gear measurement

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HELPFUL FOR SUBJECT MECHANICAL MEASUREMENT CHAPTER GEAR MEASUREMENT TO MECH. ENGG ,STUDENTS

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MECHANICAL MEASUREMENT & METROLOGY GEAR MEASUREMENT METHODS: 

By: Samir Jariwala MECHANICAL MEASUREMENT & METROLOGY G EAR MEASUREMENT METHODS

DEFINITION: : 

“A gear is a toothed wheel with the teeth cut on the periphery of a cylinder or a cone commonly used to transmit power or motion, from one shaft to another, without slip.” DEFINITION: Pinion Gear Gear Drive

CLASSIFICATION OF GEARS:: 

According to the position of shaft axis: According to the peripheral velocity of the gears. According to the type of meshing gears. CLASSIFICATION OF GEARS:

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GEARS Parallel Shaft Intersecting Shaft Non parallel & non intersecting shaft Spur gears Helical gears Rack & pinion Bevel gears Worm & worm wheel Straight bevel gears Spiral bevel gears Spiral gears

According to the peripheral velocity of the gears: : 

Low velocity gears: Low velocity gears having peripheral velocity less than 3 m/s. Medium velocity gears : These gears having peripheral velocity between 3 to 15 m/s. High velocity gears : These gears having peripheral velocity more than 15 m/s. According to the peripheral velocity of the gears:

According to type of meshing gears:: 

External gears : In these gears, the teeth of gears mesh externally with each other. Internal gears: In these gears, the teeth of gears mesh internally with each other. According to type of meshing gears:

TYPES OF GEARS: 

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

Spur gears:: 

“If teeth of the gear wheels are parallel to the axis of wheel, the gears are called spur gears.” Spur gears are used for transmitting power between two shafts when the axis of the driving and driven shafts are parallel and co-planer. Spur gears: Wheel of gear Pinion Spur Gear

External and Internal spur Gear…: 

External and Internal spur Gear…

Helical gears:: 

In helical gears, teeth are cut in the form of the helix around the gear. Their teeth are not parallel to the shaft axis. The helical gears run smoothly and more quietly at high speeds and curvilinear contact of gear teeth giving gradual engagement. Helical gears are used for transmitting power between two parallel, non-parallel, non intersecting shafts. Helical gears:

Rack and Pinion: : 

Rack is a rectangular bar consist of a series of straight teeth cut on it. Theoretically, rack is a spur gear of infinite diameter. The rack is mesh with another small gear known as 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 The rack and pinion drive is used to convert rotary motion into linear motion. Rack and Pinion: Rack Pinion

Bevel gears:: 

Teeth of the bevel gears are cut on conical surfaces. The axis of two moving gears are inclined in the bevel gear. Bevel gear teeth are varying in cross section along the tooth width. In most of cases, two bevel gears have their axes at right angle and are of equal sizes, called miter gears. Bevel gears are used for transmitting power between two shafts, when the axis of the two shafts are inclined and intersects each other. Bevel gears:

Types of Bevel gears:: 

Straight bevel gear: In straight bevel gears the teeth are formed on cones, and they are parallel to the axis of the gear. Types of Bevel gears: Bevel pinion Bevel gear Straight bevel gear

CONT….: 

Spiral bevel gear : In a spiral bevel gear, the teeth are formed at an angle with respect to its axis. The contact between two meshing teeth is gradual and smooth from start to end, as in case of helical gears. CONT…. Spiral bevel gear

Spiral gears:: 

The teeth of spiral gears are same as helical gears and it cut along helical curved path. In spiral gear, there is a point contact while curvilinear contact in case of helical gear drive. Spiral gears are used to transmit power between two non-parallel, non intersecting shafts. Spiral gears: Spiral gear

Worm and worm wheel:: 

Worm gears are suitable for transmission of power when a high velocity ratio is required. worm gears are used for transmitting power between two shafts having their axes at right angles and non-coplanar. Worm and worm wheel: Worm Worm Wheel

Gear Terminology:: 

Gear Terminology:

NOMENCLATURE OF SPUR GEARS: 

NOMENCLATURE OF SPUR GEARS

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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°.

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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.

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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 D 1 and D 2 are the diameters of the two meshing gears having the teeth T 1 and T 2 respectively, then for them to mesh correctly,

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Diametral pitch. 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 dedendum circles of a gear. It is equal to the sum of the addendum and dedendum.

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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.

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The analytical inspection of gears consists in determining the following teeth elements in which manufacturing errors may be present. MEASURMENT & TESTING OF SPUR GEAR The tooth thickness is defined the length of the arc of the pitch circle between opposite faces of the same tooth.

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1. RUNOUT Total variation of the distance between a surface of revolution and a reference surface measured perpendicular to the surface of revolution is called Runout . It may be checked with the help of gear testing machine and a master gear. The runout is characterised by periodic variation in sound during each revolution and by tooth bearing shifting progressively around the gear from heel to toe and toe to heel.

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2. PITCH MEASURMENT

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A.TOOTH TO TOOTH PITCH MEASUREMENT (STEP BY STEP METHOD) In this method, variations in pitch between successive teeth of the gears are measured. Base pitch measuring instrument used for measurement of base pitch errors. The portable hand-held instrument has three tips. It’s position can be adjusted by a screw and the further movement of it is transmitted through a leverage system to the dial indicator It is meant for the stability of the instrument and its position can also be adjusted by a screw .

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BASE PITCH MEASURING INSTRUMENT 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. The properly set up instrument is applied to the gear so that all the tips contact the tooth profile. The reading on dial indicator is the error in the base pitch.

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B. DIRECT ANGULAR MEASUREMENT It is the simple method of determining pitch errors. In this method, two dial gauges on adjacent are used with the gear mounted at centres. The gear is indexed through successive pitches to give a constant reading on dial A. Any change in the reading on dial B indicates the pitch errors. The actual errors can be determined by deducting the individual reading on dial B from the mean of the reading.

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3. PROFILE CHECKING The portion of tooth flank between the outside circle and the specified from circle of diameter approximately equal to pitch circle diameter minus twice the dedendum is called Profile checking The following methods are used to check the involute profile of a spur gear

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(A) OPTICAL PROJECTION METHOD In this method, optically magnified profile of the gear is compared against a master diagram or template may be used on the gears with sharp edges. This method is quick and suitable for checking the profile of small thin instrument gears.

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(B) USING INVOLUTE MEASUREMENT MACHINE This machine is designed for checking the involute profiles of the spur and other gears. If a straight edge is rolled around a base circle without slipping, the stylus of the dial gauges attached to the straight edge would traverse a true involute. A ground circular disc having exactly the same diameter as the base circle of gear under test and along with the gear to be tested are mounted on the mandrel. The straight edge of the instrument is brought in contact with the base circle of the disc. As the gear along with disc are rotated, the straight moves over the disc without slip.

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The stylus of the dial gauges is brought in contact with a tooth profile. When the gear and disc are rotated, the stylus is slided along the involute curve . The deviation of the tooth profile from the correct involute I indicated by a dial indicator accuracy 0.0001mm. A master involute template is also provided with the machine for setting and calibration of the machine.

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(C) USING DIVINDING HEAD AND HEIGHT GAUGE This method is used for large and when special purpose involute measuring equipment is not available. In this method , the gear is rotated through small angular increments and the readings of the vertical measuring or the height gauges are compared with the theoretically calculated values at about five to ten places along the tooth flank, and the required increments of angular setting may be established by trail. This method is very time consuming but is best suited for calibration of master involute, so it is used only for very precision components.

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The measured values of the vertical setting may be calculated as follow. (a)Initial set up (b) (c) (d) L1-L2= rb θ 1-rb θ 2 L1-L2= rpcos φ ( θ 1- θ 2) Similarly, L3-L1= rp cos φ ( θ 3- θ 1)

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4.MEASUREMENT OF CONCENTRICITY A concentricity of teeth should be checked to ensure that the set up and equipments is in good order. If teeth are not concentric then fluctuating velocity will be noticed on the pitch line while transmitting motion. Tooth concentricity can be checked by:

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5. ALIGNMENT CHECKING If alignment of gear tooth is not proper, the load will not be distributed evenly over its face. The alignment of gear with respect to the axis of mounting may be checked by placing a parallel bar between the gear teeth. The gear being mounted between centres. Height readings are taken at the two ends of the bar. Differences in the readings of either end of the parallel bar will indicate presences of misalignment.

The tooth thickness is defined the length of the arc of the pitch circle between opposite faces of the same tooth. Following are the various methods of measuring the gear tooth thickness: : 

The tooth thickness is defined the length of the arc of the pitch circle between opposite faces of the same tooth . Following are the various methods of measuring the gear tooth thickness: Using gear tooth vernier caliper. Base tangent method. Constant chord method

GEAR TOOTH VERNIER CALLIPER:: 

GEAR TOOTH VERNIER CALLIPER:

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A gear tooth vernier is widely used to measure the tooth thickness . As the tooth thickness varies from top to the bottom, any Instruction for measuring on a single tooth must : Measure the tooth thickness at a specified position on the tooth .. Fix that position at which the measurement is taken . The gear tooth vernier caliper is instrument similar to the ordinary vernier caliper but having a second beam at right angles to the main beam. This additional beam carries a tongue sliding between the jaws, which can vertically slid up & down so that when it rests on the top of a tooth the tips of the jaws are at the correct distance from the tooth flanks for the required measurement. The reading on the horizontal vernier scale gives the value of chordal thickness (w) & the reading on the vertical vernier scale gives the value of chordal addendum (h). These measured values are then compared with the calculated values. GEAR TOOTH VERNIER CALLIPER:

The value of width (w) and addendum height (h) can be obtained as follows: From fig., AB=w, and CE=h : 

The value of width (w) and addendum height (h) can be obtained as follows: From fig., AB=w , and CE=h

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Now , AD+DB=w But, AD=DB W=2*AD ……..( 1) From ∆ADO, SinѲ =AD/AO AD=AO*SinѲ=RSinѲ Angle AOD=Ѳ=360/( 4N), Where N=number of teeth Ѳ=90/N, AD=R*sin (90/N ) Substituting value of AD in eq.-(1 ), W=2*Rsin (90/N) ……..( 2 )

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Module,m=Pitch Circle Diameter/Number of teeth M=2R/n R = (N*m)/ 2 Substituting value of R in eq.-(2) W=2*(N*m/2)*sin (90/N ) Width, w=N*m sin (90/N) ……..( 3 ) The height h , can be calculated as follow : From the fig, OC=OE+EC But OE=R=N*m/2, and EC=addendum=module=m OC= (N*m/2) +m ……..( 4) Now, OC=OD+DC ……..( 5)

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From ∆ADO, CosѲ=OD/R OD=RcosѲ OD= (N*m/2)*cos (90/N) ……..( 6 ) Substituting value of OC & OD in eq.-(5 ), (N*m/2) +m =( N*m/2)*cos (90/N) + DC But DC=h DC=h =( N*m/2) + m- (N*m/2)*cos (90/N ) Depth, h= (N*m/2) [1+ (2/N) – cos (90/N)]

Limitations:: 

Limitations: Accuracy is limited by the least count of instrument, the vernier itself is not reliable closer than 0.05 mm or perhaps 0.025 mm with practice. The measurements depend on 2 vernier readings, each of which as a function of the other. The wear during use is concentrated on the jaws, the caliper has to be calibrated at regular intervals to maintain the accuracy of measurement.

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In this method,the span of convenient number of teeth is measured with the help of a David brown tangent comparator. This 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. The base tangent length is adjusted by setting the fixed anvil at a desired place with the help of locking ring and setting tubes. Base Tangent Method:

Base Tangent Method: : 

Base Tangent Method :

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The advantage of this method is that, it depends only on one vernier reading unlike gear tooth vernier calliper where we require two vernier reading. The number of teeth over which measurement is to be made for a particular gear is selected from gear hand book.

From fig. 5.14, Base tangent length =arc AB+arc BC =arc AB+S*∏mcosø BASE TANGENT LENGTH= N*mcosø [(tanø-ø)+ ∏/2N+S ∏/N] Where , N= number of teeth m= module ø = pressure angle in radian S= number of tooth spaces in base tangent length : 

From fig. 5.14, Base tangent length =arc AB+arc BC =arc AB+S*∏ mcosø BASE TANGENT LENGTH= N* mcosø [( tanø -ø)+ ∏/2N+S ∏/N] Where , N= number of teeth m= module ø = pressure angle in radian S= number of tooth spaces in base tangent length

CONSTANT CHORD METHOD:: 

CONSTANT CHORD METHOD:

Definition: A constant chord is defined as the chord joining those points on opposite faces of tooth which make contact with the mating teeth when centre line of the tooth lies on the line of gear centers. : 

Definition: A constant chord is defined as the chord joining those points on opposite faces of tooth which make contact with the mating teeth when centre line of the tooth lies on the line of gear centers. Description: As the number of teeth varies in the gear tooth vernier calliper method the value of tooth thickness ‘w’ and the depth ‘d’ can be changed. Constant chord of gear is measured where the tooth flanks touch the flank of the basic rack. The teeth of the rack are straight and inclined to their center lines at the pressure angle. When the gear rotates and all the teeth come in the contact with the rack then for the given size of tooth, the contact always takes place at point ‘A’ and ‘B’ i.e. distance AB remains constant. And hence called as……“CONSTANT CHORD”…

Derivation for calculating the chord length ‘AB’:: 

From fig. l(DE ) = l(DF) = Arc DG And Arc DG = ¼(circular pitch) = ¼(pi)( m) l(DE) = l(DF) = ¼(pi)(m) Now consider ; Triangle DAE = y; Cos y = AD/DE So, AD = DE cos y AD = ¼(pi)(m)( cos y) Now consider ; Tri DCA = y; Cos y = CA/AD CA = AD cos y CA = ¼(pi)(m)( cos y)( cos y) = cos^2y(pi)(m)\4 Derivation for calculating the chord length ‘AB ’:

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From fig. Chord length AB = 2(l)(CA) = 2(cos^y)(pi)(m)/4 = (pi)(m)(cos^y)/2 Depth H can be calculated as follow, From Tri DAC, Sin y = CD/AD CD = Ad sin y = ¼(pi)(m)( cos y)(sin y) Now; GD = GC+CD Where GD = addendum = module GD = m And CD = ¼(pi)(m)( cos y)(sin y) And GC = depth = h Therefore; m = h+(1/4)(pi)(m)( cos y)(sin y) h = m-(1/4)(pi)(m)( cos y)(sin y) h = m[1-(1/4)(pi)( cos y)(sin y)]

Principle: 

A master gear is mounted on a fixed vertical spindle and the gear to be tested on another similar spindle mounted on a sliding carriage. These gears are maintained in mesh by spring pressure. If spring loaded pair of gears into close mesh are rotated, any errors in the tooth form , pitch or concentricity of pitch line, will cause a variation of centre distance. Thus, movements of the carriage, as indicated by the dial gauge, indicate errors in the gear under test. Principle PARKINSON’S GEAR TESTER

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PARKINSON’S GEAR TESTER

Construction: 

A gear tester for testing spur gears is shown in the figure. This type of the tester are also available for bevel, helical and worm gears. The gears are mounted on two spindles so that they are free to rotate without measurable clearance. Construction PARKINSON’S GEAR TESTER

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The master gear is mounted as an adjustable carriage whose position ca be adjusted to enable a wide range of gears diameters to be accommodated and it can be clamped in any desired position. The gear under test is mounted on a floating spring loaded carriage so that the master gear and the gear under test may be meshed together under controlled spring pressure. Construction PARKINSON’S GEAR TESTER

Working: 

Using gauge blocks between the spindles set the dial gauge to read zero at the correct centre distance, and adjust the spring loading. Set limit marks on dial gauge. Mount the master gear and the gear to be tested, and note the variation in the dial indicator reading when the gears are rotated. Working PARKINSON’S GEAR TESTER

Working: 

If it falls outside the limit marks, the gear is not acceptable. The variation in dial gauge indicator readings are a measure of any irregularities in the gear under test, alternatively a recorder can be fitted, in the form of a waved circular chart and records made of the gear variation in accuracy of mesh. Working PARKINSON’S GEAR TESTER

Limitation: 

Friction in the movement of the floating carriage reduces the sensitivity. It is not suitable for gear with more than 300 mm diameter. Measurements are directly dependent upon master gear or reference gear. Errors are not clearly identified for type profile, pitch, helix and tooth thickness and are indistinguishably mixed. The accuracy is of the order of ± 0.001 mm. Limitation PARKINSON’S GEAR TESTER

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