Flexible Gear Research Articles

Study on rigid-flexible coupling modeling of planetary gear systems: Incorporation of the pass effect and random excitations

A rigid-flexible coupling model for the planetary gear system is developed, in which the flexibility of the ring gear, input shaft, and carrier are considered. Subsequently, rotational modal projection is proposed to simulate the meshing of the flexible ring gear at any angle of planet gear revolution, and the coordinate transformation equations are presented to establish the coupling between rigid body and rotating flexible body. These two approaches incorporate the pass effect into the coupling model. Additionally, a method employing pre-emphasized noise to simulate random excitations is introduced. The model is validated by comparing computed modal frequencies and dynamic responses with those from ANSYS software and experiment, respectively. Results indicate that the proposed method accurately simulates the modulation signal observed in the experiment. Closely matched resonances excited by random excitations are apparent in experimental and simulated acceleration spectra, highlighting the validity of the proposed method and aiding in the determination of operational system modes. In addition, analyses of parameter influences are conducted, which further reveal the dynamic characteristics of the system.

Vat Photopolymerization of Sepiolite Fiber and 316L Stainless Steel-Reinforced Alumina with Functionally Graded Structures.

Alumina (Al2O3) ceramics are widely used in electronics, machinery, healthcare, and other fields due to their excellent hardness and high temperature stability. However, their high brittleness limits further applications, such as artificial ceramic implants and highly flexible protective gear. To address the limitations of single-phase toughening in Al2O3 ceramics, some researchers have introduced a second phase to enhance these ceramics. However, introducing a single phase still limits the range of performance improvement. Therefore, this study explores the printing of Al2O3 ceramics by adding two different phases. Additionally, a new gradient printing technique is proposed to overcome the limitations of single material homogeneity, such as uniform performance and the presence of large residual stresses. Unlike traditional vat photopolymerization printing technology, this study stands out by generating green bodies with varying second-phase particle ratios across different layers. This study investigated the effects of different contents of sepiolite fiber (SF) and 316L stainless steel (SS) on various aspects of microstructure, phase composition, physical properties, and mechanical properties of gradient-printed Al2O3. The experimental results demonstrate that compared to Al2O3 parts without added SF and 316L SS, the inclusion of these materials can significantly reduce porosity and water absorption, resulting in a denser structure. In addition, the substantial improvements, with an increase of 394.4% in flexural strength and an increase of 316.7% in toughness, of the Al2O3 components enhanced by incorporating SF and 316L SS have been obtained.

A vibration model of a flexible multiple shaft gear system with the tip relief modification

The fixed-shaft gear system (FSGS) is one critical part in gear transmission systems (GTSs), whose vibrations can significantly influence performances of GTSs. To reduce the vibrations of rigid FSGS caused by installation and manufacture errors, the tooth profile modifications without the shaft deformation were widely introduced. This paper establishes a flexible multiple shaft gear system (FMSGS) model of an unmanned underwater vehicle, which can obtain vibrations of rotor at different axial positions. However, the previous rigid FSGS model cannot obtain those vibrations. In the FMSGS model, the Timoshenko beam elements are applied to the establishment of shaft segments considering flexibility. The meshing stiffness for helical gears with different ranges of tooth profile modification are quantitatively expressed by a gear slicing method. Based on the kinetic relationship between the gear pairs, shaft segment, and bearings, the dynamic equations of FMSGS are derived. By comparing the time-domain waveforms and spectra of FMSGS, the effects of the tooth profile modification amounts and lengths on the vibrations of FMSGS are revealed. The proposed FMSGS model is validated by an experiment. This study extends the dynamic methods of FSGSs, and some suggestions on the vibration control of FSGSs are given.

Modeling of flexible bevel gear rotor systems: Modal and dynamic characterization

Bevel gears, a crucial part of aircraft transmission systems, are more susceptible to wheel body vibration issues as lightweight requirements rise. In the past, the gear wheel body was often considered rigid while assessing the dynamic properties of gear systems. Constructing a bevel gear model with a thin-walled structure might not be appropriate for this modeling technique; this research suggests a dynamic model that considers the flexibility of bevel gears. The web and teeth structure of the gear are preserved by realistic modeling using three-dimensional hexahedral components. The component mode synthesis (CMS) approach reduces the model order for increased computational efficiency. To confirm the accuracy of the modeling method, the modal frequencies and vibration shapes of the proposed model single-gear shaft are compared with results from experiments and ABAQUS. By contrasting ABAQUS system-level meshing modal frequencies and vibration shapes, the accuracy of the system model assembly is further confirmed. The model examines the impact of bevel gear flexibility on the modal frequencies, modal vibration shapes, and system dynamic properties. The mode shape diagram at dangerous modal frequencies found using the modal strain energy technique and the vibration displacement cloud maps at resonance speeds computed using the Newmark-β method are mutually verified, and this demonstrates that lightweight bevel gears are more susceptible to excitation due to nodal diameter type vibrations. Proposed and traditional models anticipate substantially different resonance speeds since the traditional model assumes that the gear, being a rigid disk, can only excite the shaft's bending mode of vibration. The proposed model provides a more comprehensive description of the dynamic characteristics of bevel gear systems, providing a theoretical basis and optimization tool for the high-performance design, vibration reduction, and noise control of high-speed lightweight gear transmission systems.

3D walkable DNA gears for ultrasensitive detection of multiple microRNAs in lung cancer cell lysates

As a tumor biomarker with therapeutic application potential, microRNA (miRNA) was crucial for the accurate and sensitive detection of early-stage tumors. Herein, a unique three dimensional (3D) DNA nanomachine (DNM) was created, which was capable detecting lung cancer-related biomarkers miRNA-21, miRNA-205 and miRNA-125b in lung cancer cell lysates with extreme sensitivity. The 3D DNM was composed of DNA scissors and three flexible walkable DNA gears modified with various species of silver nanoclusters (AgNCs). Based on the flexibility of DNA scissors and the walkability of DNA gears, neighboring DNA gears closed the distance between different species of AgNCs by walking in the presence of targets, generating fluorescence resonance energy transfer (FRET) effect and emitting different kinds of fluorescence to complete the highly sensitive detection of single targets and multiple targets. The findings demonstrated that a linear model provided an excellent match for the association between fluorescence signal and target miRNAs. For miRNA-21, miRNA-205, and miRNA-125b, the limits of detection (LODs) (signal/noise = 3) were 4.2 pmol/L (pM), 6.3 pM, and 10.2 pM, respectively. Their recoveries in A549 cell lysate samples ranged from 95.3 to 108.8 % with relative standard deviations of 1.26 %–4.88 %. Satisfactorily, the 3D DNM displayed exceptional analytical performance with high sensitivity and stability, strong specificity and reproducibility, which was triumphantly employed to identify miRNAs in tumor cell lysates, providing a workable technique in creating adaptable nanostructure for dependable bioanalysis and clinical diagnosis of cancer biomarkers.

Meshing characteristics and dynamic characteristics of planetary transmission system with new tooth-type flexible ring gear

As one of the important components of the planetary transmission system, dynamic meshing characteristics of ring gear directly affect the performance of planetary transmission system load sharing and dynamic load factor. With the help of the flexibility of ring gear, the planetary gear system with flexible ring gear (FRG) can compensate for the uneven transmission torque of each branch caused by the machining error and installation error and improve the system's load sharing and dynamic load performance. An L-shaped FRG was developed in Italy to improve the traditional ring gear and was used in the latest AW101 helicopter with good feedback. By increasing the ring flexibility, the load distribution between planetary gears is more uniform, and the load-sharing performance of the system is significantly improved. Tooth wear and fracture caused by uneven load distribution can be improved. However, the structure has problems such as unbalanced loading, strength weakening, and stress concentration. In this article, the FRG's meshing and structural characteristics are analyzed in detail by constructing the parametric finite element model. Differences, advantages, and disadvantages of FRG and traditional ring gear are compared. A new type of tooth-type FRG is proposed. It has excellent structural flexibility meshing characteristics of tooth surface and avoids generating stress concentration. It improves the planetary gear train's load-sharing performance and overcomes tooth surface unbalanced loading and large amplitude fluctuation of loaded transmission errors.

Influence of ring gear flexibility on the fatigue reliability of planetary gear systems in heavy helicopters

Flexibility of ring gear rims significantly affects the mechanical properties of planetary transmissions at both levels of gear tooth meshing and system power sharing, and is one of the important design factors determining the service reliability of large aviation planetary systems. Therefore, to analyze the mechanism by which the flexibility of ring gear rims affects the fatigue reliability of planetary systems, in the framework of the stress-strength interference theory, a reliability assessment model for the planetary system is constructed based on a calculation logic extension for the full probability formula. Starting from balancing evaluation accuracy and evaluation cost, a hybrid finite element method and a gear tooth lifetime transformation test are employed to provide load and strength input variables for the reliability model respectively. Finally, a mapping relationship from ring gear rim flexibility to planetary system fatigue reliability is established. For the specific design scheme of planetary systems, a lower limit of the ring gear rim thickness can be determined according to the requirements of reliability indexes, so that the balance between reliability and lightweight can be achieved to some extent.

Dynamic modeling and analysis of high-speed flexible planetary gear transmission systems

Modern planetary gear transmissions are often made with flexible components and operated at high or varying speed. Despite advances in understanding their dynamic performance, they remain vulnerable to problems leading—in some cases—to subsequent system failure. In this study, using angular and translational displacements as generalized coordinates, we establish lumped-parameter dynamic sub-models of the sun and planet gears that accurately consider gear-tooth dynamic behavior; we also develop reduced-order finite-element sub-models that fully consider the flexibility of the housing and carrier. Investigating the coupling between these sub-models in depth enables us to construct a complete hybrid dynamic model that can be used for coupling-dynamics analysis of flexible planetary gears under high- and variable-speed conditions. The accuracy of our planetary-gear-dynamics model is verified by comparing simulation data in the time and frequency domains to the results of experiments conducted on a planetary gear transmission system test bench specially built for this purpose. Finally, the dynamic characteristics of high-speed flexible planetary gears are studied at low speed, high speed, and high acceleration.

Vibration characteristics analysis of flexible helical gear system with multi-tooth spalling fault: Simulation and experimental study

Gear systems operating at high speeds and under heavy loads are susceptible to continuous multiple tooth surface spalling. The time-varying meshing stiffness (TVMS) model of helical gear pair with multi-tooth spalling fault is established by combining image recognition method and loaded tooth contact analysis (LTCA) method to target the actual form of the spalling fault, and its effectiveness was verified through finite element method (FEM). The flexible helical gear dynamic model is established by utilizing 8-node shell model and Timoshenko beam model to simulate the gear foundations and shafts, the TVMS in multi-tooth spalling fault condition is introduced as the excitation. The mapping relationship between the meshing process, TVMS and vibration response under the influence of rotational speed, spalling surface morphology scale, spalling depth and location of spalling occurrence is analyzed by combining simulation and experimental results. As the rotational speed increases, the specific meshing frequency coincides with the natural frequency of the gear system, leading to the phenomenon of superharmonic resonance. Continuous multi-tooth spalling fault results in continuous time-domain shocks and the meshing frequency modulation of the rotational frequency of the gear with spalling fault. In the absence of bottoming out, the increase in spalling surface morphology scale exerts a more pronounced influence on the vibration characteristics of the helical gear system compared to the increase in spalling depth. The research results can provide theoretical basis for gear system fault diagnosis.

Calculation of tooth pair stiffness by finite element analysis for the multibody simulation of flexible gear pairs with helical teeth and flank modifications

Calculation of tooth pair stiffness by finite element analysis for the multibody simulation of flexible gear pairs with helical teeth and flank modifications

Vibration attenuation characteristics of squeeze film dampers in spiral bevel gear systems

A central drive bevel gear system of aero-engines extracts power from a high-pressure rotor. The high speed of the high-pressure rotor aggravates the gear system's vibration. This work adopts squeeze film dampers (SFD) as damping devices to suppress excessive vibration of the spiral bevel gear rotor system. This paper establishes the general Reynolds equation of SFD and calculates the nonlinear oil-film force of SFD in real-time based on the finite element method. Besides, the finite element method and Timoshenko beam element are employed to model the flexible gear shaft. Then, the dynamic model of the spiral bevel gear system supported by SFDs is established, including the nonlinear oil-film force of SFD and time-varying meshing stiffness of the gear system. The dynamic response of the spiral bevel gear system is analyzed theoretically and experimentally to study the vibration attenuation characteristics of SFD. The findings indicate that SFD can effectively suppress the vibration amplitude of the system at high speeds. The theoretical analysis and experimental amplitude are within an order of magnitude, and the changing trend is consistent.

Dynamic modeling of GTF star gear-rotor coupling system considering structural flexibility

This paper establishes a dynamic model of Geared turbofan (GTF) star gear-rotor coupling system, in which the flexibility of shaft, disk, shell, diaphragm coupling, ring gear, and carrier are all taken into consideration. Additionally, an internal meshing model for flexible ring gear is developed, and the matrix reduction techniques is introduced to enhance the computational efficiency. Based on the dynamic model, the modal characteristics of the coupling system are extracted, and the influence of structural flexibility are investigated. Considering gyroscopic effect of the rotor, the Campbell diagram and the critical speeds are obtained. In addition, the vibration amplitudes under unbalanced excitation and time-varying mesh stiffness (TVMS) excitation are calculated and compared. The results of modal characteristics analysis indicate that many of the star gear train models are greatly affected by structural flexibility. Besides, the counter-rotating between the low-pressure rotor and the fan rotor results in frequency veering in the Campbell diagram, which is rarely observed in parallel gear-rotor system. The vibration responses indicate that unbalanced excitation of the rotor has relatively less effect on the gear vibration, while the low frequency excitation at star gear train is capable of exciting resonant vibration of the rotor.

Dynamic behavior analysis of planetary gear transmission system with bolt constraint of the flexible ring gear

Dynamic behavior analysis of planetary gear transmission system with bolt constraint of the flexible ring gear

Dynamic modeling and vibration analysis of a flexible gear transmission system

Vibrations of gear transmission systems (GTSs) are the key problems in the machinery industry. In the previous vibration analysis of GTS, the rotor is usually regarded as a rigid part. The rigid-shaft gear-transmission dynamic system RGDS) model cannot solve the differences of vibrations of rotor at different axial positions. To solve this problem, a flexible-shaft gear- transmission system dynamic (FGDS) model is established by using the finite element method. In the FGDS, the GTSs is separated into some flexible shaft segments, gear meshing unit and bearing unit. The bearing stiffness, bearing contact force, time-varying meshing stiffness and damping force of gear are considered. The time- and frequency-domain vibrations of FGDS and RGDS model under different rotational speeds are compared and analyzed. Note that the FGDS can obtain more accurate results than the RGDS model. The vibrations from FGDS are less than those from RGDS model. This paper can give some new approach for the dynamic modeling and vibration analysis of flexible GTSs.

A Contact Load Distribution Model to Capture the Influence of Structurally Compliant Rotating Ring Gear on the Dynamic Response of Epicyclic Gear Sets

AbstractEpicyclic gears, also commonly referred to as planetary gears, are power transfer components that are commonly used in several industrial applications. The structural compliance of thin-rimmed annular ring gear can significantly influence the performance of an epicyclic gear set. As powertrain components are continually being optimized to their design limits, this influence becomes prominent and can no longer be ignored. Therefore to capture the influence associated with ring gear flexibility, the current study will incorporate a finite element-based ring gear formulation into the three-dimensional planetary dynamic load distribution model (Ryali, and Talbot, 2021, “A Dynamic Load Distribution Model of Planetary Gear Sets,” Mech. Mach. Theory, 158, p. 104229). The proposed contact model employs a modified simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several components and system-level design variations without the need for an empirical mesh stiffness formulation or transmission error excitation of the system. The developed formulation will be used to study the dynamic response of planetary gear sets where the ring gear is a rotating member. The discussed results demonstrate the fidelity of the developed model, thus making it an excellent tool for the design and analysis of planetary gears.

Flexible Tuning of Friction on Atomically Thin Graphene.

The tuning of flexible microscale friction is desirable for the reliability of wearable electronic devices, tactile sensors, and flexible gears. Here, the tuning of friction of atomically thin graphene on a flexible polydimethylsiloxane (PDMS) substrate was obtained with the elastic modulus using a 1H,1H,2H,2H-perfluorodecyltrichlorosilane (FDTS) self-assembly monolayers (SAMs)-modified microsphere probe with the diameter of 5 μm at the microscale. The friction can be tuned at a large scale with the difference in the elastic modulus of PDMS and thickness of graphene. The hydrophobic property of the FDTS SAMs-modified probe decreased friction by reducing interfacial adhesion and preventing the effect of capillary interaction; thus, the friction decreased with the increase in the elastic modulus of the PDMS substrate due to decreasing indentation depth and thus the interfacial contact area; and also, the enhanced out-of-plane stiffness effectively decreased the interfacial contact quality with the increase of the thickness of graphene. The flexible tuning of friction on graphene was further verified by the theoretical calculation from the aspects of the friction arising from the normal and lateral deformation around the contacting area. This work is meaningful for promoting the design and reliability of flexible micro-devices.

Study on the Nonlinear Dynamic Behavior of Rattling Vibration in Gear Systems

To reveal the nonlinear dynamic behavior of gear rattling vibration caused by gear backlash, a 2-DOF oscillator model with spring and damping elements was established. Based on the theory of discontinuous dynamical systems, the phase plane of gear motion was divided into three parts: the domain of tooth surface meshing motion, the domain of free motion and the domain of tooth back meshing motion. Introducing the global mapping and local mapping dynamics method, the process of gear teeth from impact to meshing and then impact and meshing was accurately described. The influence of different restitution coefficients on gear impact-meshing motion was studied by numerical simulation. The results showed that the grazing bifurcation caused by gear backlash will lead to complex mapping structures of the system and even chaos. The restitution coefficient directly affects the impact-meshing behavior. The introduction of meshing stiffness and restitution coefficient can reasonably characterize the elastic deformation and energy loss during gear meshing, which provides a theoretical model for the application of the theory of discontinuous dynamical systems to a more complex multi-degree of freedom flexible contact gear transmission system.

Effects of gear flexibility on the dynamic characteristics of spur and helical gear system

The gear foundation is commonly assumed to be a rigid body in analyzing the dynamic characteristics of the gear system. This modeling approach may not be appropriate for building the gear model with lightweight features. Therefore, this paper proposes a gear dynamic model considering the flexible gear. The shell element with gyroscopic effect is employed to establish the gear finite element model, retaining the gear foundation and teeth structure. The fixed interface modal synthesis method is used to improve computational efficiency. The proposed model is verified by comparing it with the results calculated by Ansys. Based on the proposed model, the effects of gear flexibility on the dynamic characteristics of the spur and helical gear system are investigated. Numerical results show that the developed model can degenerate into the classical gear dynamic model. Due to the assumption of the gear as rigid discs, the predicted resonance speed by the conventional gear dynamic model is larger than the proposed model. Gear flexibility affects the dynamic characteristics of the spur and helical gear system differently. It's worth noting that the dynamic axial meshing force can excite the nodal diameter vibration in the helical gear system. The proposed model provides the theoretical basis and optimization tools for the high-performance design and vibration and noise reduction of high-speed lightweight gear transmission systems.

Deformation and Response Analysis of Spur Gear Pairs with Flexible Ring Gears and Localized Spalling Faults

For the analysis on the deformation of flexible ring gears in spur gear pairs, the complete flexible ring is discretized, and the boundary condition is added to the connecting points to develop a calculation method for the flexible deformation. The ovality index is used to describe the deformation degree of flexible ring gears, then the influences of ring-gear width and the spalling defects on the flexible deformation of ring gears are discussed. The result shows that the flexible deformation of ring gears is caused by the gear pair meshing force, and the deformed shape is close to an ellipse. In the single-tooth meshing interval of gear pairs, the main form of deformation is being stretched, and while in the double-tooth meshes, the main form is bending deformation. When the width of the ring gear rims is increased, the flexible deformation of the ring gears can be effectively suppressed, and the vibration amplitude of the gear pairs can be reduced. Additionally, when there is a localized spalling fault on gear pairs, the sudden changes in the deformation of flexible ring gears are generated by the shock of the meshing force. Finally, through the finite element analysis model and the experiment, the mathematical model of gear pairs with flexible rings is confirmed.

Study on Structural Vibration Characteristics of L-Shaped Flexible Ring Gear and Establishment of System Coupling Vibration Model

L-shaped flexible ring gear is a new solution to the non-uniform load distribution of planetary transmission systems. At present, the research on L-shaped flexible ring gear is still focused on its meshing characteristics and dynamic load sharing performance, and its structural vibration characteristics and dynamic coupling vibration characteristics with the system are not involved. Considering that the structural flexibility of the L-shaped flexible ring gear is significantly higher than that of the traditional ring gear, the structural vibration will obviously affect the load sharing and dynamic load factor performance of the transmission system, as well as the safety and reliability of the mechanism. Due to its strong structural flexibility and structural particularity, the existing dynamic analysis model is difficult to meet the requirements of analysis and design. In this paper, the coupling vibration model of L-shaped flexible ring gear planetary transmission systems is established, and the structural vibration characteristics of L-shaped flexible ring gear and its influence on the dynamic performance of the systems are deeply analyzed. The model foundation and theoretical guidance are provided for the design of L-shaped flexible ring gear and the analysis of the dynamic characteristics of flexible ring gear systems.