6. Gear Measurement And Testing

Transcription

1 6. Gear Measurement And Testing

2 Introduction Gears are mainly used for transmission of power and motion. They are used in various automobiles, machines, equipments, electronic systems, etc. We already know that gears are used for decreasing or increasing speed. They are also used for changing direction of motion.

3 Types of Gears Spur Gear : It is a cylindrical gear whose tooth traces are straight lines. Helical Gear : It is a cylindrical gear whose tooth traces are straight helices. Spiral Gear : A gear whose tooth traces are curved lines. Straight Bevel : A gear whose tooth traces are straight line generators of a cone. It is Gear conical in form operating on intersecting axes usually at angles. Worm Gear Pair: The worm and mating worm wheel have their axes non-parallel and nonintersecting.

4 Terminology of Spur Gear

5 Base Circle - It is the circle from which involute form is generated. Only the base circle on a gear is fixed and unalterable. Pitch Circle - It is an imaginary circle most useful in calculations. It may be noted that an infinite number of pitch circles can be chosen, each associated with its own pressure angle. Pitch Circle Diameter (P.C.D.) - It is the diameter of a circle which by pure rolling action would produce the same motion as the toothed gear wheel. This is the most important diameter in gears.

6 Module - It is defined as the length of the pitch circle diameter per tooth. Thus if P.C.D. of gear be D and number of teeth N, then module (m) = D/N. It is generally expressed in mm. Diametral Pitch - It is expressed as the number of teeth per inch of the P.C.D. Diametral Pitch = 1/m = N/D pitch Circular Pitch (CP.) - It is the arc distance measured around the pitch circle from the flank of one tooth to a similar flank in the next tooth..-. CP. = πd/n = πm Addendum - This is the radial distance from the pitch circle to the tip of the tooth. Its value is equal to one module. Clearance - This is the radial distance from the tip of a tooth to the bottom of a mating tooth space when the teeth are symmetrically engaged. Its standard value is m.

7 Dedendum - This is the radial distance from the pitch circle to the bottom of the tooth space. Dedendum = Addendum + Clearance = m m = 1.157m. Tooth Thickness - This is the arc distance measured along the pitch circle from its intercept with one flank to its intercept with the other flank of the same tooth. Normally tooth thickness = C.P./2 = πm/2 But thickness is usually reduced by certain amount to allow for some amount of backlash and also owing to addendum correction.

8 Face of Tooth. It is that part of the tooth surface which is above the pitch surface. Flank of Tooth. It is that part of the tooth surface which is lying below the pitch surface. Pressure Angle It is the angle between path of contact and normal drawn to the line joining centers of base circle. Helix Angle : It is the acute angle between the tangent to the helix and axis of the cylinder on which teeth are cut. Lead Angle : It is the acute angle between the tangent to the helix and plane perpendicular to the axis of cylinder Back Lash : The distance through which a gear can be rotated to bring its non-working flank in contact with the teeth of mating gear.

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10 Analytical Inspection of Gears Gear manufacturing process involves various steps which may need in process inspection. A gear blank, at starting of an operation should be checked for dimensional accuracy of face width, bore, length, diameter, etc. The analytical method of gear involves checking of various parameters of an individual gear. It involves checking concentricity of gear teeth, alignment of each tooth, hardness of gear blank, etc.

11 It also involves the factor that involves accuracy of measurement of these parameter. Analytical method is tedious and it is not preferred by industries because the values of errors in pitch, profile cannot give the error of overall operation of the gear. The analytical method is of useful for students for study and to understand the concept. It will be useful for research and development work in industries and laboratories.

12 Functional Method It involves, mainly checking of gear running with another gear during operation or at actual work. For testing function of gear, master gear is used in combination of manufactured gear. Functional method is used for determining composite errors in vibration, noise during working of gear. If the gear does not satisfy the rolling test, individual or analytical test is carried out. To carry out functional test of the gear, Parkinson gear tester or automating gear rolling machines are used.

13 Rolling Test Rolling test of gears give the composite error analysis of gears. In rolling test, gear to be tested is rolled with the master gear. This test reveals any errors in tooth form, pitch and concentricity of the pitch line. This is the fact, economical and accurate method of gear testing. Results of rolling test of gears are carefully observed and conclusions are drawn regarding the angular rotation per teeth, eccentricity as the error, individual tooth error, etc.

14 Measurement of tooth thickness by gear tooth vernier calliper

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16 It is used to measure the thickness of gear teeth at the pitch line or chordal thickness of teeth and the distance from the top of a tooth to the chord. The thickness of a tooth at pitch line and the addendum is measured by an adjustable tongue, each of which is adjusted independently by adjusting screw on graduated bars. The effect of zero errors should be taken into consideration. This method is simple and inexpensive.

17 However it needs different setting for a variation in number of teeth for a given pitch and accuracy is limited by the least count of instrument. Since the wear during use is concentrated on the two jaws, the calliper has to be calibrated at regular intervals to maintain the accuracy of measurement.

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19 The tooth thickness is generally measured at pitch circle and is, therefore, referred to as pitch-line thickness of tooth. The gear tooth vernier has two vernier scales and they are set for the width (w) of the tooth and the depth (d) from the top, at which w occurs. Considering one gear tooth, the theoretical values of w and d can be found out which may be verified by the instrument.

20 In Fig , it may be noted that w is a chord ADB, but tooth thickness is specified as an arc distance AEB. Also the distance d adjusted on instrument is slightly greater than the addendum CE, w is therefore called chordal thickness and d is called the chordal addendum.

21 In the above sketch d is chordal addendum which can be calculated as d = [(N m)/2] [1+(2/N)-cos(90/N)] N Number of teeth M module Tooth thickness can be calculated using gear tooth vernier. By setting d in vertical vernier, horizontal vernier gives w and can be verified by w = N m sin(90/n)

22 Measurement of tooth thickness by Constant Chord Method. In the above method, it is seen that both the chordal thickness and chordal addendum are dependent upon the number of teeth. Hence for measuring a large number of gears for set, each having different number of teeth would involve separate calculations, thus the procedure becomes tedious and timeconsuming one.

23 The constant chord method does away with these difficulties. Constant chord of a gear is measured where the tooth flanks touch the flanks of the basic rack. The teeth of the rack are straight and inclined to their centre lines at the pressure angle as shown in Fig

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25 Also the pitch line of the rack is tangential to the pitch circle of the gear and,- by definition, the tooth thickness of the rack along this line is equal to the arc tooth thickness of the gear round its pitch circle. Now, since the gear tooth and rack space are in contact in the symmetrical position at the points of contact of the flanks, the chord is constant at this position irrespective of the gear of the system in mesh with the rack.

26 The measurement of tooth thickness at constant chord simplified the problem for all number of teeth. If an involutes tooth is considered symmetrically in close mesh with a basic rack form, then it will be observed that regardless of the number of teeth for a given size of tooth (same module), the contact always occurs at two fixed point A and B. AB is known as constant chord.

27 The constant chord is defined as the chord joining those points, on opposite faces of the tooth, which make contact with the mating teeth when the centre line of the tooth lies on the line of the gear centers. The value of AB and its depth from the tip, where it occurs can be calculated mathematically and then verified by an instrument. The advantage of the constant chord method is that for all number of teeth (of same module) value of constant chord is same. In other words, the value of constant chord is constant for all gears of a meshing system.

28 The Base Tangent Method Or David Brown tangent comparator Or Flange Micrometer

29 The purpose of tangent tester is to determine the mean value and variation in base tangent length. It is measured between two parallel measuring surfaces tangential to unlike gear teeth falnk. In this method, the span of a convenient number of teeth is measured with the help of the tangent comparator. This uses a single vernier caliper and has, therefore, the following advantages over gear tooth vernier which used two vernier scales : (i) the measurements do not depend on two vernier readings, each being function of the other.

30 (ii) the measurement is not made with an edge of the measuring jaw with the face. Consider a straight generator (edge) ABC being rolled back and forth along a base circle. The tangent length can be calculated as d = N m cos ø [tan ø ø (pia/2n) + (pia S/N) Where, N Number of teeth M module Ø Pressure angle S No. of teeth between two anvils.

31 Direct values of d are available for different S, N and m. N (Teeth on Gear) S (Teeth to be spanned) 10 to to to to to to The instrument essentially consists of a fixed anvil and a movable anvil. There is a micrometer on the moving anvil side and this has a very limited movement on either side of the setting.

32 The distance is adjusted by setting the fixed anvil at desired place with the help of looking ring and setting tubes. The movable anvil can be also locked by using slip gauges for setting proper calculate distance. Difference of reading which is set and measured can be calculated using micrometer.

33 Parkinson s Gear Tester

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35 The principle of this device is to mount a standard gear on a fixed vertical spindle and the gear to be tested on another similar spindle mounted on a sliding carriage, maintaining the gears in mesh by spring pressure. Movements of the sliding carriage as the gears are rotated are indicated by a dial indicator, and these variations are a measure of any irregularities in the gear under test; alternatively a recorder can be fitted, in the form of a waxed circular chart and records made of the gear variation in accuracy of mesh.

36 Construction One fixed spindle and other movable spindle is mounted on flat base. The movable spindle moves along with base by rolling action on the main base plate as shown in figure. A master gear is mounted on the fixed spindle whereas a gear to be tested is mounted on a movable spindle. The dial gauge is set to note the errors whose pointer touches the floating body.

37 Working When master gear is rotated slowly, a gear to be tested will also get rotation movement because of their meshing. Errors in the manufactured gear cause the gear to move away from the centerline of spindle. When the on test moves, the floating body also moves by the same distance. Because of displacement of floating body, dial gauge gives displacement. The variations in the readings can be observed and platted in the graphical format.

38 Limitations Maximum 300 mm diameter gears can be tested. The floating body is very sensitive and hence readings are to be taken very carefully. Accuracy up to 1µm can be possible while measurement. Only composite errors in the gears can be checked not individual one. Measurement depends upon the master gear.

39 Involute Measurement Involute is a curve plotted by a point on a straight line which rolls around a circle without slipping. Involute measurement is done by 1) By profile projector 2) By Involute measuring machine

40 Involute Measuring Machine

41 The basic principle of working is that if a straight edge is rolled around a base circle without slipping, the stylus of the dial gauge attached as above, gives a involute. The gear to be tested is mounted on a mandrill. The circular disc of the same size as that of PCD is also to be mounted on the same mandrill. The straight edge on the disc, which is tangent rolls around the disc, generates a involute and the variation is recorded by dial gauge. A electronics plotter can be used instead of dial gauge for recording purpose.

42 Pitch Measuring Machine

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44 This instrument has three tips. One is the fixed measuring tip, other one is the sensitive tip whose position can be adjusted by a screw and the further movement of it is transmitted through a leverage system to the dial indicator and the third tip is the supplementary adjustable stop which is meant for the stability of the instrument and its position can also be adjusted by a screw. The distance between the fixed and sensitive tip is set to be equivalent to the base pitch of the gear with the help of slip gauges.

45 The properly set-up instrument is applied to the gear so that all the three tips contact the tooth profile. The reading on dial indicator is the error in the base pitch.

46 Procedure of Measurement The distance between tip (1) and (2) is set to a standard using slip gauges when dial gauge is showing a readings considered as zero. The machine is then applied to the gear under test. All three tips are made contact to gear under test. Reading of dial indicator shows the variation in pitch. Repeat the procedure for next pair of gear tooth.

47 Errors in Gear Following are various gear errors that can be checked while analytical inspection is carried out. 1) Profile 2) Spacing 3) Pitch 4) Run out 5) Gear Tooth Thickness 6) Lead 7) Backlash. The Errors are 1) Cumulative pitch error 2) The tooth thickness error 3) Cyclic error 4) Run out 5) Radial Run out 6) Backlash

48 Cumulative pitch error - It is defined as the actual length between corresponding flanks of teeth not adjacent to each other. The tooth thickness error It is the difference in actual tooth thickness and required tooth thickness. Cyclic error - An error occurring during each revolution of the element under consideration. Run out - It is the total range of reading of a fixed indicator with the contact point applied to a surface rotated, without axial movement about a fixed axis.

49 Radial Run out - It is the run-out measured along a perpendicular to the axis of rotation. Backlash It is the play between the matting tooth surfaces i.e. the distance through which a gear can be rotated to bring its nonworking flank in contact to teeth of mating gear. Axial run-out (wobble) - It is the run-out measured parallel to the axis of rotation, at a specified distance from the axis.

50 ? MSBTE QUESTIONS Describe with a neat sketch the use of Vernier gear tooth caliper to measure the chordal thickness of gear tooth on the pitch circle. Describe with neat sketch Parkinson gear tester. Explain principle of measurement of gear tooth thickness using a gear tooth vernier. State and explain any four types of errors in gear. Explain how will you check the involute profile of a spur gear using involute measuring machine.

51 Explain following errors in gears i) Backlash ii) Run out Explain constant chord method for measuring tooth thickness of gear.

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