- v The Society shall not be responsible for star f, - opinions advanced in papers or

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1 ^pc^ntenn/q( y _ P _ > 4. rftr ME^^ s 80-GT-162 AiIW'I 345E - v The Society shall not be responsible for star f, - opinions advanced in papers or ^ _ - THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 47 St., New York, N.Y ,n d^scuss^on at meetings of the Society or f D.r,rons or Sections. or printed in its Pub lications. Discussio n is printed only l ii - published in an ASME journal or Proceedings Released for genera f i t I,', i iji%on ;; resentation. Full credit should be giver, IC,"^`: f.1e tr _- loomii Giv Sion, and the au h or(s1. Copyright 1980 by ASME L ProgramManager Elastomer Damper Performance A Comparison with a Squeeze G. Burgess Film for a Supercritical Power Project Engineer Mechanical Technology Inc., Latham, N.Y. Mems. ASME R. Cunningham Research Engineer, NASA-Lewis Research Center Latham, N. Y. Mem. ASME Transmission Shaft This paper describes the design and testing of an elastomer damper on a supercritical power transmission shaft. The elastomers were designed to provide acceptable operation through the fourth bending mode and to control synchronous as well as nonsynchronous vibration throughout the operating range. The design of the elastomer was such that it could be incorporated into the system as a replacement for a squeeze-film damper without a reassembly, which could have altered the imbalance of the shaft. This provided a direct comparison of the elastomer and squeeze film dampers without having to assess the effect of shaft imbalance changes. INTRODUCTION A shaft is described as "supercritical" if it runs above one or more of its lateral flexural critical speeds. The need for supercritical shafting arises because of increases in shaft speed or a reduction in lateral critical speeds. With higher rotational speeds, higher power levels can be transmitted and shaft torques can be reduced. Lower system lateral critical speeds are caused by an increase in unsupported shaft lengths which allows a reduction in system weight and number of parts. Unfortunately, rotors which operate in a supercritical regime tend to be more susceptible to nonsynchronous (particularly subsynchronous) vibrations and, accordingly, may require some form of damping to stabilize vibrations. A test rig was designed and built for demonstrating the use of supercritical shafting. During the operation of this test rig, nonsynchronous vibrations from a variety of sources were observed. The test rig was run first with a minimum amount of external damping and then with a larger amount of external damping. In this way, the effect of external damping on nonsynchronous vibration and rotordynamic stability was observed. The external damping was provided by a self-contained, oil-squeezefilm damper and an elastomer damper, both designed to permit operation through the fourth bending mode. TEST FACILITY The test facility was designed to evaluate supercritical power transmission shafting. Tests were performed to identify any problems, needed technology, or limitations inherent in the use of such shafting. One of the principal areas of interest involved the demonstration of balancing of supercritical shafts. The tests included the balancing of a very flexible shaft with both damped and undamped supports. During the course of these tests, severe nonsynchronous vibrations were observed and identified. A sketch of the test rig is presented in Figure 1. A 224-kW (300 horsepower) electric motor is the prime mover for this test rig. The motor drives a variable-speed magnetic coupling, whose output speed was continuously variable from 50 to 3,600 rpm. A gearbox with a ratio of approximately 5.7 to 1 was used to produce a drive-shaft speed of up to 20,000 rpm. The drive shaft was formed from a section of aluminum tubing, 7.62 cm (3 in.) in diameter and 3.66 m (12 ft) long with a wall thickness of mm (0.125 in.). SUPERCRITICAL SHAFT VIBRATION CONTROL BY DAMPING Early testing without a damper did not permit rig operation above 1,200 rpm due to the instability of the subsynchronous excitation of the 16-Hz first critical speed. Stability problems which occurred during this stage of testing clearly established that some form of external damping, coupled with balancing, would be required for control of vibrations. Several methods for applying external damping were investigated, and an oil-squeeze-filmtype damper was first chosen based upon its flexibility and predictability in the level of damping achieved - see [1], [2], [3] and [4]*. Contributed by the Gas Turbine Division of The American Society of Mechanical Engineers for presentation at the Gas Turbine Conference & Products Show, New Orleans, La., March 10-13, Manuscript received at ASME Headquarters January 3, Copies will be available until December 1, *Numbers in brackets refer to references which can be found at the end of this paper.

2 DAMPER DESIGN AND ANALYSIS Use of a damper is a proven and effective method to control flexible rotor vibration. A number of conflicting factors, however, must be given due weight in the design of a damper application. Some of these factors are: The damper must he located at a point which participates, to a significant extent, in all critical speeds where resonance is to be controled. The dynamic characteristics (stiffness, damping and added mass) of the damper itself must allow similar participation in the critical speeds after installation. The damper must, at the same time, provide damping levels which will cause significant reductions in amplitude response at all critical speeds to be controlled. The damper must be able to tolerate the amplitudes to which it will be exposed, without failure due to overheating or overstressing with the components. The damper must be connected to the shaft by a bearing which can survive the imposed loads and speeds. For this particular application, additional considerations for the design of the damper arise. They are as follows: The damper must be easily added to the existing test rig. The damper must be compact and self-contained to be practical in helicopter drive shaft applications. The damper must provide support stiffness as well as damping. Consideration of these factors requires a good analysis of the rotor's dynamic characteristics with and without the damper and interaction of this analysis with parameter studies to find the damper configuration which provides both required dynamic characteristics and strength. The approach selected was to flexibly couple an extension shaft with a damper to the present test shaft and to perform an undamped critical speed analysis of the new shaft geometry. Figure 2 shows the predicted mode shapes and critical speeds for the first five modes. It should be noted that, for all of these modes, there is some significant amplitude at the location of the damper as represented by bearing number 2. This is important to achieve the necessary dissipation of vibration energy at the damper. The initial model of the test rig included a support of 1.75 x 10 5 N/m (1,000 pounds per inch). A damped natural frequency analysis was conducted using a series of damping values from 875 to 10,000 N-s/m (5 to 6.0 pounds-seconds per inch) with this stiffness. The second critical speed was found to be critically damped. The log decrement was plotted as a function of damping for the remainder of the first five critical speeds in Figure 3. The optimum value of damping appears to be about 8,750 N-s/m (50 pounds-seconds per inch). The damped natural frequency analysis was conducted for a series of values of support stiffness from 1.75 x 10 5 to to 10 N/m (1,000 to 15,000 pounds per inch) with a constant damping value of 8,750 N-s/m (50 pound-seconds per inch). Again, the second critical speed was critically damped. Log decrement was plotted as a function of stiffness for the remainder of the first five critical speeds in Figure 4. The only critical speed for which there was a substantial detrimental effect from increasing support stiffness was the first critical speed. However, this effect was serious enough to require that the support stiffness be kept below x 10 5N/m (5,000 pounds per inch). EZE-FILM DAMPER DESIGN AND TESTS The decision, based on the rotor-dynamic analysis, was made first to design a hydraulic mount for a stiffness of 7 x 10 5 N/m (4,000 pounds per inch) using an 0-ring as the spring member. Studies recently performed by Smalley, Darlow, and Mehta [5] reveal that this is about as low as can be practically achieved for this configuration. The squeeze-film damper was designed to be a sealed damper with no circulation of the oil. In this way, the damper would require no support hardware (such as oil supply pumps) which would prohibit its use in helicopter or other space- and weightlimited applications. A sketch of the test rig damper is shown in Figure 5. The hydraulic damper was evacuated, filled and sealed, and pressurized by the use of a bladder. The damper was predicted to generate less heat than the bearings, so the dissipation of heat was not expected to be a serious problem. The 0-ring retainers are radially adjustable, so that the hydraulic damper may be centered manually to compensate for static deflection of the 0-rings. The damper was designed to achieve a level of damping in the range of 8,750 N-s/m (50 pound-seconds per inch) for silicone oil with a viscosity of about 80 centistokes, using the short bearing theory and assuming no cavitation. The radial clearance is mm (25 mils), and the length and diameter are 7.62 cm (3 in.) and cm (4 in.), respectively. Although the hydraulic damper was designed to allow for the two 0-rings, it was used initially with just one 0-ring to obtain a low parallel support stiffness of 7 x 10 5 N/m (4,000 pounds per inch) for a continuously supported 0-ring. Testing showed that the dynamic stability of the test rig was improved as a result of the squeeze-film damper. However, the addition of external damping alone could not provide complete control of all test shaft vibrations. The test shaft also had to be balanced to achieve safe operation throughout its speed range. Through the combined use of external squeezefilm damping and balancing, the rig was safely run to over 12,000 rpm while negotating the first four flexural critical speeds of the test shaft. This speed was over 10 times that which could be achieved without any external damping. At 12,000 rpm, substantial synchronous growth of the response of the fifth critical speed occurred. There was also a very large subsynchronous response of the first and fourth critical speeds. In fact, the subsynchronous response of the first critical speed, while running at 12,000 rpm, was such that the test rig could not be run higher in speed. It is possible that subsynchronous response of the first critical speed was due to internal damping, similar to that observed with the undamped test rig. If this is the case, then the effect of the added damping was to raise the threshold of this instability from just over one time the first critical speed to almost 13 times the first critical speed, which was indeed a substantial improvement. The subsynchronous response of the fourth critical speed was most significant at the rotational speed

3 of about 11,800 rpm, as illustrated by the frequency spectrum plot at the top of Figure 6. However, at a rotational speed of 12,000 rpm, the subsynchronous response of the first critical speed became predominant, while that of the fourth critical speed had become much less significant, as illustrated by the frequency spectrum plot presented at the bottom of Figure 6. In any case, it was demonstrated that the test rig could be run to more than 11,000 rpm with no large synchronous or nonsynchronous responses of the test shaft. Additional details of the observed nonsynchronous effects noted with the power transmission shaft were provided by Zorzi and Darlow [6]. ELASTOMER-DAMPER DESIGN AND TESTS The design of the Viton-70 elastomers utilized in the supercritical shaft was based upon extrapolated data obtained from 0-ring testing during previous elastomer testing [5], and the stability analysis performed is shown in Figure 3. The supercritical shaft, squeeze-film damper (Figure 7) was modified to accept replacement elastomer dampers. The design requirements included consideration of shaft disassembly and reassembly imbalance changes. The elastomer dampers were required to replace the squeeze-film damper without the necessity of shaft/ damper disassembly. This permitted a direct comparison of elastomer and squeeze-film performance. The six Viton-70 buttons, Figure 8, were cm (0.25 in.) in diameter and cm high. Six buttons provided a stiffness of approximately 7 x 10 N/m (4,000 pounds per inch) with a loss factor of 0.75 used for design purposes. Figure 9 shows the elastomer button as assembled in the squeeze-film damper housing (Figure 7). The elastomer consistently permitted higher operational speeds than the hydraulic mount. Figure 10 illustrates the synchronous response measured when the power transmission shaft was balanced through the third critical with an elastomer damper. A change to the hydraulic mount did not permit operation through the third mode. With the squeeze film operable, trim balancing of the first and third mode was continued, and the elastomer was again installed. Figure 11 illustrates the fact that the elastomer once again outperformed the hydraulic mount, although the elastomer did not reduce vibration through the first mode as well as did the squeeze film for this run. Later balancing with the elastomer permitted operation to 13,000 rpm (Figure 12), which is 1,000 rpm higher than that achieved with the squeeze film (Figure 6). However, as was the case with the squeeze film, the unstable subsynchronous excitation of the 16-Hz first critical was again the factor which limited higher-speed operation of the power transmission shaft (Figure 13). the sponsor of this program, Mr. W. Spodnewski for his support during the testing phases of this program, and Mrs. Gillham who performed the rotor analysis for this program. REFERENCES 1 Thomsen, K.K., and Anderson, H., "Experimental Investigation of a Simple Squeeze-Film Damper." ASME Paper No. 73-DET Vance, J.M., and Kirton, A.J., "Experimental Measurement of the Dynamic Force Response of a Squeeze-Film Bearing Damper," Journal of Engineering for Industry, Trans. ASME, Series B, Vol. 97, No Sharma, R.K., And Botman, M., "An Experimental Study of the Steady-State Response of Oil-Film Dampers," ASME Paper No. 77-DET Marmol, R.A., and Vance, J.M., "Squeeze-Film Damper Characteristics for Gas Turbine Engines," ASME Paper No. 77-DET Smalley, A.J., Darlow, M.S., and Mehta, R.K., "The Dynamic Characteristics of 'O-rings'," ASME Paper No. 77-DET-27, June, Darlow, M.S., Zorzi, E.S., "Nonsynchronous Vibrations Observed in a Supercritical Power Transmission Shaft," ASME 79-9T Darlow, M.S., and Smalley, A.J., "Design and Application of a Scale Model Test Rig for Supercritical Power Transmission Shafting," MTI Report 78- TR41, June, CONCLUSIONS From these results it is concluded that elastomer dampers can control nonsynchronous as well as synchronous vibration of high-speed rotating machinery. Furthermore, the 0lastomer damper used in this application continually outperformed the squeeze film and permitted higher-speed operation of the supercritical shaft. ACKNOWLEDGMENTS The author acknowledges the aid of NASA-Lewis, 3

4 TORQUING GEARBOX (2500 HP) LOW SPEED SHAFT DRIVE-.. - GEARBOX FLOOR LEVEL - LUKE RESERVOIR ^ ^' f MAGNETIC COUPLING \ -S _ ^'y1 SPEED CONTROL.4. S 300 HP. 1800/3600 RPM DRIVE MOTOR - r. / ^ '2 TRANSMISSION SHAFT TEST SECTION i l `^. ' (SECTIONS UP TO 30-FT LONG ^'^.^`. ^^ CAN BE TESTED AT SPEEDS r TO RPM) Ii^-10 /. ^^_6 Fig. 1 Drive train technology test rig configuration for high-speed shaft balancing It u u m mto Il 2nd ROTOR CRITICAL SPEED rpm u alt Mmm I I 4th ROTOR CRITICAL SPEED rpm It flit. r u i n u C7 ^^ m mm ^ 1 I I N M ` Ist ROTOR CRITICAL SPEED rpm u ^ C^C^ a ii co m I 3rd ROTOR CRITICAL SPEED rpm :r\i?\7r 5th ROTOR CRITICAL SPEED 13,506.7 rpm Fig. 2 Mode shapes of the first five critical speeds, original shaft with extension to carry squeeze-film dampers 4

5 W 18 K=1000 1st CRITICAL SPEED ("-800 rpm) th CRITICAL SPED 7450 rpm) rd CRITICAL SPEED yzj (^-3600 rpm).10 /.08 / O ^ (^-7500 rpm) 7 / I I _.L.04 '.02r j 5th CRITICAL SPEED (^13,000 rpm).06-4th CRITICAL SPEED DAMPING lb-sec/in ,125 17,500 DAMPING N - s/m Fig. 3 Log decrement as a function of damping (stiffness = 1.75 x 10 5 N/m (1000 lb/in.)) ti r4.10 U W.08 O rd CRITICAL (ti 3500 rpm) 5th CRITICAL SPEED (^-13,200 rpm) SPEED. Ist CRITICAL SPEED (ti 850 rpm) Jili 0 I DAMPER SUPPORT STIFFNESS (x 103) lb in DAMPER SUPPORT STIFFNESS (x 105) N/m Fig. 4 Log decrement as a function of support stiffness (damping = 8750 N-s/m (50 lb-sec/in.)) Fig. 5 Sketch of squeeze-film damper designed to suppress vibrations in supercritical power transmission shaft a a / 125 Hz RPM (200 Hz) First r 4th Critical i 1/Rev. Critical 400 Hz Cage / 2/Rev. r Freq. j/ a X 16 Hz First Crit. SQUEEZE FILM CLEARANCE ELASTOMER BUMPER SCREWS PROBE LOCATION 12,000 RPM (200 Hz) 1/Rev. 400 Hz 2/Rev. ' 1 0'-RING _ DAMPER ELASTOMER SAFT (6 CIRCUMFERFNTIAL ^ LOCATIONS DOUBLE ROW PERMITTED) D 500 Hz Fig. 6 Frequency spectrum plots of test shaft vibrations with a damper running near 12,000 rpm Fig, 7 Elastomer damper/squeeze-film damper schematic 5

6 50 MILS P j._.p N,> A 1,SLVi"LY NJ J I----SQUEEZE FILM ELASTOMER f I LAS uymi L^TEN A Hz 51 Fig. 10 Synchronous response mow», 25 MILS SQUEEZE FILM Fig. 8 Elastomer damper assembly w H J FIRST I THIRD CRITICAL RITICAL ELASTOMER L PIll Aw: '. [MUM SPEED 7400RPM 0 Hz 20( Fig. 11 Synchronous response,platen 50 MILS EL ASTOMER C CRITICAL Fig, 9 Elastomer damper installed in rig,third AXIMUM SPEED 13,000 RPM 0 Hz 50 Fig. 12 Synchronous response on elastomer damper 6

7 I0 MILS 216 Hz I/REV 6Hz ^ FIRST CRITICAL 433Hz " 2/RE Hz 500 Fig. 13 Frequency spectrum at 13,000 rpm with elastomer paper operational