Meshing Pair Research Articles

Study on meshing and dynamic characteristics of herringbone gear pair considering tooth surface wear and modification

Due to errors and tooth surface wear of herringbone gear is inevitable. And tooth surface modification is the key technology to improve gear performance. Therefore, this paper studies the influence of tooth surface uneven wear and modification on herringbone gear pair's meshing and dynamic characteristics with errors. Firstly, herringbone gear pair meshing characteristic analysis model based on discrete tooth surface is established. Secondly, herringbone gear pair bending-torsion coupling dynamic characteristic analysis model considering friction is established, and the dynamic frictional force analysis process is given. Thirdly, combined with Archard's wear theory, the tooth surface uneven wear amount is obtained. The tooth surface uneven wear amount is substituted into meshing matrix as a tooth surface deviation. Finally, the meshing and dynamic characteristics of herringbone gear pair considering tooth surface wear and modification are studied by using the established analysis model of meshing characteristics and dynamic characteristics. The calculation results show that without tooth surface modification, tooth surface wear will deteriorate the meshing and dynamic characteristics rapidly. However, reasonable tooth surface modification can effectively improve meshing and dynamic characteristics of gear pair, so that the gear pair can still maintain stable transmission under wear condition.

Meshing pair geometry of the intersecting-axis internally geared screw compressor

The Intersecting-Axis Internally Geared Screw Compressor (IISC) is an emerging advanced positive displacement machine showing the potential to greatly broaden the application of screw compressor technology. The core component of the IISC is an internally geared meshing pair with the intersecting-axis gearing, while its design methodology has not been disclosed yet. To fill the gap, this paper established the geometry model for the meshing pair and discussed the influence of its core parameters on geometric performance. First, the generation model of meshing pairs was presented, and the complete parameters set of meshing pairs was defined. The established model was verified by a meshing pair manufactured by 3D printing and CNC techniques. Next, the geometric analysis model of IISCs was established such as working volume and leakage channels, which was verified by commercial 3D software. Using the analysis model, the mesh pair parameters (rotor profile, cone angle, wrap angle, and L/D ratio) were discussed to reveal the design methodology of IISCs. Finally, the variable-pitch technology was discussed, and a novel variable-pitch method was proposed to further enhance the performance of IISCs. This paper could effectively guide the design of IISCs to further promote the development of the screw compressor technology.

Effect of meshing-induced deformation on lubrication for journal planet gear bearings

To increase the power density and reliability of wind turbine gearboxes (WTGs), journal planet gear bearings (JPGBs) are increasingly employed in their low-speed planet stages. Except for the pressure- and temperature-induced deformations, the JPGB is also structurally deformed by the gear pair meshing in this application, complicating the lubrication and deformation characteristics. Considering the above meshing-induced deformation, a thermo-elasto-hydrodynamic (TEHD) model is proposed for the JPGB, whose deformation is predicted using a self-programmed procedure based on the finite element method (FEM). Besides, this model is verified through a lubrication experiment of the JPGB in the WTG. It is found that the appropriate meshing-induced deformation, varying periodically in the meshing process, can improve the TEHD and misalignment behaviors of the JPGB due to the load-carrying region expansion or twice hydrodynamic action. This phenomenon becomes increasingly obvious with increasing the WTG's input power and the planet's inner radius.

A novel analytical model of the tooth pair meshing duration of orthogonal face gears

A novel analytical model of the tooth pair meshing duration of orthogonal face gears

Dynamic modeling and failure mechanism study of herringbone gear planetary transmission system for wind turbine under gear cracks

The herringbone gear planetary transmission system (HGPTS) is a common component in the gearbox of wind turbines. Studying the dynamic performance of gear systems is the key to improving their stability. To reveal the influence of cracks on the dynamic characteristics of the HGPTS, using slicing method, we explore the influence of different crack factors on the time-varying meshing stiffness (TVMS) of the system. A 55-degrees of freedom bending torsion axis pendulum dynamic model was constructed using the centralized mass parameter method; in the model, factors such as TVMS of cracks as well as receding groove and errors are considered. The Runge–Kutta method was used to solve the dynamics, and the evolution diagram of the vibration and load distribution characteristics of the system under crack changes was obtained. Vibration tests were conducted on the system studied in this work. The results show that under the influence of cracks, the TVMS of the external and internal meshing pairs of the system will decrease, and as the cracks intensify, the fluctuation of the TVMS will decrease. Cracks can lead to regular impact behavior in the system. A modulation sideband centered on the meshing frequency appears in the vibration response, and the vibration trajectory of the gears will also become disordered, at the same time, under the influence of cracks, there are significant excitation factors in the load-sharing characteristics of the system. As the cracks continue to intensify, the vibration of the system becomes increasingly evident, and the load-sharing characteristics show a trend of first decreasing and then increasing. The vibration test results are in good agreement with the theoretical predictions. The correctness of the established model is verified. The research results can provide reference for the reliability research of wind turbine HGPTS.

An involute gear pair meshing stiffness model considering time-varying friction under mixed lubrication

An involute gear pair meshing stiffness model considering time-varying friction under mixed lubrication

Repulsive Shells

This paper develops a shape space framework for collision-aware geometric modeling, where basic geometric operations automatically avoid inter-penetration. Shape spaces are a powerful tool for surface modeling, shape analysis, nonrigid motion planning, and animation, but past formulations permit nonphysical intersections. Our framework augments an existing shape space using a repulsive energy such that collision avoidance becomes a first-class property, encoded in the Riemannian metric itself. In turn, tasks like intersection-free shape interpolation or motion extrapolation amount to simply computing geodesic paths via standard numerical algorithms. To make optimization practical, we develop an adaptive collision penalty that prevents mesh self-intersection, and converges to a meaningful limit energy under refinement. The final algorithms apply to any category of shape, and do not require a dataset of examples, training, rigging, nor any other prior information. For instance, to interpolate between two shapes we need only a single pair of meshes with the same connectivity. We evaluate our method on a variety of challenging examples from modeling and animation.

Analytical method for time-varying meshing stiffness and dynamic responses of modified spur gears considering pitch deviation and geometric eccentricity

Pitch deviation and geometric eccentricity are almost inevitable in gear transmission systems. Tooth profile modification (TPM) is a common method used to improve gear contact properties. However, the coupling interaction between the tooth profile deviation introduced by TPM and manufacturing errors is complex. There is a lack of an analytical model that can clarify the dynamic behaviors of the modified gear pair affected by multiple manufacturing errors, specifically pitch deviation and geometric eccentricity. To fill this gap, a comprehensive analytical gear mesh model is proposed considering TPM, pitch deviation, and geometric eccentricity. The calculation formulas for the time-varying meshing stiffness (TVMS) and load sharing factor (LSF) are derived considering the iterative change of gear pair meshing parameters with phase under the influence of multiple manufacturing errors. Then, the translation-torsion coupling dynamic model of the spur gear pair based on the lumped mass method is established to investigate the dynamic transmission error (DTE) and vibration characteristics. Results show that TPM is an effective method for improving the comprehensive stiffness of a gear pair within the meshing range containing pitch deviation, but it reduces the meshing phase that includes only geometric eccentricity. Compared with the unmodified gear pair, the suppression effect of changing the modification length on the maximum DTE and vibration acceleration is more significant than that of the modification amount. TPM increases the overall fluctuation threshold range of DTE for gear pairs with only geometric eccentricity. It is expected that the proposed method can provide a theoretical basis for exploring vibration suppression in gear pairs with geometric eccentricity and pitch deviation errors.

Generated realistic noise and rotation-equivariant models for data-driven mesh denoising

3D mesh denoising is a crucial pre-processing step in many graphics applications. However, existing data-driven mesh denoising models, primarily trained on synthetic white noise, are less effective when applied to real-world meshes with the noise of complex intensities and distributions. Moreover, how to comprehensively capture information from input meshes and apply suitable denoising models for feature-preserving mesh denoising remains a critical and unresolved challenge. This paper presents a rotation-Equivariant model-based Mesh Denoising (EMD) model and a Realistic Mesh Noise Generation (RMNG) model to address these issues. Our EMD model leverages rotation-equivariant features and self-attention weights of geodesic patches for more effective feature extraction, thereby achieving SOTA denoising results. The RMNG model, based on the Generative Adversarial Networks (GANs) architecture, generates massive amounts of realistic noisy and noiseless mesh pairs data for data-driven mesh denoising model training, significantly benefiting real-world denoising tasks. To address the smooth degradation and loss of sharp edges commonly observed in captured meshes, we further introduce varying levels of Laplacian smoothing to input meshes during the paired training data generation, endowing the trained denoising model with feature recovery capabilities. Experimental results demonstrate the superior performance of our proposed method in preserving fine-grained features while removing noise on real-world captured meshes.

Influence of gear modification on dynamic characteristics of star gearing system in geared turbofan (GTF) gearbox based on a closed-loop dynamic analysis method

The star gearing transmission system is a key component of a geared turbofan (GTF) aero-engine. Accurate prediction of the dynamic characteristics of the star gearing transmission system, especially after gear modification, is important for the design of high-performance engines. Firstly, this paper establishes a dynamic time-varying mesh stiffness (TVMS) and a comprehensive transmission error (TE) calculation model for herringbone gear pair considering changes in the meshing state. Then, the dynamic internal excitation calculation model is combined with the lumped parameter dynamic model of the system to form the “excitation–response–feedback” closed-loop coupling dynamic analysis method of the GTF star gearing system. Compared with traditional analysis methods, this method takes into account the effect of contact state changes on internal excitation during the calculation process and corrects internal excitation in real time. Finally, the effect of different topology modification schemes on the system's dynamic characteristics is investigated based on this method. The results show that the closed-loop coupled dynamics analysis method is able to capture contact state changes of the same gear pair at different moments and between different gear pairs at the same moment. Modified #2 is only to modify the planet gear. This scheme can effectively reduce the vibration displacement of the ring gear, and reduce the peak-to-peak value of the ring gear's vibration displacement in all directions by more than 70%. At the same time, the scheme also reduces the load-sharing coefficient of the internal and external meshing pairs of the system by 1.92% and 2.01%, respectively, and the peak-to-peak value of the dynamic factor of the internal and external meshing pairs can be reduced by 57.91% at most.

Establishment of the dynamic BTAP model and load-sharing analysis of herringbone gear planetary system with cracks

To reveal the influence of component cracks on the dynamic load-sharing characteristics of the herringbone gear planetary system (HGPS), a 55-DOF bending-torsional-axial-pendular (BTAP) nonlinear dynamic model of the system was constructed, taking into account parameters of different crack degrees (depth, angle, length), as well as factors such as manufacturing error (ME) and installation error (IE), time-varying mesh stiffness (TVMS), time-varying support stiffness, damping, and friction. The TVMS model of components with cracks was established using the cumulative potential energy method, and the mathematical quantification relationship between different crack parameters and TVMS was studied. Based on the theory of elastohydrodynamic lubrication (EHL), calculate the time-varying friction coefficient and friction force of each gear pair. Using the nonlinear elastic theory of rolling elements and raceways, the time-varying support stiffness of each component is obtained. Using the Runge-Kutta numerical integration method to solve the dynamic differential equations, and analyzed the load-sharing characteristics and sensitivity influence law of the system when the sun gear, planetary gear, and internal gear ring contain cracks respectively. Built a vibration test bench for the HGPS with cracks, and the experimental results were compared with the theoretical results. The results show that as the crack intensifies, the TVMS value decreases at the crack tooth. When the sun gear contains cracks, there will be obvious protruding excitation in the system’s load-sharing curve, and the internal meshing load-sharing characteristics are better than the external meshing load-sharing characteristics. At the same time, as the degree of cracks increases, the system load-sharing characteristics first improve and then deteriorate. At the same crack, as manufacturing and installation errors increase, the load-sharing characteristics of the internal and external meshing pairs deteriorate. When the internal gear ring contains cracks, the dynamic load-sharing coefficients of the internal and external meshing pairs of the system are 7.96 and 4.10, respectively, which have the highest impact on the dynamic load-sharing coefficient and sensitivity of the internal and external meshing pairs of the system. The experimental results are consistent with the theoretical results, verifying the correctness of the model.

Manufacturing and contact characteristics analysis of a novel 2K-H internal meshing planetary reducer with involute-cycloid combined tooth profiles

Rotate Vector (RV) reducer involves multiple crankshafts to drive the cycloidal-pin transmission in parallel, leading to an over-positioning structure and high manufacturing and assembly requirements for the reducer, restricting the development of industrial robots. In view of the above problems, a novel configuration of Abnormal Cycloidal Gear (ACG) reducer with a 2K-H internal meshing planetary transmission is proposed. The design innovatively replaces the multiple crankshafts with a pin mechanism, thereby addressing the over-positioning and simplifying the manufacturing and assembly processes. To improve the performance of the reducer, the “epicycloid-involute-hypocycloid” combined tooth profiles are designed and adopted as the ACG reducer’s drive teeth. The configuration principle of the ACG reducer is conducted. Next, a manufacturing method utilizing a rack cutter to generate the profile of drive teeth is presented. Finally, the meshing performance and mechanical behaviors of the designed internal meshing pair for the ACG reducer are evaluated. Results show that ACG reducer has the advantages of a simple structure and large transmission ratio. The combined tooth profiles can be machined at one time using the designed cutter, simplifying the tooth machining process. The internal meshing pair is linear contact and exhibits an obviously multi-teeth meshing effect, which benefits the carrying capacity and transmission performance of the ACG reducer.

Contact Analysis for Cycloid Pinwheel Mechanism by Isogeometric Finite Element

Cycloid drives are generally used in precision machinery requiring high-reduction ratios, such as robot joint (RV) reducers. The contact stress of cycloidal gears greatly affects lifetime and transmission performance. Traditional finite element method (FEM) has less computational efficiency for contact analysis of complex surface. Therefore, in this paper, isogeometric analysis (IGA) was employed to explore the multi-tooth contact problem of the cycloid pinwheel drive. Based on the nonuniform rational B spline (NURBS) curved surface generation method, the NURBS tooth profile of the cycloid gear was reconstructed. In addition, the NURBS surface of the cycloid gear–pin tooth–output pin was generated via the element splicing method. A geometrical analysis model of cycloid pinwheel drive was established to solve the contact force of the meshing pair under different input angles and compared with the finite element method in terms of convergence, resultant accuracy, and solving timeliness. The results show that isogeometric analysis has higher accuracy and efficiency than the finite element method in calculating the contact stress and contact force. The error of the IGA is only 8.8% for 10 × 10 elements in contact, while the error of the finite element method reaches about 40%. The method can improve the contact simulation accuracy of the cycloid drive and provides a reference for the design evaluation of RV reducer.

Quantitative assessment for tooth crack of the sun gear in a planetary gearbox

The sun gear in a planetary gearbox is prone to generate tooth crack due to its much more severe load conditions than other gears. The cracked sun gear will evolve into distinct tooth breakages and thus may deteriorate the operation status and even cause catastrophic loss of the whole transmission system. To avoid tooth crack induced malfunction of the planetary gearbox, the tooth crack of sun gear should be accurately identified during the early stage. Therefore, a novelty quantitative assessment methodology for tooth crack damage is proposed, which is a mathematical model for crack propagation of the sun gear in planetary gearboxes based on vibration acceleration signal. Firstly, the quantitative relationship between the crack propagation parameters along the gear thickness and width directions and the time-varying mesh stiffness is analytically formulated. The analytical time-varying mesh stiffness formulation is incorporated into a translational–torsional dynamic model to reveal the effects of crack propagation on the vibration signal of internal and external meshing pairs in the planetary gearbox. Secondly, a quantitative mapping function is established by taking the cracked section area as the variable and the residual of the summed envelope spectrum amplitude of the vibration acceleration signal as the assessment index. Finally, a numerical simulation as well as an experimental test is conducted and compared to verify the correctness of the proposed assessment methodology. We believe that the established model and the corresponding index provide a physically intuitive yet mathematically quantitative reference for diagnosing tooth crack in planetary gearboxes.

Crowned spur gears for constant mesh stiffness: A conceptual approach

Flank line crowning is a gear surface geometry modification that can be applied as a measure to accommodate contact imperfections along the gear teeth facewidth, that are a consequence of misalignment from either geometric defects or elastic deflection. Due to flank line crowning, the contact stiffness between the teeth of an ideal spur gear changes, thus modifying the gear mesh stiffness. Gear mesh stiffness fluctuations are one of the main driving factors behind gear performance, such as transmission error, dynamic overload and overall system vibration. Regardless of manufacturing feasibility, a set of analytical equations, derived from the classical elliptical contact theory is presented aiming to find the flank line crowning values along the path of contact that eliminate gear mesh stiffness fluctuations. This is achieved by transforming the shape of single teeth pair mesh stiffness through the contact stiffness, making it similar to the shape of the load sharing. A direct method to find the load sharing of spur gears with flank line crowning is also presented.

Dynamic characteristics of the rack and pinion lift mechanism of the combined command cabin

This paper presents a novel approach to accurately simulate the dynamic characteristics of a rack and pinion lifting mechanism while accounting for the coupling effect of meshing tooth pair stiffness and grease characteristics in real-world environments. A structure-grease coupling meshing stiffness model is established based on the deformation coordination conditions of the tooth pair meshing. The model incorporates the effect of the grease stiffness term on the time-varying meshing stiffness of the rack and pinion. By analyzing the dynamic characteristics of the combined command cabin lifting mechanism using this model, we find that the total meshing stiffness of the gear teeth is lower when the transient thermoelastic flow effect of the grease is considered. Furthermore, the total stiffness value decreases as the normal meshing force at the meshing point decreases. This research reveals that the worst lubrication conditions are typically found on the gear wheel teeth near the base circle, where the grease film temperature rise is highest, the grease film pressure is highest, and the grease film thickness is thinnest.

Cutter design and the machining strategy to resolve the tooth wear issue for both paired components of single-screw compressors

A single screw compressor consists of paired components of the primary screw rotor and two star-wheel. It is widely applied in enormous industrial applications and is growing continuously. However, the manufacturing for both paired components, including the tooth surface wear issue, must be solved. This paper proposes geometric modeling of cutter design and the analytical cutting for both paired components, in addition to optimizing the contact area to resolve the tooth wear issue. The geometric modeling of the components was determined in LEMP and CEMP models. The cutter profile designs were designed according to gear enveloping theory and pair meshing conditions. The contact area on the tooth flank was successfully enhanced by applying a uniform design and RBF pseudo model. The virtual machining was accomplished in VERICUT, and the machining strategy for both paired components was verified and suitable for actual CNC machining. In addition, the geometric model's correctness for both cutters was confirmed since the profile deviation on both components satisfied the ISO-3650 standard.

Study on the Selection of Single-Screw Steam Compressors in Industrial Steam Supply

Both direct and indirect heating compression methods were proposed to satisfy the requirement of industrial steam compression and supply. The compression process in a single-screw compressor was analyzed with the determination of different inlet and outlet boundary conditions. Considering the misalignment of meshing pairs caused by the offset of the star wheel axis and screw origin, the differential expansion of the vertical meshing pair was further analyzed. The inner ring of the sealing end face, the wall of the inner ring of the bearing at the inlet and outlet ends, and the bottom surface of the bracket were analyzed by different coordinate systems and different constraints, thus facilitating the design and selection of the single screw. The critical point for the design of a steam-type single-screw compressor is an outlet temperature of 350 °C and an outlet volume flow rate of 130 m3/min. At a flow rate of 130 m3/min, when the temperature exceeds 350 °C, the reliability of the compressor is still limited, and the differential expansion of the meshing pair exceeds 0.3 mm. In addition, superheating of steam can be improved by applying a centrifugal compressor with cascade compression and centrifugal compression in conjunction with reflux adjustment at the compression outlet.

Approximate expression for the single tooth pair slice mesh stiffness

In many gear mesh stiffness models, the single tooth pair mesh stiffness is commonly approximated as having a parabolic-like symmetric shape along the path of contact with a fixed or contact ratio dependent amplitude. Even though this is a valid approximation under certain conditions, there is an asymmetry being disregarded and an amplitude being roughly approximated. In this work, a new straightforward analytical expression for the single tooth pair slice mesh stiffness is defined resorting to a parabolic approximation of the tooth pair structural stiffness that requires the definition of the asymmetry, relative amplitude and maximum value as a function of the gear parameters. In order to validate the developed work in terms of applicability and accuracy, a random sample of gears have their tooth pair structural stiffness approximation tested. The established asymmetry, relative amplitude and maximum value allow, in a fast and simple fashion, to obtain an accurate approximation. Different formulations of the single tooth pair slice mesh stiffness are compared, highlighting the importance of including the asymmetry and showing the improvements due to the new parameters.

Inv3D: a high-resolution 3D invoice dataset for template-guided single-image document unwarping

Numerous business workflows involve printed forms, such as invoices or receipts, which are often manually digitalized to persistently search or store the data. As hardware scanners are costly and inflexible, smartphones are increasingly used for digitalization. Here, processing algorithms need to deal with prevailing environmental factors, such as shadows or crumples. Current state-of-the-art approaches learn supervised image dewarping models based on pairs of raw images and rectification meshes. The available results show promising predictive accuracies for dewarping, but generated errors still lead to sub-optimal information retrieval. In this paper, we explore the potential of improving dewarping models using additional, structured information in the form of invoice templates. We provide two core contributions: (1) a novel dataset, referred to as Inv3D, comprising synthetic and real-world high-resolution invoice images with structural templates, rectification meshes, and a multiplicity of per-pixel supervision signals and (2) a novel image dewarping algorithm, which extends the state-of-the-art approach GeoTr to leverage structural templates using attention. Our extensive evaluation includes an implementation of DewarpNet and shows that exploiting structured templates can improve the performance for image dewarping. We report superior performance for the proposed algorithm on our new benchmark for all metrics, including an improved local distortion of 26.1 %. We made our new dataset and all code publicly available at https://felixhertlein.github.io/inv3d.