BACK TO BASICS . . .
`
`
`
`Curvio Coupling Design
`
`Gleason Works
`
`Rochester, New York
`
`
`
`Fig. 1- Lett. a terms-section view taken perpendicular to the axis ot a con-
`cave Cur-vi: Coupling. Right. the mating convex C urvic Coupling. Note the
`curved teeth.
`
`Introduction
`
`Curvic Couplings were first introduced in 1942 to meet the
`need for permanent couplings and releasing couplings
`{clutches}, requiring extreme accuracy and maximum load
`carrying capacity. together with a fast rate of production.
`The development of the Curvic Coupling stems directly
`from the manufacture of Zero]"3 and spiral bevel gears
`since it is made on basically similar machines and also
`uses similar production methods. The Curvic Coupl-
`ing can therefore lay claim to the same production
`advantages and high precision associated with bevel gears.
`The term "Curvic Couplings" refers to toothed connection
`members with the teeth spaced circumferentially about the
`face and with teeth which have a characteristic curved shape
`when viewed in a place perpendicular to the coupling axis
`{see Fig. 1.}. This curvature exists because the members are
`machined with a face—mill cutter or a cup—type grinding wheel.
`One member is made with the outside edge of the cutter or
`wheel as shown at the left of the figure, and a concave. or
`an hour glass shaped tooth is produced. The mating member
`is usually cut or ground with the inside edge, thus produc-
`
`34 Gear homotopy
`
`
`
`ing a convex, or barrel-shaped tooth. The radius of the cuts
`ter or the grinding wheel surface is chosen in such a way that
`the teeth will either mate along the full face width of the tooth
`or along only a section of the face width. as desired.
`The three basic types of Curvic Couplings are ill the Fixed
`Curvic Coupling. t2} the Semi-Universal Coupling. and {3)
`the Releasing Coupling (or clutch}. The coupling provides a
`positive drive along with precision centering and high load
`can‘ying capacity.
`
`Fixed Curvic Couplings
`
`The Fixed Curvic Coupling is a precision face spline for
`joining two members, such as two sections of a shaft. to form
`a single operating unit.
`The fixed Curvic Coupling is used extensively in the con-
`struction of built-up turbine and compressor rotors for air-
`
`
`
`Fig. 2— A compressor rotor assembly for an aircraft jet engine. The Find
`Curvic Coupling is used to accurately position the separate interchangeable
`disc"
`SONY Exhibit 1021
`SONY Exhibit 1021
`SONY v. FUJI
`
`SONY v. FUJI
`
`

`

`
`
`Fig. 3— A turbine rotor assembly tor .J stationary masturbme Note tht- Fm-d
`Cum" (““91” "fl“ WW?" “‘h “l“
`
`
`
`
`
`
`craft and industrial gas or steam turbine engines as shown
`in Figs. 2. 3. and 4. Figs. 5 and b show a method of joining
`a turbine impeller or a bevel gear to a shaft. Crankshafts can
`be made of separate.
`interchangeable parts by means of a
`coupling as shown in Fig. 7.
`The Fixed Curvic Coupling is also used today by many
`major machine tool manufacturers for precision in‘
`clearing mechanisms as illustrated in Figs. 3 and 9.
`
`Semi-Universal Couplings
`
`The Semi-Universal Coupling is also a precision
`face spline loosely coupled to permit up to 2“
`misalignment of shafts together with axial free-
`dom. The teeth of one member usually have
`a curved profile to keep the load lOCalized
`in the middle of the tooth and to transmit
`
`more nearly uniform motion.
`semi—
`Fig. 10 illustrates an application of
`universal couplings and shows the typical tooth
`shape.
`
`
`
`Releasing Couplings (Clutches)
`
`The Releasing Couplings are designed and made so
`that the proper tooth contact is maintained while the clutch
`engages and disengages. 1n the larger sizes, a helical surface
`is used to accomplish this. On small clutches, this action is
`
`
`
`
`
`
`
`
`approximated by a special localized tooth bearing. The two
`members ot a shitt or overload clutch are usually held
`in position by spring pressure. By adjusting the amount
`oi pressure.
`the amount of
`torque which can be
`transmitted without disengagement ot
`the clutch
`can be controlled. Shift clutches are used today
`in a wide variety ot applications including
`aircraft. automotive.
`tarm equipment and
`power tools.
`11 can be
`The application shown in Fig.
`produced by cutting or grinding, depending
`on accuracy required.
`
`Design Features
`
`The basic geometry of the Curvic Coupling
`has been given in Fig.
`i. The grinding wheel
`sweeps across the face of the coupling contacting
`one side of one tooth and the opposite side of another
`tooth in a single engagement. During one complete
`revolution of
`the work,
`the machining of
`the Curvic
`Coupling is completed.
`The radius of the grinding wheel. the number of teeth. and
`the diameter of the Curvic Coupling are all interdependent
`as shown in Fig. 12.
`
`
`
`35
`Nowember/December 1956
`
`
`

`

`Fig. ll — A stationary gas turbine rotor showing the through bolts used for
`clamping the Fixed Curvit Coupling members together.
`
`
`
`
`Fig. 5 — A Fixed Curt-Pic Coupling used in assembling a turbine impeller and
`shaft.
`
`36 Gear Technology
`
`
`
`
`Fig. 6 - C urvie Couplings are used to enable separate manufacture 0t bevel
`gear and long shalt.
`
`Fig. 7—A section of a crankshaft showing the Fixed Curvic Coupling.
`Crankpins. crankWebs and roux-rials were made separately for ease oi manufac-
`ture and handling.
`
`The basic relationship is as follows:
`nx=number of half pitches included between two
`engagements of grinding wheel.
`
`N= number of teeth in Curvic Coupling.
`
`r =radius of grinding wheel.
`
`A= mean radius of Curvic Coupling.
`
`then fi=90§(m
`and r -.A tan 5.
`
`The radius of the grinding wheel can be changed by chang-
`ing n, as we]! as by changing N and A. The diameter of the
`grinding wheels used varies between nominal values of 6'
`
`

`

`
`
`Fig. 8 and 9— The precision accuracy of Fixed Curvic Couplings permits the precise
`indexing and repeatability required on this horizontal turret lathe
`(Fig. 5) and vertical turret lathe (Fig. 9).
`
`
`
`and 21 '. The maximum Curvic Coupling diameter produced
`is 50‘ and the smallest diameter is 0.375".
`
`Curvic Coupling teeth can be produced with a wide range
`of pressure angles to suit the application.
`A View of ground Fixed Curvic Coupling teeth at the out-
`side diameter is shown in Fig. 13. The chamfer on the top
`of the teeth is automatically ground as the tooth slot is being
`ground. The chamfer permits a larger fillet radius to be used,
`thus strengthening the teeth. Also shown is the characteristic
`gable bottom which eliminates any possibility of forming a
`stress-raising step in the root of the tooth. Fig. 14 shows the
`tooth configuration of a typical Curvic Coupling.
`As can be seen in Figs. 1 and 12, the space between two
`adjacent Curvic teeth is ground at two different locations on
`the wheel to obtain the proper taper of the tooth toward the
`coupling center. The grinding wheel
`then must be wide
`enough to cover at least half of the tooth space width at the
`outside diameter and still be narrow enough to pass through
`the space at the inside.
`To do this, the inside diameter of the coupling must be
`equal to. or greater than. 75% of the outside diameter.
`Another design feature of Fixed Curvic Couplings permits
`localization of the tooth contact area. The tooth contact for
`
`most applications should be centrally located and the length
`of contact should be approximately 50% of the face width
`when checked with the mating control coupling under light
`pressure. The type of application and method of bolting deter-
`mine the tooth bearing length which should be used. Under
`pressure of the bolting load the tooth bearing area will in—
`crease, thus insuring a uniform distribution of contact over
`the entire tooth surface.
`
`Because the grinding wheel sweeps across the face of the
`
`33 Goort’echnology
`
`coupling, it is usually necessary that the blank design con-
`tain no projections beyond the root line of the teeth. For
`proper clearance, the nearest projection should be at least ‘t'g'
`below the root line.
`
`In designing a Fixed Curvic Coupling it is essential to con-
`sider the method of bolting or clamping the two members.
`The tension in the bolt or bolts must be sufficient to keep
`the coupling teeth in full engagement under all conditions of
`operation. Furthermore.
`the bolts must have clearance
`throughout their entire length so that centering is accom-
`plished only by the Fixed Curvic Coupling teeth.
`in selecting the required coupling size, three items deter-
`mine the load which the coupling teeth will carry. The teeth
`must {1} be strong enough so they will not shear. {2) have
`sufficient surface area to prevent pitting, galling, and fret-
`ting corrosion. and (3) be supported by adequate material
`to withstand tension across the root of the tooth space.
`The shear strength is dependent upon the cross-sectional
`area of all the teeth. Since there is no backlash in a Fixed
`
`Curvic Coupling, the teeth are in intimate contact so that half
`of the metal
`is ordinarily removed in both members.
`regardless of the number of teeth or their depth. With this
`condition. the torque load is carried over a shear area ap-
`proximately half as large as in a one-piece hollow shaft.
`The allowable surface loading will depend on the contact
`area of the coupling teeth. Standard tooth proportions are
`used to maintain a constant area for a given coupling diameter
`regardless of the number of teeth. This area is sufficient to
`carry a load corresponding to the safe load in shear. and the
`proportions are varied only in special cases.
`The third factor affecting the load carrying ability of the
`coupling is related to the bolt tension. Tension in the bolt
`
`

`

`
`
`
`Fig. 10 — A Curvic Coupling of the semi-universal type is employed at both
`ends of this intermediate drive shalt
`
`Fig. 11 — A shift clutch tor a truck application. The tops of the teeth have
`generated helical surfaces.
`
`forces the coupling members together causing a wedging ef-
`fect between the mating teeth. This wedging effect creates a
`tensile stress in the blank under the tooth space. An increased
`amount of backing material will decrease this stress within
`limits.
`
`Design Procedure
`
`After considering the type of Curvic Coupling required to
`meet the needs of a given application, it is possible to deter~
`mine the approximate size which is necessary to transmit a
`specified load.
`For initial size determination on Fixed Curvic Couplings
`either Graph 1 or the following formula can be used:
`
`D
`
`{I T where D=coupling diameter (inches)
`1310
`T= torque (lb-inches)
`
`I.
`
`This assumes that the face length is .125 times the coupl-
`ing diameter or .875". whichever is smaller, and a material
`with an ultimate strength of 150.000 P.S.l.
`is employed.
`Graph 2 applies to Semi-Universal Curvic Couplings and
`Graph 3 covers shift and overload clutches which engage or
`disengage under load. For a shift clutch which is engaged or
`
`
`
`Fig. 12 — Diagram illustrating the basic geol'netr).r of the Cunric Coupling.
`
`disengaged only while standing still. use the Graph 1. Graphs
`2 and 3 are based on the use of case-hardening steel at 60
`Rockwell ”C".
`
`The maximum torque value during operation should be
`used in the above determination. If. however. there is a peak
`starting torque or other peak overload torque which occurs
`very infrequently during the life of the unit and does not ex-
`ceed 5 seconds duration at any one time, this peak value
`should be divided in half and compared with the maximum
`Operating torque. The higher of these two values should be
`used to determine Coupling size.
`
`
`
`ClRCtE A-‘la ON READER REPLY CARD
`
`
`
`November/Decanter I986 39
`
`

`

`Curvic Coupling Design
`
`it
`Having chosen the initial size of the Curvic coupling,
`is necessary to determine the number of teeth and the face
`width. Pressure angle and whole depth will be considered in
`later sections. When using standard tooth proportions. the
`surface contact area of the Curvic teeth will remain constant
`
`for a given coupling diameter, regardless of the number of
`teeth. Also. the shear area remains substantially constant for
`a given coupling diameter. regardless of the number of teeth.
`Couplings are usually designed with a diametral pitch rang-
`ing from 3 to 8. Graph 4 shows a recommended range for
`diametral pitch in relation to outside diameter. This curve
`is intended only as a guide. and the designer may depart from
`it if special requirements exist. Diametral pitch is taken at
`the outside diameter and,
`therefore.
`the number of teeth
`
`equals the diametral pitch multiplied by the outside diameter
`of the coupling.
`The face width of the Curvic coupling is the radial distance
`between the outside and inside radii of the coupling.
`it
`is
`almost directly proportional to the stress when the outside
`diameter is held constant. Often,
`the configuration of the
`assembly or weight considerations will dictate the face width
`to be used. The face width is generally .125 of the outside
`diameter of the coupling in order to produce the Curvic
`coupling with proper tooth taper.
`
`Curvic Design
`
`The initial Curvic Coupling dimensions which have been
`chosen in the preceding section should now be checked us-
`ing the stress formulas for this particular type of coupling.
`it is first necessary, however. to list the standard tooth pro-
`portions for Fixed Curvic Couplings. Fig. 15 shows a cross-
`section view of the teeth at the outside diameter and is the
`
`standard form for a Fixed Curvic Layout. It shows the sym-
`bols used for the various tooth dimensions. Standard depth
`proportions are recommended for all heavily loaded applica-
`tions. The 70% of standard tooth proportions are usually
`satisfactory where less surface contact area is acceptable for
`the lighter loads.
`
`Fig. 13 - Fixed Curvic Coupling teeth viewed at the outside diameter. Note
`the gable bottom.
`
`
`
`5.!th 8431' r. in
`
`[In [T HAD-inn
`
`40 Gear technology
`
`
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`shown on this marine radar part.
`
`$333551?i
`
`
`

`

`c =clearance
`
`c,=charnter height
`
`hI =whole depth
`a =addendum
`
`b =dedendurn
`
`A pressure angle of 30' has been found to be most prac-
`tical for most Fixed Curvic Couplings and is the standard.
`This pressure angle is the best compromise between a low
`pressure angle. with its corresponding light separating force.
`and a high pressure angle with its greater strength. Also, the
`axial and radial runout oi the Curvic coupling can be held
`more accurately at higher pressure angles. such as 30". since
`the tooth spacing accuracy is constant tor all pressure angles.
`and the axial component of a given spacing error decreases
`as pressure angle increases.
`1! special design conditions require it. the pressure angle
`for a Fixed Curvic Coupling can be as low as 10L or as high
`as 40. The strength tormulas given are applied to pressure
`angles between 20" and 40". For tower pressure angles.
`in—
`crease the calculated stress up to 25%.
`For pressure angles 20" and lower. the amount of clearance
`should be doubled.
`
`The fillet radius. the tooth thickness and the height ot the
`gable bottom (see Figs. 13 and 15! are calculated on the
`worksheets Ior machine settings.
`A calculation for shear stress and for surface stress should
`
`DEBURRS GEARS
`FAST
`
`[818] 4422898
`
`* SET-UPS
`
`TAKE
`
`SECONDS
`
`‘k INTERNAL-EXTERNAL
`
`SPUR 8. HELICAL GEARS
`
`TO 20 INCHES DIAMETER
`
`H707 McBean Drive. El Monte, CA 917.32
`
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`AItemate Tooth
`
`Proportions
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`The final values should be rounded to the next higher even
`thousandth.
`
`I’d=dtametral pitch at the outside diameter.
`
`a:
`
`ES
`2
`
`b =h, —a
`
`D-coupling outside diameter
`
`CIRCLE A-28 ON READER REPLY CARD
`
`
`
`November/December 1986
`
`
`41
`
`

`

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`tinuous operation at higher stresses is likely to result in tooth
`breakage or surface distress on the Curvic teeth.
`The allowable limits listed above are based on the use of
`
`steel with an ultimate tensile strength of 150.00 psi. minimum
`at operating temperatures. For steel with a lower ultimate
`strength and for other materials such as aluminum, titanium,
`and various heat-resistant alloys. the allowable limits should
`be altered in direct proportions to the ultimate strength values
`at operating temperature.
`
`A pair of Fixed Curvic Couplings must be tightly clamped
`together in assembly so that the teeth are in actual contact
`under all conditions of operation. This clamping action is
`usually provided by a single through bolt or multiple bolts.
`However, other means such as a special clamp can be used
`provided the above condition is met. It is important that the
`clamping arrangement and clamping force be carefully
`chosen. The bolt or bolts should have clearance throughout
`their entire length so that centering is accomplished only by
`the Fixed Curvic Coupling teeth.
`The clamping force should be at least one and one-half to
`two times the sum of all the separating forces acting on the
`Curvic coupling teeth. These separating forces usually include
`
`
`
`Fig. lS—Fixed Cun'ic Coupling
`
`be made according to the following formulas:
`
`Shear stress s,= T2
`IA F
`
`Surface stress sc=L
`AFN h“
`
`2
`
`D-F
`
`where T=torque.
`
`lbs. inches
`
`A=mean radius of coupling, inches=
`
`F=faCe-width, inches
`
`N-number of teeth
`
`ho=contact depth. inches=(h.-c—2c.)
`
`The recommended allowable limit for shear stress is 15,000
`
`psi. when there is combined torsion and bending. The recom-
`mended allowable limit for shear stress is 30.000 psi. when
`there is pure torsion and no bending. The recommended
`allowable limit for surface stress is 40,000 psi. for all applica-
`tions. These limits are suitable for continuous operation.
`Higher stresses may be permiSSible for very short periods
`which occur only infrequently during the life of the unit. Con-
`
`42 Gear Technology
`
`FtKED CUHWC COUPLING
`TEETH
`PRESSURE ANG LE
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`VIEW At uuTSIDE
`
`

`

`
`
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`CIRCLE A-9 ON READER REPLY CARD
`
`November xDacambat 1936 43
`
`
`TFll-CJFIDINATE CORPORATION
`
`REMANUFACTURED DETROIT CNC GEAR GRINDE RS
`
`A TOTALLY IKE-ENGINEERED 8:
`REMANUFACTURED CNC GEAR
`GRINDING SYSTEM
`
`FEATURES:
`1. PR“ ISIUN BAH?“ HUN-'5 & [INIAR 5t ,\[[5
`BOTH AXI'5
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`
`

`

`CURVIC SHIFT CLUTCH
`_ TEETH
`0" PRESSURE ANGLE
`
`CONVEX TEETH
`(MATE CONCM‘EI
`
`CONCAVE
`MEMEER
`
`VIEW A! OUTSIDE
`
`'—1
`
`sin
`'—1
`Ls.‘ __li'
`
`J1:
`
`Hg. rs—Curvic Shirt Clutch.
`
`(1) the separating force produced by the action of the torque
`on the Curvic teeth. (2) the separating force produced by any
`bending moment on the assembly. and (3) other separating
`forces. such as those produced by gas pressure. thrust loads.
`or other external operating characteristics.
`The separating force produced by torque is found as
`follows. neglecting the effect of Friction:
`
`Fl-T'i—tan a
`F, -separating force caused by torque
`
`where
`
`T -torque
`
`A -mean radius of coupling
`
`o-pressure angle
`
`'Ihernaximumseparatingtorceproduoedbyabmdingmo—
`ment acting on the coupling assembly is
`
`F _ 5DM
`‘
`(or?
`
`where
`
`M-bending moment. inch lbs.
`
`This maximum separating foroe produced by a bending
`
`44 GoorTeottnology
`
`
`
`moment occurs only at one point on the periphery of the Cur-
`vic coupling. The value of separating force drops off on either
`side of this point in proportion to the distance from the
`neutral axis. It is assumed that the coupling represents the
`cross-sectionofabeamwiththeneutralaxisattheaxisof
`
`the coupling. The neutral axis may actually be nearer the
`coupling periphery, but the above choice gives a higher
`separating force and, thus, a more conservative design ap-
`proachAftertheclampingiorceischosentomeet thesecon-
`ditions, the resulting surface stress on the Curvic coupling
`teeth should be calculated according to the following formula:
`
`1
`
`2 tan dt +3
`
`T
`
`s"-(NFI'I‘,
`
`F5
`
`where
`
`sg-equivalent surface stress, drive side. psi.
`N-nurnber of teeth
`
`F-face width. inches
`
`ho-contact depth. inches
`
`lie-clamping force. lbs.
`
`T-torque, lbs. inches
`
`o-pressure angle
`
`A-mean radius of coupling, inches
`
`This calculated surface equivalent stress should not exceed
`the compressive yield strength at the operating temperature
`of the material being used.
`As with any design consideration, it is important that the
`calculated clamping force be applied to the actual assembly.
`Where multiple bolts are used. they should all be elongated
`by the same amount within 1 943. To assist the shop in main-
`taining these values. it is helpful for the designer to provide
`a convenient means for measuring or gaging the final bolt
`lengths at assembly. The use of a hollow bolt facilitates
`assembly by allowing a heating element to be inserted to
`elongate the bolt a predetermined amount. The nut is then
`tightened by hand and, after cooling, the required amount
`of tension is obtained.
`
`When the bolts must pass through the region of the Cur-
`vic teeth, it is possible to use a split-face Curvic. This type
`of coupling has an inner and outer row of teeth separated
`by a groove for the bolt holes. The same stress formulas are
`used. with the sum of the two sections of face width inserted
`for the face width value.
`
`Rotor Design
`
`Turbine and compressor rotors make up the largest pro-
`portions of Fixed Curvic Coupling applications at present.
`Typical construction with multiple clamping bolts is shown
`in Figs. 2. 3 and 4. Generally, multiple clamping bolts are
`perferred for rotors where the coupling outside diameter is
`greater than 10 inches. Satisfactory rotors have been built
`with a single through bolt. but this requires a heavier sec-
`tion in the end member to transfer the clamping force from
`the region of the bolt to the region of the Curvic coupling.
`Also. a single bolt tends to be affected by bending moments
`on the rotor. whereas multiple bolts simply adjust to changes
`in the preload as the assembly rotates.
`Any suitable material can be used for turbine and com-
`
`

`

`'—
`
`
`
`pressorrotorssinoetheCurvicCouplingGi-inderscanbepro-
`vided with the optimum automatic grinding cycle for the
`material chosen. To date. all varieties of heat-resistant alloys.
`stainless steel. alloy steel. steilite, aluminum. aluminum
`bronze. and titanium have been ground satisfactorily.
`The useofunlilte materialsin matingCurviccouplingrotor
`discs creates a condition where the two couplings tend to ex—
`pandat different rateusthetemperattue increases. Thestan-
`dardCurvictoothwithanaverageamountoflengthwisecur—
`vature has been found to provide sufficient locking action
`for most applications to date.
`ifaspedaldesimrequirementmakesitnecessarytoper-
`rnit relative movement. the Curvic coupling can be designed
`with teeth which have a “half-barrel” shape.
`This removes the radial restraining force and permits one
`member to expand with respect to the other. Since the ex-
`pansion maintains the same tooth angle,
`regardless of
`diameter. the centering action of the Curvic coupling remains
`unchanged. It should be noted. however, that the clamping
`foroeeinertsaverysuongfractional forcewhichteruktoresist
`relative movement. regardless of the tooth shape.
`Many aircraft rotor designs are composed of extremely
`light-weight sections which require additional locking action
`in the Curvic teeth to resist the effect of centrifugal force.
`Here. amullerdiametergrindingwheelcan be used topro-
`vide more lengthwise curvature on the teeth. Some designs
`haveseparatelight-weightspacersbetwemthediscsandthese
`spacers are supported against centrifugal force only through
`the Curvic coupling teeth. A variation of the “half-barrel”
`shaped toothisusedinsuchcasesto provideextra resistance
`to this centrihrga] force which is always acting in the same
`relativedirection. When theamount of the relativeoentrifugal
`force is known, the included angle made by lines tangent to
`the two sides of a tooth can be determined to provide the
`maximum locking action, while keeping the separating force
`produced by this action within safe limits.
`A turbine or compressor rotor which requires a series of
`different Curvic coupling diameters to fit a tapering rotor con-
`figuration can often be made so that three or four diameters
`can be taken from the same basic coupling development. In
`this way. fewer developments are required with a resulting
`saving in machine set-up time and tooling. in the case of the
`split-face coupling. these Curvic coupling teeth must have
`special calculations for balanced tooth area.
`Whencoolingairisrequiredtobetransmittedtothein-
`terior of a rotor.
`it
`is usually possible to provide extra
`clearanceat the roots of the Curviccoupling teeth. By using
`the addendum and diamfer values found from the alternate
`
`tooth proportions and the whole depth value from the stan-
`dard tooth proportions. a practical amount of additional
`clearancecanbedetermined. For faoewidthsbelowthe max-
`
`imumlimit. it isoften practical toexceed thestandarddepth
`toobtainrnoredearancearea. Theremovalotteethfrom
`
`a Curvic coupling to provide cooling air passage should be
`avoided if poaible.
`In the opposite case. where the Curvic teeth must be com-
`pletelysealedtopreventthepmageoiair. itispossibieto
`Irv-chine a narrow drorlar groove in the face of both members
`before the Curvic teeth areground. At assembly, a flexible
`
`metallicsealingstripcanbe inserted in thisgroovearrd the
`members mated to form a sea]. It is important that the seal-
`ing strip be flexible enough so that no centering action will
`take place to oppose the centering action of the Curvic
`coupling.
`ThenumberofCurvicteeth shotddbemadeanemuullti-
`
`ple of the number of clamping bolts to make it possible to
`assemble thepartsolseveral differentmeshpoints.’l"l'temull
`practice for rotor assembly is to first balance the individual
`discsandtomarktheheavypointoneachdbe.Ataaunbly.
`the heavy points are placed 180“ apart on each succeeding
`disc to obtain the best assembled balance.
`
`For best control of runout at the periphery of the disc. the
`disc diameter before blading should not exceed 2.5 times the
`Curvic coupling outside diameter.
`
`Design Examplefi Rotors
`
`Suppose it is required to design a Curvic coupling for an
`aircraft compressor rotor to transmit a maximum torque of
`340.000 lbs. inches. The design configuration requires that
`the Curvic coupling outside diameter should be from 10.5“
`to 11" with a face width of O. 375". (The use of the brutal.
`
`
`
`D-dldr:10
`
`indicatesthatamuchsmallercouplingcouldbeusedtocarry
`the load but other design factors have determined the size.)
`The material selected has a yield strength of 100.000 psi.
`at operating temperature and an ultimate strength of 150.!!!)
`psi.
`We calculate the stresses for a 10.875" 0.0. and a .375"
`
`face width. and a premue angle of 30". From Graph 4 we
`findthatthesuggesteddiametralpitchrangeforthisdiametu
`is from 4.9 to 5.6. We will choose 54 teeth for this example.
`
`Pd-B-m-IIW
`-..-%-f§g- 124'
`'c
`lp-Zo-fT93-314'
`'q %3-%- 014”
`A _ D_;-if _ 103752—375 _ 5.25
`
`h, - (h.—-c—-2c.) - .124—.014—2(.014) - 092
`
`“r _
`340000
`" " rA’F
`rxts.25)’x.375 " ”“70 ”L
`
`1‘
`340.000
`
`5‘ " Atom. " stsx 375x54x.002 ' 39'” P"
`' Nhlfl Tl
`5" — 2 ms
`1
`150000 + 34.3000)
`'s-rx .375x .082 2x 57735
`
`-.602 {129.9m+64.8mi-.602 (mend-117.200 pit
`
`'mmnowm“.w.
`
`Number/m 1906 Q!
`l__—_—_
`
`

`

`Semi-Universal Curvic Couplings
`
`Having chosen the Curvic coupling diameter from Graph
`2 or formula and the number of teeth.
`the tooth loads on
`
`this type of coupling should be checked according to the
`following formula:
`
`F3 : LZAF
`
`where
`
`F3=tooth loading.
`
`lbs. per '1
`
`inch face.
`
`A =mean radius of coupling.
`
`inches.
`
`F =face width,
`
`inches.
`
`For satisfactory operations. "F3" should not exceed 2500
`lbs. per 1” face width when the coupling teeth are made of
`case-hardened steel with a minimum hardness of 60 Rockwell
`""C.
`
`Successful operation of the semi-universal Curvic coupl-
`ing is largely dependent on the profile curvature which is in—
`troduced on the convex member. The pressure angle is always
`DC at the pitch plane. When properly designed. this curvature
`keeps the tooth contact safely pesitioned within the bound—
`aries of the tooth surface. It also increases the number of teeth
`
`in contact at any instant. The load calculation, however. is
`based on having two teeth in contact. Angular misalignment
`must not exceed 2:. Parallel offset of the shafts is limited to
`one-half the amount of backlash.
`
`To determine the required profile curvature on the con-
`
`vex member. calculate the value of ASP which is the bear-
`ing shift above or below center on the two diametrically op-
`posite teeth in contact.
`
`A sin .33
`ASP_ '2 sin Eli,
`
`where
`
`AE=angular misalignment
`
`A =mean radius of coupling
`A
`t n26u = —
`a
`no
`
`Rp=profile radius of cutter
`
`It must be remembered that 35,. represents the shift of the
`center of the tooth contact and should not be permitted to
`travel to the edge of the tooth. The height of profile contact
`can be found as follows:
`
`h, = \ ’o'fmie it,
`
`From these calculations.
`follows:
`
`the addendum is obtained as
`
`a
`
`= ASQ+%+Q+ .015”
`
`The clearance at the roots of the teeth must be at least as
`
`large as the fillet radius plus the axial component produced
`by the angular misalignment plus the amount of axial freedom
`required in the coupling. The entire tooth design must be ex-
`ecuted by trial. As a first assumption. choose a profile radius
`equal to the cutter radius. If the required tooth depth is greater
`than 1.25 times the circular tooth thickness at the outside
`
`46 Gear Technology
`
`diameter, another trial should be made with a different pro-
`file radius or cutter diameter.
`
`A typical Semi-Universal Curvic coupling tooth applica-
`tion is shown in Fig. 10. Suitable arrangements must be made
`for lubricating the assembled unit. An enclosed design can
`be packed with grease or pressure lubricated.
`
`Shift and Overload Clutches
`
`The number of tooth shapes which can be designed for shift
`and overload clutches is practically unlimited. and it will only
`be possible to outline the basic design procedure.
`In general.
`shift clutches can be considered in three
`categories: (1) clutches having 0* or negative pressure angles.
`(2) clutches having 10'; or positive pressure angles and [3}
`saw-tooth clutches.
`
`Overload clutches fall primarily in the second category,
`with pressure angles usually in the range of 30" or 45‘. and
`some overload clutches are in the form of saw-tooth clutches.
`
`Special chamfers and helical surfaces can be added to the teeth
`of these three basic types.
`The layout form for a Curvic shift clutch with 0“ pressure
`angle is shown in Fig. 16. A typical clutch of this type is
`shown in Fig. 1]. This type of shift clutch produces no axial
`thrust and.
`in fact. requires a substantial force to disengage
`it when operating under load in order to overcome the effect
`of friction. lf vibration exists during operation and if there
`are slight errors in concentricity and parallelism when the
`members are assembled. there exists a tendency for the clutch
`to slowly work out of engagement during operation. To over-
`come this pOssibility. a clutch with a slight negative pressure
`angle is often employed, usually from 2" to 5° negative. and
`this creates a thrust force working to keep the coupling
`members engaged.
`To facilitate disengagement of the clu