Internal Gear Research Articles

Geometric design and contact analysis of internal meshing gears with elliptical contact path

This study proposes a design method of internal meshing gear with elliptical contact path, and its contact characteristics are analyzed. The tooth profile of the internal meshing gear is actively designed based on elliptical meshing line (EML). Firstly, the elliptic meshing line is established according to the principle of differential geometry. The intersection points of the index circle and the tooth top circle of the internal meshing gear are on the meshing line. And the length of the minor axis of the elliptical meshing line can be set arbitrarily. Secondly, based on the rack equation and plane coordinate transformation, the tooth top profile equation of the EML gear was derived. Finally, the root tooth profile equations are derived from the top tooth profile equations based on the gear meshing principle. The theoretical model of EML gear is verified by finite element method. The contact stress, meshing stiffness and transmission error of minor axis of elliptic meshing line under different lengths are analyzed. The results show that by adjusting the length of the minor axis appropriately, the contact stress, mesh stiffness and transmission error of the EML gear will be reduced accordingly. Compared with involute gears, the contact stress of EML gears is reduced by 58.76%, the mesh stiffness is increased by 68.38%, and the transmission error is reduced by 40.62%. The contact performance of internal gears is greatly improved. By modifying the minor axis length of the elliptic meshing line of EML gear, the tooth profile of EML gear can be automatically modified through the equation relationship between the minor axis length and the tooth profile, so that the tooth profile design is more efficient. This study provides a reference for improving the performance of internal meshing gears.

Profile design of grinding wheel and temperature field analysis of internal gear with parabola curve configuration

Profile design of grinding wheel and temperature field analysis of internal gear with parabola curve configuration

Modelling Method and Meshing Characteristics of a Novel Curve-Surface Conjugate Internal Gear Drive

Space exploration has become a major focus in the field of technology, with gear transmissions in aerospace equipment playing a crucial role. In the extreme environment of space, gear transmissions face challenges like large temperature differentials, deformation and maintenance difficulties, which will severely impact transmission accuracy and service life. To meet the growing demands for high-performance gear transmissions with high transmission efficiency and error adaptability in the aerospace field, this paper proposes a novel curve-surface conjugate internal gear drive consisting of an involute internal gear and a curve-surface gear. The fundamental theory of curve-surface conjugation is introduced, and the construction method for curve-surface gear based on a selected contact path and meshing tube is presented. The analysis models including induced curvature, sliding ratio and tooth contact analysis with errors (ETCA) are simulated to evaluate the meshing characteristics. Additionally, prototypes are manufactured and experimental setups are established to validate the transmission performance. These results indicate that as the rotational speed increases, the transmission efficiency of the curve-surface conjugate internal gear drive improves, which is contrary to the trend observed in involute gear drives. And the transmission efficiency of the curve-surface conjugate internal gear drive surpasses that of the involute gear drive at higher rotational speeds. Moreover, this novel gear drive exhibits excellent error adaptability, maintaining intact contact paths and high transmission efficiency even in the presence of assembly errors. This study provides new ideas for the design and manufacture of high-performance gear transmissions from the perspective of spatial geometric elements.

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.

Computerized design and analysis of a novel high load bearing internal gear drive with curved meshing line

A novel high load bearing internal gear drive with curved meshing line is presented in this paper, and its performance is compared with that of an involute internal gear drive by finite element calculation. First, the novel gears’ meshing line is an S-shaped curve composed of two parabolas. Second, the novel gears’ tooth profiles based on the curved meshing line are designed using differential geometry and gear meshing theory. Third, three-dimensional mesh models of the novel gears are created by procedures, then using finite element calculation to analyze the stress of gear meshing. Finally, numerical examples demonstrate that the novel gears have lower stress and a smoother sliding coefficient than involute gears, implying that the former has a greater benefit in bearing capacity and wear performance. Meanwhile, tooth modifications can improve stress concentration, hence increasing the load-bearing capability of the novel gears.

Experimental and Numerical Test of Radial Internal Magnetic Spur Gear

Experimental and Numerical Test of Radial Internal Magnetic Spur Gear

The Grinding and Correction of Face Gears Based on an Internal Gear Grinding Machine

This paper presents a method of calculating and correcting grinding face gears on an internal gear grinding machine. The generating principle of face gears is studied, and the feasibility of grinding motion on an internal gear grinding machine is analyzed. Then, the motions that need to be followed for grinding are analyzed based on the gear machine tool structure. Four main error sources causing tooth surface deviation in the grinding movements are proposed. The mathematical modeling of the grinding of face gears containing proposed error sources on an internal gear grinding machine is accurately established. The influence of the error sources on the topological deviations of the tooth surface is explored. A sensitivity matrix is established for the influence of various error factors on the tooth surface deviations. The correction values of each error factor are obtained in the case of existing tooth surface deviations. Finally, a virtual machining experiment is conducted, which proves the accuracy of the proposed method for characterizing grinding and realizing corrections.

Research on Three-Dimensional Simulation of the Internal Arc Gear Skiving

Research on Three-Dimensional Simulation of the Internal Arc Gear Skiving

Active design method and performance prediction of internal gear pairs with low sliding ratio

Active design method and performance prediction of internal gear pairs with low sliding ratio

Numerical Analysis of Tooth Contact and Wear Characteristics of Internal Cylindrical Gears with Curved Meshing Line

In order to improve the contact strength and reduce the sliding friction of the gear pair, an internal cylindrical gear pair with a curved meshing line is studied in this paper. Firstly, a curved meshing line is designed. The tooth profiles of the internal gear pair with the designed meshing line are calculated by using differential geometry and the gear meshing principle. Secondly, a wear model is established by combining the finite element method and the Archard wear formula. Then, a numerical simulation is conducted; the relative curvature, sliding coefficient, sliding distance, maximum contact pressure, transmission error, and wear depth are calculated. Ultimately, the variation law of tooth surface wear of new gear with and without installation errors is observed under different stress cycles. On this basis, the influence of tooth modification on tooth surface wear is further researched. Through the results, the advantages of the introduced novel internal cylindrical gears in wear resistance are further demonstrated. The study in this paper provides new research ideas and methods for gear wear research and gear design.

A Triboelectric-Electromagnetic Hybrid Nanogenerator with Magnetic Coupling Assisted Waterproof Encapsulation for Long-Lasting Energy Harvesting.

Ocean energy harvesting based on a triboelectric nanogenerator (TENG) has great application potential, while the encapsulation of triboelectric devices in water poses a critical issue. Herein, a triboelectric-electromagnetic hybrid nanogenerator (TE-HNG) consisting of TENGs and electromagnetic generators (EMGs) is proposed to harvest water flow energy. A magnetic coupling transmission component is applied to replace traditional bearing structures, which can realize the fully enclosed packaging of the TENG devices and achieve long-lasting energy harvesting from water flow. Under the intense water impact, magnetic coupling reduces the possibility of internal gear damage due to excessive torque, indicating superior stability and robustness compared to conventional TENG. At the waterwheel rotates speed of 75rpm, the TE-HNG can generate an output peak power of 114.83mW, corresponding to a peak power density of 37.105Wm-3. After 5h of continuous operation, the electrical output attenuation of TENG is less than 3%, demonstrating excellent device durability. Moreover, a self-powered temperature sensing system and a self-powered cathodic protection system based on the TE-HNG are developed and illustrated. This work provides a prospective strategy for improving the output stability of TENGs, which benefits the practical applications of the TENGs in large-scale blue energy harvesting.

Przykłady Małej Architektury w oparciu o System Arm-Z

Arm-Z is a conceptual hyperredundant robotic manipulator composed on linearly joined number of identical modules. Each of them has one-degree-of-freedom (1-DOF) – the relative twist. Since modules are congruent, Arm-Z presents potential economical advantages and enhanced robustness. The modules can be mass produced and easily replaceable. The control of Arm-Z, however, is difficult and not intuitive. Therefore it most often requires the use of computational intelligence techniques. This article presents selected concepts for kinetic street furniture based on Arm-Z: a helical column of adjustable height, a sun tracking shade or solar energy harvesting device, bio-mimicing sculpture, sprinkler or fountain. All these ideas are based on low-tech approach. For this purpose, the initial unit in the chain is fixed to the solid foundation. For simplicity, the drive is applied directly to the first unit and transferred by the means of internal gears to the following modules. All of them are equipped with a set of cylindrical and bevel gears with straight teeth with involute profile (for connecting the modules).

Study on the mathematical model of the novel drum worm pair

Abstract A lot of work is needed to investigate the design method of planar internal gear enveloping drum worm (PIGEDW). Firstly, based on the gear meshing theory, the meshing equation is deduced. Secondly, the PIGEDW mathematical model is established by MATLAB. Finally, the influence of the inclination angle of the generating plane on the meshing performance of PIGEDW is analyzed. The results show that appropriate changes in geometric parameters are beneficial in enhancing the performance of PIGEDW, which provides a way to optimize its design.

Hydrostatic bearing groove multi-objective optimization of the gear ring housing interface in a straight-line conjugate internal meshing gear pump

The lubrication performance of a straight-line conjugate internal meshing gear pump is poor under the low-speed, high-pressure operating conditions of the volumetric servo speed control system, and it is difficult to establish a full fluid lubricating oil film between the gear ring and the housing. This leads to significant wear and severe heating between the gear ring and the housing. The lubrication performance of the interface moving pair of the electro-hydraulic actuator pump gear ring housing can be improved by designing a reasonable lubrication bearing structure for the gear ring housing. In this study, a multi-field coupling multi-objective optimization model was established to improve lubrication performance and volumetric efficiency. The whole model consists of the dynamic model of the gear ring components, the fluid lubrication model of the gear ring housing interface, the oil film formation and sealing model considering the influence of temperature, and the multi-objective optimization model. The comprehensive performance of the straight-line conjugate internal meshing gear pump was verified experimentally using a test bench. The results show that the lubrication performance is improved, the mechanical loss is reduced by 31.52%, and the volumetric efficiency is increased by 4.91%.

Performance reliability evaluation of high‐pressure internal gear pump

AbstractWith the development of the high‐end equipment technology, the performance requirements of the internal gear pump (IGP) under high pressure are also increasing. However, the increase of working pressure will lead to the instability of gear pump performance in terms of volumetric efficiency, noise, reliability and so on, it is necessary to reasonably evaluate the reliability level of high‐pressure IGP. The reliability analysis of the high‐pressure IGP is carried out from the aspects of flow, noise, and gear strength in this paper. First, the output flow rate and far‐field flow‐induced noise of the high‐pressure IGP were obtained through fluid numerical simulation, and experimental verification was conducted. Then, based on the time‐varying meshing stiffness, backlash function and static transmission error of the gear pair, a nonlinear dynamic model of the internal meshing gear pair was established. The time‐varying meshing force was obtained through the dynamic model of the gear pair, and then the tooth contact stress and tooth root bending stress were obtained. Finally, considering the uncertain factors affecting the performance of the high‐pressure IGP, Latin hypercube sampling (LHS) combined with dendrite network (DD) was used for random response modeling. The performance reliability of the high‐pressure IGP, including output flow rate, far‐field flow‐induced noise, and the strength of gear pair, were estimated based on the fourth moment‐based saddlepoint approximation (FMSA). The reliability analysis results can provide a theoretical basis for the structural optimization design of the high‐pressure IGP.

Continuous Carbon Fiber Reinforced SiC Ceramic Matrix Composites by Vertical Fiber Laying Combined with Material Extrusion 3D Printing

3D printing is reported in the fabrication of continuous carbon fiber reinforced silicon carbide ceramic matrix composites (Cf/SiC CMCs), however, there are layer defects in the 3D printed materials, manifested as weak mechanical properties between layers. Therefore, it is essential and urgent to study how to improve the mechanical properties of 3D printed Cf/SiC CMCs at the layers. In this article, a novel processing technique which combined vertical fiber laying method with material extrusion (ME) 3D printing is proposed to manufacture Cf/SiC CMCs. A self‐developed 3D printing fixed‐axis rotating lifting synchronizer is adopted. The vertical fiber laying of continuous carbon fibers (Cf) in Z‐direction is introduced into the X−Y printing plane. Five cycles of precursor infiltration and pyrolysis (PIP) are performed to achieve the densification of Cf/SiC CMCs. The effects of Cf bundle numbers on the flexural strength and fracture work of Cf/SiC CMCs are studied. The best performing composite is Cf/SiC CMC with six bundles, and the maximum flexural strength and fracture work is 63.84 ± 6.62 MPa and 1291.99 ± 161.39 J m−3, respectively. Compared with pure SiC, the fracture work of Cf/SiC CMC with 6 bundles Cf is increased by 2.54 times.

Research of the Meshing Performance of New Concave-convex Ball Teeth

Aiming at the limitations of the existing hydraulic pumps, a new type of bidirectional water-hydraulic internal ball gear pump using concave-convex ball teeth meshing to transfer power is proposed. In this paper, the principle of internal gear pump is utilized to establish the model of internal ball gear pump, and its mechanical properties and dynamic meshing characteristics are numerically investigated by using the finite element method. The results show that (a) the concave-convex ball gears run smoothly without any interference, and (b) increasing the number of gear rows can effectively reduce the maximum stress and meshing impact under a given load and speed. This study provides a basis for the development of high-performance ball gear pumps.

A novel electro-hydraulic unit design based on a shaftless integration of an internal gear machine and a permanent magnet electric machine

In recent years, increasingly stringent emission regulations have spurred an electrification trend in off-highway vehicle technology. To address challenges such as the high cost of power electronics components, limited battery capacity, and the substantial modifications required for the vehicles, there is a pressing need to develop high-speed, cost-effective, compact, and efficient electro-hydraulic units capable of powering vehicle functions. In response to these demands, this paper introduces an innovative morphology for an electro-hydraulic unit and outlines the integration method for a crescent-type internal gear machine with a permanent magnet synchronous electric machine. The proposed morphology aims to minimize component count through a shaftless solution while incorporating a cooling system that utilizes the same working fluid as the hydraulic machine. The design approach utilizes a genetic algorithm optimization process to maximize overall energy efficiency and compactness. Insights gained from the optimization results shed light on the relationship between key design parameters and unit performance, enhancing the understanding of this electro-hydraulic unit. A prototype of the unit was manufactured and tested, demonstrating a volumetric efficiency ranging from 81 % to 97 % at a maximum rotational velocity of the pinion of 6000 rpm. These results validate both the morphology and the design approach, indicating the feasibility of designing compact electro-hydraulic units that leverage hydraulic machines with higher maximum rotational velocities than commercially available counterparts as a mean to enhance efficiency and compactness.

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.

The influence of gear load distribution based on coupled systems on gearbox meshing noise

Introduction: With the rapid development of the gearbox manufacturing industry, the internal gear response has received attention, and the control of meshing noise during gear operation has been studied. Conventional noise reduction methods are usually based on gear order, and with the improvement of gearbox manufacturing technology, this method gradually becomes difficult to cope with a wide range of data.Methods: To expand the search domain of noise control systems, this study combines gear response and gear order, and adds the condition of gear uniform load. For common noise reduction problems in composite systems, this study improves the time-varying stiffness excitation mechanism and generates a coupled system.Results: Finally, this study conducts experiments on the Gmnoi dataset and compares it with three systems including quantum genetics to verify the superiority of the proposed system. The suppression effects of the four systems on gear meshing noise were 98.4%, 95.8%, 93.5%, and 92.7%, respectively. Their highest performance for different gear groups was 623, 514, 406, and 423, respectively.Discussion: The experimental results showed that the proposed coupling system has strong robustness and high accuracy in controlling gearbox meshing noise, and is of great significance in reducing noise pollution and improving the working environment of the gearbox.