Meshing Pair Research Articles

Dynamic analysis on single-rotor multi-input helicopter main gearbox related with structural parameters

Combined with the finite element method and the lumped mass method, the integral node dynamic model of a single-rotor multi-input helicopter main gearbox is established. The influence of shaft parameters on dynamic characteristics is analyzed, and each torsional shaft is regarded as a finite element node to derive the system dynamic equation. In addition, the dynamic model of the meshing pair element is established by lumped mass method, and these elements not only include internal excitations such as time-varying meshing stiffness and transmission error, but also carry the external load. The differential equations of the system are solved by the Fourier series method. The dynamic responses of the converging element and the planetary gear train are obtained. The load-sharing coefficients of these elements are calculated by the influence of the shaft structural parameters. A parameter optimization method is proposed to improve the system load characteristics, which provides a theoretical support for the design of helicopter main transmission system.

Modeling the effect of misalignment and tooth microgeometry on helical gear pair in mesh

Understanding the effect of misalignment and microgeometry is important for gear designers and those have the main interest is gear manufacturing and maintenance. Unavoidable misalignment and microgeometry are both important factors to be considered in gear design which influence the resulted stresses, transmission error, and dynamic response. Analyzing the stress concentration on the tooth root and tooth flank areas is important to predict the failure modes that may occur. The current research work concentrates on modeling engaged gear teeth, analyzing the generated stresses and shows the importance of introducing the micro-geometry modifications. To do so, three different cases have been studied. The first case (case 1) considers the basic microgeometry modifications, the second case (case 2) considers the misalignment effect, and the last case (case 3) is to add some more micro-geometry modifications to compensate for the misalignment effect.It was observed that the gear calculating tools resulted in significantly higher stresses than the FE software. The obtained results from different software tools have been discussed to understand the differences for the three studied cases. However, the results from case 2 as compared to case 1 showed that the introduced misalignment results in shifting the stress pattern into one side of the gear tooth and significantly higher stresses than case 1. Case 3 showed that the use of micro-geometry modifications can result in compensating the effect of the misalignment in operation.

Force Analysis for a Variable-Pitch Rotor Meshing Pair in Twin-Screw Vacuum Pump Generating on CNC Turning Machine

The variable pitch twin-screw vacuum pump has more advantage than the uniform pitch twin-screw vacuum pump. Its energy efficiency and volumetric compression ratio are specifically high. Under the cyclic gas pressure and working temperature, the rotors of vacuum pump often deform and interfere that lead to noise, vibration and rotor abrasion. In this paper, a 3D model of the variable pitch rotor generating by CNC turning process is constructed to reasonably estimate the rotor load and deformation in operation. The contact force have been analyzed to show the advantages of variable pitch rotors.

Geometric characteristics analysis for inner surface of working chamber in single screw compressor with multicolumn envelope meshing pair

In single screw compressor (SSC), the inner surface of the working chamber has always been a key issue that affects oil application and heat transfer. However, the geometric characteristics for the inner surface of the working chamber in SSC with Multicolumn Envelope Meshing Pair (MEMP) have not been carried out yet. Therefore, in this paper, a geometric model of working chamber inner surface for the SSC with MEMP is established to predict the geometric characteristics of the working process. The presented model is verified as a powerful tool for geometric characteristics analysis by the simulation results. With the validated model, the geometric characteristics of the working process and the effect of MEMP structural parameters on the geometric characteristics and the working performance for the SSC with MEMP have been analyzed. Through the comparison of the inner surface area with different structural parameters, optimization analysis of the structural parameters can be obtained. All of this work can provide the basis for the later heat transfer analysis and optimization structural design of the SSC.

Consistent Shape Matching via Coupled Optimization

AbstractWe propose a new method for computing accurate point‐to‐point mappings between a pair of triangle meshes given imperfect initial correspondences. Unlike the majority of existing techniques, we optimize for a map while leveraging information from the inverse map, yielding results which are highly consistent with respect to composition of mappings. Remarkably, our method considers only a linear number of candidate points on the target shape, allowing us to work directly with high resolution meshes, and to avoid a delicate and possibly error‐prone up‐sampling procedure. Key to this dimensionality reduction is a novel candidate selection process, where the mapped points drift over the target shape, finalizing their location based on intrinsic distortion measures. Overall, we arrive at an iterative scheme where at each step we optimize for the map and its inverse by solving two relaxed Quadratic Assignment Problems using off‐the‐shelf optimization tools. We provide quantitative and qualitative comparison of our method with several existing techniques, and show that it provides a powerful matching tool when accurate and consistent correspondences are required.

An investigation on the influence of modification parameters on transmission characteristics of planetary gear system

A new gear tooth modification model of planetary gear system was established by considering the characteristics of tooth longitudinal crowning modification and tooth profile modification. Using this model, the influences of modification parameters on the time-varying mesh stiffness, transmission error, contact spots and dynamic response of the planetary gear system were analyzed through numerical analysis. The results show that tooth profile modification can effectively restrain the mesh stiffness sudden variation in the single and double tooth alternation of both the internal and external mesh pairs, and significantly decrease the transmission error fluctuation. However, longitudinal crowning modification has no marked influence on mesh stiffness sudden variation or transmission error fluctuation. The tooth profile modification can significantly reduce the sudden variation of tooth surface load during gear mesh course. Longitudinal crowning modification can make the tooth surface load evenly distributed in tooth width direction. When the external meshing pairs are modified at the tooth profile individually, the magnitude values of main response resonance peaks of internal meshing pairs have a great reduction, but those values of external meshing pairs change slightly. In the case of tooth profile modification of the internal meshing pairs, the phenomenon is reversed. By contrast with tooth profile modification, longitudinal crowning modification has little influence on the resonance peaks of internal and external meshing pairs.

Thermoelastic Stress-Strain Analysis of the Meshing Pairs of a Two-Tooth Difference Swing-Rod Movable Toothed Drive

Temperature distribution, thermal strain and thermal stress, as the major thermal characteristics influence considerably the performance of a two-tooth difference swing-rod movable toothed drive. By principles of heat transfer and tribology became the basis for deriving the calculation formulae for the frictional heat flux of meshing pairs, convective heat transfer coefficient of a meshing toothed surface, and end face under slip conditions to construct the movable teeth finite element model for the thermal analysis. Thermal strain and thermal stress distributions of a single tooth meshing model of the meshing pair were analyzed by thermal structural coupling using ANSYS package. The meshing stiffness in the case of thermal elastic deformation is also discussed. The surface heat transfer coefficient of the movable teeth is shown to be high, under favorable heat transfer conditions. In this region, the heat transfer coefficient of a ring gear becomes lower as the temperature is growing. Numerical simulation of thermal strain demonstrated a considerable reduction in the stiffness of meshing pairs. The above describes the effect of thermal behavior of the movable teeth transmission system on its dynamic performance.

Theoretical study on wear characteristics of single screw refrigeration compressor with multicolumn envelope meshing pair

In single screw refrigeration compressor (SSRC), the wear of meshing pair has always been a key issue that restricts its development. In order to solve this problem, a Multicolumn Envelope Meshing Pair (MEMP) was proposed. However, the theoretical research on wear resistance of MEMP has not been carried out yet. Therefore, in this paper, a theoretical calculation model describing the influence of the MEMP profile parameters on wear characteristics of the SSRC with MEMP is established to predict the wear resistance. The presented model is verified as a powerful tool for wear characteristics analysis by the experimental results. With the validated model, the effect of MEMP profile parameters on the wear characteristics of SSRC has been analyzed. Optimization analysis shows that in the design stage more envelope columns with a larger center distance and larger envelope column diameter should be chosen for the MEMP to get a better wear resistance.

Planet bearing fault diagnosis using multipoint Optimal Minimum Entropy Deconvolution Adjusted

The vibration signals of planet bearings exhibit periodic impulsive features and are modulated by various effects, including: 1) time-varying vibration transfer path; 2) load zone passing; 3) time-varying angles between gear pair mesh lines of action and impact force vector; and 4) bearing fault. At the same time, slippages of rolling elements in bearings can lead to randomized periods of impulses and blurs in the Fourier spectrum of planet bearing vibration signals. As a result, common methods have limitations in analyzing planet bearing signals. In this paper, we establish a model of planet bearing vibration signal considering slippages in rolling elements, then derive its Fourier spectrum to illustrate the impact of slippages on Fourier spectrum. In order to extract the features of impulses caused by faults, we apply a deconvolution algorithm called Multipoint Optimal Minimum Entropy Deconvolution Adjusted (MOMEDA), which is good at deconvoluting signals with periodic impulses. For adaption to planet bearing vibration, we redesign the target vector of MOMEDA to simulate the actual stochastic impulses caused by slippages. To quantify the severity of slippages and describe the randomness of impulses, we propose the slippage parameter and utilize negentropy to determinate it. Lastly, the proposed method is validated using both numerical simulation and experimental data. We detect faults in outer race, rolling element and inner race of planet bearings, respectively. Compared with traditional Fourier and envelope spectra as well as kurtogram filtering method, MOMEDA shows specific applicability for fault diagnosis of planet bearings.

A New Mathematical Modeling Method for Four‐Stage Helicopter Main Gearbox and Dynamic Response Optimization

A new mathematical modeling method, namely, the finite element method and the lumped mass method (LMM‐FEM) mixed modeling, is applied to establish the overall multinode dynamic model of a four‐stage helicopter main gearbox. The design of structural parameters of the shaft is the critical link in the four‐stage gearbox; it affects the response of multiple input and output branches; however, only the meshing pairs were frequently shown in the dynamic model in previous research. Therefore, each shaft is also treated as a single node and the shaft parameters are coupled into the dynamic equations in this method, which is more accurate for the transmission chain. The differential equations of the system are solved by the Fourier series method, and the dynamic response of each meshing element is calculated. The sensitivity analysis method and parameter optimization method are applied to obtain the key shaft parameters corresponding to each meshing element. The results show that the magnitude of dynamic response in converging meshing pair and tail output pair is higher than that of other meshing pairs, and the wall thickness has great sensitivity to a rotor shaft. In addition, the sensitivity analysis method can be used to select the corresponding shaft node efficiently and choose parameters appropriately for reducing the system response.

On Dynamic Mesh Force Evaluation of Spiral Bevel Gears

The mesh model and mesh stiffness representation are the two main factors affecting the calculation method and the results of the dynamic mesh force. Comparative studies considering the two factors are performed to explore appropriate approaches to estimate the dynamic meshing load on each contacting tooth flank of spiral bevel gears. First, a tooth pair mesh model is proposed to better describe the mesh characteristics of individual tooth pairs in contact. The mesh parameters including the mesh vector, transmission error, and mesh stiffness are compared with those of the extensively applied single‐point mesh model of a gear pair. Dynamic results from the proposed model indicate that it can reveal a more realistic and pronounced dynamic behavior of each engaged tooth pair. Second, dynamic mesh force calculations from three different approaches are compared to further investigate the effect of mesh stiffness representations. One method uses the mesh stiffness estimated by the commonly used average slope approach, the second method applies the mesh stiffness evaluated by the local slope approach, and the third approach utilizes a quasistatically defined interpolation function indexed by mesh deflection and mesh position.

Relationship between the engaging force of planetary gear train and the position‐correlated modal properties

Planetary gear train (PGT) is widely used in a variety of fields such as helicopters and aircraft engines. The failure of meshing gear often happens in the PGT due to the working condition of high speed, variable load, high-frequency excitation, assembly error etc. However, the causes of gear failure are still insufficiency, especially in the condition of high speed and high-frequency excitation. In this work, the engaging force between gear meshing pair of the PGT under high-frequency excitation is studied using the proposed position-correlated modal properties calculation method, which is established by incorporating the effect of meshing position and meshing phase difference of each contact pair into the free vibration model to study the modal properties of the PGT at different meshing positions. The corresponding engaging force responses based on the position-correlated modal properties are investigated. The simulation results show that the higher-order natural frequencies of the system are greatly affected by the meshing position. The peaks of engaging force occur at meshing positions where the natural frequencies are equal to the excitation frequency, which can be the potential cause of the gear damage.

Exploring RGB-D Cameras for 3D Reconstruction of Cultural Heritage

RGB-D cameras have a great potential to solve several problems arising during the digitization of objects, such as cultural heritage. Three-dimensional (3D) digital preservation is usually performed with the use of high-end 3D scanners, as the 3D points generated by this type of equipment are in average millimeter up to sub-millimeter accurate. The downside of 3D scanners, in addition to the high cost, is the infrastructure requirements. It requires its own source of energy, a large workspace with tripods, special training to calibrate and operate the equipment, and high acquisition time, potentially taking several minutes for capturing a single image. An alternative is the use of low-cost depth cameras that are easy to operate and only require connection to a laptop and a source of energy. There are several recent studies showing the potential of RGB-D sensors. However, they often exhibit errors when applied to a full 360 degrees 3D reconstruction setup, known as the loop closure problem. This kind of error accumulation is intensified by the lower accuracy and large volume of data generated by RGB-D cameras. This article proposes a complete methodology for 3D reconstruction based on RGB-D sensors. To mitigate the loop closure effect, a pairwise alignment method was developed. The proposed approach expands the connectivity graph connections in a pairwise alignment system, by automatically discovering new pairs of meshes with overlapping regions. Then the alignment is more evenly distributed over the aligned pairs, avoiding the loop closure problem of full 3D reconstructions. The experiments were performed on a collection of 30 artworks made by the Baroque artist Antonio Francisco Lisboa, known as Aleijadinho, as part of the Aleijadinho Digital project conducted in partnership with IPHAN (Brazilian National Institute for Cultural and Artistic Heritage) and United Nations Educational, Scientific and Cultural Organization (UNESCO). Experimental results show 3D models that are favorably compared to state-of-the-art methods available in the literature using RGD-D sensors. The main contributions of this work are: a new method for 3D alignment dedicated to attenuate the RGB-D camera loop closure problem; the development and disclosure of a complete, practical solution for 3D reconstruction of artworks; and the construction of 3D digital models of an important and challenging collection of Brazilian cultural heritage, made accessible by a virtual museum.

Coupling bending-torsional vibration model of gear - rotor

A rotor - bearing model of 5 degrees of freedom was established by finite element method, and a gear pair meshing model of 5 degrees of freedom was established by Newton’s second law. By introducing the azimuth, the gear rotor system could be designed with the gear pair arranging at will. Then through the transformation of coordinate system, the coordinate system of rotor-bearing model and gear pair model were unified, and the two were coupled together, and a complete gear-rotor model with uniform coordinate system was established.

Dynamic Mesh Forces in Accounting of the Time Variable Mesh Stiffness of a Gear Train

The paper considers the problems connected with the periodic variation of the tooth stiffness during the engagement in a spur gear train that arise due to the different number of teeth involved in torque transmission. Thus, the process of engagement is accompanied by a redistribution of the dynamic forces between the teeth at the boundaries of the engagement phases from the one-pair contact to the double-pair contact. As a result, it can cause forced and parametric vibrations. The dynamic mesh forces caused by kinematic error and time variable mesh stiffness are associated with the periodic mesh of the teeth. It is further shown that the load on the meshing pairs of teeth can be several times higher than the nominal forces. As a result, the operation of a machine is accompanied by high level of noise and vibration.

Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach

Time-dependent mesh stiffness is a most important reason of vibration and dynamic excitation in gear sets. In this research, analytical formulas of the helical gear set and the planetary gear system are combined to calculate the time-dependent mesh stiffness of the helical planetary gear system. For this purpose, at the first step, the analytical equations are derived for the spur gear pair. Then by dividing a helical tooth into the several independent thin spur tooth slices, the helical gear pair mesh stiffness is extracted. Finally, these equations are extended to the helical planetary gear system. The suggested analytical results and those which obtained by the finite element method (FEM) are compared and are in good agreement when the helix angle is less than 15 degrees. Also, the helical planetary gear system mesh stiffness in different cases such as fixed carrier, fixed sun gear and fixed ring gears is calculated. These results show that the value of mesh frequency ratio in each case scales the mesh stiffness shapes in the rotation angle direction. In other words, mesh frequency ratio parameter determines the number of meshing period in each rotation of planets.

Multiple-Traces Surface Integral Equations for Electromagnetic Scattering From Complex Microstrip Structures

In this communication, a new multiple-traces Poggio–Miller–Chang–Harrington–Wu–Tsai (MT-PMCHWT) equation is proposed to simulate the electromagnetic scattering from microstrip structures. Based on the surface equivalent principle, the original object can be decomposed into two independent domains, i.e., the exterior region (free space) and interior region (microstrip). Different from the traditional EFIE-PMCHWT method, in this new multiple-traces method, dielectric surface is discretized with two pairs of meshes, and Robin transmission conditions (TCs) are enforced on the interface between the exterior and interior regions to ensure the continuity of fields. In comparison with the traditional EFIE-PMCHWT, this new MT-PMCHWT has a better iteration convergence property. Additionally, a new multiple-traces electric field/combined field integral equation with better iteration convergence is also proposed. Because the continuity of fields is ensured by TCs, the exterior and interior regions can be discretized with nonconformal meshes, which improves the flexibility and efficiency of the proposed methods substantially.

Optimization study on multicolumn envelope meshing pair of single screw compressor based on leakage characteristics

The Multicolumn Envelope Meshing Pair (MEMP) is a significant influence factor of single screw compressor (SSC) performance. It is necessary to carry out an optimization study on MEMP to improve the SSC performance. In this paper, a theoretical calculation model containing three leakage influencing factors is presented to research the influence of the MEMP profile parameters on the leakage characteristics of the SSC. Experiment investigations on the performance of a SSC with MEMP are carried out to verify the theoretical calculation model. With the validated model, the effect of MEMP profile parameters on the leakage characteristics of SSC has been analyzed. Optimization analysis shows that in the design stage more envelope columns with smaller center distance and larger radius should be chosen for the front side of the MEMP, but less envelope columns with smaller center distance and smaller radius should be chosen for the back side of the MEMP.

Analysis of non-Hertz contact stress and bearing capacity on meshing pairs in a real-time non-clearance precision ball transmission

Considering the friction on meshing pairs in a real-time non-clearance precision ball transmission, a modified meshing mechanical analysis model was established, and the normal meshing force and tangential friction acting on each meshing pair were calculated accurately via the contact stiffness coefficient method. The ball–tooth contact was equivalent to the contact model of an ellipsoid and semi-infinite elastic solid according to non-Hertzian theory, and the contact stress of meshing pairs was analyzed by the discrete convolution and fast Fourier transform (DC-FFT) technique. Furthermore, the bearing-capacity estimation method for a transmission system was established based on the Mises yield criterion. The results show that the tangential distribution force has a significant effect on the contact stress field of a meshing pair, with the maximum Mises equivalent stress being approximately 0.621 times the central contact pressure at different meshing positions. Moreover, the bearing capacity of the planetary plate is weaker than that of the center plate; hence, the bearing capacity of a transmission system should be determined by the planetary plate.

A synergy-column envelope meshing pair profile for single screw compressors

Multi-column envelope engaging couples have been proposed for single screw compressors to reduce the friction and prolong the operational life. However, little is mentioned about the relationship between columns at opposite sides of the star-wheel teeth. An imbalance in the lubricant film forces would appear and influence the lubrication between the tooth and the groove. During a real design process, it is necessary to try several times for each different type of compressor to find the optimal combination of columns. In part, due to the large number of columns, it also makes both manufacturing processing and product testing difficult. In this paper, a synergy-column design method and its related manufacturing methods are presented. The locations and relationships of the designed columns can be prescribed by given the tooth width. Manufacturing of the rotor and star-wheel shows the new design method can be more efficient through processing. The stable operation results prove that the synergy-column envelope meshing pair can solve the star-wheel’s wear-out problem.