BACK TO BASICS...
`
`
`
`Curvic Coupling Design
`
`Gleason Works
`Rochester, New York
`
`
`
`Fig. 1—Left, a cross-section view taken perpendicular to the axis of a con-
`cave Curvic Coupling. Right, the mating convex Curvic 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 Zerol® andspiral 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 havea 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 memberis made with the outside edge of the cutter or
`wheel as shownat 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 Technology
`
`
`
`ing a convex, or barrel-shaped tooth. The radius of the cut-
`ter or the grinding wheelsurface 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 (1) the Fixed
`Curvic Coupling, (2) the Semi-Universal Coupling, and (3)
`the Releasing Coupling (or clutch). The coupling provides a
`positive drive along with precision centering and high load
`carrying capacity.
`
`Fixed Curvic Couplings
`The Fixed Curvic Coupling is a precision face spline for
`joining two members, such as twosections ofa shaft, to form
`a single operating unit.
`The fixed Curvic Coupling is used extensively in the con-
`struction of built-up turbine and compressorrotors forair-
`
`
`
`Fig. 2—A compressor rotor assembly for an aircraft jet engine. The Fixed
`Curvic Coupling is used to accurately position the separate interchangeable
`
`“=
`
`SONYExhibit 1021
`SONY Exhibit 1021
`SONY v. FUJI
`SONYv. FUJI
`
`

`

`
`
`
`craft and industrial gas or steam turbine engines as shown
`in Figs. 2, 3, and 4, Figs. 5 and 6 show a method ofjoining
`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-
`dexing mechanismsasillustrated in Figs. 8 and 9.
`
`Fig. 3— A turbine rotor assemblyfor a stationary gas turbine. Note the Fixed
`Curvic Coupling teeth between each disc
`
`
`
`
`
`Semi-Universal Couplings
`The Semi-Universal Couplingis also a precision
`face spline loosely coupled to permit up to 2°
`misalignmentof 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.
`Fig. 10 illustrates an application of semi-
`universal couplings and showsthetypical 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. In the larger sizes, a helical surface
`is used to accomplish this. On small clutches, this action is
`
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`approximated by a special localized tooth bearing. The two
`members of a shift or overload clutch are usually held
`in position by spring pressure. By adjusting the amount
`of pressure,
`the amount of
`torque which can be
`transmitted without disengagement of
`the clutch
`can be controlled. Shift clutches are used today
`in a wide variety of applications including
`aircraft, automotive,
`farm equipment and
`powertools.
`11 can be
`The application shown in Fig.
`produced bycutting or grinding, depending
`on accuracy required.
`
`Design Features
`The basic geometry of the Curvic Coupling
`has been given in Fig.
`1. The grinding wheel
`sweeps across the face of the coupling contacting
`oneside 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.
`Theradius of the grinding wheel, the number of teeth, and
`the diameter of the Curvic Coupling areall interdependent
`as shownin Fig, 12.
`
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`
`
`
`35
`November/December 1986
`
`
`

`

`Fig. 4—A stationary gas turbine rotor showing the through bolts used for
`clamping the Fixed Curvic Coupling members together.
`
`
`
`
`Fig. 5— A Fixed Curvic Coupling used in assembling a turbine impeller and
`shaft.
`
`36 Gear Technology
`
`
`gear and long shaft.
`
`Fig. 6—Curvic Couplings are used to enable separate manufacture of bevel
`
`Fig. 7—A section of a crankshaft showing the Fixed Curvic Coupling.
`Crankpins, crankwebs and journals were made separately for ease of manufac-
`ture and handling.
`
`The basic relationship is as follows:
`n,=number of half pitches included between two
`engagements of grinding wheel.
`N= numberof teeth in Curvic Coupling.
`r =radius of grinding wheel.
`A= meanradius of Curvic Coupling.
`90° Xn,
`then 8 = ae
`andr =Atan 8.
`
`The radius of the grinding wheel can be changed by chang-
`ing n, as well as by changing N and A. The diameter of the
`grinding wheels used varies between nominal values of 6”
`
`

`

`
`
`Fig. 8 and 9—Theprecision accuracy of Fixed Curvic Couplings permits the precise
`indexing and repeatability required on this horizontal turret lathe
`(Fig. 8) 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 groundas the toothslot is being
`ground. The chamfer permits a largerfillet 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 showsthe
`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 twodifferent 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 coveratleast half of the tooth space width at the
`outside diameter andstill 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
`whenchecked with the mating control coupling underlight
`pressure. The type of application and method ofbolting 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
`
`38 Gear Technology
`
`coupling,it is usually necessary that the blank design con-
`tain no projections beyond the root line of the teeth. For
`properclearance, the nearest projection should be atleast '/32”
`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 underall 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 ofall 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 constantarea 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 shaft
`
`Fig. 11—A shift clutch for a truck application. The tops of the teeth have
`generated helical surfaces.
`
`forces the coupling members together causing a wedgingef-
`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 ofa 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 ‘ T where D=coupling diameter (inches)
`“i310
`T = torque(Ib-inches)
`
`This assumes that the face length is .125 times the coupl-
`ing diameter or .875”, whicheveris smaller, and a material
`with an ultimate strength of 150,000 P.S.I.
`is employed.
`Graph 2 applies to Semi-Universal Curvic Couplings and
`Graph3 covers shift and overload clutches which engage or
`disengage under load.Fora shift clutch which is engaged or
`
`CIRCLE A-13 ON READER REPLY CARD
`
`
`
`November/December 1986 39
`
`Fig. 12 — Diagram illustrating the basic geometry of the Curvic 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 S 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.
`
`
`KING
`
`tan-
`if your $
`to date:
`
`manutacturers
`500
`
`Beat
`
`

`

`Curvic Coupling Design
`Having chosen the initial size of the Curvic coupling,it
`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 Curvicteeth will remain constant
`for a given coupling diameter, regardless of the numberof
`teeth. Also, the shear area remains substantially constant for
`a given coupling diameter, regardless of the numberof 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
`Theinitial 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,tolist the standard tooth pro-
`portions for Fixed Curvic Couplings. Fig. 15 showsa cross-
`section view of the teeth at the outside diameter andis the
`standard form for a Fixed Curvic Layout. It shows the sym-
`bols used for the various tooth dimensions. Standard depth
`proportions are recommended forall 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.
`
`
`
`GABLE BOTTOM
`
`CHAMFER
`
`FILLET RADIUS
`
`40 Gear Technology
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`
`Fig. 14—The tooth configuration of the Fixed Curvic Coupling is clearly
`
`iste
`shown on this marine radar part.
`
`

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`Standard Tooth
`Proportions
`
`Alternate Tooth
`Proportions
`
`Py
`h,
`
`c
`
`©
`
`N/D
`800
`Py
`100
`Py
`-090
`Py
`
`N/D
`616
`Py
`070
`Py
`063
`Pq
`
`The final values should be rounded to the next higher even
`thousandth.
`
`P,=diametral pitch at the outside diameter.
`h—c
`2
`
`a=
`
`c =clearance
`
`c,=chamfer height
`h,=whole depth
`a =addendum
`
`b =dedendum
`
`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 correspondinglight separating force,
`and a high pressure angle withits greater strength. Also, the
`axial and radial runout of the Curvic coupling can be held
`more accurately at higher pressure angles, such as 30°, since
`the tooth spacing accuracyis constantforall pressure angles,
`and the axial component of a given spacing error decreases
`as pressure angle increases.
`If special design conditions require it, the pressure angle
`for a Fixed Curvic Coupling can be as low as 10° oras high
`as 40°. The strength formulas given are applied to pressure
`angles between 20° and 40°. For lower 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 of the
`gable bottom (see Figs. 13 and 15) are calculated on the
`worksheets for machine settings.
`A calculation for shear stress and for surface stress should
`
`DEBURRS GEARS
`FAST,
`
`(818) 442-2898
`
`* SET-UPS
`TAKE
`SECONDS
`*& INTERNAL-EXTERNAL
`SPUR & HELICAL GEARS
`TO 20 INCHES DIAMETER
`
`11707 McBeanDrive, El Monte, CA 91732
`
`b =h,-a
`D=coupling outside diameter
`
`
`
`CIRCLE A-28 ON READER REPLY CARD
`
`November/December 1986
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`
`41
`
`

`

`UE] nT UT siehnnernaiat
`
`aoe
`
`FIXED CURVIC COUPLING
`TEETH
`PRESSURE ANGLE
`
`o
`
`va
`CONVEX TEETH
`(MATE CONCAVE
`
`F
`
`CONCAVE MEMBER
`
`VIEW AT OUTSIDE
`
`eee ea
`CUcan con
`Hasttel te
`
`efeaten
`
`peas
`
`eeoe ae
`
`Fig. 15—Fixed Curvic Coupling.
`
`be made according to the following formulas:
`
`Shearstress s,=—STA‘F
`Surface stress i=—
`AFN h,
`
`lbs. inches
`where T=torque,
`A=mean radius of coupling, inches=
`
`D—F
`
`F=face-width, inches
`
`N=numberof teeth
`
`h,=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
`allowablelimit 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 thelife of the unit. Con-
`
`42 Gear Technology
`
`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 ultimatetensile 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 mustbe 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 asa special clamp can be used
`provided the above conditionis met. It is importantthat 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
`
`
`
`

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`momentoccurs 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-section of a beam with the neutral axis at the axis of
`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-
`proach. After the clamping force is chosen to meet these con-
`ditions, the resulting surface stress on the Curvic coupling
`teeth should be calculated according to the following formula:
`
`po)SeCe SE:
`
`CURVIC SHIFT CLUTCH
`— TEETH
`O° PRESSURE ANGLE
`
`VIEW AT OUTSIDE
`
`‘ (rt 2tan@ A
`
`where
`
`S..= equivalent surface stress, drive side, psi.
`N=numberof teeth
`
`F=face width, inches
`h,=contact depth, inches
`F,=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%. 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 nutis 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 groovefor the bolt holes. The same stress formulas are
`used, with the sum of the twosections 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 totransfer 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
`onthe rotor, whereas multiple bolts simply adjust to changes
`in the preload as the assembly rotates,
`Anysuitable material can be used for turbine and com-
`
`CONVEX TEETH
`(MATE CONCAVE)
`
`CONVEX
`MEMBER
`
`CONCAVE
`MEMBER
`
`9. Pe ey
`Kg [Te
`
`L
`
`Fig. 16-—-Curvic Shift 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 bygas pressure,thrust loads,
`or other external operating characteristics.
`The separating force produced by torque is found as
`follows, neglecting the effect of friction:
`F,=—Ltan ¢
`F, =separating force caused by torque
`T =torque
`A =mean radius of coupling
`$=pressure angle
`
`where
`
`The maximum separating force produced by a bending mo-
`ment acting on the coupling assembly is
`
`F,
`
`__5DM
`(D-FY
`M=bending moment, inch lbs.
`
`where
`
`This maximum separating force produced by a bending
`
`44 Gear Technology
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`

`

`_.
`
`
`
`
`
`Design Example — Rotors
`Suppose it is required to design a Curvic coupling for an
`aircraft compressor rotor to transmit a maximum torque of
`340,000 Ibs. inches. The design configuration requires that
`the Curvic coupling outside diameter should be from 10.5”
`to 11” with a face width of 0.375”. (The use of the formula
`
`2dm
`
`indicates that a much smaller coupling could be used to carry
`the load but other design factors have determined the size.)
`The materialselected has a yield strength of 100,000 psi.
`at operating temperature and an ultimate strength of 150,000
`psi.
`Wecalculate the stresses for a 10.875” O.D. and a .375”
`face width, and a pressure angle of 30°. From Graph 4 we
`find that the suggested diametral pitch range for this diameter
`is from 4.9 to 5.6. We will choose 54 teeth for this example.
`
`10,470 psi.
`
`39,000 psi.
`
`metallic sealing strip can be inserted in this groove and the
`pressor rotors since the Curvic Coupling Grinders can be pro-
`
`vided with the optimum automatic grinding cycle for the members mated to formaseal. It is important that the seal-
`ing strip be flexible enough so that no centering action will
`material chosen. To date,all varieties of heat-resistant alloys,
`stainless steel, alloy steel, stellite, aluminum, aluminum
`take place to oppose the centering action of the Curvic
`bronze, and titanium have been ground satisfactorily.
`coupling.
`The use of unlike materials in mating Curvic coupling rotor
`The number of Curvic teeth should be made an even multi-
`ple of the number of clamping bolts to make it possible to
`discs creates a condition where the two couplings tend to ex-
`pand atdifferent rates as the temperature increases. The stan-
`assemble the parts of several different mesh points. The usual
`practice for rotor assembly is to first balance the individual
`dard Curvic tooth with an average amountof lengthwise cur-
`discs and to mark the heavy point on each disc. At assembly,
`vature has been found to provide sufficient locking action
`the heavy points are placed 180° apart on each succeeding
`for most applications to date.
`disc to obtain the best assembled balance.
`If a special design requirement makes it necessary to per-
`mit relative movement, the Curvic coupling can be designed
`Forbest control of runoutat the periphery of the disc, the
`with teeth which have a “half-barrel” shape.
`disc diameter before blading should not exceed 2.5 times the
`This removes the radial restraining force and permits one
`Curvic coupling outside diameter.
`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
`force exerts a very strong fractional force which tends toresist
`relative movement, regardless of the tooth shape.
`Manyaircraft 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, a smaller diameter grinding wheel can be used to pro-
`vide more lengthwise curvature on the teeth. Some designs
`have separate light-weight spacers between the discs and these
`spacers are supported against centrifugal force only through
`the Curvic coupling teeth, A variation of the “half-barrel”
`shaped toothis used in such cases to provide extra resistance
`to this centrifugal force which is always acting in the same
`relative direction. When the amountof the relative centrifugal
`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,
`When cooling air is required to be transmitted to the in-
`terior of a rotor,
`it
`is usually possible to provide extra
`clearance at the roots of the Curvic coupling teeth. By using
`the addendum and chamfer values found from the alternate
`tooth proportions and the whole depth value from the stan-
`dard tooth proportions, a practical amount of additional
`clearance can be determined. For face widths below the max-
`imum limit, it is often practical to exceed the standard depth
`to obtain more clearance area. The removal of teeth from
`a Curvic coupling to provide cooling air passage should be
`avoided if possible.
`In the opposite case, where the Curvic teeth must be com-
`pletely sealed to prevent the passage of air,it is possible to
`machine a narrow circular groove in the face of both members
`before the Curvic teeth are ground. At assembly, a flexible
`
`Py = D ~ 10.875 ~ 4.97
`yo Sa ft ue
`*"c ct = re -014"
`>< oe = 014"
`te aa p= re 10.875- B73. cos
`ho = (h-c—2c)) = .124—.014—2(.014) = .082
`T
`340,000
`5" ar
`x X (5.25)? X .375
`T
`>
`340,000
`s AR
`:25X .375X54 X .082
`az (eee
`*e
`2 <3
`ae
`_150,000_ + 3.00
`
`November/December 1986 45
`eeeel
`
`= .602 (129,900 +64,800) = .602 (194,700) 117,200 psi
`
`"Use value to the nearest even 002”.
`
`~ 54.375 x .082
`
`|2X.57735
`
`

`

`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:
`
`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.
`
`2AF
`
`where
`
`inch face.
`F,;=tooth loading, Ibs. per 1
`A =mean radius of coupling,
`inches.
`F =face width,
`inches.
`
`For satisfactory operations, “F;” 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
`"Cs
`Successful operation of the semi-universal Curvic coupl-
`ing is largely dependent on the profile curvature whichis in-
`troduced on the convex member. The pressure angle is always
`0° at the pitch plane. When properly designed, this curvature
`keeps the tooth contact safely positioned within the bound-
`aries of the tooth surface. It also increases the numberofteeth
`in contact at any instant. The load calculation, however,is
`based on having twoteeth 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 AS, whichis the bear-
`ing shift above or below center on the two diametrically op-
`posite teeth in contact.
`
`where
`
`A sin AZ
`a5,= 2 sin O,
`AE=angular misalignment
`A =meanradius of coupling
`A
`tanz0,= =
`an20o=
`R-
`R,=profile radius of cutter
`
`It must be remembered that AS,, 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 asfollows:
`
`h, =V0.002 R,
`
`From these calculations,
`follows:
`
`the addendum is obtained as
`
`a
`
`= AS,+22+c+ .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 misalignmentplus the amountof axial freedom
`required in the coupling. The entire tooth design must be ex-
`Caramel
`ecuted bytrial. As a first assumption, chooseaprofile radius
`equal to the cutter radius. If the required tooth depthis greater
`than 1.25 times the circular tooth thickness at the outside
`
`Your ad reaches
`over 5,000 potential customers.
`Call GEAR TECHNOLOGY for details.
`
`CIRCLE A-30 ON READER REPLY CARD
`
`46 Gear Technology
`
`Shift and Overload Clutches
`The number of tooth shapes which can be designed forshift
`and overload clutches is practically unlimited, andit 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 andhelical 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
`shownin Fig. 11. This type of shift clutch produces no axial
`thrust and,
`in fact, requires a substantial force to disengage
`it when operating underload in order to overcometheeffect
`offriction. If vibration exists during operation andif 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-
`comethis 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,
`Tofacilitate disengagement of the clutch members, as well
`as engagement, a pressure angle of 10° is often used. Ex-
`perience has shown that
`the separating force with a 10°
`pressure angle is approximately equal to the forceof friction
`so that only a light load on the shifter mechanism is needed
`(continued on page 48)
`
`PROFITS ARE BEING MADE
`by advertising
`The Journal of
`
`* Unique capabili
`* Machinequality
`wanted
`
`
`
`

`

`
`asu= te tan } *
`AS, =bearing shift lengthwise on the tooth
`
`where
`
`h, =contact depth
`
`6
`
`=pressure angle
`
`re =cutter radius
`
`A =meanrad