Gear Mesh Research Articles

Influence of the Rotation Speed on the Internal Flow Characteristics of an Aircraft Fuel Gear Pump

A gear pump is a key rotary-displacement pump for aircraft fuel transportation in the aerospace industry. Due to the great ratio of power-to-weight condition demanded for gear pumps in aircraft fuel transportation systems, the parameter of the rotation speed is a matter of extreme concern affecting internal flow characteristics that determines the adverse effects of cavitation, fuel trapping, and vibration. However, the flow characteristics of an aircraft fuel gear pump influenced by the rotation speed have not been elaborated upon on yet. In this research, the flow characteristics of an aircraft fuel gear pump were studied by considering the influence of the rotation speed. An experiment for testing the external performance of an aircraft fuel gear pump was performed, and a corresponding numerical simulation of a gas–liquid two-phase flow was employed. Distributions of the velocity and pressure at the central cross-sections and their monitored transient developments were comparatively analyzed for different rotation speeds. It was found that a greater pressure oscillational amplitude accompanied by a higher frequency could be induced by a higher rotation speed, especially in the region of gear engagement. Additionally, cavitation evolution characteristics affected by the rotation speed in the fuel gear pump were discussed. The mechanism of cavitation generation in the region of gear engagement to withdrawal was revealed to be the quick release of a great amount of pressure. Furthermore, a dimensionless cavitation area was employed to quantify the periodic cavitation evolution, and the natural exponential development of the maximum dimensionless cavitation area with the rotation speed was determined through curve fitting. This study should be helpful for creating a deeper understanding of the internal flow characteristics of an aircraft fuel gear pump in scientific research and the external performance in aerospace industrial applications.

Data driven modeling of heavy-duty joint system for DEMO manipulators: An initial study from MPD joint simulation

This study investigates the subspace modeling method in developing surrogate model of a heavy-duty joint system in a muti-purpose deployer. The joint system is constructed in the Matlab SIMULINK Simscape environment, which includes the multibody dynamics with friction models, meshing loss models and viscous models. The input and output data generated in simulation are used to develop the subspace model. The result shows the subspace modeling method can accurately identify the system order and linear part of dynamics in this joint system. The nonlinearity contributed by the gear friction, meshing and viscosity can't be neglected in the surrogate model. Further model augmentation technics are needed to improve the capability of subspace modeling method applying in nonlinear system.

Bifurcated Polymorphic Transition and Thermochromic Fluorescence of a Molecular Crystal Involving Three-Dimensional Supramolecular Gear Rotation.

The ability of molecules to move and rearrange in the solid state accounts for the polymorphic transition and stimuli-responsive properties of molecular crystals. However, how the crystal structure determines the molecular motion ability remains poorly understood. Here, we report that a three-dimensional (3D) supramolecular gear network in the green-emissive polymorph 1G of a dialkylamino-substituted anthracene-pentiptycene π-system (1) enables an unusual bifurcated polymorphic transition into a yellow-emissive polymorph (1Y) and a new green-emissive polymorph (1G*) via 3D correlated supramolecular rotation. The 90° forward correlated rotation causes the molecular conformation between the octyl and the anthracene units to change from syn to anti, the ladder-like supramolecular columns to constrict, and the gear network to disengage. This cooperative molecular motion is marked by the gradual formation of an intermediate state (1I) across the entire crystal from 170 to 230 °C, which then undergoes bifurcated (forward or backward rotation) and irreversible transitions to form polymorphs 1Y and 1G* at 230-235 °C. Notably, 1G* is similar to 1G but lacks gear engagement, preventing its transformation into 1Y. Nevertheless, 1G can be restored by grinding 1Y or 1G* or fuming with dichloromethane (DCM) vapor. This work illustrates the correlation between the crystal structure and solid-state molecular motion behavior and demonstrates how a 3D molecular gear system efficiently transmits thermal energy to drive the polymorphic transition and induce fluorochromism through significant conformational and packing changes.

Fatigue life and transmission efficiency prediction of marine timing gears under 3D mixed lubrication state

The timing gears are the core transmission components of marine diesel engine, whose working conditions are complex and harsh, transient and coupled with the microscopic lubrication state, meshing in the mixed lubrication environment with lubrication-contact coexistence, local asperity contact brings stress concentration, further affects the fatigue life and friction loss. In this study, based on a three-dimensional (3D) line-contact mixed lubrication model, dynamic subsurface stress calculation, fatigue life prediction, and friction loss power study were carried out on timing gears, taking into account transient operating conditions and actual surface roughness. For the established simulation model, an equivalent simulation test of line-contact friction of timing gears was carried out, which can realize the measurement of friction coefficient under the condition of different slip-roll ratios, and make up for the deficiency that the traditional test equipment can only carry out the test under the fixed slip-roll ratio. Although the gear meshing process can only be simulated by the disc specimen due to the limitation of the specimen form, this limitation is similar to the simplified form of the simulation model, which can meet the needs of the verification test. The influence of structure and material on the lubrication state, fatigue life and friction power consumption are studied, which provide theoretical guidance for the tribological optimization design and reliability analysis for the marine timing gears.

Heat transfer on impingement cooled meshing spur gears: Experimental comparison of into-mesh, out-of-mesh and inclined impingement methods

Oil jet impingement cooling is the standard approach to cool high-speed high-power gears. The heat transfer between oil jets and gears is experimentally investigated in this paper. The three established methods of oil jet impingement cooling -into-mesh, out-of-mesh and inclined impingement on one of the gears- are studied. Heat transfer coefficients for these methods are experimentally determined. A loss correction approach is implemented for the evaluation of measurements. For the inclined impingement method, heat transfer on the non-impinged gear and the influence of meshing on the heat transfer coefficient are investigated. Gear meshing has an insignificant effect on the average heat transfer coefficient over the gear tooth. However, the spatial distribution of the heat transfer coefficient depends on the meshing configuration. Significant cooling on the non-impinged gear is observed with the inclined impingement method. The inclined impingement method is superior to the into-mesh and out-of-mesh methods at all measured operating points.

Dynamic characteristics analysis of gear tooth modification in a three-stage gear system

Gears serve as vital elements in high-efficiency mechanical transmissions, playing a pivotal role in vehicles. Employing gear modification has the capacity to significantly enhance the dynamic properties of the Planetary Gear Transmission (PGT) systems. In this study, the investigation has been directed toward a three-stage PGT model system with a comprehensive consideration of various vibration-related factors that affect the dynamic behavior of the system. These factors are encompassed by Time Varying Mesh Stiffness (TVMS), torsion and bending forces experienced by connecting shafts, dynamic Transmission Error (TE), impact of gear meshing eccentric load forces, inherent flexibility in the supporting shaft structure, and influence of torque and power fluctuations originating from a multi-cylinder engine. The estimation of TVMS is carried out for both external-external and external-internal teeth meshing pairs, utilizing the Potential Energy Method (PEM). Subsequently, this study employs the lumped parameter method to establish a model with a specific objective of investigating the lateral-torsional-coupling behavior within adopted PGT model system. The lateral vibration displacement characteristics of the PGT model system is deeply analyzed, revealing the influence of speed on lateral vibration and displacement frequency domain characteristics through a 3D waterfall diagram. Furthermore, a Tooth Profile Modification (TPM) method is applied utilizing two distinct parameters namely [Formula: see text] TPM parameter and [Formula: see text] TPM parameter. The objective is to mitigate vibrations and evaluate the performance of the adopted PGT model after employing each TPM parameter through both TVMS and Root Mean Square (RMS).

Geometric contact characteristics of variable hyperbolic circular-arc-tooth-trace cylindrical gear under different machine tool errors and sensitivity analysis for impact factors

Machine tool error is one of the most important research contents in gear transmission error, and contact characteristics are important factors affecting gear transmission performance. The establishment of tooth contact analysis (TCA) model of gear pair plays a guiding role in analyzing contact characteristics of gear pair. Based on the forming principle of variable hyperbolic circular-arc-tooth-trace cylindrical gear (VH-CATT gear), the structure model and coordinate system of VH-CATT gear machine tool are established. Based on the gear meshing conditions, the tooth surface mathematical model of the VH-CATT gear with machine tool error are established, and the TCA model with machine tool error is established. The influence of different machine tool errors on the geometric contact characteristics of the gear pair is analyzed. The results show that the pressure angle error, rotation error in y direction, and rotation error in z direction, translation error in y direction, and rotation error in z direction have a significant impact on the contact characteristics of tooth profile of VH-CATT gear.

Numerical modeling and experimental validation of power loss and efficiency in an electric-drive axle system

Power loss and efficiency are pivotal performance metrics significantly impacting the quality of electric-drive axles. This study outlines a numerical method for determining the electric-drive axle system power loss, which includes gear meshing, gear churning, and bearing power losses. Power loss from gear meshing was calculated by analyzing load distribution and friction coefficient. The frictional loaded tooth contact analysis method was employed to ascertain the load distribution during gear meshing. A formula based on a weighting function was utilized to compute the friction coefficient. The finite element method was used to verify the gear load distribution and meshing power loss. Subsequently, empirical formulas were used to calculate the gear churning and bearing power losses. To substantiate the proposed numerical method, an experimental apparatus was employed to measure the power loss and efficiency of an electric-drive axle under various operating conditions. The experimental study demonstrated a strong correlation between the numerical and calculated results. These findings suggest that the proposed method can be an effective tool in predicting the power loss and efficiency of electric-drive axles.

Consideration of Power Transmission Characteristics in a Micro-Gear Train.

Characteristics related to power transmission in the micro-domain, based on dry rolling contact of the gears, were investigated using a 3D-printed gear train with a pitch circle diameter of 84 µm in order to experimentally compare the power transmission efficiency in the macro- and micro-domains. For a basic gear train with two intermeshing gears, it was shown that the gear train in the micro-domain was capable of transmitting power to the same extent as in the macro-domain. However, in gear trains with complex power transmission paths, assuming a planetary gear train with multiple meshing gears, it has been shown that the power transmission characteristics of micro-domain gears differ from those in the macro-domain. The use of gear trains in the micro-region necessitates consideration of the loss of transmitted torque due to contact between tooth surfaces, which is unique to the micro-region and different from its use in the macro-region.

Vibration characterization of rolling bearings with compound fault features under multiple interference factors.

As a key component of rotating machinery power transmission system, rolling bearings in gas turbines are often required to serve in complex working conditions such as the high speed, the heavy load, the variable load, the variable rotational speed, and so on. The signals of bearing failures are easily drowned out by strong background noise and disturbances of related components. In the mechanical transmission system, the signals of bearing failures are easily submerged by the strong background noise and the disturbance of related components, especially for the composite bearing failures, which seriously hinders the effective identification of the vibration characteristics of the bearing operating state and increases the difficulty of fault diagnosis. In order to investigate the impact of interference on the bearing, through the establishment of rolling bearing composite fault vibration model, analyze the relationship between the vibration signals caused by different types of bearing failures and the corresponding vibration characteristics, to reveal the transmission system of the parts of the perturbation of the main multi-interference factors on the bearing fault signal influence law. The experimental verification shows that disturbance yp(t) caused by the sum of gear meshing frequency, and installation errors of the shaft, and coupling in the transmission system and background noise ni(t), which makes the fault frequency relatively weak and difficult to observe, and makes it difficult to accurately separate the fault information of the bearing. It provides a theoretical basis to solve the problem of damage identification and fault diagnosis of rolling bearings under multi-interference state.

The use of an artificial neural network for assessing tone perception in electric powertrain noise, vibration and harshness

The transition from internal combustion engines to electric powertrains brings new challenges for the Noise, Vibration, and Harshness (NVH) analysis of these vehicles. The tonal nature of the electromagnetic excitations and of the gear meshing mechanism are reflected in the radiated noise of electric powertrains, often leading drivers and passengers to rate the noise from electric vehicles with an increased nuisance even if they are quieter than internal combustion driven powertrains. In this paper, a flexible multi-body dynamics model is developed to calculate the vibration and forces transmitted from the bearings to the housing of an electric powertrain. Acceleration, force and sound spectra data are used to train an artificial neural network to assess the prominence of tones in the noise based on the results of the structural simulation. The results show it is possible to identify psychoacoustic metrics from the multibody dynamics simulation alone. With this new approach, it is feasible to quickly investigate how changes in the powertrain will affect the tonal perception of the noise without the need of new acoustic simulations and experiments. For the tonal perception analysis, the Prominence Ratio is used as a metric. This framework of combining multibody dynamics simulation with initial acoustic data and neural networks can be also applied to different NVH metrics as appropriate.

Research and design of internal meshing gear pump separating crescent plate

The design of the crescent block is a key factor in the high-pressure operation of the internal meshing gear pump. In order to increase the output pressure of the pump, this article designs a new type of separable crescent plate. Then, taking a certain type of high-pressure internal meshing gear pump as the research object, a nonlinear differential equation for the internal flow field of the gear pump was established, and the pressure distribution law in the transition zone of a cycle was derived. A mathematical model of the device was established based on the equilibrium conditions of the internal and external crescent block forces. Finally, experimental research was conducted on the design parameters of the separation crescent plate. The results showed that under the conditions of displacement of 100.5 ml/r, pressure of 20.5 MPa, and rotational speed of 1800 RPM, the compensation chamber angle range was 31.23°, and the pump's volumetric efficiency could reach 94.6%. There were no abnormal phenomena during the entire operation of the pump, and there was no jamming or jamming of the friction pair.

A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears

As a critical component of the joint gearbox, spur gear pairs play a crucial role in energy conversion, limiting the performance of a collaborative robot. Accurately assessing their instantaneous efficiency and torque fluctuation is essential for developing high-precision robot joint control models. This study proposes a computational model to predict the instantaneous efficiency and torque fluctuation of spur gears under typical operating conditions. The model incorporates a torque balance model, a load distribution model, and a friction model to reflect the relationship between gear meshing position and efficiency. The instantaneous efficiency and torque fluctuation of gear pairs were compared with the Coulomb friction model with an average friction coefficient and the elastohydrodynamic lubrication model with a time-varying friction coefficient. The effect of gear contact ratio on efficiency is analysed, while the instantaneous efficiency and torque fluctuation of gears are studied under varying operating conditions. The results indicate a maximum efficiency difference of 1.86 % between the two friction coefficient models. Under specific operating conditions, the instantaneous efficiency variation of the gear pair can reach 3.34 %, and the torque fluctuation can reach 5.19 Nm. Finally, this study demonstrates the effectiveness and accuracy of the proposed method through comparative analysis.

Dynamic modeling of spur gear system considering the coupling effect between bearing deflection and gear mesh stiffness

Bearing deflection has a direct impact on the mesh condition of gear systems via the center distance of the gear pair and corner contact. These factors need to be considered to accurately model the time-varying mesh stiffness and dynamic responses of gears. To address this issue, a spatial coordinate conversion is used to obtain the instantaneous spatial position of the gear pair under the bearing deflection. The tooth pair separation distance is derived through the geometric relationship analysis to model the corner contact effect. A dynamic model is established which employs a step-to-step time integration algorithm that considers the coupling effect between bearing deflection and time-varying mesh stiffness to obtain the dynamic response of the spur gear system. The simulation results of the proposed model show good agreement with the experimental results which demonstrate that the proposed model enables a proper analysis of the influence of bearing deflection on gear mesh behavior. This study provides an original dynamic model for analyzing the dynamic performance of the gear system considering the influence of bearing deflection.

Effects and optimization of bionic texture parameters on the tribological behavior of line contacts under starved lubrication conditions

PurposeGears are prone to instantaneous failure when operating under extreme conditions, affecting the machinery’s service life. With numerous types of gear meshing and complex operating conditions, this study focuses on the gear–rack mechanism. This study aims to analyze the effects and optimization of biomimetic texture parameters on the line contact tribological behavior of gear–rack mechanisms under starvation lubrication conditions.Design/methodology/approachInspired by the microstructure of shark skin surface, a diamond-shaped biomimetic texture was designed to improve the tribological performance of gear–rack mechanism under starved lubrication conditions. The line contact meshing process of gear–rack mechanisms under lubrication-deficient conditions was simulated by using a block-on-ring test. Using the response surface method, this paper analyzed the effects of bionic texture parameters (width, depth and spacing) on the tribological performance (friction coefficient and wear amount) of tested samples under line contact and starved lubrication conditions.FindingsThe experimental results show an optimal proportional relationship between the texture parameters, which made the tribological performance of the tested samples the best. The texture parameters were optimized by using the main objective function method, and the preferred combination of parameters was a width of 69 µm, depth of 24 µm and spacing of 1,162 µm.Originality/valueThe research results have practical guiding significance for designing line contact motion pairs surface texture and provide a theoretical basis for optimizing line contact motion pairs tribological performance under extreme working conditions.

Investigating tooth surface reconstruction principle of a gear rack and pinion system with variable transmission ratio pinion

Rack-and-pinion gear sets with variable transmission ratios have gradually become a standard core component in steering systems, as the harmony between portability and sensitivity in vehicle steering can be achieved with such applications. When the conventional meshing theory is adopted to calculate point clouds of variable-ratio tooth surfaces, drawbacks will occur with respect to unevenness in point cloud density, inaccessible tooth surface boundaries, and point cloud fusion at the interface between the working tooth surface and fillet. Thus, the generated point cloud of variable ratio tooth surfaces is inapplicable for computer-aided engineering (CAE) and plastic forming. In this study, the point cloud reconstruction of pinion tooth surfaces with variable transmission ratio was investigated. Meanwhile, based on the analysis of transient length in contact lines that occur during gear meshing, various criteria were proposed to determine the validity of the variable-ratio rack-and-pinion design in terms of whether continuous and reverse driving can be achieved. By adopting the proposed methods, the designed variable-ratio pinion tooth surfaces demonstrate point clouds with equidistant distributions and clear boundaries. CAE analysis results also indicate a good quality in gear meshing. The real-time gear meshing status of variable-ratio rack-and-pinion sets is characterized by the transient length of contact lines. The measured variation curves for the transmission ratios of a prototype demonstrate significant consistency with the theoretical curves, indicated by attaining transmission ratio errors within a reasonable range. The validity of the design methods proposed in this study has been verified by the aforementioned results.

Influence of Fixed Ring Gear Structural Compliance on the Quasi-Static and Dynamic Response of Epicyclic Gear Sets

Abstract The structural compliance of annular ring gear can significantly influence the quasi-static and dynamic 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. The current paper will study the impact of ring gear compliance on the dynamic response of epicyclic gear sets, in fixed ring kinematic configuration. To achieve this objective the current study will incorporate a finite element based ring gear formulation into the three-dimensional planetary load distribution model of Ryali and Talbot [1]. The proposed 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 component and system level design variations. The developed formulation is used to conduct parametric studies involving different planetary gear designs, ring gear fixtures (bolted vs. splined), and operating conditions (quasi-static, dynamic). In the case of a splined ring gear fixture, an external splined tooth contact model is developed, which will be used to validate the model against the quasi-static experiments of Ligata et al. [2]. The discussed results demonstrate the fidelity of the developed model, thus making it an excellent tool for the design and analysis of planetary gears with thin annular ring gears.

A Fully Integrated Simulation Approach of Drive Trains towards Tonality Free Wind Turbines

Wind turbine manufacturers are now facing stricter noise regulations as turbines are being placed closer to urban areas. While rotor blade aero-acoustic noise is the dominant noise component in the total sound pressure level of a wind turbine, mechanical noise originating from gears and generators are gaining importance as well, especially when producing tonal noise. To minimize the tonal noise originating from the gears it is crucial to compare different drivetrain concepts and gear designs early in the design phase and consider the NVH performance as part of the design selection criteria. Unfortunately, the software available on the market allows the prediction of the acoustic performance of a drivetrain design when all details are already known, but these software’s are unable to do this in the early concept design phase when making design choices have the biggest impact. Therefore, an integrated simulation platform has been developed to predict wind turbine tonality, considering factors like gear mesh excitation and aero-acoustic masking, which is already applicable in the design concept phase when lots of design details are not known yet. This platform, linked to optimization software, allows ZF to proactively develop strategies to mitigate Noise, Vibration, and Harshness risks, resulting in cost-effective and harmonized solutions across their product platforms.

Research on the influence on the addendum-shortened-coefficient of the first-last teeth of incomplete driving gear to avoid interference

In order to ensure the normal transmission of incomplete gears without interference during the process of gear meshing. This research first establishes the theoretical model to explore the influence of the reference circle pressure angle (α), the addendum modification coefficient, and the number of teeth on the addendum-shortened-coefficient (σ) of the incomplete driving gear's first-last teeth, and then systematically explores the influence between the key factors and the decrease of σ. The results show that: (1) When the pressure angle of the driven gear addendum circle (αa2) and the maximum critical value of the addendum radius of the driving gear to avoid interference (ra1') increases with the increase of α, σ decreases with the increase of α; (2) In the cases of high-modification gear transmission and angular-modification gear transmission, there are five conditions in which σ decreases due to the addendum modification coefficient of driving gear (x1) and the addendum modification coefficient of driven gear (x2): 1) High-modification gear transmission with one case:① x1+x2=0, x1=−x2≠0 with the increase of x2, that is: x1 and x2 are opposite number; 2) Angular-modification gear transmission with other four cases: ② x1+x2<0, x1<0 with x2=0, that is: The driving and driven gears are negative-modified and standard gears, respectively; ③ x1+x2>0, x1=0 with x2>0, that is: The driving and driven gears are standard and positive-modified gears, respectively; ④ x1+x2<0, x1≠0, x2≠0 with the increase of x2, that is: The sum of x1 and x2 are negative and neither of them is zero, there exist three kinds of addendum modification gears for the driving and driven gear, which are positive-negative, negative-positive and negative-negative. ⑤ x1+x2>0, x1≠0, x2≠0 with the increase of x2, that is: The sum of x1 and x2 are positive and neither of them is zero, there exist three kinds of addendum modification gears for the driving and driven gear, which are positive-negative, negative-positive and positive-positive. (3) While exploring the influence of α, x1 and x2 on σ, the influence of the number of driven gear teeth (Z2) on σ is greater than that of the number of driving gear teeth (Z1). It contributes to the optimization design of incomplete gears to avoid transmission interference in the study and improve its gear strength, load-bearing capacity, and transmission efficiency without reducing, etc.

Error Analysis of Instantaneous Frequency Estimation of Second-Order SST and Its Application on Analyzing Gear Meshing Stiffness From Motor Current

Error Analysis of Instantaneous Frequency Estimation of Second-Order SST and Its Application on Analyzing Gear Meshing Stiffness From Motor Current