Vision Based Measurement System for Gear Profile, Hazrat ALI- Syuhei KUROKAWA- Kensuke UESUGI 2013 EFE BERKAY GÜVEN [email protected] 69