Curvic Couplings Research Articles

Research on the dynamic variation law of the discontinuous characteristics of the curvic coupling of aero-engine rotors under working conditions

For the design of advanced aero-engine rotor systems under ultra-high rotational speeds, this paper undertakes a comprehensive investigation into the contact stiffness of curvic couplings, which are the key connection mechanism of modern aero-engine rotors, and explores the dynamic variations in the contact stiffness of curvic couplings under working conditions. Firstly, the impact of dynamic loads of aero-engine rotors under working conditions on the curvic coupling is studied; Then, the contact stiffness analytical model of curvic couplings considering three-dimensional geometric features is proposed with the effects of dynamic loads; Finally, based on the established stiffness model, the dynamic loss laws of contact stiffness of curvic couplings under different dynamic loads are investigated, and the established model is experimentally validated. The results show that the dynamic loss law of contact stiffness varies with different dynamic loads. In comparison to the contact stiffness under the static condition, dynamic loads significantly reduce the contact stiffness of curvic couplings under working conditions, which in turn leads to changes in the dynamic characteristics of the rotor with curvic couplings. For the safe integration of the discontinuous rotor system under ultra-high rotational speeds, it is essential to carefully design and regulate the operating speed, transmission torque, unbalanced mass, and preload.

Static and Dynamic Stress of the Combined Rotor with Curvic Couplings Considering the Rough Three-Dimensional Interface at Extreme Operating Conditions

The curvic coupling, as one of the common connecting structures for gas turbine combined rotors, is more susceptible to various dynamic and static loads at extreme operating conditions. But, traditional combined rotor models tend to neglect the influence of the connection structure, especially failing to consider the contribution of the curvic coupling interfaces. To address this problem, this paper establishes a solid geometric model of the combined rotor with curvic couplings considering the rough three-dimensional interfaces. The effectiveness of the proposed model method is indirectly verified through the compression tests and modal tests. Subsequently, combined with finite element calculations, the mechanical properties of the rotor with curvic couplings considering the rough interface are analyzed under static and dynamic load conditions. The results indicate that the roughness of the interface significantly affects the deformation of the contact surface under static load, but its impact on the overall deformation of the rotor is relatively insignificant. The dynamic stress at the interface exhibits periodic variations at the resonance speed. At the maximum operating speed, the dynamic stress is influenced by the magnitude of imbalance. The aforementioned methods and conclusions provide a reference for the design research and engineering application of combined rotors.

Analytical model of curvic coupling and application in nonlinear vibration analysis of a squeeze film damper - rolling bearing - rotor system

The curvic coupling has been extensively employed in the rotor system of aero-engine. Effects of the radical slip of the teeth and damping are usually neglected in the traditional models of the curvic coupling. Additionally, there are only a few researches on the vibration characteristics of the rotor system with curvic coupling, squeeze film damper (SFD) and rolling bearing. In this paper, an analytical model of the curvic coupling is proposed. The nonlinear vibration analysis of a SFD - rolling bearing - rotor system with curvic coupling is furtherly carried out. The Jenkins element is adopted to simulate the dynamic behaviors of the curvic coupling in the model. The hysteresis curves of the analytical model show good agreement with the results of the three-dimensional (3D) finite element (FE) simulation. After that, the dynamic equation of a SFD - rolling bearing - rotor system with curvic coupling is formulated. Subsequently, detailed parametric analyses, including preload, number of teeth and pressure angle, are conducted to investigate the vibration characteristics of the rotor system. Results show that the curvic coupling mainly produces stiffness loss and damping at the interface of the curvic coupling. The motion stability of the rotor system can be enhanced by increasing the preload, number of teeth at multiple curvic couplings and pressure angle. Moreover, the vibration level of the rotor system initially decreases and then increases as the number of the teeth and pressure angle increase. Finally, the numerical results are validated to be reasonable by an experimental study.

Precision Regulation in Multistage Aero-Engine Rotors With Curvic Couplings Using Line-Structured Light Array Scanning and Virtual Assembly

Precision Regulation in Multistage Aero-Engine Rotors With Curvic Couplings Using Line-Structured Light Array Scanning and Virtual Assembly

Optimizing circumferential assembly angle of rotor parts connected by curvic couplings based on acquired tooth surface error data

Due to the excellent self-centering and load-carrying capability, curvic couplings have been widely used in advanced aero-engine rotors. However, curvic tooth surface errors lead to poor assembly precision. Traditional physical-master-gauge-based indirect tooth surface error measurement and circumferential assembly angle optimization methods have the disadvantages of high cost and weak generality. The unknown tooth surface fitting mechanism is a big barrier to assembly precision prediction and improvement. Therefore, this work puts forward a data-driven assembly simulation and optimization approach for aero-engine rotors connected by curvic couplings. The origin of curvic tooth surface error is deeply investigated. Using 5-axis sweep scan method, a large amount of high-precision curvic tooth surface data are acquired efficiently. Based on geometric models of parts, the fitting mechanism of curvic couplings is uncovered for assembly precision simulation and prediction. A circumferential assembly angle optimization model is developed to decrease axial and radial assembly runouts. Experimental results show that the assembly precision can be predicted accurately and improved dramatically. By uncovering the essential principle of the assembly precision formation and proposing circumferential assembly angle optimization model, this work is meaningful for assembly quality, efficiency and economy improvement of multistage aero-engine rotors connected by curvic couplings.

Parametric Modeling of Curvic Couplings and Analysis of the Effect of Coupling Geometry on Contact Stresses in High-Speed Rotation Applications

Curvic couplings are used in applications demanding high positional accuracy and high torque transmission; therefore, improving their design and enhancing their load-carrying capacity is crucial. This study introduced the kinematic model Curvic3D, which was developed to produce the accurate geometry of both members of a curvic coupling using a CAD system. The model enabled the complete parametrization and customization of the coupling design using important geometric parameters. The couplings produced using Curvic3D were then imported into a finite element analysis model also developed as part of this study. A detailed analysis of the stresses developed on the teeth of the concave and convex parts provided information about the behavior of the coupling under different loading conditions. Finally, a series of geometric parameters, such as the number of teeth, the number of half pitches, the root fillet radius, and gable angle were examined as to their influence on the load-carrying capacity of the curvic coupling. The study concluded that all the examined parameters have a significant effect on the tooth flank and root area stresses.

Beam based rotordynamics modelling for preloaded Hirth, Curvic and butt couplings

Gas turbine and other machinery rotating assemblies are frequently manufactured as multiple components for cost and component alignment reasons. Butt joint, Hirth, and Curvic coupling are widely used for this purpose. Localized joint flexibility in these preloaded couplings introduce non-beamlike behavior which affects rotordynamic critical speeds, imbalance response and stability, rendering a conventional beam model inadequate. 3D solid finite element models of the couplings with Greenwood Williamson (GW) asperity interface features provide accurate representations of the couplings, however computational costs are impractical for use in an industrial design setting, which are limited to beam element models. A novel modeling approach for the coupling is developed that derives equivalent beam element Young's modulus and shear form factor properties, that replicate the bending behavior of the high fidelity 3D solid models, including GW based interface asperity stiffness. The equivalent beam models for butt, Hirth and Curvic couplings are validated using measured natural frequencies as a benchmark, for a range of through-bolt preloads. The equivalent beam model and the 3D solid model in this correlation incorporate GW contact models derived with experimentally measured surface roughness parameters. An Ecoupling sensitivity study for GW surface roughness parameters was conducted and showed a significant level of sensitivity. The effect of the coupling on an industrial class rotor's critical speed is included to illustrate usage of the approach.

An improved preloaded Curvic coupling model for rotordynamic analyses

Curvic couplings are commonly utilized in aircraft engines and large gas turbines for high load capacity, precision centering of stacked components in rotating assemblies. The couplings have non-axisymmetric, complex curved mating contact surfaces, which transmit torque, moment and force. Coupling contact surface roughness, and tooth and ring deformations introduce local lateral flexibilities, compared with a continuous beam model, and consequently affect rotordynamic vibration predictions. A novel approach of modeling the Curvic coupling is proposed which combines a GW contact model with a 3D solid element model of flexible teeth and coupling rings. This improves on similar approaches that assume rigid teeth and rings or omits a surface roughness – asperity model. Comparisons of the various models with experimental measurements of free-free natural frequencies of an axially preloaded shaft, demonstrate a marked improvement in accuracy with the proposed approach. A parametric study is performed which varies tooth contact pattern, tooth number, pressure angle, half pitch number, and tooth rigidity to evaluate their effects on vibration and stress. The proposed approach is also applied to an industrial rotor to illustrate the effect of the new Curvic coupling model on critical speeds. The higher fidelity flexible tooth model presented shows a significant change in critical speed relative to the rigid tooth model from the literature.

Positioning and orientation error measurement and assembly coaxiality optimization in rotors with curvic couplings

In the assembly of aero-engine rotors, coaxiality is the major technical index, which has an important influence on the performance and service life of the whole machine. This article studies the optimization problem of assembly coaxiality of multistage rotors with curvic couplings, and proposes a method for indirectly measuring the positioning and orientation errors between the mating surfaces of a single-stage rotor with curvic couplings. This method can solve the problem that the positioning and orientation errors cannot be directly measured due to the tooth structure. Then the mathematical expression between the coaxiality after assembly and the assembly phase is derived based on the positioning and orientation errors of the rotors of each stage, which can realize the prediction and optimization of the assembly coaxiality. Finally, it verifies the prediction and optimization effect through the assembly experiment of multistage rotors with curvic couplings. Results indicate that: the maximum coaxiality prediction errors for the two-stage and four-stage rotors assembly under ten different assembly phases are 15.63% and 8.62%, respectively. Compared with direct assembly, the coaxiality of optimized assembly is reduced by 83.3% and 48.7%, respectively. It proves that this method can better realize the prediction and optimization of the assembly coaxiality of multistage rotors with curvic couplings.

Modelling and stress analysis for double-row curvic couplings

This paper proposes a parameterized modelling method that considers the details of the machining process for double-row curvic couplings and presents a modified stress analytical method that can take the deep beam bending effect into account. The modified method provides a more accurate equivalent stress estimation than the classic Gleason method, which is demonstrated by the nonlinear finite element simulation. The contact stress and the contact status of the curvic couplings in high-speed rotation situations are analysed with the nonlinear FEA method under different loads. The results show that the strength of the weak regions of the double-row curvic couplings occur at the tooth root and the tooth to near the bolts. The bolt preload has the greatest influence on the contact stress and the contact status. The rotating speed reduces the bolt preload, causing the stress to decrease. The torque results in contact stress and contact status of different sides of the tooth being obviously different. Finally, the modified analytic method is recommended during the preliminary design, and the FEA method considering the contact effects is recommended for the detailing design.

A Model accounting for Stiffness Weakening of Curvic Couplings under Various Loading Conditions

Curvic couplings are frequently used in aeroengine rotors. The stiffness of the curvic couplings is of guiding significance to the engineering design of aeroengine rotors as it is significantly different from that of continuous structures. In this paper, definitions and relations of the structure parameters for a curvic coupling are firstly introduced. Based on this proposed mechanical framework, a novel mechanical model accounting for the stiffness weakening under shearing, compression, bending, and torsion is developed for curvic couplings. In this model, a three-spring system, which consists of two types of springs, is adopted to describe the equivalent stiffness of a pair of meshing teeth of curvic couplings. The spring stiffness is obtained by employing the plane strain analysis of a discretized tooth with trapezoid pieces. Subsequently, the stiffness matrix of curvic couplings is deduced based on the deformation compatibility of each tooth and the force balance of the whole structure. A series of analyses of curvic couplings with various structure types are performed to demonstrate the mechanism behind the proposed model, and the results are verified against those obtained from finite element analyses. It is shown in this study that the pressure angle is the major factor affecting the stiffness of curvic couplings, while the compression stiffness and bending stiffness are more sensitive than other stiffnesses. Furthermore, the stiffness of curvic couplings is considerably smaller compared to that of continuous structures, indicating the importance of appropriate modelling of stiffness weakening in the design of aeroengine rotors.

Simple Contact Stiffness Model Validation for Tie Bolt Rotor Design With Butt Joints and Pilot Fits

Abstract Tie bolt rotors for centrifugal compressors comprise multiple shaft components that are held together by a single tie bolt. The axial connections of these rotors—including butt joints, Hirth couplings, and Curvic couplings—exhibit a contact stiffness effect, which tends to lower the shaft bending frequencies compared to geometrically identical monolithic shafts. If not accounted for in the design stage, shaft bending critical speed margins can be compromised after a rotor is built. A previous paper had investigated the effect of tie bolt force on the bending stiffness of stacked rotor assemblies with butt joint interfaces, both with and without pilot fits. This previous work derived an empirical contact stiffness model and developed a practical finite element modeling approach for simulating the axial contact surfaces, which was validated by predicting natural frequencies for several test rotor configurations. The present work built on these previous results by implementing the same contact stiffness modeling approach on a real tie bolt rotor system designed for a high pressure centrifugal compressor application. Each joint location included two axial contact faces, with contact pressures up to five times higher than previously modeled, and a locating pilot fit. The free-free natural frequencies for different amounts of tie bolt preload force were measured, and the frequencies exhibited the expected stiffening behavior with increasing preload. However, a discontinuity in the data trend indicated a step-change increase in the contact stiffness. It was shown that this was likely due to one or more of the contact faces becoming fully engaged only after sufficient tie bolt force was applied. Finally, a design calculation was presented that can be used to estimate whether contact stiffness effects may be ignored, which could simplify rotor analyses if adequate contact pressure is used.

Analysis of contact and bending stiffness for Curvic couplings considering contact angle and surface roughness

This paper develops a method for calculating the contact and bending stiffness of a Curvic coupling, and investigates stiffness changes according to the coupling shape and surface roughness characteristics. The surface of the on-site Curvic coupling is chosen as reference for a most accurate simulation. The three parameters representing the surface roughness characteristics—the standard deviation of the asperity height distribution, the average radius of asperities, and the density of asperity on the nominal contact area—are calculated with a profile of the coupling surface through a random process: the contact problem between rough surfaces is tackled using the Greenwood-Williamson model, the Curvic coupling is modeled assuming that it has as many teeth as possible within the machining limits depending on the contact angle, and the tangential stiffness resulting from the contact angle is calculated by dividing into the stick and slip regions, and is taken into account in terms of total stiffness. With this, results showed that using Curvic couplings reduces stiffness than using flat disc couplings because of the contact angle, and that the standard deviation of rough surface height is the most crucial surface parameter affecting stiffness.

A method to achieve uniform clamp force in a bolted rotor with curvic couplings

The preloading process is essential for circumferential bolted rotors with curvic couplings and preloading effects determining the rotor performance. A nonuniform clamp load of each bolt will destroy the periodicity of the rotor and affect its strength, stiffness, and stability. In this paper, the finite element method was adopted, the influence of elastic interaction on two types of preload methods (one by one and group) was investigated and the mechanism about elastic interaction was analyzed, and a method to achieve a uniform clamp force of spindle bolts was proposed. This method is based on displacement, and by ensuring equal relative displacements of each bolt and nut during the preloading process, the uniform clamp force can be obtained. The validity of the proposed method is experimentally verified.

Stiffness Analysis of Curvic Coupling in Tightening by Considering the Different Bolt Structures

AbstractCurvic couplings are extensively used in aerospace machinery, such as helicopter, aero-engine, or other aircrafts. The aim of this paper is to reveal new insights into the behavior of bolted joint with curvic couplings according to the bolt geometry and physical parameters by an analytical model. The different cases are focused mainly on the different geometry characters of the bolt. The analytical results show that the compression stiffness of both the curvic and the ring part of the disc has some relationship with the curvic rotation. The curvic rotation angle and the curvic compression stiffness show a slight difference during the tightening regardless of the bolt structural parameters. However, the stiffness of the other disc parts present a more obvious difference in tightening because of the various bolt structural parameters.

Influence of Thin-Wall Structure on Stress Distribution of Curvic Couplings

Abstract The objective of this paper is to investigate the influence of transition structure between curvic teeth and disk on stress distribution of curvic couplings, and provide data to help improving the design of curvic couplings. In this work, the three-dimensional finite element method was used, and Augmented Lagrange Algorithm was adopted to the contact algorithm during the analysis. According to the results of this paper, designing thin-wall structure reasonably can avoid detaching of contact interface at external diameter during preload process; reduce stress fluctuation of curvic teeth caused by circumferential bolts structure; and balance stress difference of each contact pair caused by different disk quality under the action of the centrifugal force.

Development and Validation of Analytical Model for Stiffness Analysis of Curvic Coupling in Tightening

Curvic couplings are extensively used in aerospace machinery, such as helicopters, aeroengines, or other aircraft. In this paper, the behavior of bolted joints with curvic couplings is investigated to determine a method to describe the relationship between the stiffness parameters and the geometry of the parts of curvic coupling and external loads. The validity of the method is proven through experiments and finite-element simulation. Additionally, the study investigates the effects of the curvic height, curvic width, curvic thickness, pressure angle of curvic surface, and friction coefficient of curvic surfaces on the stiffness of disc parts. The analytical results show that the compression stiffness of both the curvic and ring parts of the disc has a relationship with the curvic rotation. Although the curvic compression stiffness tends to be constant in the bolt-tightening process for different curvic geometrical dimensions, the compression stiffness of the other disc parts has obvious differences owing to the various curvic geometrical parameters. By choosing appropriate pressure angles of the curvic surface or number, the stiffness of the curvic coupling can be kept stable in the bolt tightening course. The stiffness parameters of curvic couplings can be determined by the analytical model, regardless of how the geometry of the parts of curvic couplings or the external loads are changed.

Analysis of the contact stresses in curvic couplings of gas turbine in a blade-off event

The contact pressure distribution of the curvic couplings in a heavy duty gas turbine under a blade-off load condition is investigated in a three-dimensional finite element model. Several blade-off positions on each stage disk may develop the different characters on the contact pressure distributions of the curvic couplings during the application of a blade-off load. Both the position and magnitude of the applied blade-off load and the distribution of the spindle bolts have an effect on the contact pressure distribution of the curvic couplings. Further the contact stress on the left and right sides of the teeth develops different characters during the application of torque load following not only a normal centrifugal load but also a blade-off load which produces a unbalanced equivalent bending force. Furthermore the stiffness of the connection body part of the rotor between the compressor end and the turbine end associated with its section thickness is crucial in deciding the contact stress distribution on the curvic couplings. This analysis shows a change in the magnitude of contact stress of each set of the curvic couplings.

Stress distribution and contact status analysis of a bolted rotor with curvic couplings

The aim of this article is to provide some basis for the design and assembly of a bolted rotor with curvic couplings. It is well known that the key difference between a bolted rotor with curvic couplings and an integrated one is the contact interface. According to the characteristics of curvic couplings and spindle bolts, the model of a bolted rotor with curvic couplings of the turbine end of a heavy duty gas turbine was built. A method of accurately applying the preload force has been studied in this article. The three-dimensional finite-element contact method was used, non-linear behaviours such as friction and contact were also taken into account, and the dynamic contact between the spindle bolts and the sidewall of turbine wheels was included. The tendency of stress, which involved the rotor, curvic couplings, and the spindle bolts, was determined and the radial slippage trend of curvic teeth was also determined, by investigating the stress distribution and contact behaviour of the bolted rotor with curvic couplings during the course of preload, warm-up, speed-up, and running. It can be seen from the results that the contact stress of curvic couplings is dominant during the course of preload, and the bent stress is dominant when the rotating speed increased to 3000 r/min; the stress inequality on two sides of a tooth is caused by torque, so the stress proportion induced by torque should be restricted to an appropriate level to avoid anisotropy of the rotor.

1413 位相組立を用いたタービン振れの最適化(GS-10 回転機,研究発表講演)

It is important to assemble the turbine disks for minimum runout for realizing small vibration of the turbine. However the conventional disks phase assembly method to minimize runout depends on the worker's experience. So we paid attention to slight geometrical face error which exists in curvic couplings of the disks, and by modeling the turbine into the oblique swivel mechanism we enabled to presume runout of assembled rotor for any phase combination. And we established the calculation method of optimum runout considering dynamic balance.