Design and Application of Flexible Diaphragm Couplings to Industrial-Marine Gas Turbines

Transcription

1 73-GT-75 $3.00 PER COPY $1.00 TO ASME MEMBERS The Society shall not be responsible for statements or opinions advanced in papers or in discussion at meetings of the Society or of its Divisions or Sections, or printed in its publications. Discussion is printed only if the paper is published in an ASME journal or Proceedings. Released for general publication upon presentation. Full credit should be given to ASME, the Professional Division, and the author (s). Copyright 1973 by ASME Design and Application of Flexible Diaphragm Couplings to Industrial-Marine Gas Turbines N. B. ROTHFUSS Product Manager, The Bendix Corp., Fluid Power Div., Utica, N. Y. This paper discusses the common needs of different industrial-marine gas turbine systems for flexible power transmission coupling shafts and shows how the flexible diaphragm coupling has been successfully applied to such gas turbines as the TPM FT-4, G. E.'s LM2500 and several others. Most aircraft derivatives and the larger industrial gas turbines require lightweight, maintenance-free, quiet flexible couplings. The diaphragm coupling will fill this need if properly designed and applied. Materials and methods of making preliminary natural frequency calculations and computer modeling of the diaphragm coupling are also discussed. Contributed by the Gas Turbine Division of The American Society of Mechanical Engineers for presentation at the Gas Turbine Conference and Products Show, Washington, D.C., April 8-12, Manuscript received at ASME Headquarters January 11, Copies will be available until February 1, THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS, UNITED ENGINEERING CENTER, 345 EAST 47th STREET, NEW YORK, N.Y

2 Design and Application of Flexible Diaphragm Couplings to Industrial-Marine Gas Turbines N. B. ROTHFUSS INTRODUCTION Gas turbines, steam turbines, high-speed centrifugal compressors, and pumping systems in the industrial and marine field are using more flexible diaphragm metallic disk couplings because of their common need for long life, vibration-free power transmission. Having been used on aircraft for the past 20 years to transmit power between the gas turbine engine and a remotely mounted accessory, the metallic diaphragm coupling now enjoys the position of being specified and used on new mili- Fig 1 Single flexible contoured diaphragm tary aircraft in the U.S.A., primarily because of its high reliability, no maintenance and light weight. This trend toward more use of dry metallic couplings is also taking place in the industrial-marine field. A diaphragm coupling accommodates misalignment while transmitting power by material flexure. It does not require lubrication. Angular and axial movements occur in the flexible metal disk as elastic deflections. By proper design and application, the combined steady-state stresses and cyclic fatigue stresses are kept far below the material "infinite" life fatigue strength to insure years of maintenance-free service. A complete coupling has one or more flexible disks. Its capability for accommodating misalignments depend upon the number of disks, their size, and their spacing. Where the driving turbine and driven machine are separated by a significant distance, the coupling is often referred to as a flexible shaft or coupling shaft and has one or more flexible disks at each end. Fig. 1 illustrates a contoured diaphragm used in a Bendix flexible diaphragm coupling. Torque is transmitted between the rigid hub and the rigid rim through a disk of variable thickness, having,a contour of the shape approximating a hyperbola. This shape insures uniform shear stresses and minimum bending stresses. The use of a rigid rim and rigid hub with generous radii blending the profile to these rigid connecting points minimizes local stress concentrations and eliminates unexpected and unpredictable fatigue failures. Fig. 2 shows, in an exaggerated manner, the shape of a single diaphragm when subjected to angular misalignments and axial movements. It also illustrates how the diaphragms accommodate angular, axial, and parallel misalignment and how they may be added in series at each end of a coupling shaft when it is necessary to operate 2

3 Negligible Axial Expansion Torque Casing ' Expansion (a) IL] Axial Deflection --Shaft Expansion h -Casing I l -Shaft (d) --Cosing+Shaft Expansion (b) X Shaft Bearing 0 Thrust Bearing A Case Support Fig. 3 Thermal movements of shaft and casing Fc Fc Mt Angular Misalignment Parallel Offset M2 Mt thrust forces when required to provide flexibility while operating under load. Some systems also need couplings with very precise and permanent balance because they are very sensitive and a small unbalance results in excessive vibration. (c) Fig. 2 Diaphragm coupling arrangements under conditions of high misalignment. By design and material selection, the flexible diaphragm coupling is always rated for "infinite life" when operating simultaneously at the specified torque, speed, and misalignments. COMMON NEEDS OF GAS TURBINE SYSTEMS Industrial-marine gas turbines need light weight, long life, maintenance-free flexible couplings that have predictably low bending and Flexibility The flexibility requirements vary with each system. Mechanical drives, where there is a thrust bearing in the driven gear, generally require axial movements of 1/4 in. and occasionally up to 1 in., depending upon the thermal growths. Driven equipment, such as electrical generators whose rotor shafts can float axially in the bearings, do not require high axial movement, but the coupling must be capable of repositioning the driven rotor. System angular misalignments and axial movements result from installation tolerances, thermal growth of the system shafting, structure and casings, and deformation of supports. Deterioration of mountings may also add to misalignments. Generally, 1/8-deg angular misalignment is specified, but some systems require 1/2 deg at each end of the coupling shaft. Installation and Alignment Gas turbine systems require coupling shafts that are easily installed and provide for quick simple engine alignment and realignment if an engine or gear box is changed. The coupling shaft itself should be able to be replaced without moving the engine or gear box. When properly applied, the coupling can help reduce start-up

4 problems by making alignment easy and eliminating vibration. High axial movement is a limitation of the flexible diaphragm coupling and is not normally applied to match the large movements permitted by its dental coupling counterpart. Because of this, the initial system axial alignment must also carefully account for thermal expansions of both the driving turbine shaft and the driven gear. Systems are generally positioned cold so they grow into alignment when hot. Thermal expansions, causing horizontal and vertical shaft movement, result as angular misalignment and are easily accommodated by the diaphragm coupling; however, thermal expansions that change the coupling length during operation must be more accurately accounted for. Drive turbines and the driven gear generally have both shaft thrust bearings and case supports. The location of these, with respect to the coupling, is important to the steady-state and transient axial movement. Fig. 3 shows how the relative location of the thrust bearing and casing support can greatly affect the coupling axial movement at the driving end. Equal consideration must also be given to the driven side of the coupling. The total relative movement of the driving and driven shaft then represents the true axial movement required of the coupling. Note that the system in Fig. 3(d) may have a transient growth due to thermal time differences between casing and shaft. Forces During operating and shutdown conditions, the end loads, bending moments, and vibration forces caused by the flexible coupling must be within predictable pre-established limits for the life of the design. If these forces or operating characteristics change from operating time or load, frequent condition monitoring and coupling maintenance is required to guard against rapid deterioration of the coupling or other system components, such as support bearings, thrust bearings, housings etc. Critical Speed The aircraft derivative gas turbines and the larger more rugged industrial gas turbines require long turbine output shafts to reach beyond the exhaust ducting. The flexible couplings and shafting Must be light and provide low overhung moments, low imbalance, and permanent balance to insure smooth vibration-free operation, as these systems often run near a system natural frequency. The ability to make a last minute change in the torsional spring rate of the coupling in a prototype system has also proved to be invaluable. Noise On some marine systems and many new industrial systems, no noise generation is permitted and noise attenuation highly desirable. In two recent applications, the diaphragm coupling was chosen because of its noise characteristics. It avoided noise generation in one instance and provided noise attenuation in the other. There are a few very significant features of diaphragm couplings that reduce noise generation, such as its ability to transmit torque at constant velocity ratio between the turbine and the driven gear. Also, there is no backlash and no rubbing parts. Severe Environments Operation in high ambient temperatures and corrosive atmospheres are occasionally required by the aircraft derivative gas turbines. The diaphragm couplings used in the LM2500 engine on the Admiral Wm. M. Callaghan were manufactured from Inco 718, a high nickel alloy, because of its strength at high temperatures and resistance to corrosion. DIAPHRAGM COUPLING DESIGN CONSIDERATIONS Materials The flexible diaphragm coupling requires a material having high tensile and fatigue strength, also good weldability for designs employing electron beam welded joints. Vacuum melted AISI 4340 is a very popular and reliable material for industrial gas turbine applications. Its ambient temperature limit of 600 F is rarely required. When operating temperatures are above 600 F, H-11 tool steel may be used. In special high-speed applications where extreme light weight is required and in aircraft applications, 18 percent nickel maraging steel is used and for systems requiring,high corrosion resistance, Inco 718. In one instance, 6AL4V titanium was applied. There is a wide choice of materials for adapters and interconnecting tubes, ranging from standard AISI 4130 and 9310 tubing to aluminum. Often weld joint compatibility dictates the spacer tube material. Safe Life Versus Fail Safe Design Some steam and gas turbine systems require couplings with limited end float and, in rare instances, redundancy of torque transmission. Diaphragm couplings can be provided with internal 4

5 stops for limited end float. For overload protection, spline-like surfaces that are not in contact during normal operation are used. These spline surfaces are also designed to redistribute an unexpected overload to protect the diaphragm or to drive the full torque in the event of a diaphragm failure. The safe life design philosophy has been very successful. This is accomplished by keeping an adequate margin of safety at all combined operating conditions with respect to the infinite fatigue strength of the material. Overload conditions must also be below the yield point. In most systems, sensors are used to detect system conditions, and vibration sensors will normally detect an insipient coupling failure as an increase in the vibration level of the operating system. SYSTEM DESIGN CSNSIDERATIONS Lateral Critical Speed and Balance Turbine driven systems all too often seem to operate near enough to one of its lateral critical speeds that even a slight coupling and shaft adapter unbalance can result in excessive system whirl and vibration. Preventive action to avoid vibration linked with rotational speed is to calculate the various lateral, axial, and torsional resonant frequencies before the design of the system elements are finalized. For multi-. element systems, computer programs are available for reliable predictions of resonant frequencies. Coupling Balance The diaphragm coupling is designed in such a manner that the center spacer shaft or "flex unit" may be removed and either the driving turbine or the driven device can be operated independently. For this reason, among others, the coupling adapter parts are first balanced individually, then the complete coupling is balanced with corrections made on the spacer shaft. Attachments are made using body-fitted bolts or close-fitted pilot diameters, insuring repeatable unbalance between factory arbors and field conditions, also, repeatable balance after field disassembly and reassembly. Unbalance requirements vary considerably between turbine manufacturers and between manufacturers of centrifugal compressors, gear boxes, etc. Marine installations generally specify the unbalance requirement in MIL-STD-167 (Ships): U (in.-oz) = 4W/N. This formula was developed many years ago when heavy dental couplings were used at low speeds. With the advent of the highspeed turbine and the lightweight, high-speed flexible coupling, this formula often results in an unrealistically low unbalance. 20 W/N or 40 W/N are now being used, and one centrifugal compressor manufacturer specifies the unbalance on a constant velocity basis in inches per second (ips) at each end of the coupling. This is defined as the rotational surface speed of the coupling whirling about its eccentricity, i.e., single amplitude of vibration when on the balance machine. Lately, the trend is to define the allowable unbalance as a function of the speed squared: Exceptionally low unbalances have been specified for the individual parts of dental (gear) couplings, but, when assembled in a system, the radial clearance required in the teeth for proper operation, multiplied by the weight of the spacer shaft, causes a system unbalance that exceeds that specified for the components by a factor of 10 to 100. This, of course, is one of the major advantages of a metal disk coupling. It does not have radial or torsional backlash. Naturally, the final evaluation of coupling unbalance is just how smooth does the system work and will the system stay smooth throughout its operating life. As previously stated, the closer a system is operating to a critical speed, the more critical is the coupling unbalance. Centrifugal Force The centrifugal force acting on each support of a rigid body is a function of unbalance and speed. Note that the units of unbalance are generally oz-in. or gm-in. U = 16 We (1) W = weight of body at each support (lb) e = eccentricity -- distance between center of rotation and center of gravity (in.) U = unbalance (in.-oz) each end where: Fc = 1.78 x 10-6 UN2 (2) F c = centrifugal force each support (lb) N = speed (rpm) Note: The force at each end is a function of the weight at each end. Reaction Loads -- Fig. 2(c) The reaction loads on the connected equipment, due to the diaphragm coupling bending spring rate, are often so low as to have no effect upon the machines. In any event, these loads may be readily calculated as they are strictly a func- 5

6 In addition to the, reaction load resulting from bending spring rate, there will be a bending torque moment (Mt) applied to the driving and driven shafts if there is angular misalignment in combination with torque. This additional bending moment is not related to the type of coupling as it exists with all types of couplings or coupling shafts and occurs in a plane 90 deg to the plane of bending angle (0). where M t = Tsin 0 (5) M t = bending moment from torque (lb-in.) T = torque (lb-in.), (b) L (d) Fig. 4 Rigid body vibrations tion of elastic deflection of the diaphragm and are independent of transmitted torque or rotational speed except for the unbalance and centrifugal force considerations. The bending moment reaction (M), which is transferred to the machine bearings, is simply equal to the bending spring rate of the coupling times the angle (0) at which the coupling'is deflected. The transverse shear load (F) on one machine is equal to the sum of the end moments divided by the distance (L) between the centers of articulation. where M = Kc B (3) F = (M 1 + M2)/L (4) M = bending moment (lb-in.) 0 = coupling angle (deg) Kc = coupling bending spring rate (lb-in./deg) Axial Loads and Axial Preloading Changes in length of the coupling by flexure of the diaphragms require a force proportional to the deflection from the neutral or free length. The amount of this force is dependent upon the axial spring rate of a single diaphragm and the number of diaphragms in the coupling. The total axial spring rate of a two diaphragm coupling, when the diaphragms are in series, is 1/2 of the individual diaphragm rate. Multiple diaphragm couplings have a spring rate equal to that of one diaphragm divided by the number of diaphragms in the coupling. For installations where the axial deflection required for a given coupling is greater than would be permissible from a stress or axial load viewpoint, it is possible to install the coupling in a preloaded condition. This will enable the axial movement to move the coupling from the preload position, througn neutral, to a load position, thus doubling the axial deflection capability. This technique is especially valuable in connecting machines whose shafts grow toward each other a known amount due to thermal expansion. Lateral Vibrations and Rotational Critical Speeds During the preliminary system design and selection of diaphragm coupling size, various rigid body "stick mode" vibrations and simple lateral whirl frequencies should be calculated to insure they are outside the operating speed range. The finalized system must then be completely calculated, using multi-element computer methods. Fig. 4 illustrates two conditions of rigid body lateral vibrations (c) and (d) and one of simple lateral whirl (e), the flexible diaphragm being depicted by a circle on the line schematic. When a single diaphragm is used, the flexible joint may be treated as a pin joint having an 6

7 AXIAL VIBRATION C 0-0J 7 (o) Fig. 6 Axial vibration of spacer g = 386 (in./sec 2 ) (o n = frequency (cpm). (b) (c) (d) Fig. 5 Rigid body vibrations It is very desirable to have these frequencies out of the operating speed range by a significant margin, 50 to 100 percent or more. Fig. 4(d) shows a condition of simple dynamic whirl, first critical speed of the spacer shaft. This can be calculated using the following equation which has also been derived assuming the single flexible diaphragm acts as a pin joint with infinite lateral spring rate (i.e., simple support). Nc = 7r 2 [EI/UL4] 1/2 60/2v (7) where infinite radial spring rate for simple calculations. When used in a computer model, it is best E = material bending modulus (psi) treated as a pin joint with infinite radial spring I = shaft bending moment of inertia (in. 4 ) rate and a specific bending stiffness (lb-in./deg). u = mass per unit length, i.e., total weight/gl The diaphragm bending stiffness can be accurately (1b-sec2/sq in.) calculated and is linear within the range of angu- L = shaft length lar deflections normally used. Nc = critical speed (cpm). Figs. 4(b) and 4(c) show two modes of rigid body motion, and K1 represents the lateral spring In this case, every attempt is made to keep the rate of the support bearings. If the coupling calculated whirl critical at least two times weight is distributed equally at each support and the maximum operating speed. if the support spring rates are equal, then the Fig. 5(a) illustrates a flexible diaphragm vibration modes will appear as shown in the sche- coupling shaft having two flexible diaphragms matics. The various frequencies can be approxi- arranged in series at each end. An infinite mated by the following formula. lateral spring rate cannot be used for this type of flexible joint. The following equation gives (o n = [Kied l'60/2-rr (6) the formula for calculating the lateral spring rate of this type of coupling. where Kd = 360 KID /TrL (8) K1 = support spring rate (lb/in.) W = effective weight of coupling at the where support (lb), a function of cg loca- Kb = single diaphragm bending spring rate tion and mode shape (lb/in.)

8 Fig. 7 TPM FT-4 Euroliner system showing diaphragm couplings Fig. 8 TPM FT-4 Marine engine module L c = distance between diaphragm center -lines (in.) Kd = coupling lateral spring rate (1b/in.) Knowing how the weight of the spacer shaft is distributed at each coupling and the lateral spring rate (Kd ) of each coupling, the natural frequency illustrated by Figs. 5(c) and 5(d) can be calculated using the following formula. Again, the reader must be reminded that the weight (W) is the effective weight as seen by the coupling. w n = Kdg/ 1/260/2, (9) Fig. 5(d) again depicts the simple whirl mode deflection. The critical speed of this system should be approximated using multi-element computer methods because the lateral stiffness of the diaphragm coupling at each end and the modulus and stiffness of the spacer shaft have a large effect upon each other. In most instances, however, it has been found that the approximation used in equation (7) is applicable. 8

9 For complete system computer modeling, this multiple-element coupling can be reduced to finite elements two ways, the equivalent quill shaft method shown by equations (10) and (11) or the preferred pin joint with bending stiffness method as previously described. In this case, the computer model will have a pin joint at each diaphragm. The element connecting the pin joints should have an EJ, length and weight, etc., identical to the actual parts. The "equivalent quill" method simply replaces the coupling with a simple solid shaft having an equivalent bending, shear spring rate and EI. OD = [584 Kb Lq/E] 4 (10) Lq = L cv7 Note that the equivalent length of the quill (Lq ) isartlonger than the actual diaphragm spacing. It is also important to point out that this method will not result in an equivalent torsional spring rate. The length (Lc) should always be kept as short as possible. Axial Vibrations The center tube of a flexible diaphragm type coupling is usually connected only to the two diaphragms, Fig. 6; thus, it represents a mass freely suspended on springs. The total axial spring rate, as seen by the spacer tube, in this case is twice the diaphragm spring rate. The center tube will respond to an axial input vibration and will vibrate at its resonant frequency. Generally, this vibration does not cause trouble unless a significant amount of amplitude is present at exactly the resonant frequency. Operation at the rotational speed corresponding to the resonant axial frequency could cause an axial vibration, and, although it is not normally severe, such operation should not be continuous. The following formula can be used to calculate the axial resonant frequency. where Nn = [Kg /W ]i 60/27r (11) K = sum of axial spring rate of each coupling (lb/in.) W s - weight of spacer tube (lb) w n = frequency (cpm). Nonlinearity of axial spring rate with axial de- Fig. 9 Euroliner diaphragm coupling flection must be considered when applying the formula. GAS TURBINE APPLICATIONS The flexible diaphragm coupling is being used with many different gas turbine systems, such as the TPM FT-4, G.E. LM2500, Lycoming TF-25A, DDAD (Allison) 501, Deltex/DeLaval Turbopac 1400 with LM1500 gas generator, and others. TPM is using diaphragm couplings with their FT-4 Twin Pac electrical generator systems, marine drive propulsion systems for the four Seatrain gas turbine driven ships, Euroliner, Eurofreighter, Asialiner, and Asiafreighter, for the U. S. Coast Guard Ice Breaker and for special mechanical drives, such as centrifugal compressors and pump drives as well as mobile generator sets. Fig. 7 is a partial cross section of the TPM FT-4 engine showing the power turbine extension shaft and flexible diaphragm coupling connect ed to a reduction gear. A similar system will be used to drive the new USCG Ice Breakers. The coupling at the gear end has two very flexible diaphragms. These absorb 0.34-in. thermal growth of

10 Fig. 10 G.E. LM2500 Admiral Wm. M. Callaghan installation showing diaphragm coupling Fig. 11 Single diaphragm used in G.E. LM2500 coupling for the Admiral Wm. M. Callaghan the power turbine extension shaft and the angular misalignment. The relative angular and parallel misalignment between the engine and the gear is very low, well within the capability of the single diaphragm flange at the turbine end. TPM selected a flexible diaphragm coupling because they needed a coupling that would absorb angular and axial movement due to thermal growth and have a lightweight and low unbalance to reduce the overhung moment on the bearings, thus increasing the lateral critical speed of the power turbine extension shaft and eliminating vibration caused by unbalance. The no-lubrication feature, which eliminates potential seal leakage problems, is another reason for their selection of a dry coupling. Engine alignment is very quick and easy because of tine short length of the coupling (5.5 in.). The gap width, parallelism, and shaft concentricities can be measured with a simple dial indicator, rotating the free turbine by hand. The alignment procedure developed by TPM can be completed in approximately one half day, and their experience shown that changing of a gas generator or power turbine has not required engine realignment, although provisions are made for minor realignments after the frame has been initially aligned and grouted or chocked in position. The alignment specifications are developed by calculating the thermal growth of the free turbine output shaft and of the driven gear box shaft, axially and vertically, based upon the average horsepower for the application. Shaft hydrodynamic offsets are also calculated. Fig. 8 shows the TPM FT-4 marine engine module for Sea Train Lines with the power turbine extension shaft and flexible diaphragm coupling. The diaphragm couplings (Fig. 9) on the Euroliner are approaching 10,000 hr each and the two on the Eurofreighter, 5000 hr each. This performance is notable because they have been completely free of any maintenance or inspection requirements. Fig. 10 is a cutaway section of the LM2500 showing the power turbine outboard support bearings, turbine power output shaft, and flexible diaphragm couplings. This system was designed for relatively high angular, parallel, and axial misalignments between the engine module and the reduction gear, and two diaphragms are used in series to make up a coupling. In December 1969, the port engine of the Admiral Wm. M. Callaghan was changed to an LM2500 engine, and these diaphragm couplings have not been changed, having accumulated over 17,000 hr as of October The reasons for selecting flexible diaphragm couplings for this gas turbine installation were very similar to those discussed with the FT-4, 1 0

11 Fig. 12 Stewart & Stevenson DD963 gas turbine generator set Lowspeed Shaft 120 rpm Test Gear Slave Gear Drvej Highspeed Shafts 3600 rpm Fig. 14 Schematic of DD963 reduction gear test stand -- Westinghouse Marine Division Fig. 13 Flexible diaphragm million in.-lb torque capacity although in this case, the high-temperature environment, estimated to be 750 F, required the selection of a material that had high fatigue strength at the high temperature witb corrosion resistance For this reason, General Electric selected Inco 718. Fig. 11 shows one of the 22-in. OD flexible diaphragms having provisions for bolting at the rim and the hub. Structure-borne noise is becoming an important consideration on many new gas turbine systems. One recent application for flexible diaphragm couplings is on the Shi; Service generator system to be supplied by Stewart & Stevenson to Litton Industries for the DD963. This systell as illustrated in Fig. 12. uses a DDAD (Allison) 501 gas turbine driving through a Philadelphia Gear reduction box and an Electro Dynamics electric generator. The flexible diaphragm coupling is located on the lowspeed side of the system between the gear box and the generator. In this position, the coupling accommodates all of the misalignments between the generator and the gear box. Fig. 13 shows a 64-in-dia diaphragm capable of transmitting 15,000,000 in.-lb of torque at 120 rpm. These couplings were selected by Westinghouse, Marine Gear Division, Sunnyvale, for their DD963 reduction gear test stand to attenuate 'the transmission of noise between the slave gear and test gear. This back-to-back test stand is shown schematically in Fig. 14 and uses flexible diaphragm couplings on both the high-speed and lowspeed interconnecting shafts.

12 CONCLUSION The future utilization of flexible diaphragm couplings in high-speed and low-speed gas turbine and marine systems appears excellent. Their features of light weight, low and permanent imbalance, zero backlash and no maintenance essentially provide the common requirements of different gas turbine systems. Relatively large diaphragms now being manufactured will be evaluation tested for marine line shafting, and one can foresee growth in the use of metal couplings to isolate forces and bending moments and attenuate vibrations between the reduction gear and the thrust bearing for many marine propulsion systems. ACKNOWLEDGMENTS The author wishes to acknowledge and extend gratitude to David O'Neil and Bill Wurtz of TPM, W. Swanson of General Electric Company, Leon Kasbaum of Stewart & Stevenson, and Dan McAllister and Henry Miller of Westinghouse Marine Division, for providing drawings and operating information. 12