Meshing Pair Research Articles

Transform of parameter and teeth surface modification for non-standard planetary spur gear train with X-gears

In view of the lack of ready formulae for modification calculation of non-standard planetary spur gear trains, the paper is focused on new modification methods of non-standard planetary spur gear trains with X-gears. Firstly, a novelty transform method from the parameters on the pitch circle to the parameters on the reference circle for a non-standard planetary spur gear train with X-gears is proposed in order to study the modification method. Secondly, a scheme of teeth surface modification for non-standard planetary spur gear train with X-gears is put forward. Thirdly, the calculation method of loaded transmission error and flash temperature on the tooth surface under mixed elastohydrodynamic lubrication for external meshing spur gear pairs is proposed using tooth contact analysis as well as loaded tooth contact analysis. Then, a new modification optimization method for non-standard planetary spur gear train with X-gears is proposed, and formulae of the maximal modification length along the tooth height are derived. Finally, the effectiveness of the modification optimization method is confirmed by an example, and the transform formulae of the optimized modification parameters for sun gear are derived.

Research on dynamics and failure mechanism of herringbone planetary gearbox in wind turbine under gear surface pitting

In this paper, the herringbone planetary gear system in wind turbine gearbox with tooth surface pitting is modelled, and the time-varying mesh stiffnesses of the gear meshing pairs are calculated. The results show that the aggravation of tooth surface pitting weakened the mesh stiffnesses in different levels based on the pitting condition. Based on the dynamic model of the transmission system, the vibration signal model of the gearbox is established, considering the vibration transmission path and attenuation. The gearbox vibration acceleration signals under tooth surface pitting in different conditions are simulated, the obtained time-domain signals reveal abnormal fluctuations, and the frequency-domain signals illustrate abundant sidebands near harmonics of meshing frequency and low frequency area. For different pitting conditions, the fault frequencies vary, the results provide theoretical basis for the fault analysis and diagnosis of the gearbox. Furthermore, the theoretical analysis results are validated against experimental test results based on the test bench of herringbone planetary gearbox with tooth surface pitting in sun gear.

Theoretical study on leakage characteristics of water-injected single screw vapor compressors with a multicolumn envelope meshing pair

For a water-injected single-screw vapor compressor (SSVC), leakage is an important issue that affects the compressor performance. However, the leakage mechanism of an SSVC with a multicolumn envelope meshing pair (MEMP) is unclear. In this paper, leakage characteristic mathematical models of an SSVC with MEMP are established and solved, including the orifice plate model, parallel plate model covered by a water-vapor two-phase film and Laval nozzle model considering the flash evaporation process. The calculation results are compared and verified by experimental data, and the error of the exhaust temperature and leakage coefficient is within 5%. Based on the verified mathematical model, the leakage characteristics of an SSVC with MEMP and the influence of the operating parameters and structural parameters on them are analyzed and discussed. Of all leakage channels, only the path between the front side of the screw groove and wall is inward leaking. The leakage of the plate channel is mainly water, while the Laval nozzle and orifice plate channels are mainly two-phase. The volumetric efficiency of SSVC can be increased by 6.5% and 2.65% by reducing the rotational speed and evaporation pressure by 50%, respectively. This study can provide a theoretical basis for the compressor performance analysis.

Preliminary comparison of close-range photogrammetric and microCT scanning: Surface Deviation Analysis of 3D digital models of hominin molar crowns

This study is a preliminary assessment of the viability of close-range photogrammetry in comparison to microCT scanning for the construction of 3D models of isolated molar crowns. Photogrammetric scanning is more cost-effective and less time-consuming than CT scanning, and in paleoanthropological contexts eliminates the possibility of exposing fossils to doses of radiation that affect ESR dating. Samples of fossil (Homo naledi), archaeological, and contemporary human molars were scanned via microCT and close-range photogrammetric scanning. The photogrammetric scans included 96 digital images per tooth and the resulting models were compared to their corresponding CT models using point-to-point Surface Deviation Analysis. The surface difference between the CT mesh models before and after processing functions such as smoothing and retriangulation was also assessed. Signed-rank tests comparing the surface difference between the two sets of mesh pairs show no significant difference in the level of deviation within the archaeological and contemporary molar samples. The Dinaledi sample demonstrates complementary results, as the majority of the photogrammetric meshes fall within a devised acceptable range of difference when compared to the processed CT meshes. A total of 81% of specimens in the study with suitable characteristics—a stained and unreflective crown surface—provided photogrammetric meshes that fell into this devised range. Crown characteristics that produced unsuitable models had unstained and reflective surfaces. Areas of higher deviation tend to occur in crenulations and fissures. The exploratory results suggest that sufficient reflectance and color contrast data must be present on the tooth enamel to create viable photogrammetric surface models, however further study is needed to fully understand the capabilities and limitations of close-range photogrammetry in comparison to microCT scanning.

An Automatic Generalization Method for a Dense Road Network Area Considering Spatial Structural Features as Constraints

Road networks are the skeletal elements of topographic maps at different scales, and road selection is a prerequisite for implementing continuous multiscale spatial representations of road networks. The mesh-based approach is a common, advanced and powerful method for road selection in dense road areas in which small meshes are removed and road segments with the least importance in each mesh are eliminated. However, small meshes in a map can be classified into two types: aggregated small meshes and isolated small meshes. The number of the former is small, and that of the latter is large. Existing methods are generally applicable for the latter, and some or even most spatial characteristics will be lost when they are applied to the former; as a result, the road selection quality will be affected. Therefore, as a supplement to the mesh-based selection method, this paper proposed an automatic generalization method of dense road network areas (areas formed by aggregated small meshes) considering spatial structural features as constraints. First, the aggregated areas of small meshes were identified based on the number of adjoining small meshes, and the boundaries of aggregated areas are extracted and used as hard constraints during mesh elimination. Second, the starting meshes were redefined by simultaneously considering the edge features and mesh density of small meshes, and an ordinal elimination algorithm was proposed to eliminate the meshes in the stroke connection direction. Third, road selection was implemented by identifying the starting meshes and sequentially processing the related mesh pairs. This iterative process continued until all mesh densities of the newly formed meshes are beyond the threshold or the problem becomes a simple elimination problem involving two adjoining small meshes or one isolated small mesh. Finally, a 1:10,000 standard topographic road map for Jiangsu Province, China, was used for validation. The experimental results showed that in the aggregated areas with two small meshes, 31% of the areas obtained the same selection results by using the mesh-based method and the proposed method, and the remaining 69% obtained a more compact result with the proposed method. Moreover, for all aggregated areas with more than two small meshes, the spatial distribution structure of small meshes was preserved better by the proposed method.

Multi-meshing-state and disengaging-proportion analyses of a gear-bearing system considering deterministic-random excitation based on nonlinear dynamics

Backlash induces gear-teeth separation or back-side tooth mesh (BTM), resulting in gear disengagement (GD), which heavily aggravates the dynamic performance and transmission quality of gear drivetrains. This study focuses on the disengaging proportion (DP) characteristics of a gear- bearing systems based on a multi-meshing-state (MMS) model. A new nonlinear dynamic model of gear-bearing system with MMS and deterministic-random external excitation is established considering the synergistic effect of backlash and non-integer contact ratio. A modified time-varying mesh stiffness with temperature stiffness is included in the model. Afterwards, the effect of the gear pair meshing vibration on bearing radial vibration is studied. The bifurcation and evolution of the MMS behavior are investigated changing the system parameters. An algorithm of DP is proposed in the time domain based on the established MMS model. The characteristics of DP are systematically discussed with the effects of dynamic response type, phase trajectory topology, bifurcation and chaos, and correlation between parameters. The results demonstrate that grazing bifurcation reduces the number of GD and chaos is prone to BTM. The disengaging proportion is highly dependent on the phase trajectory topology and generally increases from period-1 to quasi-periodic and then to chaotic responses. Bifurcation changes the variation trend of DP, thus there is a peak near period-doubling bifurcation and a trough near grazing bifurcation. The chaotic response leads to a jump in DP. The correlation between parameters considerably dominates the DP. This study provides a reference for revealing the mechanism of gear system disengagement and improving the dynamic performance.

Two Calculation Verification Metrics Used in the Medical Device Industry: Revisiting the Limitations of Fractional Change

Abstract Quantifying the fractional change in a predicted quantity of interest with successive mesh refinement is an attractive and widely used but limited approach to assessing numerical error and uncertainty in physics-based computational modeling. Herein, we introduce the concept of a scalar multiplier αGCI to clarify the connection between fractional change and a more rigorous and accepted estimate of numerical uncertainty, the grid convergence index (GCI). Specifically, we generate lookup tables for αGCI as a function of observed order of accuracy and mesh refinement factor. We then illustrate the limitations of relying on fractional change alone as an acceptance criterion for mesh refinement using a case study involving the radial compression of a Nitinol stent. Results illustrate that numerical uncertainty is often many times larger than the observed fractional change in a mesh pair, especially in the presence of small mesh refinement factors or low orders of accuracy. We strongly caution against relying on fractional change alone as an acceptance criterion for mesh refinement studies, particularly in any high-risk applications requiring absolute prediction of quantities of interest. When computational resources make the systematic refinement required for calculating GCI impractical, submodeling approaches as demonstrated herein can be used to rigorously quantify discretization error at a comparatively minimal computational cost. To facilitate future quantitative mesh refinement studies, αGCI lookup tables herein provide a useful tool for guiding the selection of mesh refinement factor and element order.

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.

Geometry design, meshing analysis and error influences of face-hobbed cycloidal bevel gears with double circular-arc profile for a nutation drive

As the core components of nutation drive, the internal meshing pair of bevel gear must be delicately designed to achieve desirable operational performances for the transmission device. For this purpose, this paper designs a face-hobbed internal meshing pair of cycloidal bevel gears with double circular-arc profile (DCAP). First, a cutter head with DCAP cutting edges is designed to generate the tooth surface of internal gear pair. Then, the tooth geometry of the external and internal bevel gears are derived according to the meshing theory. Finally, a finite element model is developed to simulate the meshing characteristics of the gear pair. The simulation results reveal that the proposed face-hobbed cycloidal bevel gear pair with DCAP has higher contact/bending strength, better load sharing and smaller transmission error compared with the logarithmic spiral bevel gear pair with DCAP. The effects of four typical manufacturing errors on meshing characteristics of the proposed bevel gear pair are investigated to provide fundamental references for the tolerance design of cycloidal bevel gears.

Coefficient of friction behavior of gear oils and significance for the meshing process of spur gears

The mechanical properties of oils are determined using test methods. There are standardized test methods for determining viscosity and density. The characterization of transmission oil based on its dynamic viscosity alone is not sufficient for the physical explanation of different levels of noise emissions in vehicle transmissions. For this reason, the test procedure for determining the coefficient of friction is used in the following to enable a further differentiation between the oils according to mechanical properties.In gear transmissions with involute gear teeth, rolling friction occurs in the gear pair meshing along the line of action due to the variation in the equivalent curvature radii throughout the meshing cycle. This is rolling friction on which a sliding friction component, so-called slip, is superimposed. Pure rolling friction only occurs in the pitch point. From the pitch point to the start and end of the meshing, there is a superimposed sliding friction component that increases with increasing distance from the pitch point. Slip values occur in the range of 5–50% depending on tooth geometry.These friction conditions during tooth flank lubrication can be assessed using the Stribeck curve. The Stribeck curve represents the coefficient of friction as a function of the speed. A mini traction machine from PCS Instruments with a ball/plate measurement setup was used to determine the coefficient of friction behavior of gear oils. This allows the coefficient of friction of an oil to be assessed at low speeds in the range from boundary and mixed friction to elastohydrodynamic fluid friction at high speeds.The investigations show that the coefficient of friction behavior of a gear oil depends on the oil viscosity and above all on the chemical composition. The lower the coefficient of friction, the less energy is required to shear the lubricating film and the lower the power transmission through the fluid. The coefficient of friction is a property that is dominated by the type of base oil and the type of VI improver in the area of mixed and fluid friction, especially with additional sliding in contact.It will be shown in the paper that the use of a gear oil that has been optimized with regard to the coefficient of friction curve can reduce the entry impacts of meshing gear pairs under vibration excitation and the gear transmission thus generates lower noise emissions.

Analysis of circumferential gas force on star-wheel in a single screw expander

Service life of a star-wheel directly affects operation stability of a single screw expander. In addition, since star-wheel tooth of a single screw expander is prone to wear, circumferential force of the star-wheel rotor is investigated in this paper. Geometric gap models between the meshing pair with a single line envelope profile at different rotation angles are established and meshed section pressure fields and velocity fields of a referent tooth flank are simulated. Circumferential gas torque calculation model of a referent tooth and multi-tooth are established, and torque influencing factors are analyzed. Results indicate that the pressure difference between the expansion cavity and low-pressure cavity as well as gap geometry shape have a significant influence on the pressure field and velocity field. Both gas forces that act on the meshed section and the unmeshed section of the tooth have significant effects on the circumferential torque. Due to multi-tooth coupling, total gas torque periodically changes with the star-wheel rotation angle. Moreover, the negative values indicate that the gas torque on the left side of the star-wheel is greater than that on the right side. Unbalanced gas torque can cause star-wheel teeth deviation towards the side with less force. This consequently results in wear increase.

Skin3D: Detection and longitudinal tracking of pigmented skin lesions in 3D total-body textured meshes

We present an automated approach to detect and longitudinally track skin lesions on 3D total-body skin surface scans. The acquired 3D mesh of the subject is unwrapped to a 2D texture image, where a trained objected detection model, Faster R-CNN, localizes the lesions within the 2D domain. These detected skin lesions are mapped back to the 3D surface of the subject and, for subjects imaged multiple times, we construct a graph-based matching procedure to longitudinally track lesions that considers the anatomical correspondences among pairs of meshes and the geodesic proximity of corresponding lesions and the inter-lesion geodesic distances. We evaluated the proposed approach using 3DBodyTex, a publicly available dataset composed of 3D scans imaging the coloured skin (textured meshes) of 200 human subjects. We manually annotated locations that appeared to the human eye to contain a pigmented skin lesion as well as tracked a subset of lesions occurring on the same subject imaged in different poses. Our results, when compared to three human annotators, suggest that the trained Faster R-CNNdetects lesions at a similar performance level as the human annotators. Our lesion tracking algorithm achieves an average matching accuracy of 88% on a set of detected corresponding pairs of prominent lesions of subjects imaged in different poses, and an average longitudinal accuracy of 71% when encompassing additional errors due to lesion detection. As there currently is no other large-scale publicly available dataset of 3D total-body skin lesions, we publicly release over 25,000 3DBodyTex manual annotations, which we hope will further research on total-body skin lesion analysis.

Geometric Design of a Face Gear Drive with Low Sliding Ratio

A design method of low sliding ratio face gear drive is presented. The rack and gear meshing pair with a low sliding ratio is obtained by constructing the contact path. The face gear is then formed by this gear, and its tooth width characteristics are analyzed. Combined with the explicit solution of the meshing point of the tooth surface, a method to solve the sliding ratio of the proposed face gear pair is given, and the effects of relevant design parameters on the sliding ratio are analyzed. Moreover, the rationality of the tooth profile design is verified by 3D modeling and motion simulation. The proposed face gear pair has a lower sliding ratio, as well as larger tooth width, than those of traditional face gear drive (the pinion is involute spur gear) with the same basic parameters. The results of this study can provide points of reference for reducing friction and improving the mechanical efficiency of face gear drives.

A Virtual Measurement Method of the Transmission Error Based on Point Clouds of the Gear

Abstract As the most widely used gear measuring instrument, the gear measuring center can measure the individual deviations of a gear tooth flank other than the comprehensive deviations of the gear. However, gear transmission error is an important transmission performance indicator in the gear meshing process. It is an important trend of gear measuring to obtain the transmission error from individual deviations. In this study, a calculation method of gear transmission error is proposed based on the point clouds of the gear obtained by optical sensors. According to the gear meshing principle, a method is introduced to determine the contact status between the tooth flanks formed by the point clouds. According to this introduced method, the single tooth pair meshing process and the meshing process of multiple tooth pairs are analyzed to determine the gear transmission error curve. The comparison results of tooth contact analysis and gear measurement experiments verify the proposed virtual measurement method.

Study on two‐phase lubrication characteristics of the meshing pair in a single‐screw compressor

AbstractIn this paper, the lubrication state of the meshing pair in a single‐screw compressor is analysed. The two‐phase lubrication flow field numerical calculation model and the multi‐tooth coupling circumferential torque calculation model are established. The oil film pressure and the circumferential torque of multi‐tooth at 0%–60% air volume fraction (AVF) inlet are studied. Results show that the AVF at the inlet plays an important role in the promotion of the peak and average pressures of the oil flow field for certain star‐wheel rotation angles. For other star‐wheel rotation angles, the aforementioned pressure may even be weakened. For multi‐tooth coupling, the star‐wheel circumferential torque with inlet AVF of 20%, 40% and 60% is 15.3%, 13.1% and 6.8% higher than that with inlet pure oil, respectively. This shows that the existence of bubbles at the inlet increases the unbalanced circumferential torque of the star‐wheel and increases the possibility of wear of the teeth.

Dynamic Modeling and Analysis of Nonlinear Compound Planetary System

In the vehicle composite planetary gear transmission system, nonlinear excitations such as time-varying meshing stiffness, backlash and comprehensive error would lead to large vibration and noise, uneven load distribution, unstable operation and other problems. To address these issues, this work focuses on compound planetary gears and develops the bending-torsion coupling nonlinear dynamic model of the system based on the Lagrange equation. There are internal and external multi-source excitations applied to the system. This model is used to study the bending-torsion coupling meshing deformation relationship of each meshing pair along with the translational and torsional directions. The natural frequencies and vibration modal characteristics of the system are extracted from the model, and the influence of rotational inertia and meshing stiffness on the inherent characteristics of the system are studied. The coupling vibration characteristics of the system under operating condition are analyzed in terms of the inherent characteristics and time–frequency characteristics of the system. The simulation results exhibit that the planetary gear system has three modes. The change in natural frequency trajectory has two phenomena: modal transition and trajectory intersection. The main frequencies include engine rotating frequency, meshing frequency and its double frequency, and the rotation frequency and harmonic frequency of the engine have a great influence on the vibration response of the system. Finally, the virtual prototype of the composite planetary system is used to verify the accuracy of the established model from speed, inherent characteristics, meshing force and frequency composition.

Establishment and analysis of nonlinear frequency response model of planetary gear transmission system

Abstract. Based on the lumped parameter theory, a nonlinear bending torsion coupling dynamic model of planetary gear transmission system was established by considering the backlash, support clearance, time-varying meshing stiffness, meshing damping, transmission error and external periodic excitation. The model was solved by the Runge–Kutta method, the dynamic response was analyzed by a time domain diagram and phase diagram, and the nonlinear vibration characteristics were studied by the response curve of the speed vibration displacement. The vibration test of the planetary gearbox was carried out to verify the correctness of frequency domain response characteristics. The results show that the vibration response in the planetary gear system changes from a multiple periodic response to a single periodic response with the increase in input speed. Under the action of the backlash, time-varying meshing stiffness and meshing damping, the speed vibration displacement response curves of internal and external meshing pairs appear to form a nonlinear jump phenomenon and have a unilateral impact area, and the system presents nonlinear characteristics. The nonlinear vibration of the system can be effectively suppressed by decreasing the mesh stiffness or increasing the mesh resistance, while the vibration response displacement of the system increases by increasing the external exciting force, and the nonlinear characteristics of the system remain basically unchanged. The backlash is the main factor affecting the nonlinear frequency response of the system, but it can restrain the resonance of the system in a certain range. The spectrum characteristics of the vibration displacement signal of the planetary gearbox at different speeds are similar to the simulation results, which proves the validity of the simulation analysis model and the simulation results. It can provide a theoretical basis for the system vibration and noise reduction and a dynamic structural stability design optimization.

Study on screw rotor thermal machining method of single screw compressor

Single screw compressor (SSC) is a type of rotary compressor with excellent performance. However, under high temperature conditions, the hot deformation of the screw rotor and the star wheel cause the change of the gap of the meshing pairs, which seriously degrades the compressor performance. In order to solve the problem of the gap variation of the meshing pairs, a new hot-state machining method is proposed to study the deformation characteristics of the screw rotor in the hot-state machining process, which provides some reference data for the pre-deformation of the rotor in the machining process. Numerical calculation model of thermal machining process for screw rotor was established by using finite element method. With the validated model, the deformation characteristics in the process of hot working were studied by changing the number of heating holes, diameter of heating holes and temperature of heating holes. Results show that screw rotor deformation will increase with the increase of heat source temperature and diameter, and the deformation distribution of the screw rotor is not significantly affected by the heat source temperature and diameter, but will be more uniform with the increase of heat source quantity. The research work in this paper can provide theoretical basis for hot machining of screw rotor for SSC.

A Data‐Driven Approach to Functional Map Construction and Bases Pursuit

AbstractWe propose a method to simultaneously compute scalar basis functions with an associated functional map for a given pair of triangle meshes. Unlike previous techniques that put emphasis on smoothness with respect to the Laplace–Beltrami operator and thus favor low‐frequency eigenfunctions, we aim for a basis that allows for better feature matching. This change of perspective introduces many degrees of freedom into the problem allowing to better exploit non‐smooth descriptors. To effectively search in this high‐dimensional space of solutions, we incorporate into our minimization state‐of‐the‐art regularizers. We solve the resulting highly non‐linear and non‐convex problem using an iterative scheme via the Alternating Direction Method of Multipliers. At each step, our optimization involves simple to solve linear or Sylvester‐type equations. In practice, our method performs well in terms of convergence, and we additionally show that it is similar to a provably convergent problem. We show the advantages of our approach by extensively testing it on multiple datasets in a few applications including shape matching, consistent quadrangulation and scalar function transfer.

Study of the thermo-mechanical couple deformation of the meshing pairs of a single-screw compressor

Single-screw compressor has attracted attentions from the scientific community due to its excellent performance. However, thermal deformations of the star wheel, screw, and casing substantially affect the clearance between the components, and hence reduce the performance of the single-screw compressor. In this study, the thermal deformation of a meshing pair of the single-screw compressor was investigated using a finite-element-based thermo-mechanical coupled model. This model was developed based on measured thermal boundary conditions during compressor operation. The effect of thermal deformation on the compressor sealing clearance was then studied. The results showed that the thermal deformation of the casing, screw, screw shaft, and star wheel significantly affected the clearance between the tooth tip and the groove bottom as well as the meshing pair clearance distribution. The change of clearance between the casing and screw is up to 0.03 mm while the change of the clearance between the star wheel tooth tip and screw groove is up to 0.05 mm. Furthermore, it was found that the spatial position meshing error caused by the thermal deformation was one of the major reasons for the wear of the meshing pair of the single-screw compressor. The simulated thermal deformation results agreed well with the experimental data. The clearances of the compressor were modified based on the thermal deformation in a single-screw compressor with a capacity of 6 m3/min and the results showed that the modified compressor can operate reliably. This indicated that the developed model could be used in the design of the single-screw compressor. It provides guidance for the design and optimization of large single-screw compressors.