Non-circular Gear Research Articles

Advanced design strategies and applications for enhanced higher-order multisegment denatured pascal curve gears

The existing Pascal curve gears suffer from limited flexibility in pitch curves and restricted changes in transmission ratios. This has impeded the application in a range of mechanical systems that require more adaptable gear solutions. For this, a design procedure for higher-order multisegment denatured Pascal curve gear is proposed. This innovative design offers greater flexibility in pitch curves and allows for a broader range of transmission ratios. The analysis of the transmission ratio confirms the theoretical predictions and highlights the effectiveness of the proposed gear design in achieving variable transmission ratios. The transmission mechanism of the higher-order multisegment denatured Pascal curve gear is analyzed and the unified mathematical expression of the families of Pascal curve gear is derived. The non-circular gears with free-form pitch curves can be obtained from higher-order multi-segment denatured Pascal curves by adjusting design parameters to unify different types of pitch curves. This approach provides significant flexibility in achieving specific transmission characteristics. Then the transmission characteristics are discussed. To further validate the design, the visual analysis and design software of the higher-order multisegment denatured Pascal curve gear is compiled based on Visual Basic, and is verified with the example. The novelty Pascal curve gears is applied to drive the differential velocity vane pump. The displacement, instantaneous flow rate, and pulsation rate of the differential velocity vane pump are calculated. The novelty drive mechanism could meet the requirements and have good performance. The application shows that the higher-order multisegment denatured Pascal curve gear is feasible in practice.

Experimental Study of the Kinematics of a Double-Row Planetary Mechanism Using Two Elliptical External Gears

Introduction. Mechanisms with non-circular gears are of wide interest to researchers and inventors due to their compactness and the implementation of a wide range of transfer functions. The development of this area is stimulated by the advancements and reduction in cost of mechanical processing and additive manufacturing technologies, as well as the use of applied mathematical modeling packages for the analysis and synthesis of non-circular gears. Traditionally, noncircular gears are used to transmit rotational motion between parallel axes with a variable ratio of angular velocities. However, their use in planetary gear schemes provides implementing various types of output link motion. The analysis of the papers on the research area shows that gears with movable rotation axes have not been sufficiently studied from the point of view of kinematics and dynamics. Most research papers reveal the theory of such mechanisms without verifying the results obtained in practice. This work is aimed at the experimental verification of the kinematics of a planetary mechanism with two external engagements, which contains elliptical gears.Materials and Methods. The kinematic model of the mechanism under study is built on the basis of the velocity diagram of its links, which made it possible to obtain expressions for finding an analogue of the angular velocity and the position function of the output shaft. The experimental study of kinematics was performed on a laboratory stand containing a model of a planetary mechanism with a set of replaceable gear wheels, absolute encoders on the input and output shafts of the mechanism, a controller, and a PC for recording and processing the signal. The analysis of the obtained results was performed on a computer using statistical analysis methods.Results. As a result of kinematic analysis, position functions were constructed for three alternative planetary mechanisms, which had different geometric parameters of the gears and made it possible to implement various types of motion of the output shaft: swinging motion, discontinuous motion, and unilateral uneven rotation.Discussion and Conclusion. The analysis of the experimental results showed the adequacy of the constructed mathematical model of kinematics to real mechanisms. The confidence interval of measuring errors at a reliability level of 95% was 0.16±0.08° for the first version of the mechanism, 0.57±0.22° — for the second version, and 0.08±0.26° — for the third. The proposed planetary mechanism with elliptical gears for implementing various types of motion can be used in drives of process equipment in numerous industries: chemical and food (mixers), oil refining (pumping units for crude production), mechanical engineering (compressors, pumps, automated machines), and others. The conducted kinematic studies of the planetary mechanism and their experimental analysis are needed for further dynamic and force investigations, as well as for the design of drives based on the proposed transmission.

Research on pitch error measurement method of non-circular gear based on digital twin

Aiming at the challenge of measuring errors in non-circular gears, it is proposed to establish the mathematical model of gear measuring center based on digital twin technology, and research on the detection method of pitch error of non-circular gears. The mathematical model simulates the operation of the gear measuring center, replacing traditional hardware with a 3D model and simulation software. By calculating the trajectory of the probe based on the unique characteristics of non-circular gears, the Portal program framework is developed. This framework allows for precise calculation of pitch errors and comparison with actual measurements to achieve accurate detection and analysis of the non-circular gear errors. The proposed approach reduces reliance on traditional experimental methods, offering a more efficient and accurate means of analyzing non-circular gear errors.

Structural Analysis of Gear–Lever Cyclic Mechanisms with Noncircular Gears

Structural Analysis of Gear–Lever Cyclic Mechanisms with Noncircular Gears

STRUCTURAL DESIGN OF NON-STANDARD GEAR TRANSMISSION

Non-standard gear transmissions are increasingly finding their applications in practice, primarily being designed for various applications. While standard circular gears are designed for a constant gear ratio, non-standard gears have a variable gear ratio that changes. This paper addresses the issue of designing non-circular gears for a specific range of gear ratios. An elliptical shape for the gears was chosen. The uniqueness of the proposed solution lies in selecting an ellipse as the evolute for creating the involute curve of the gear tooth.

Advanced design strategies and applications for enhanced higher-order multisegment denatured Pascal curve gears

The existing Pascal curve gears are limited by inflexible pitch curves and constrained transmission ratio changes, which hinders the application in a range of mechanical systems that require more adaptable gear solutions. To address this, a design procedure for higher-order multisegment denatured Pascal curve gear is proposed. A unified mathematical expression for the Pascal curve gear family is derived, enabling the construction of non-circular gears with free-form pitch curves by adjusting key parameters and offering more flexible pitch curve and a wider range of transmission ratios. Compared with elliptical gears and eccentric circular gears, its transmission ratio range can be expanded by up to 35%. Then the transmission characteristics of these gears are analyzed in detail. To validate the design, the visual analysis and design software of the gear is compiled based on Visual Basic, and is verified with the example. The novelty Pascal curve gears is applied to drive the differential velocity vane pump. The displacement, instantaneous flow rate, and pulsation rate of the differential velocity vane pump are calculated. The comparison with the differential pumps driven by eccentric non-circular gears and Fourier non-circular gears shows that when the pitch curves are not concave, the displacement driven by Pascal curve circular gears is the highest (compared to differential pumps driven by eccentric non-circular gears, and Fourier non-circular gears, their flow rates increased by 50.6%, and 175.7%, respectively), and the instantaneous flow pulsation rate of single pump is the smallest.This study shows that the higher-order multisegment denatured Pascal curve gear provides a viable solution for systems requiring flexible transmission mechanisms and improved operational performance.

Investigation of contact ratio and dynamic characteristics of non-circular planetary gear train in hydraulic motor

As a basic component of the non-circular gear hydraulic motor (NGHM), the non-circular planetary gear train (NPGT) offers a number of advantages, including low velocity, high output torque and compact design. Two different types of NPGT pitch curves have been designed using the 4–6 type of NGHM as an example. Aiming at two kinds of pitch curves, the contact ratio solution methods for the planetary gear meshing respectively with the sun gear and the inner gear ring are proposed. A comparative analysis of an integrated pitch curve design and a segmented pitch curve design is conducted to evaluate the effects of varying addendum coefficient (AC) and tool tooth profile angle (TTPA) on the contact ratio. Furthermore, the influence of load, velocity, and contact ratio on the dynamic characteristics (DC) of the NPGT with a segmented pitch curve is investigated through dynamic simulation. The results show that AC and TTPA significantly affect the contact ratio, with an increase in contact ratio observed as TTPA decreases and AC increases. Additionally, the load has a notable impact on the dynamic meshing force and its fluctuation. A higher contact ratio is associated with greater transmission stability in the gear train. This study provides a theoretical foundation for the design and optimization of NGHMs, and expands the potential application of contact ratio effects on NPGTs in this field.

Design of and research on a noncircular gear with a high-contact-ratio composite tooth profile

Design of and research on a noncircular gear with a high-contact-ratio composite tooth profile

Design of a 2R Open-Chain Plug Seedling-Picking Mechanism and Control System Constrained by a Differential Non-Circular Planetary Gear Train

With a focus on the problems of complex structure and accumulated lateral clearance in the single degree of freedom non-circular wheel system seedling-picking mechanism, which leads to poor motion accuracy, trajectory, and attitude, this study developed a 2R open-chain chili plug seedling-picking mechanism (SPM) constrained by a differential non-circular wheel system. The picking arm was driven by a single-stage non-uniform speed transmission mechanism to reproduce the seedling-picking trajectory and attitude. A protruding seedling-picking device, SPM control system, and test bench were designed. A kinematic model of a differential non-circular gear system was established, and an optimization design software for the SPM was developed based on kinematic analysis. The kinematic characteristics of the SPM were analyzed under optimal parameters. This study completed the seedling-picking performance test of the SPM on the control panel. The test showed that the designed chili SPM can sequentially complete the processes of seedling picking, conveying, retracting, pushing, and returning under the automatic control of the test bench without damaging the main root. The lateral root damage rate was 15.7%, effectively ensuring the integrity of the seedling bowl substrate.

A unified optimization design method for multi-stage non-circular gear transmission based on periodic B-spline interpolation

This research introduces a novel and unified optimization design method for multi-stage non-circular gear transmission (MNCGT) to address the challenges in designing MNCGT for complex motion requirements. The method optimizes non-circular gears comprehensively, reducing design and manufacturing difficulties while ensuring the realization of specified transmission requirements. A unified parameterization method, grounded on periodic B-spline interpolation, is introduced to establish the transmission function of non-circular gears and map it to a finite unified variable space. This innovative approach effectively reduces the difficulty and constraints of MNCGT optimization design. The proposed method takes into account crucial factors such as non-circularity, smoothness, processing conditions, and contact ratio, which significantly impact the transmission performance and manufacturing feasibility of non-circular gears. The effectiveness and superiority of this method are demonstrated through two practical examples and a real-world application in a planetary gear transplant mechanism, highlighting its potential for solving complex engineering problems.

Translation torsion coupling dynamic modeling and nonlinearities investigation of non-circular planetary gear systems

Translation torsion coupling dynamic modeling and nonlinearities investigation of non-circular planetary gear systems

Dynamics analysis of noncircular planetary gears

Noncircular planetary gear has simple structure and wide application, but its dynamics research is still blank. Therefore, this paper designs and establishes a 3–4 noncircular planetary gear model, and takes a deep dive into its dynamic characteristics. Firstly, the torsional vibration mechanical model of noncircular planetary gear is established, and the key factors in the planetary gear system are fully considered, such as time-varying meshing stiffness, backlash, meshing damping and excitation frequency. These factors have an important impact on the vibration characteristics of the system. Then, the vibration differential equation of the system is established, and the vibration characteristics of the system under different parameter conditions are analyzed. The results show that the noncircular planetary gear system with large damping and appropriate stiffness can maintain a more stable operating state at a larger excitation frequency. In addition, shortening the acceleration time of the system can effectively reduce the damage caused by the unstable state to the system. These findings provide a solid theoretical basis for the subsequent optimization and analysis of noncircular planetary gears.

ОБОСНОВАНИЕ РАЦИОНАЛЬНОЙ КОНСТРУКЦИИ КРИВОШИПНОГО МЕХАНИЗМА КОЛЕСНО-ШАГАЮЩЕГО ДВИЖИТЕЛЯ

The article substantiates the rational design of the crank mechanism of a wheel-step mover. Kinematics analysis of a prototype of the wheel-step mover revealed the presence of oscillations in the vertical coordinate of the central axis during movement. To eliminate this drawback, differential geometry methods were used, thanks to which a method for calculating the non-circular profile of support shoes was created. Studies of the dynamics of the crank mechanism of the wheel-step mover showed that even in a steady state of motion, periodically acting inertial forces arise. To reduce their effect, non-circular gears should be used in the mover power drive. The dimensions of the crank mechanism links have been calculated, at which the cross-country ability of the running system, its kinematics and dynamics characteristics are improved, energy costs when laying a track are reduced, as well as the negative impact of the machine on the fertile soil layer. The polar coordinates of the involute points have been calculated. They are needed to construct the tooth profiles of non-circular gears. As the power drive of the crank mechanism, non-circular gears have symmetrical geometric parameters along two axes and provide a constant movement speed. Thus, the wheel-step running system can be used in agriculture, the timber industry, mining, and when working in emergency situations. The mover design being developed is intended for unmanned ground vehicles. This type of unmanned vehicles is at the initial stage of its development, inferior in frequency to air and marine unmanned vehicles. A targeted concentration of production and financial resources is necessary to ensure that domestic industry has a leading position in the production and sale of unmanned ground vehicles.

Wave energy converter with mechanical motion rectifier, motion regulator, and energy storage element.

In this work, a novel design of an oscillating body-type Wave Energy Converter (WEC) is proposed with an efficiency of 48.73 %. Innovative features of the new design include the integration of Mechanical Motion Rectifier (MMR), Motion Regulator (MR), Energy Storage Element (ESE), and Electric Generator (EG) with the operation controlled by a microcontroller, limit switches, and linear actuator. Lab experiments conducted with a prototype ensured a peak voltage of 8.1 V and peak power of 4.3 W. Experimental and MATLAB theoretical simulation results demonstrated the average power of 55.2-148.3 mW for a wave height of 50-125 mm. In comparison to the conventional operation, where the electric generator is directly driven by wave motion, the proposed design will ensure higher peak power and better energy utilization characteristics of the generated voltage waveform. Simulation results are presented with the incorporation of non-circular gears that ensure modification of the voltage waveform for better energy utilization.

Mechanism Analysis and Optimization Design of Exoskeleton Robot with Non-Circular Gear–Pentabar Mechanism

To address the complex structure of existing rod mechanism exoskeleton robots and the difficulty in solving the motion trajectory of multi−rod mechanisms, an exoskeleton knee robot with a differential non−circular gear–pentarod mechanism is designed based on non−circular gears with arbitrary transmission ratios to constrain the degrees of freedom of the R-para-rod mechanism. In this study, the kinematic model of a non-circular gear–five−rod mechanism is established based on motion mapping theory by obtaining the normal motion positions of the human lower limb. An optimization design software for the non-circular gear–five−rod mechanism is developed using the MATLAB 2018b visualization platform, with the non−circular active gear as the sole input variable. A set of ideal parameters is obtained through parameter adjustment and optimal parameter selection, and the corresponding trajectories are compared with human trajectories. The three−dimensional model of the mechanism is established according to the obtained parameters, and the motion simulation of the non−circular gear–five−bar mechanism demonstrates that the mechanism can better reproduce the expected human knee joint motion posture, meeting the working requirements of an exoskeleton knee robot.

Geometric working volume of a satellite positive displacement machine

This article describes a method for determining the geometric working volume of satellite positive displacement machines (pump and motor). The working mechanism of these machines is satellite mechanism consisting of two non-circular gears (rotor and curvature) and circular gears (satellites). Two variants of the satellite mechanism are presented. In the first mechanism, the rolling line of the rotor is a sinusoid "wrapped" around a circle. In the second mechanism, the rolling line of the rotor is a double sinusoid "wrapped" around a circle. A method for calculating the area of the working chamber as a function of the rotor rotation angle is presented, based on mathematical formulae of the rotor, the curvature and the satellite rolling lines. It has been shown that the second variant of the satellite mechanism is advantageously characterised by a larger difference between the maximum area of the working chamber and the minimum area of this chamber. New mathematical formulas have been proposed to calculate the area of the working chamber for any angle of rotation of the shaft (rotor) based on the maximum and minimum values of the area of this chamber. It was thus confirmed that the geometric working volume depends on the maximum and minimum area of a working chamber and on the height of the satellite mechanism. The analyses of the area of the working chamber were carried out both for the mechanism without gears (the area delimited by the rolling lines of the elements of the mechanism) and for the real mechanism with gears. Differences in the values of these fields were also detected.

Synthesis of 1-DOF mechanisms for exact regular polygonal path generation based on non-circular gear transmissions

Design of one-degree-of-freedom (1-DOF) mechanisms is of paramount interest. This work deals with the generation of exact regular polygonal paths by using two particular 1-DOF mechanisms. The design of two-bar and three-bar mechanisms including non-circular gears is presented and evaluated. Differences in the kinematics of both mechanisms are discussed. The three-bar mechanism allows derivable velocity and acceleration curves during the whole trajectory, including the polygon vertices, a feature that cannot be achieved with the simpler two-bar mechanism. Hence, the three-bar mechanism makes it possible to generate perfect vertices using non-circular gears. To the best of the authors’ knowledge, this mechanism is the first 1-DOF mechanism with articulated links and a non-circular gear transmission that can generate exact regular polygonal paths. The proposed mechanisms can also be applied to generate two straight lines with a given angle, which is another novel contribution of this work. A prototype of the three-bar mechanism has been developed for experimental validation.

Research on the calculation and evaluation method of transmission efficiency of noncircular planetary gear

The torque fluctuation characteristics of noncircular planetary gear (NPG) systems are difficult to obtain, and there is no clear analysis method and evaluation method for transmission efficiency, which seriously affects their service performance. Given that, this article establishes a torque fluctuation model for NPG systems based on the principle of gear meshing and differential geometry theory and methods, taking into account factors such as actual working conditions and speed loads. And proposed, the comprehensive transmission rate, a new method for evaluating the efficiency of NPG systems. By analyzing the actual working conditions of NPG systems, the influence mechanism of alternating load and speed on torque fluctuation and transmission efficiency was explored. The research results indicate that the alternating load can cause an increase in system impact and vibration. The comprehensive transmission rate of NPG systems decreases with increasing rotational speed and increases with increasing load, and is more sensitive to changes in rotational speed. The trend of comprehensive transmission rate and transmission efficiency of NPG systems is basically consistent, indicating that the proposed method of using comprehensive transmission rate to evaluate transmission efficiency is a practical and feasible analysis method. The research results can provide a new method for dynamic measurement and evaluation of torque and transmission efficiency of non-circular gear transmission systems.

A Synthesis Method of Open-Chain Coupled Serial Linkage Mechanism Fusing Trajectory and Posture

In order to meet the motion characteristics requirements of multi-objective fusion of execution components, a synthesis method of open-chain coupled serial linkage mechanism fusing trajectory and posture is proposed. According to periodic change characteristics of the execution component trajectory and posture of the linkage mechanism, the motion characteristics equation including trajectory and posture information is established by using Fourier series. The harmonic parameters of the link trajectory and posture are calculated according to the principle of discrete Fourier transform. The complex vector theory is applied to determine the functional relationship between the harmonic parameters of the trajectory and posture and the independent variable of the linkage mechanism, and furthermore the motion synthesis equation of the open-chain linkage mechanism fusing trajectory and posture information is established. The linkage mechanism parameters are calculated using Mathcad Prime software. The single-degree-of-freedom open-chain coupled serial linkage mechanism fusing trajectory and posture information is obtained by using a noncircular gear planetary gear train to couple the connection points of the linkage mechanism. The correctness of the method is verified through an example.

Service Performance Optimization and Experimental Study of a New W-W Type Non-circular Planetary Gear Train

To address the vibration problem in traditional W-W-type non-circular planetary gear trains during operation, this study proposes two new combinations of W-W-type non-circular planetary gear trains. The study focuses on analysing the transmission error and improving service performance. By utilizing the conjugate theory and the coordinate transformation theory, an accurate mathematical model for non-circular gears is derived. The transmission error models for the two combination forms of the non-circular planetary gear train are established using the incremental meshing line method. The analysis also examines the influence of eccentricity on the transmission error. Kinematic analysis of the multi-body dynamics model confirms that the new W-W type non-circular planetary gear train, formed by combining non-circular gears and cylindrical gears, exhibits superior transmission performance. Furthermore, a test analysis is conducted on the roller pumping unit test platform and the indicator diagrams of the pumping unit under various working conditions are obtained. The study concludes that the optimal matching mode for the sucker rod counterweight and motor frequency of the reversing device of the pumping unit is 20 kN and 20 Hz, and the dynamic balance of the pumping unit load can be achieved by adjusting the motor frequency.