solid model rotor dynamics

Transcription

1 solid model rotor dynamics A traditional practice in the rotor dynamics analysis is to use beam models for both the lateral and the torsion analysis. Such an analysis limits the capabilities for the modern day design of high-speed machinery. Veeresh Vastrad QuEST Global

2 contents 1.0 Abstract Understanding Rotor Dynamics in an Everyday Environment Understanding the Market Need to Adopt Solid Model Rotor Dynamics Process Description and Product Lifecycle Stages The Challenge Method Results Limitation of Solid Model Rotor Dynamics Conclusion Author Profile About QuEST Global 09

3 Abstract A traditional practice in the rotor dynamics analysis is to use beam models for both the lateral and the torsion analysis. Such an analysis limits the capabilities for the modern day design of high-speed machinery. The beam type one-dimensional models require good modeling techniques to approximate the three dimensional rotors. An analysis of this type is usually followed for most of the steam turbine and compressor rotors. The accuracy of the beam modeling analysis is limited to how best the mass and stiffness terms in the system are captured. For a complex geometry such as that of the rotor, it is difficult to accurately capture these terms in the rotor dynamics beam model. Solid model rotor dynamics provides an accurate solution for such problems. Solid model rotor dynamics analysis is demonstrated within QuEST through the uses of the ANSYS finite element code. The solid models allow significant advantages by eliminating tedious, time-consuming, equivalent beam modeling procedures. in the rotor dynamics analysis which are not considered in the conventional beam element modeling. The spin softening effect has significant influence on the backward whirl modes and the stress stiffening effect on the forward whirl modes. Another significant advantage of the solid models lies in the fact that all the coupled modes of shafts, disks, and other mounted parts can be accounted in one analysis, which otherwise cannot be handled by the beam models. With the enhancement of element capabilities introduced in ANSYS, it is now possible to include the effects of gyroscopes in the solid element models. With the provision of applying different speeds to different elemental components, it is possible to simulate the rotor dynamics analysis considering the effect of the casings. This provides an efficient real-life rotor dynamics simulation of the present day rotors which is more accurate than the conventional modeling approach. A specific advantage of solid models is the inclusion of stress stiffening, spin softening, and temperature effects Understanding Rotor Dynamics in an Everyday Environment Most of the modern day equipments, be it for power generation applications or for industrial applications, employ one or the other rotating components called rotors which are the main elements for the power transmission. Rotor dynamics is a collective term for the study of the vibration of these rotors. For the effective running of these units and to ensure the integrity of the unit, accurate rotor dynamics analysis is essential. Rotor dynamics is a system level analysis unlike the vibration analysis of the individual components. To meet the weight and the cost requirements, the present day rotors are made extremely flexible; this makes rotor dynamics as an essential part of the design. It involves the prediction of the critical speeds or the safe operating speed limits for the rotors, based on the evaluation of natural frequencies and plotting them on the Campbell diagram. The alternate option is to decide upon the variables in the design such as bearing specifications in terms of stiffness, bearing span, and coupling specifications, to keep the critical speeds away from the operating regime. However accurately these rotors are balanced, there will be some unbalance still left in the system. The response of the rotor due to the residual unbalance to make sure that the rotor does not rub against the casing, is an important aspect of the rotor dynamic analysis. Most of these rotors can develop excessive stresses in torsion because of the low torsional natural frequencies of the system involving the flexible couplings. Therefore, the accurate prediction of torsional frequencies and the response of the rotor to the transient torsional excitations such as an electrical disturbance, are required. It is an established fact that the casing has an effect on the dynamics of the rotor. The interaction between the dynamics of the rotors with that of the casing is an essential aspect of the rotor dynamics. 3

4 Understanding the Market Need to Adopt Solid Model Rotor Dynamics The specific need to go for solid model rotor dynamics arises due to the accuracy of the results observed in comparison to the test results. The solid element rotor dynamic models can be used for the entire frequency range of the system and taking into consideration all the real-life effects like stress stiffening, spin softening and so on. The laborious process of breaking the complex system into a large number of stations, and then the complexity of the calculation of the stiffness and the mass of different stations and lumping it at a station, is not required in the solid model rotor dynamics. All the assumptions and inaccuracies involved in the multi-station beam model consisting of the beam, the mass, and the stiffness elements are eliminated with the solid rotor dynamic model. Therefore, the results obtained by the solid model rotor dynamics are more comparable to the test results than the conventional beam model results. Process Description and Product Lifecycle Stages Solid model rotor dynamics is a method of performing the rotor dynamics analysis by solid elements instead of the conventional beam models. Therefore, in the product development process, there is no change in the stage at which it occurs. As rotor dynamic analyses are system level studies, they are performed prior to any structural design, once the design from the flow and the aerodynamic considerations is acceptable. The Challenge The conventional beam elements are incapable of simulating the spin softening and stress stiffening effects. For a complex geometry such as that of the rotor (for example, the rotor of a cryogenic turbo pump with inducers), it is difficult to simulate the rotor characteristics by the beam element approximations. The solid model rotor dynamics provides an accurate solution to such problems Method To demonstrate the advantages of the solid model rotor dynamics, a study was undertaken at QuEST by considering a dual rotor system (Ref 2). A dual rotor system is generally employed in the aircraft engines to save space and keep the weight to a minimum by having a hollow outer spool which mounts the high pressure compressor and the turbine running at a relatively higher speed through which an inner spool rotor mounts the low pressure compressor and turbine rotors. An example is taken (Ref 1) as shown schematically in Figure 1. ROTOR cm 2.54 cm r E6 N/m E6 N/m E6 N/m E6 N/m ROTOR cm r 4 Distances: 1-2 = 7.62 cm; 2-3 = cm; 3-4 = cm; 4-5 = 5-6 = 7-8 = 9-10 = 5.08 cm; 8-9 = cm Masses 2 = 4.904; 5 = 4.203; 8 = 3.327; 9 = kg Inertials IP 2 = ; 5 = ; 8 = ; 9 = kgm² ID = IP/2 E = GPa; Density = 8304 kg/m³ ² = 1.5 ¹ Figure 1: Example of a twin spool rotor

5 The above problem was simulated in ANSYS using two separate modeling approaches. First by the beam elements (Beam 4 elements in ANSYS) and then by the solid elements, and finally the results were compared considering the different effects like stress stiffening and spin softening. The bearing stiffness properties are simulated using the Combin 14 elements in ANSYS. The beam model developed is shown in Figure 2. Mass 21 elements Rotor 1 Rotor 2 Y Z X Beam 44 elements Combin 14 elements Figure 2: Beam element model of dual rotor system An equivalent solid rotor model for the example of Figure 1 is made. The dimensions of this model are given in Figure 3, which gives the same masses and inertias of Figure 1. It may be noted that Figure 1 can represent in a unique manner an equivalent beam model of the solid model of Figure 3, even though several other solid models can be derived for the Figure 1 beam model. This is the main limitation of the beam model analysis, as an equivalent derived beam model may represent the dynamics of different solid models. An actual physical model in solid form eliminates this approximation. Y Rad = cm Length = 1.7 cm Rad = cm Length = 1.38 cm Rad = cm Length = cm Rad = cm Length = 1.66 cm Figure 3: Example of a twin spool rotor Results For the beam model of Figure 2, a vibration analysis was carried out including the Gyroscopic effects, and the Campbell diagram was generated. The analysis results were compared with the theoretical work mentioned in the reference. Below is the Campbell diagram for the beam model. Figure 1: Example of a twin spool rotor 5

6 3000 WHIRL SPEED (rad/s) Mode 1B Mode 1F Mode 2B Mode 2F Mode 3B Mode 3F Tmode 1B Tmode 1F Tmode 2B Tmode 2F Tmode 3B Tmode 3F 1 *REV (omega1) 1 *REV (omega2) ROTOR 1 SPIN SPEED (rad/s) Figure 4: Campbell diagram for the beam model with gyroscopic effects Solid lines in the diagram are from the beam analysis results and the dotted lines are from the theoretical work. The split of the forward and the backward whirl modes is clearly observed. Now for the solid model of the same rotor as shown in Figure 3, a vibration analysis was carried out including the effects of gyroscopes and spin softening. The Campbell diagram was constructed from the results and compared with the theoretical work as shown in Figure 5. From the results observed it clearly shows that due to the effect of spin softening, both the forward whirl and the backward whirl frequencies decrease with speed. The effect of decrease in frequency with the increase in speed is more for the backward whirls than the forward whirls. The beam models are incapable of capturing such effects WHIRL SPEED (rad/s) ROTOR 1 SPIN SPEED (rad/s) 3000 Mode 1B Mode 1F Mode 2B Mode 2F Mode 3B Mode 3F Tmode 1B Tmode 1F Tmode 2B Tmode 2F Tmode 3B Tmode 3F 1 *REV (omega1) 1 *REV (omega2) Figure 5: Campbell diagram for the solid model with gyroscopic and spin softening effects One more analysis was carried out with the solid model of Figure 3, considering the combined effect of stress stiffening and spin softening. The Campbell diagram was constructed from the results and compared with the theoretical work as shown in Figure 6. 6

7 3000 WHIRL SPEED (rad/s) Mode 1B Mode 1F Mode 2B Mode 2F Mode 3B Mode 3F Tmode 1B Tmode 1F Tmode 2B Tmode 2F Tmode 3B Tmode 3F 1 *REV (omega1) 1 *REV (omega2) ROTOR 1 SPIN SPEED (rad/s) Figure 6: Campbell diagram for the solid model with gyroscopic, spin softening and stress stiffening effects From the above Campbell diagram results it can be observed that because of the stress stiffening effects, the frequency of the forward whirl modes increases with the speed, however, the backward whirl modes continue to decrease in frequency with the increase in speed and eventually disappear after a certain speed. The conventional beam models fail to capture these real-life effects of spin softening and the stress stiffening of the rotors. Limitation of Solid Model Rotor Dynamics The only limitation with the solid model rotor dynamics is the computational time and the hardware resources. To solve the large model, more computational resources in terms of the hardware requirements are needed in comparison to the beam models. With advancements in the computational resources, this is not a concern any more. Conclusion A specific advantage of the solid models is the inclusion of stress stiffening and spin softening effects in the rotor dynamics analysis which are not considered in the beam models. The spin softening effect has significant influence on the backward whirl modes and the stress stiffening effect on the forward whirl modes. Another significant advantage of solid models lies in the fact that all the coupled modes of shafts, disks, and other mounted parts can be accounted in one analysis which otherwise cannot be handled by the beam models. The study was carried out with a simple dual rotor system with the simplified mass and inertia representation of the rotors. The simulation of a real-life complex geometry of the rotor by the beam model is a tedious, error prone, and time consuming job. Solid model rotor dynamics offers a time effective and accurate solution to the real-life rotor dynamic problems. References 1) Rajan, M., Nelson, H. D. and Chen, W. J., Parameters Sensitivity in the Dynamics of Rotor-Bearing Systems, J Vib. Acoust. Stress and Rel. Des., Trans. ASME, vol. 108, 1986, p ) Rao, J. S., Sreenivas, R. and Veeresh, C. V., 2002, Solid Model Rotor Dynamics, Paper presented at the Fourteenth U.S. National Congress of Theoretical and Applied Mechanics, Blacksburg, VA, June

8 Author Profile Veeresh Vastrad Veeresh Vastrad is specialized in the structural analysis of Mechanical & Gas Turbine Structures. He has extensive experience in Finite Element Method analysis, linear and nonlinear structural analysis, vibrations and rotor dynamics. He is amply proficient with ANSYS and the various rotor dynamics tools. Veeresh has a Bachelor of Engineering degree in Mechanical Engineering from Karnataka University, (Dharwad) and a Master of Science degree in Mechanical Engineering from Manipal University. He has approximately 11 years of experience at QuEST in the gas turbines, industrial, and aerospace component structural analysis areas. Veeresh is credited with the following achievements: QuEST Technical Excellence Champion (2011) for succeeding in reducing the internal defects against desired targets, and for diligent effort in training and mentoring the stress team Co-author of the Solid Model Rotor Dynamics paper along with Dr. J. S. Rao which was presented at the 14th U.S. National Congress of Theoretical and Applied Mechanics, (Blacksburg, VA) June 23-28, 2002 Employee of the Month, (May 2002) for the value addition provided to the customer on the project First Prize winner for the presentation on the Solid Model Rotor Dynamics using ANSYS paper at the ANSYS Users Symposium, (Bangalore) December 6, 2001 At QuEST, his role includes: Meeting the compliance requirements of the technical review process Appraising the technical deliverables by the stress team Managing the knowledge management repository Evaluating the competency levels of the stress team Maintaining the competency at the required level Identifying the training needs of the team and coordinating the training program In addition, he is also actively involved in mentoring the new recruits on the job-specific requirements. veeresh.vastrad@quest-global.com 8

9 About QuEST Global QuEST Global is a focused global engineering solutions provider with a proven track record of over 17 years serving the product development & production engineering needs of high technology companies. A pioneer in global engineering services, QuEST is a trusted, strategic and long term partner for many Fortune 500 companies in the Aero Engines, Aerospace & Defence, Transportation, Oil & Gas, Power, Healthcare and other high tech industries. The company offers mechanical, electrical, electronics, embedded, engineering software, engineering analytics, manufacturing engineering and supply chain transformative solutions across the complete engineering lifecycle. QuEST partners with customers to continuously create value through customer-centric culture, continuous improvement mind-set, as well as domain specific engineering capability. Through its local-global model, QuEST provides maximum value engineering interactions locally, along with high quality deliveries at optimal cost from global locations. The company comprises of more than 7,000 passionate engineers of nine different nationalities intent on making a positive impact to the business of world class customers, transforming the way they do engineering.