Cc loi khp ni trc trong cng nghipJune 9, 2010byNguyn Thanh Sn4 CommentsKhp ni trc l mt b phn c kh ni v truyn momen xon gia hai thnh phn chuyn ng, thng thng l ni gia 2 trc (bi ny ch yu ni v mc ch ny). C rt nhiu ng dng ca khp ni, v d d thy nht l trong t chng ta c khp ni cc ng ni truyn t ng c ti cu trc pha sau. Ngoi ra, khp ni cn c tc dng nh iu chnh tc , ngn nga qu ti hay ng m cc c cu c kh, v.v

Nu phn loi theo ng dng th c rt nhiu loi khp ni, nhng ni chung chng phn ra 3 loi chnh sau:1. Khp ni cng (Rigid coupling)2. Khp ni linh ng (n hi) hay khp ni b (Flexible or Compensating Couplings)3. Khp ni ly hp (cho php ni hoc tch cc trc my)Mt s c im ca 3 loi ny:1. Khp ni cng (Rigid coupling):ni cc trc c ng tm trn cng mt ng thng v khng di chuyn tng i vi nhau. C cc loi sau:- Khp ni ng:kt cu n gin, lp rp hi kh, r tin, ch dng cho trc c ng knh nh hn 70mm.

- Khp ni bch: n gin l ni trc tip hai bch ca hai trc my bng buloong.

2. Khp ni linh ng (n hi) hay khp ni bDng ni cc trc c sai lch tm do bin dng n hi ca cc trc, do sai s ch to v lp t. Cc sai lch ny s c b li nh kh nng di ng ca cc chi tit trong khp ni.Trong kt cu ca khp ni trc, chi tit lin kt c kh nng bin dng n hi ln, gi l khu n hi. Nng lng va p, rung ng c tch lu vo khu n hi, sau gii phng dn ra. Do hn ch c cc chn ng c truyn t trc ny sang trc kia.- Khp ni a (Disc coupling): y l loi s dng ph bin nht cho cc thit b quay ca nh my cng nghip nh bm, qut, my nn, tuabin, my pht,v.v..kt cu cng kh n gin gm cc a kim loi, nh cc a ny c m c th b mt phn cho lng mt ng tm trc v khong di trc ca hai my:

Nu c 1 mt b(flexible) th s ch b c gc( lch trc)Nu c 2 mt b: s b c khong di trc v lch trc

- Khp ni rng (Gear Tooth Coupling): lm iu kin ti ln, ng knh trc ln

- Khp ni xch-Khp ni n hi (Elastomeric Couplings)or( jaw flexible coupling)

Ngoi ra mt s thit b khi lng ln cn gia tc m i, iu kin lm vic khc nghit (nh my xc khai thc m, truyn ng cho bng ti, my nghin bt giy ), c th iu chnh tc v i hi kh nng sn sng cao ngi ta dng khp ni thy lc (Fluid Coupling).Khp ni thy lc khng truyn lc trc tip qua cc c cu c kh m bng du thy lc hay c th gi l s kt ni mm v truyn cng sut t trc dn ng sang trc b dn nh bin i mmen ca cht lng v c th thay i s vng quay bng cch thay i lng cht lng cung cp.

Nguyn l:khi ng c dn ng quay s lm cnh bm ca khp ni quay vi tc ng c v y du v pha cnh tuabin (pha trc my c dn) lm tuabin quay v ko my c dn quay. Nh vy c s chuyn nng lng c hc sang nng lng thy lc v ngc li

Nhc im: gi thnh u t cao, kt cu phc tp, cng knhu im: lm vic m i, t bo trTham kho thm v khp ni thy lc ti: www.voithturbo.comChn khp ni:Chn loi khp ni: Da vo ti trng, s vng quay, tnh cht lm vic ca my chn kiu khp niDa vo ng knh d (trc ch ng) ca on cn lp khp ni v moomen xon T trn trc, tra bng tm khp ni thch hpTc dng ca khp ni:thng khp ni n hi mc ch gim chn ng gia cc chi tit, tng mmen t t lm vic m, thng thng ng c n>1000 th dng khp n hiKhp ni lm nhim v truyn chuyn ng gia hai trc, ni cc trc ngn thnh mt trc di, khp ni cn c tc dng ng m cc c cu (ly hp), ngn nga qu ti, gim ti trng ng, b sai lch ca cc trc. T s truyn qua khp ni bng 1.Ni trc l loi khp ni lin kt 2 trc vi nhau. Ch c th thc hin ni hoc tch ri hai trc khi dng my. C 3 loi ni trc: cht, b, n hi.Ni trc n hi. Trong kt cu ca ni trc, khu lin kt c kh nng bin dng n hi ln, gi l khu n hi. Nng lng va p, rung ng c tch lu vo khu n hi, sau gii phng dn ra. Do hn ch c cc chn ng c truyn t trc ny sang trc kia.Nhiu ni trc n hi ng thi cng l ni trc b. Do bin dng ca khu n hi, ni trc c kh nng la theo cc sai lch ca trc lm vicng knh ca trc vo v trc ra thng thng l bng nhau, trong mt s trng hp l khc nhau.Chn khp ni cn theo trnh t:Chn loi khp ni: Da vo ti trng, s vng quay, tnh cht lm vic ca my chn kiu khp niDa vo ng knh d (trc ch ng) ca on cn lp khp ni v moomen xon T trn trc, tra bng tm khp ni thch hp

Ti khng bit g v truyn ng nhng on chng " khp ni n hi " l "flexible coupling " nn google th xem th c nhiu ti liu lm ! du sao cng tn cng search nn cng post li ,hy vng khng b lc .V l thuyt th nhiu ,in hnh nh :

http://books.google.com/books?id=b2Q...esult&resnum=1

Cu hi ca khoa246 l"Cho em hi l khp ni n hi ni 2 trc c ong knh ln hn nhau khong bao nhiu?v khi chn th chn theo trc dn phi khng ah."

Cu hi c hai phn,phn sau l: "v khi chn th chn theo trc dn phi khng ah "

Lovejoy corporation l nh sn xut coupling ln nn ta tm cu tr li phn " technical resources " website ca cng ty ny.

Sorting Out Flexible Couplings

http://www.lovejoy-inc.com/content.aspx?id=598

Cn vn u tin ca cu hi " Cho em hi l khp ni n hi ni 2 trc c ong knh ln hn nhau khong bao nhiu? "

Anh DCL tr li : " t tin chc rng hi t hc th trong sch c ni r iu ny, schby gith t khng bit "Ta li tm xem by gi th t l nh th no y:

http://www.lovejoy-inc.com/content.aspx?id=286

Trong ny c on :

The Beam, Bellows and Mini Disc designs all have a single piece construction, so only one part needs to be selected.The GS curved jaw, Oldham, Mini Soft, and Mini Jawdesigns have a three piece constructions, consisting of two hubs and an insert. When the shaft size of the driver and driven are the same diameter, the hubs will be the same.When the shaft diameters differ, the hubs selected will differ accordingly

Nh vy cc loi c bi m c dng ni trc khc kch c.Ta li vo catalog xem :

http://www.lovejoy-inc.com/uploadedF...V7wocovers.pdf

Th thy nh sau :

Nh vy t l kch thc ca hai trc khc bit kh nhiu.Cn vt liu cht do m anh DCL nhc n chc l ci Elastomeric coupling.

Ti ang lm thy bi on m,nu ti on sai cm t " khp ni n hi" th xin c xem y l ti liu tham kho thm nh.FL Jaw Flexible CouplingFLJaw Flexible CouplingsProducts details1 Applicable to all types of machinery and hydraulics2 Small volume and large transmitted torque3To be plugged in axially, easy assembly, maintenance free4 Balancing axiad, radial and angular misalignment5 Dimensions are available on customer request.6 Applicable from -40to +100 C, max temperature 120 CApplication fieldMixer, brewing machinery, centrifugal blower, centrifugal compressor, transport machinery, centrifugal fan and pump, generator sewage treatment equipment, clay processing machinery, crane, washing machines, woodworking machinery, machine tool, rotary grinding machine, paper mill machinery, the spinning jenny, reciprocating transports, crushing machine, shake conveyor, rubber machinery (equipped with mixed refine sensor and grinding machine, reciprocating compressor). Commonly used in air compressor machine.A. COUPLINGS

1.0 Introduction

Couplings are divided into categories: Rigid and Flexible. As compared with flexible couplings, rigid couplings have limited application. Rigid couplings do not have the ability to compensate for shaft misalignments and are therefore used where shafts are already positioned in precise lateral and angular alignment. Any misalignment between shafts will create high stresses and support bearing loads.

Rigid couplings by virtue of their simple rugged design are generally able to transmit more power than flexible couplings of comparable size but this is not an Important advantage except in high horsepower applications.

This section will be devoted to the small to medium size flexible type couplings which cover a much larger field of applications. Flexible shafts, which are closely related to flexible couplings will also be discussed. This writeup is divided into the following categories.

Application Considerations Torque and Horsepower Shaft Misalignment Lateral and Axial Flexibility of Coupling Torsional Flexibility Backlash Service ConditionsTypes of Flexible Couplings Universal Joints Oldham Couplings Flexible Shaft Couplings Miscellaneous Couplings Rotational Velocity Error

2.0 Application Considerations

Flexible couplings are designed to accommodate various types of load conditions. No one type of coupling can provide the universal solution to all coupling problems;hence many designs are available, each possessing construction features to accommodate one or more types of application requirements. Successful coupling selection requires a clear understanding of application conditions. The major factors governing coupling selection are:

(a) Torque and HorsepowerThe strength of a coupling is defined as its ability to transmit a required torque load, frequently in combination with other factors. Hence a coupling may be selected whose rated torque capacity is many times greater than needed. For example, in a Coupling subject to wear and increasing backlash, a useful torque rating would depend chiefly on backlash limitations rather than strength. For manually operated drives, the torque Imposed through Improper handling may be In excess of the drive torque required. Couplings are frequently specified In horsepower capacity at various speeds. Horsepower is a function of torque and speed, and it can be readily determined from the formula on page T63.

(b) Shaft MisalignmentShaft misalignment can be due to unavoidable tolerance build-ups in a mechanism or intentionally produced to fulfill a specific function.Figure 1illustrates the various types of shaft misalignments often encountered.

(c) Lateral and Axial Flexibility of CouplingsLateral and axial flexibility of couplings are factors frequently overlooked. The term flexible does not mean that the Coupling gives Complete freedom of movement to coupled shafts with no transmissible force. More properly, flexible couplings give limited freedom of movement with transmitted force. Simply stated: Forces are needed to make a flexible coupling flex. These forces are either lateral (at right angles to the shafts) or axial in nature or a combination of both. Lateral forces may produce a bending moment on the shafts and a radial toad on the support bearings. Axial force can produce undesirable thrust loads if not considered in the original design. Universal joints and Oldham couplings impose relatively little lateral load on bearings. The elastomeric type of couplings will produce lateral forces in proportion to their stiffness. Small lateral force calls for soft rubber and in turn reduces torque capacity.

(d) Torsional FlexibilityTorsional flexibilty of a coupling is the elastic deformation induced in a flexible coupling while transmitting torque. In some applications using encoders, it may be essential that the torsional flexibility sometimes be very low so as not to introduce reading errors caused by angular displacements. On the other hand torsional deflection may be desirable for reducing peak torque In driving high inertia loads.

(e) BacklashBacklash is the amount of rotational play inherent in flexible couplings which utilize moving parts. In some applications this slack may not be objectionable, but In an application such as described In the previous paragraph backlash would rule out couplings of this type.

(f) Rotational Velocity ErrorIn addition to the types of error already described, universal joints produce an error because of their kinematic behavior. If the input speed Into a single universal joint is held constant, then the output will produce cyclic fluctuations in direct relation to the operating angles of the input and output shafts. This Will be described more fully in the section dealing with Universal Joints.6 Couplings and Universal Joints1233.0 Types of Flexible Couplings

Most small to medium size couplings are basically one of three types.

3.1 Universal Joints

A universal joint is a linkage consisting of two yokes, one on each shaft, connected by spider as shown onFigure 2. Since universal joints are frequently used, and thee r analysis is complex, a separate section is devoted to them following this section.

By substituting an elastomeric member in place of the conventional spider and yoke construction Such as in the design shown inFigure 3backlash is eliminated. Lubrication is no longer a consideration because there are no moving parts and a fairly large amount of lateral misalignment can be accommodated. The Illustrated coupling is available in the product section of the catalog. Please refer toFigures 4and5for specific design data for this type of Coupling.

COUPLINGS Introduction Application Considerations Types of flexible couplings Oldham Coupling Flexible Shaft Misc. CouplingsUNIVERSAL JOINTS General Kinematics Joint Selection Secondary Couples3.2 Oldham Coupling

Oldham couplings consist of three members. A floating member is trapped by 90 displaced grooves between the two outer members which connect to the drive shafts as shown inFigure6.

Oldham couplings can accommodate lateral shaft misalignments up to 10% of nominal shaft diameters and up to 3 angular misalignments. Lubrication is a problem but can in most applications be overcome by choosing a coupling that uses a wear resistant plastic or an elastomer in place of steel or bronze floating members.

Oldham couplings have the following advantages:a. No velocity variation as with universal jointsb. High lateral misalignments possiblec. High torque capacityd. Ease of dismantling

Disadvantages:a. Limited angular displacement of shaftsb. Need for periodic lubrication due to relative sliding motion unless nylon or rubber construction is employedc. Possible loss of loose members during disassembly

3.3 Flexible Shafts

Flexible shafts are stiff in torsion and very compliant in bending and lateral misalignments. A good example of this is in their use on automotive speedometer drives.Flexible shafts Consist of: Shaft the rotating element consisting of a center wire With several wire layers wrapped around it in alternating directions. Casing the sleeve made from metal or non-metals to guide and protect the shaft and retain lubricants. Case End Fitting connects the casing to the housing of the driver and driven equipment. Shaft End Fitting connects the shaft to the driving and driven members.Flexible shafts are also supplied without a casing when used for hand operated controls or intermittent powered appiications. Flexible shafts as shown in the product section of the catalog are often substituted in place of more expensive gear trains and universal joints in applications where the toad must be moved in many directions. They are extremely useful where the load Is located in a remote position requiring many gear and shafting combinations. The basic design considerations are torque capacity, speed, direction of rotation, bend radii and service conditions.

Torque capacity is a function of the shaft size. Operating conditions must be considered in power drive applications such as starting torque, reversing shocks, and fluctuating loads. These conditions constitute overloads on the shaft. If they are substantially greater than the normal torque load, a larger shaft must be selected. Since in power applications torque is inversely proportional to speed, it is beneficial to keep the torque down thereby reducing shaft size and cost. Ordinarily speeds of 1750 to 3600 RPM are recommended. However there are applications in which shafts are operating successfully from 600 to 12,000 RPM. The general formula for determining maximum shaft speed is:

Flexible shafting for power transmission is wound for maximum efficiency when rotating in only one direction the direction which tends to tighten the outer layer of wires on the shaft. Direction of rotation is identified from the power source end of the shaft. Torque capacity in the opposite direction is approximately 60% of the wind direction. Therefore if the power drive shaft must be operated in both directions, the reduced torque capacity will require a larger shaft than would normally be selected for operation in the wind direction.

Because flexible shafts were developed primarily as a means of transmitting power where Solid Shafts cannot be used, most applications involve curves. Each shaft has a recommended minimum operating radius which is determined by the shaft diameter and type. As the radius of curvature Is decreased, the torque capacity also decreases and tends to shorten shaft life.

Lastly, service conditions such as temperature present no special problems to flexible shafts when operating in the -65 to +250F range. Plastic casing coverings are able to cover this temperature range and provide additional protection from physical abrasion as well as being oil and water tight. Sometimes it is desirable if not essential that a flexible shaft coupling be as short as possible and still retain most of the features previosly described.Figure 7illustrates such a coupling, available in the Product Section of the catalog.

The flexible Shaft center section consists of three separately would square wire springs. Individual spring layers are opposingly wound to provide maximum absorption of vibration, load shock and backlash. The hubs are brazed to the springs for maximum strength. Design data is available in Figure 8 as well as in the Uni-Flex catalog page in this catalog.

Figure 8- Uni-Flex Couplings Selection DataSeriesNumberMax.TorqueLb.in.H.P. Capacity*At Varying Speeds (R.P.M.)

100300600900120015001800240030003600

1825375018343982.03.05.06.13.09.15.18.39.18.30.36.78.27.45.541.2.36.60.701.5.45.75.902.5.912.3.71.21.43.91.51.83.911.824.6

*Based on service factor of one only

Service Factors: Light, even load 1 Irregular load without shock, rare reversals of direction 1.5 Shock loads, frequent reversals 2Unflex Selection Procedure: Select the service factor according to the application. Multiply the horsepower or torque to be transmitted by the service factor to obtain rating. Select the coupling With an equivalent or slightly greater horsepower or torque than shown in the table.3.4 Miscellaneous Couplings

This group of couplings incorporate design features which are frequently unique, approximations or combinations of universal, Oldham and flexible shaft couplings. Two widely used couplings in this category are the Jaw and Sleeve types, both of which are available in the Product Section of our catalog.

Jaw type couplings Consist of two metal hubs which are fastened to the input and output shafts. Trapped between the hubs is a Urethane spider whose legs are confined between alternating metal projections from the adjacent hubs. The spider is the wearing member and can be readliy replaced without dismantling adjacent equipment. The coupling is capable of operating without lubrication and is unaffected by oil, grease, dirt or moisture. Select the proper size for your application fromthe table inFigure 10and the selection instructions.

Figure 10- Jaw Type Couplings Selection DataCouplingSeriesNo.RatedTorquein Lbs.ServiceFactorHorsepower capacity at Varying Speeds (R.P.M.)

100300400900120015001800240030003600

0353.51.01.52.0.0056.0037.0028.017.011.009.034.023.017.05.033.25.067.045.033.084.056.043.13.087.065.10.067.05.17.113.0252.13.10

05025.21.01.52.0.04.03.02.12.08.06.24.16.12.36.24.18.48.32.24.60.40.30.72.48.36.96.64.421.2.80.601.44.96.70

07037.837.81.01.52.0.06.04.03.18.12.09.36.24.12.54.36.27.72.48.36.90.60.451.08.72.541.44.96.721.81.2.902.161.441.08

07575.61.01.52.0.12.08.06.36.24.18.72.48.361.08.72.541.44.96.721.801.20.902.161.441.082.881.921.443.62.41.84.342.882.10

090126.1.01.52.0.20.13.10.60.40.301.2.20.601.81.2.902.41.61.23.02.01.53.62.41.84.83.22.46.04.03.07.24.83.6

Service Factors1.0 _______ Even Load No Shock infrequent Reversing with Low Starling Torque1.5 _______ Uneven Load Moderate Shock Frequent Reversing with LOW Start Torque2.0 _______ Uneven Load Heavy Shock Hi Peak Loads Frequent Reversals with High Start Torque

Jaw Type Coupling Selection Procedure: Select the service factor according to the application. Multiply the horsepower or torque to be transmitted by the service factor toobtain rating. Select the coupling with an equivalent or slightly greater horsepower or torque than shown in the table. Turn to the Product Section page illustrating the same coupling and make your specific selection in that number series.A sleeve type Coupling consists of two splined hubs with a mating intermediate member of molded neoprene. Because of its construction features, it is capable of normal operation with angular shaft misallgnments up to 7.112.

Lubrication is not required. All parts are replaceable without disturbing adjacent equipment provided sufficient shaft length is allowed by slide coupling hubs clear of the sleeve member during disassembly. Select the proper size for your application from table In Figure 12 and follow the selection instructions.Sleeve Type Coupling Selection Procedure: Determine motor characteristic. Determine service conditions. Select the series coupling with an equivalent or slightly greater horsepower than shown in the table. Turn to Powergrlp couplings in the Product Section and select the specific assembly or individual components in that number series.Other types of couplings are also available and are fully described along with technical specifications in this catalog.

B. UNIVERSAL JOINTS

1.0 GENERAL

A universal joint is a positive, mechanical connection between rotating shafts, which are usually not parallel, but intersecting. They are used to transmIt motion, power, or both.

The simplest and most common type is called the Cardan joint or Hooke joint. It is shown inFigure 1. It consists of two yokes, one on each shaft, connected by a cross-shaped intermediate member called the spider. The angle between the two shafts is called the operating angle. It Is generally, but n01 necessarily, constant during operation. Good design practice calls for low operating angles, often less than 25, dependIng on the application. Independent of this guideli ne, mechanical interference In th e construc tio n of Cardan joints limits the operating angle to a maximum (often about 37), depending on its proportions.

2.0 Applications

Typical appllcatlons of universal joints include aircraft, appliances, control mechanisms, electronIcs, Instrumentation, medical and optical devices, ordnance, radio, sewing machines, textile machInery and tool drives.

Universal joints are available in steel or in thermoplastic body members. Unlversal joints made of steel have maximum load-carrying capacity for a given size. Universal joints with thermoplastic body members are used in light industrial applications in which their self-lubricating feature, light weight, negligible backlash, corrosion resistance and capability for high-speed operation are significant advantages.

Universal joints of special construction, such as ball-jointed universals are also available. These are used for high-speed operation and for carrying large torques. They are available both in miniature and standard sizes.

3.0 General Characteristics of the Cardan Joint

A basic characteristic of the Cardan joint is the nonuniformity of motion transmission through the joint. The angular-velocity ratio between input and out put shafts varies cyclically at two cycles per revolution of the input shaft. This fluctuation, which is accompanied by corresponding angular accelerations, increases with the operating angle and can be as much as 15% of peak angular velocity (in the case of a 30 operating angle). In selecting a joint the effect of these fluctuations on static torque, inertia torque and system performance needs to be kept in mind.

COUPLINGS Introduction Application Considerations Types of flexible couplings Oldham Coupling Flexible Shaft Misc. CouplingsUNIVERSAL JOINTS General Kinematics Joint Selection Secondary Couples

The non uniformity of the transmission can be eliminated by using two appropriately phased universal joints in series, as shown inFigure 2. In such cases the velocity variation induced by one joint can be made to cancel that of the ot her, thereby transmitting a constant (1:1) angular velocity ratio between shafts. The angular velocity fluctuation of the intermediate shaft, however, cannot be avoided. Two universal joints in series also permit coupling of two laterally displaced shafts (single Cardan joints are limited to intersecting shafts).Single Cardan joints have the following advantages: Low side thrust on bearings. Large angular displacements are possible. High torsional stiffness. High torque capacity.They have the following disadvantages: Velocity and acceleration fluctuation increases with operating angle. Lubrication is required to reduce wear. Shafts must lie in precisely the same plane. Backlash difficult to control.4.0 Kinematics

For a uniformly rotating input shaft, the output shaft angular - velocity and angular acceteration undergo two cycles per revolution of the input shaft. The angular displacement of the output shaft does not precisely follow that of the input shaft but leads or lags, again with two cycles per revolution. The angular-velocity variation as a function of operating angle is illustrated inFigure 3.

The peak displacement lead (or laq). peak angular-velocity ratios (max. and min.) and peak angular-acceleration ratios are shown as a function of operating angle in Table 1, which is reproduced from "The Analytical Design of Universal Joints" by S.J. Baranyi, Design News, Sept. 1, 1969.

The table should always be consulted for exact numerical values. As a qualitative guideline, it may be kept in mind that for small operating angles (say up to 10), the angutar-displacement error (max. lead or lag), the deviation of the max. and min. angular velocity ratios from unity, and the maximum angular acceleration ratio are very nearly proportional to the square of the operating angle.

The static torque transmitted by the output shalt is equal to the product of the input to torque and the angular-velocity ratio. The angular acceleration gives rise to an inertia torque, as well as to vibrations. The inertia torque typically would be equal to the sum of the product of the angular acceleration of the output shaft (rad/sec) and the polar mass moment of inertia of the output shaft (in-lb-sec) and the output torque (with the units indicated the torque would be given in in-Ibs).

The inertia loading often determines the ultimate limit on the speed of operation of the joint. Recommended speed limits vary depending on operating angle, transmitted power and nature of the applicatlon. Recommended peak angular accelerations of the driven shaft vary from 300 rad/sec to over 2000 rad/sec in power drives. In light instrument drives, the allowable accelerations may be higher. For an accurate determination of allowable speed, a stress determination is necessary.

4.1 Example 1: Determining the Maximum Inertia Torque

A universal joint operates at 250 RPM with an operating angle of 10. Find the max. angular displacement lead (or lag), max. and min. angular-velocity of output shaft and max. angular acceleration of output shaft. If the system drives an inertia load so that the total inertial load seen by the output shaft (including its own inertia) can be represented by a steel, circular disc attached to the output shaft (radius r = 3", thickness t = 1/4"), find the max. inertia torque of the drive. From Table 1 with ( = 10, the max. displacement lead (or lag) = 0.439 = 26.3'. The max. and min. angular-velocity ratios are given as 1.0154 and 0.9848, respectively. Hence, the corresponding output-shaft speeds are:

|

TABLE 1 - The Effect of Shaft Angle () on Single Universal Joint Performance For Constant Input Speed*

According to Table 1, the max. angular acceleration ratio is

Inertia torque = (21.0) (0.0233) = 0.489 in-lbs. This inertia torque is a momentary maximum. The inertia torque fluctuates cyclically at two cycles per shaft revolution oscillating between plus and minus 0.489 in-lbs.

When system vibrations and resonances are important, it may be required to determine the harmonic content (Fourier series development) of the output shaft displacement as a function of the displacement of the input shaft. The amplitude of the mthharmonic (m > 1) vanishes for odd values of m, while for even values of m it is equal to (2/m) (tan1/2 )m, where denotes the operating angle.

5.0 Joint Selection (Torque Rating)

The capacity of a universal joint is the torque which the joint can transmit. For a given joint, this is a function of speed, operating angle and service conditions. Table 2 shows use factors based on speed and operating angle for two service conditions: intermittent operation (say, operationl or less than 15 minutes, usually governed by necessity for heat dissipation) and continuous operation. The torque capacity of a single Cardan joint of standard steel construction is determined as follows:

i. From the required speed in RPM, operating angle in degrees, and service condition (intermittent or continuous), find the corresponding use factor from Table 2.ii. Multiply the required torque, which is to be transmitted by the input shaft, by the use factor. If the application involves a significant amount of shock loading, multiply by an additional dynamic factor of 2. The result must be less than the static breaking torque of the joint.iii. Refer to the torque capacity column in the SOP catalogue and select a suitable joint having a torque capacity not less than the figure computed in (ii), above. If a significant amount of power is to be transmitted and/or the speed is high, It is desirable to keep the shaft operating angle below 15. For manual operation operating angles up to 30 may be permissible.

TABLE 2 Use Factors for the Torque Rating of Universal Joints

5.1 Example 2: Universal Joint Selection for Continuous Operation

A single universal joint is to transmit a continuously acting torque of 20 in-lbs, while operating at an angle of 15 and at a speed of 600 RPM. Select a suitable joint. From Table 2 for continuous operation, the use factor is given as 68. Note that there are blank spaces in the table. If the combination of operating angle and speed results in a blank entry in the table, this combination should be avoided. The required torque Is (68)(20) = 1360 in-Ibs. There is no shock load and the dynamic factor of 2 does not apply in this case.

From the catalogue, it is seen that there are two joints meeting this specification: 508-0500 and 508-0516, both with a torque capacity of 1700 in-lbs. The first has a solid-shaft construction and the second a bored construction. The choice depends on the application.

5.2 Example 3: Universal Joint Selection for Intermittent Operation With Shock Loading

A single universal joint is to transmit 1/4 horsepower at 300 RPM at an operating angle of 15. Select a suitable joint for Intermittent operation with shock loading. Here we make use of the equation:

loads (300 RPM, 15), the use factor is 16. Due to shock loading there should be an additional dynamic factor of 2. Hence, the rated torque = (52.5) (16) (2) = 1680 in-lbs. Thus the same joints found in the previous example are usable in this case.

5.3 Example 4: Determining the Maximum Speed of an Input Shaft

A universal joint is rated at 250 in-lbs, and operates at an angle of 12. driving a rotating mass, which can be represented (together with the inertia of the driven shaft) by a steel, circular disc, radius r = 6", thickness t = 1/2", attached to the driven shaft. How fast can the input shaft turn if the inertia torque is not to exceed 50% of rated tourque?

From Table 1, for = 12, we have max/ = 0.0442. The weight, W, of the disc is r t y. where y = 0.283 lbs/in and denotes the density of steel. Thus W = (6) (0.5) (0.283) = 16 Ibs. The polar mass moment of inertia, I, of the disc is given by

Hence, if the inertia torque is not to exceed its limit, the max. speed of the input shaft is 588 RPM. For joints made with thermoplastic material, consult the catalogue, which contain design charts for the torque rating of such joints.

6.0 Secondary Couples

In designing support bearings for the shafts of a Cardan joint and in determining vibrational characteristics of the driven system, it is useful to keep in mind the so-calledsecondary couplesorrocking torques, which occur in universal joints.

These are rocking couples in the planes of the yokes, which tend to bend the two shafts and rock them about their bearings. The bearings are thus cyclically loaded at the rate of two cycles per shaft revolution. The maximum values of the rocking torques are as follows:

where Tindenotes the torque transmitted by the input shaft and the operating angle. These couples are always 180 out of phase. The bearing force induced by these couples is equal to the magnitude of the rocking couple divided by the distance between shaft bearings.

For example if the input torque, Tin, is 1000 in-Ibs. and the operating angle is 20, while the distance between support bearings on each shaft is 6", the max. secondary couple acting on the input shaft is (1000) (tan 20) = 364 in-Ibs. and on the output shaft it is (1000) (sin 20) = 342 in-Ibs. The radial bearing load on each bearing of the input shaft is 364/6 = 60.7 lbs. and it is 342/6 = 57 lbs. for each bearing of the output shaft. The bearings should be selected accordingly.

It has been observed also that due to the double frequency of these torques, the critical speeds associated with universal drives may be reduced by up to 50% of the value calculated by the standard formulas for the critical speeds of rotating shafts. The exact percentage is a complex function of system design and operating conditions.

1.0 Joints in Series

As mentioned in paragraph 3, universal joints can be used in series in order to eliminate velocity fluctuations, to connect offset (non-intersecting) shafts, or both.Figure 2shows a schematic of such an arrangement.

7.1 Phasing

In order to obtain a constant anqular-velocity ratio (1:1) between input and output shafts, proper phasing of the joints is required. This phasing can be described as follows: two cardan joints in series will transmit a constant angular-velocity ratio (1:1) between two intersecting or non-intersecting shafts (seeFigure 2), provided that the angle between the connected shafts and the intermediate shaft are equal ( = ') and that when yoke 1 lies in the plane of the input and intermediate shafts, yoke 2 lies in the plane of the in terrnedtate shaft and the output shaft.

If shafts 1 and 3 intersect, yokes 1 and 2 are coplanar. When the above phasing has been realized, torsional and inertial excitation is reduced to a minimum. However, inertia excitation will inevitably remain in the intermediate shaft 2, because this shaft has the angular acceleration of the output shaft of a single universal joint (the first of the two joints in series). It is for this reason that guidelines exist limiting the max. angular acclerations of the intermediate shaft. Depending on the application values between 300 rad/sec and values in excess of 1000 rad/sec have been advocated. In light, industrial drives the allowable speed may be higher. For an accurate determination of allowable speed, a stress determination is necessary.

7.2 Example 5: Determining the Maximum Speed of an Input Shaft in a Series

In a drive consisting of two universal joints in series, phased so as to produce a constant (1:1) angular velocity ratio between input and output shafts, the angle between the intermediate shaft and input (and output) shaft is 20. If the max. angular acceleration of the intermediate shaft is not to exceed 1000 red/sec, what is the upper limit of the speed of the input shaft?Hence, the speed of the input shaft should not exceed 854 RPM, When the joint angle is less than or equal to 10, Table 3 can be used as an alternative.

7.3 Example 6

Same as problem 5, except operating angle is 10, Here we can use Table 3. The intersection of ( = 10 and the 1000 sec curve yields N 1800 RPM. Hence, the speed of the input shaft should not exceed 1800 RPM. A more exact calculation, as in Example 5, yields N = 1726 RPM, For practical purposes however, the value obtained from Table 3 is entirely satisfactory.