External Gear Research Articles

Analysis of the tooth-root stress of external spur gears with high effective contact ratio

For spur gears with contact ratio close to 2, the extension of the contact interval resulting from loaded tooth deflections and local contact deformations may result in an effective contact ratio above 2. In these cases, the load is transmitted by at least two tooth-pairs, the maximum load and tooth-root stress decrease, and therefore the calculation methods of the gear rating Standards ISO and AGMA provide very conservative results. In this work, two models are applied to the calculation of the tooth-root stress of load-induced high contact ratio external gears: (i) an analytic model of load sharing, based on the minimum energy method, and (ii) a finite element model, which validates the results obtained from the previous model. Obtained values of the stress are compared with those provided by ISO and AGMA rating methods, which do not account for the stress reduction due to the higher contact ratio. A new modification coefficient is proposed to correct these conservative values, which allows the AGMA and ISO geometry factors to remain as no load-dependent factors and keep their actual calculation methods and significance.

Simulation and validation of the transmission error, meshing stiffness, and load sharing of planetary spur gear transmissions

Although the load sharing between planets of sequentially phased planetary gear transmissions has been studied in the past, the required solving techniques based on the Finite Element Method result in long time consuming and high computational cost. This limits the possibilities of undertaking extensive studies that take into consideration a high number of cases allowing optimal solutions to be sought or general conclusions drawn. In addition, the determination of the curves of transmission error, time-varying mesh stiffness, and load sharing among tooth pairs in simultaneous contact are also complicated. In this work an analytical model has been developed for the simulation of the time-varying mesh stiffness, quasi-static transmission error, and load sharing ratio between planets and tooth pairs of planetary spur gear transmissions. It is based on similar models for external and internal spur gears previously developed and has been validated by comparison with a hybrid model based on the Finite Element Method and theoretic-experimental correlation.

Effect of hydraulic oil temperature on the flow output quality of external gear pump

Effect of hydraulic oil temperature on the flow output quality of external gear pump

Flow characteristics and factors affecting flow pulsation of external meshing herringbone gear pump

To enhance the outlet flow stability of the external herringbone gear pump, an analysis was conducted on the main influencing factors, key geometric parameters were identified, and a numerical model was developed for fluid analysis. A numerical model was then established for fluid analysis. The accuracy of the numerical model was verified by comparing it with experimental results, with simulation errors of displacement and volumetric efficiency being < 5%, ensuring the simulation's accuracy. The simulation results indicated that the pump's head (49.7808 m) and outlet pressure (4.9285 bar) remained stable. At 700 rev/min, the simulated volumetric efficiency was 82.94%. Subsequently, the impact of helix angle, changes in center distance, and tip clearance on outlet flow stability were analyzed. The analysis revealed that increasing the helix angle from 27° to 30° could reduce flow pulsation. A slight reduction in center distance from 180.3 (δ = +0.3 mm) to 179.9 mm (δ = −0.1 mm) effectively decreased mass flow difference and outlet pressure pulsation, enhancing outlet output stability. Reducing tip clearance from 0.25 to 0.12 mm, while meeting design requirements, resulted in more stable pressure and lift output. These results ensured smooth pump operation, improved outlet output stability, and met low-flow pulsation requirements. This study offered valuable insights into the design and production of the external meshing herringbone gear pump.

Experimental uncertainty evaluation by measuring a micro gear standard using focus variation

Abstract Micro gears play an increasingly important role in various industrial applications, and the minimization of their deviations is challenging for metrology and manufacturing. A promising method is the focus variation technology, which enables areal measurements of micro gears. Practice-related standards are used to determine measurement uncertainties by comparison with calibration values. In this work, the external micro gear standard of the Physikalisch-Technische Bundesanstalt (PTB) is used to evaluate experimental measurement uncertainties of a focus variation coordinate measurement system for the first time. The traceable standard with modules between 0.1 and 1 mm is calibrated using micro tactile coordinate measurements. Optical and tactile measurements are then compared. As a result, small expanded measurement uncertainties of less than 4 µm are achieved.

Construction of the contact zone of a helical cylindrical external gear pair with straight top land meridians

The study deals with the construction of the contact zone of helical cylindrical external gears. The shape and size of the contact zone determine the phenomena that occur even in the case of error-free tooth design, installation error exemption and load-induced error exemption Such a phenomenon is the vibration excitation resulting from the connection, which also affects the identification of the drive elements. It is possible to deviate from the regular rectangular shape of the contact zone by modifying the top land surfaces. The change can mean a combination of the change in the total length of the contacting generating lines and the change in the contact ratio. This study deals with the construction of the generalized contact zone.

The Influence of the external meshing gears’ contact ratio on the contact stress in the transmission system

Abstract Using the Hertz contact theory, the calculation method of tooth contact stresses at different boundary points within the double tooth meshing zone for high contact ratio external meshing gear pair is investigated. The radius of curvature and pressure angle at each boundary point of the external meshing gear with a high contact ratio is given. The boundary point meshing coefficients are introduced to convert the comprehensive radius of curvature at the boundary point into the radius of curvature at the node, to make it in line with the form of calculation of the national standard. The analysis examines how the parameters affect the contact stress at different boundary points of the gear pair with a high contact ratio. When the contact ratio of the gears is 2, there is a sudden change in the contact stress on the tooth surface, and HCR gears have smaller contact stress than LCR gears.

Advanced 2D Computational Fluid Dynamics Model of an External Gear Pump Considering Relief Grooves

The article presents an advanced two-dimensional (2D) computational fluid dynamics (CFD) model of an external gear pump which considers relief grooves. Relief grooves are limiting design features for the flow process of this type of pump, and their influence in existing studies is considered by a three-dimensional (3D) model only. The structural modification proposed by the authors is beyond the possibilities of real implementation, but it gives the possibility to precisely model the pump’s design features. In contrast to the existing studies (using 3D CFD), the proposed advanced 2D model requires significantly fewer computing resources. Numerical experiments were carried out using the 2D model at different pump operating modes depending on the rotation frequency (950–1450 min−1) and pressure load (5–150 bar). The numerical results were validated by a real-world experiment for the same pump operating modes using an existing laboratory experimental setup. An analysis of the CFD model and real experiment results was carried out by determining a quantitative index of match (FIT), which varies in the range of 97.93–99.82%. This proves the performance of the proposed CFD model, which can be further used as a part of more complex hydraulic systems models.

Reflections of the EU Normative Agenda toward First and Second Russia-Chechen Conflicts

Over the decades, the normative approach has been considered as the decisive external policy gear of the EU. But, the limitation of the policy divulges its future application to an external country, promoting the question: Is the EU a normative power, or has it failed to implement its normative policy towards an external country? This paper aims to analyze the normative strategy of the EU and its constraints during the first and second Russia-Chechen conflicts. It investigated the EU normative policy regarding the conflicts and revealed the strategic chemistry of the EU-Russia relation, which fluctuated from time to time. It argues the EU normative discourses toward conflicts were sporadic in character and consisted of verbal and, at best, some written criticisms occasionally. Predominantly, The EU largely disregards the application of its normative values to the Chechen case; instead, it prioritizes its economic and bilateral relations with Russia. However, the 9/11 incident in the USA and the post 9/11 Russian hostage crisis developed the EU normative policy as a less important policy for Chechen conflicts.

Physics-Constraint Variational Neural Network for Wear State Assessment of External Gear Pump.

Most current data-driven prognosis approaches suffer from their uncontrollable and unexplainable properties. To address this issue, this article proposes a physics-constraint variational neural network (PCVNN) for wear state assessment of the external gear pump. First, a response model of the pressure pulsation of the gear pump is constructed via a spectral method, and a compound neural network is utilized to extract features from the pressure pulsation signal. Then, the response model is formulated into an objective function to softly constrain the learning process of the neural network, forcing the learned features to have explicit physics meaning. Meanwhile, to characterize the system uncertainty, the variational inference is utilized to extend a Kullback-Leibler (KL) divergence into the objective function. Finally, the wear state is evaluated based on the distance of learned physics features. Experimental results on an external gear pump validate the merits of the proposed method in explainable representation learning and system uncertainty estimation. It also offers a controllable and explainable perspective to understand the dynamic behavior of the system.

INVESTIGATING CAVITATION PHENOMENON IN EXTERNAL GEAR PUMPS

External gear pumps find widespread application across various industries owing to their simplicity, efficiency, and reliability in fluid transfer tasks. However, cavitation poses a significant challenge to these pumps, potentially impairing their performance and leading to premature failure. This article delves into innovative approaches for mitigating cavitation effects, with a specific focus on material selection and surface coatings. By harnessing advanced materials and coatings, enhanced durability of pump components can be achieved, minimizing cavitation-induced damage and ultimately improving pump performance and longevity. Keywords: cavitation, external gear pump, cavitation between gears, hydraulic equipments.

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The article considers the issue of updating the machines designed for the cultivation of near-trunk and near-vine spaces. From the prospect of complete satisfaction of the agrotechnological and technical requirements of the mentioned machines, the rotary tillers with vertical rotation axis are preferable, which, however, need to get structurally developed. On this account, it is recommended to select planetary mechanism with external gear as a driving mechanism, which enables to ensure high rotation numbers of the tiller in case of relatively low rotation numbers of the rotor. The kinematic analysis of the driving mechanisms has been conducted, analytical expressions have been derived, which enable to determine the trajectory, speeds and accelerations of the tiller’s blades depending on the frequency of rotor’s rotation and the gear ratio of the mechanism. Based on the analytical expressions resulted from the kinematic research of the mechanism force analysis of the rotary tiller has been conducted. The estimated expressions of the general resistance moment value applied to the shaft of the moving rotor of the machine, as well as the value of resistance moments generated on the planet gear (satellite) rotors have been derived, which enable to identify the optimal kinematic and geometric parameters for the mechanism and rotary through the theoretical calculation method ensuring the optimal values of traction resistance force and other force factors in conditions of the stated working rules.

Analytical model of meshing stiffness, load sharing, and transmission error for internal spur gears with profile modification

The influence of the teeth geometry on the load distribution, transmission error, and meshing stiffness of internal spur gears is very similar to that of external gears. Therefore, the formulation of the models for strength and dynamic calculations for internal and external gears is also similar. However, the internal gears have usually greater values of the contact ratio, frequently above 1.8, even 1.9. In these cases, the lengthening of the contact interval due to the elastic deflections of the teeth may result in an effective contact ratio greater than 2, with the subsequent changes in the load sharing and transmission error. These changes are not properly described by the theoretical models for high contact ratio spur gears. In this paper, a model of load sharing, quasi-static transmission error, and time-varying meshing stiffness for internal spur gears with profile modification is presented, which has been applied to low contact ratio internal gears which, due to the transmitted load, become high contact ratio internal gears. The influence of the variations of the transmitted load on the load capacity is also studied.

Tooth profile design and meshing characteristics analysis of internal meshing gears based on variable center meshing line

A design method of internal meshing gear based on variable center meshing line (VCML) is presented in this paper. The meshing line is an arc line connecting the intersection of the indexing circle connecting the inner and outer gears and the intersection of the tooth top circle, and the center of the line of engagement freely slides on the vertical bisection line of the line connecting the two intersection points. The top tooth profile equation of internal and external gears is derived by rack equation. According to the normal method of gear profile, the equation of gear root meshing line is derived by using the tooth top profile equation of the gear. According to the principle of plane meshing, the root profile equation of gear is derived by using the root meshing line equation of gear. The tooth profile of VCML gear can be deduced quickly by adjusting the center position of the meshing line. The stress, meshing stiffness, transmission error, contact ratio and sliding ratio of the VCML gears are analyzed by finite element method, and the area of significant performance improvement of the meshing line center of the VCML gears is found. The research results show that compared with involute gears, the maximum average stress of VCML gears is reduced by 64.99%, the meshing stiffness is increased by 193.67%, and the transmission error is reduced by 65.95%. This method improves the efficiency of new tooth profile design and transmission performance. By changing the center coordinates of the meshing line, the tooth profile of the VCML gear can be quickly redesigned, which greatly improves the efficiency of the new tooth profile design and transmission performance. This design method provides a new idea for the tooth profile design of internal meshing gear.

Design optimization of external engagement cylindrical gear flowmeter under uncertainty

Design optimization of external engagement cylindrical gear flowmeter under uncertainty

Integrated CFD-FEM approach for external gear pump vibroacoustic field prediction

In this work, a three-dimensional fluid-structural and vibro-acoustics coupled model of a gear pump is presented. Gear pumps represent the majority of the positive displacement machines used for flow generation in fluid power systems. Typically, the dynamics of gear pumps are dependent on the characteristics of the fluid dynamics inside the pump, which translates into vibrations to the housing. These vibrations then propagate to the surrounding medium and emit sound. The purpose of this study is to propose a three-dimensional fully integrated computational model to simulate the complete gear pump behaviour from the fluid dynamics to the structural vibrations, up to the vibroacoustic response. In this hybrid configuration, a transient CFD (Computational Fluid Dynamics) model is first developed to simulate the 3D flow field with a deforming and re-meshing approach to take into account the variation of the volume between the gears. Second, the internal pressure field calculated at each time step is then used as a loading into a structural FEM (Finite Element Method) model of the gear pump to compute the actual stresses and deformations of the housing. Third, the results of the structural response are used as excitation in a vibroacoustic sub-model to simulate the radiated noise using a high-order FEM technique. The comparison between the numerical and experimental flow curves validates the CFD model. The sound power calculations from the vibroacoustic model show good comparison with the sound intensity measurements around the pump casing, confirming the validity of the proposed coupled model. The described CFD-FEM approach proves to be a powerful gear pump design tool: it provides a reliable estimate of gear pump working parameters such as fluid power and vibroacoustic characteristics, starting from the CAD (Computer-Aided Design) geometry of the components. Furthermore, being one of the first multi-domain simulation models of a gear pump, this work can be useful to researchers as a starting point to correlate the noise emitted with the internal flow in full 3D conditions.

Effect of Rim and Web Thickness on Tooth Root Stress of Spur Gear

This study investigated the impact of spur gear rim and web thickness on root stress. A finite-element analysis model (FEM) was utilized and validated through a gear-bending test. Four gears with different rim and web specifications, including a solid gear, were designed and tested using strain gages to measure their root stress. The 3D FEM was validated by comparing the measured root stresses with that analyzed by the developed FEM. Using this model, a parametric study was conducted by varying the web position, pressure angle, and module to investigate the effect of the backup ratio on the root stress ratio of the gear. A stress-ratio map was generated based on the results. This stress-ratio map was compared with the rim thickness factor (YB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${Y}_{B}$$\\end{document}) for external spur gears specified in ISO 6336-3. The comparison reveals that the rim thickness factor specified in ISO 6336 is overly conservative compared to values obtained in this study. Our results suggest that the thickness of both the rim and web should be considered to reduce the weight of spur gears. These findings can be applied to the design of lightweight spur gears.

Numerical simulation of flow behavior in a urea liquid external gear pump with immersed solid method

Numerical simulation of flow behavior in a urea liquid external gear pump with immersed solid method

CFD Modeling and Experimental Validation of the Flow Processes of an External Gear Pump

This article presents computational fluid dynamics (CFD) modeling of the flow processes at a certain specimen of an external gear pump. The purpose of the developed two-dimensional (2D) CFD model is to carry out a numerical study to obtain the main characteristics of the pump flow rate, especially the flow rate as a function of the pressure and the flow rate as a function of the time. A numerical study was carried out at forty-two different operating modes that were expressed as a variation of two parameters: rotational frequency (950–1450 min−1) and pressure (5–150 bar). The validation of the numerical results was carried out through an experimental study. For this purpose, a laboratory experimental setup equipped with a modern data acquisition (DAQ) system was designed and implemented. It allows the gear pump to be tested at the same operating modes as the numerical study. A validation analysis was performed by comparing the numerical and experimental results using the average relative error index (FIT). A detailed description of the 2D CFD model development (CAD model, mesh, general settings, boundary conditions, etc.) is provided. Based on the 2D CFD model, an original methodology was proposed to take into account the influence of the discharge channels on the displacement volume of the pump by adjusting the face width of the gears. Despite the limitations of the simple 2D CFD model, which are discussed in this article, a very good match between numerical and experimental results is analyzed by calculating the FIT level, which is in the range of 93–97%.

Quasi-Static Force Analysis and Tooth Profile Modification Optimization of the Cycloid Speed Reducer

This article proposes a new method for optimizing tooth profile modification amounts of cycloidal reducers. By optimizing transmission error and transmission ratio fluctuation, the objective optimization function is determined, and the influence of optimized modification amount on various transmission performances is studied. In addition, this article also conducted mechanical analysis on the cycloidal reducer and obtained the results of tooth contact force. The mathematical model for the mechanical analysis of the cycloidal reducer was established, and the variation law of force distribution between the internal and external gears of the cycloidal reducer was calculated. The results indicate that the needle tooth force, bearing force, transmission ratio, and transmission error obtained through the mechanical analysis model using optimized modification quantities tend to stabilize and exhibit periodic changes, which corresponds to the actual scenario.