Non-circular Gear Research Articles

Research on the seedling picking trajectory error of the gear train seedling picking mechanism considering tooth backlash

AbstractThe research investigated the tooth backlash influences the error in seedling picking trajectories of the gear train SPM. First, a sine function and the sum of random errors are taken into account is utilized to fit the tooth backlash of the firstly and secondary transmissions. Additionally, the analysis established the relationship between the fitting parameters and the tooth backlash of the firstly and secondary transmissions, in order to determine the appropriate fitting parameters. Next, the relationship between the tooth backlash of the firstly and secondary transmission in the seedling picking mechanism (SPM) and the x, y coordinates, as well as the velocity and acceleration of the seedling needle tip (SNT), is examined. This analysis is based on the error and movement variance of the coordinate and kinematic parameters of SNT. The results indicate that the tooth backlash of the firstly transmission has a more significant influence on the error of the seedling picking trajectory compared to the tooth backlash of the secondary transmission. When the tooth backlash of the noncircular gear in the firstly transmission reaches its maximum value of 0.24 mm, the x and y coordinates of the SNT can reach maximum values of 1 and 3.5 mm. The test of the jumping of the needle tip and idling trajectory description indicated that noncircular gears with larger tooth backlash exhibit higher positional jumping at the tip of the seedling needle.

Generating processing method and tooth surface deviation characteristics of non-circular face gear based on disk cutter

Generating processing method and tooth surface deviation characteristics of non-circular face gear based on disk cutter

Flow fluctuation abatement method and flow characteristics of lobe pump by external noncircular gear drive

Flow fluctuation abatement method and flow characteristics of lobe pump by external noncircular gear drive

Tooth Profile Construction and Experimental Verification of Non-Circular Gear Based on Double Arc Active Design

The double arc pitch curve is a novel way for creating a non-circular gear tooth profile. Aiming at the problems of the rounding of non-integer teeth and the nonlinear equation system in the construction of double circular arc tooth profile, an active design method based on planetary gear transmission kinematics and gear-meshing theory is proposed. By studying the double arc pitch curve of the three engagement positions, combined with the uniform theory of the relative curvature of surfaces, the distribution characteristics of the solution of the nonlinear equation system are analyzed in depth, leading to the optimal solution of the characteristic parameter values of the pitch curve. Combined with UG modeling and ADAMS motion simulation, the gear engagement force and the angular velocity of the planetary gear around the center are compared and analyzed in the case of integer tooth ratio and non-integer tooth profile. The results show that the engagement force of the gear pair constructed by integer teeth is reduced by about 17%. The optimal combination of the numbers of teeth is determined by orthogonal experiments, on which trial production and hydraulic load tests are based. The results reveal that the torque of the product at a rated speed is about 2.6% higher than that of foreign prototypes, which verifies the effectiveness of the design method proposed in this paper.

Cutting Force Fluctuation Suppression and Error Homogenization of Noncircular Gear Hobbing Based on the Tool Shifting Method

The current research on noncircular hobbing mainly focuses on the linkage model and motion realization. However, the intermittent cutting characteristics of hobbing would increase uncertainties in the manufacturing process. In this paper, a hobbing machining model with tool-shifting characteristics was proposed to solve the problems of cutting force fluctuation and inconsistency of tooth profile envelope accuracy at different positions of the pitch curve in noncircular gear hobbing. Based on the unit cutting force coefficient method, the undeformed chip volume generated by interrupted cutting was used to characterize the fluctuation trend of the hobbing force. The fluctuation characteristics of the cutting force generated by different hobbing models were compared and analyzed. Using the equivalent gear tooth and hob slotting numbers, an analysis model of the tooth profile envelope error of the noncircular gear was constructed. Subsequently, the tooth profile envelope errors at different positions of the pitch curve were compared and analyzed based on the constructed model. The transmission structure of the electronic gearbox was constructed based on the proposed hobbing model, and the hobbing experiment was conducted based on the self-developed noncircular gear CNC hobbing system. This paper proposes a hobbing method that can effectively suppress the fluctuation of the peak and whole circumference cutting force and reduce the maximum envelope error of the whole circumference gear teeth.

Kinematic synthesis and optimization design of a rice pot seedling transplanting mechanism

To achieve the precise operation trajectory and posture required for pot seedling transplanting and solve the problem that the partial reversal of the transplanting arm’s output in the double planet carrier transplanting mechanism, which is unconducive to the realization of the seedling pushing action, a motion synthesis method for a double planet carrier gear train mechanism with attitude constraints based on the output angle and four exact task poses is proposed. First, the ideal transplanting trajectory is planned according to the transplanting agronomic requirements, and the position and attitude information of the four key points on the ideal trajectory are extracted as the constraints of the mechanism design. Then, based on the relative displacement equation, a comprehensive design equation of the motion of the plane 3R mechanism (simplified model of the transplanting mechanism) about the output rotation angle and the precise four pose constraints is established, and the mechanism parameters that meet the constraint requirements are obtained by solving the multicellular homotopy method. A mathematical model of the roundness of the non-circular gear was also established, and the roundness of the transmission non-circular gears in the gear-train transplanting mechanism was optimized by using the genetic algorithm. Finally, the structural design, virtual simulation, and experimental analysis of the double-planet carrier gear train transplanting mechanism were completed. The results show that the actual trajectory and attitude are consistent with the theoretical design, and when then the mechanism was under the transplanting efficiency of 120 and 180 plants/min, the success rates of picking seedlings were 91.53% and 87.46%, respectively, meeting the design requirements.

Multi-Joint Bionic Mechanism Based on Non-Circular Gear Drive.

Aiming at the nonlinear expansion/contraction drive problem between different cables in multi-joint cable drive mechanisms, a mechanical drive method based on a non-circular gear drive was proposed, which could replace the servo-sensing control system and minimize the system's complexity and cost. A multi-joint single-degree-of-freedom (DOF) bending mechanism was constructed with several T-shaped components and cross-shaped components. The principle of the multi-joint mechanism driven by non-circular gears was clarified. The corresponding relationships between the joint bending angle, cables' extension/retraction amount and non-circular gear transmission ratio were established. Using the Bowden cable driving, a multi-DOF bending mechanism decoupling scheme was proposed. Considering the adverse effect of non-circular gear hysteresis on the motion of multi-joint mechanisms, a non-circular gear backlash elimination method was proposed. The expression of the backlash of the non-circular gear with respect to the axial movement amount was deduced, which could enable the precise control of the backlash. A two-DOF multi-joint bionic mechanism driven by the non-circular gear was developed. The experimental results show that the mechanism can achieve coordinated bending motion by precisely controlling the line extension/contraction through non-circular gears. This multi-joint bionic mechanism driven by non-circular gears has the characteristics of reliable structure and simple control, and it is expected to be applied to bionic fish and bionic quadruped robots in the future.

Design of Linear Functional Noncircular Gear with High Contact Ratio Used in Continuously Variable Transmission

Continuously variable transmission (CVT) of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency. The key technology of CVT with noncircular gear has been broken through some countries, and is in the stage of deep application research. Although the characteristics and design methods of noncircular gear pairs have been continuously studied in China, the noncircular gear CVT is still in the preliminary exploration and research stage. The linear functional noncircular gear pair, whose transmission ratio is a linear function in the working section, to realize continuously variable transmission was the research object in this paper. According to the required transmission ratio in the working section, the transmission ratio function in the non-working section was constructed by using a polynomial. And then the influence of pitch curve parameters in the working section on which in the non-working section was also analyzed to obtain the pitch curve suitable for transmission of this gear pair. In addition, for improving the stability and bearing capacity of gear transmission, the noncircular gear pair transmission with high contact ratio was designed. Furthermore, the accurate value of the contact tooth length was calculated based on the gear principle and the characteristics of the involute tooth profile, from this the contact tooth length error was calculated by comparing the accurate value with its actual value obtained by the rolling experiment. Finally, an indirect method to verify the contact ratio by detecting the contact length error of the tooth profile was proposed.

Design and Analysis of the Differential Pump Driven by the Novel Eccentric Non-Circular Gears

In order to obtain a better driving mechanism of the differential pump, a high-performance differential velocity vane pump was presented. The pump was driven by the novel eccentric non-circular gears. The working principle and structure of the differential pump were studied. The transmission mechanism of the high-order multisegment deformed eccentric non-circular gears were established, then the transmission characteristics were discussed. Finally an example was given. The example showed that the high-order multisegment deformed, eccentric non-circular gears could meet the large displacement requirements of the differential velocity vane pump.

Influence of the Fixed Angle of the Non-Circular Gears on the Intermediate Shaft on the Gear Ratio Function Characteristics

The paper shows the influence of the fixed angle of non-circular gears (NCGs) on the gear ratio function characteristics of the compound non-circular gear (CNCG) train. The research established a mathematical model describing the centrodes of a typical CNCG train. The fixed angle β of non-circular gears on the intermediate shaft is changed to evaluate its effect on the gear ratio of the CNCG train. The results show that changing the fixed angle of non-circular gears on the intermediate shaft changes the transfer function law of the system and can increase the speed variation range on the output shaft. With the parameters of the designed CNCG train, changing the angle β can increase the amplitude of the gear ratio function to 30.19%. A CNCG train with a speed variation range from 1.37 to 5.11 has been experimentally designed and manufactured with an improved cycloid profile considering the tooth number distribution and satisfying the condition of avoiding undercutting. On that basis, an experimental system to determine the gear ratio of the CNCG train based on the meshing between the gear pairs in the CNCG train has been designed and manufactured. The experimental results showed that the maximum error of the gear ratio function is about 7.63% compared with theoretical ones. In this study, we have not considered the influence of force and torque on the experimental gear ratio. We can apply the results of this research to transmission systems to obtain a speed variation.

Mutually different tooth surface contact characteristics of a noncircular face gear with intersecting axes

Mutually different tooth surface contact characteristics of a noncircular face gear with intersecting axes

Transmission performance evaluation of non-circular spur bevel gear based on a novel isochronal measurement method

This paper aims to study the transmission performance evaluation of non-circular spur bevel gear (NCSB-gear) based on a novel isochronal measurement method. Firstly, the mathematical model of NCSB-gear is established. Then a novel isochronal measurement method is proposed, and the actual tooth surfaces are reconstructed by non-uniform rational B-spline interpolation. The advantages of the proposed method are discussed based on the geometric characteristics of tooth surface and measurement fitting error. A pair of forged NCSB-gears is measured through a coordinate measurement machine and the maximum tooth surface fitting error by the proposed method reduces 2μm compared with the traditional method. Moreover, deviation tooth contact analysis (DTCA) and load tooth contact analysis (LTCA) are conducted to evaluate the transmission performance. Finally, the transmission performance of measured NCSB-gear is obtained by a gear rolling tester. By comparing the TCA calculation of different measurement methods, it is found that the relative error of the maximum transmission error based on the isochronal measurement method reduces 4.719% compared with the traditional measurement method, thus verifying the validity of the proposed measurement method.

Optimization Synthesis of Hybrid Six-Bar Mechanism With Non-Circular Gear Constraints

AbstractA novel hybrid six-bar mechanism with non-circular gear constraints and its optimal synthesis method for complex multi-pose rigid body guidance tasks are proposed. An innovative optimization module is proposed to optimize the non-circularity and smoothness of non-circular gear pitch curves. The optimization synthesis of this mechanism is divided into two steps. The first step is to conduct multi-objective constraint optimization with pose error and non-circular gear pitch curve as optimization objectives to obtain the required diversified non-inferior solution set. Second, a set of solutions are selected from the solution set to construct the optimization function of non-circular gear pitch curves. The non-circularity and smoothness of the pitch curve are optimized to the maximum extent, and the pose change is ensured to be small. Finally, the multi-pose picking and planting of vegetable pot seedlings were realized using the proposed mechanism and optimization synthesis method. The final optimization design results show that the error between the actual pose and the required pose of the compact hybrid mechanism is small. The optimization effect of non-circularity and smoothness of non-circular gear pitch curves is pronounced. The effectiveness of the mechanism is verified via kinematic simulation.

The mathematical model of non-circular crossed-axis gear

Non-circular crossed gear can be regarded as the general form of the single stage gear, which can be converted into hypoid gearing, non-circular bevel gearing, non-circular external gearing, and non-circular internal gearing with specific parameters. This paper established its mathematical model, deduced equation of its axode, and put forward a new method of tooth profile generation with introduction of relative velocity. In term of the theory above, the 3D model of a pair of conjugated gears was built, and its output angular velocity was obtained in analysis of ADAMS. Finally, the physical prototype of the gearing was developed and output angular velocity was measured as well. Both the simulation and measurement results show the motion is in good condition, which confirms the correctness of the theory and algorithm.

Precise Shrink Fitting Design of the High Strength Gear Mold for the Precision Forging of Noncircular Spur Bevel Gears

Shrink fitting of forging mold (SFFM) is an effective method for improving mold strength, extending the mold's service life and reducing the manufacturing cost of forging mold. However, due to the asymmetric geometry and complex stress distribution, the precise design of SFFM for the precision forging of noncircular bevel gears is very difficult. In this paper, a new precise design method of SFFM for the precision forging of noncircular bevel gears is proposed, which mainly includes the following five parts. First, a new design method for the mold parting surface-the curved surface parting method-is proposed to design the forging mold of noncircular spur bevel gears. Then, new dimension design methods for the gear mold and shrink rings based on the uniform shrinkage force are proposed. Third, a new design method for the inhomogeneous interference value between shrink rings and the gear mold is developed to provide a precise, uniform shrinkage force. After that, a strength correction method for the shrink-fitted gear mold is proposed to ensure the gear mold and shrink rings have sufficient strength both in the assembly process of the shrink-fitted gear mold and precision in the forging process of noncircular spur bevel gears. Ultimately, finite element simulations and verification experiments are performed to verify the proposed precise design method of SFFM for the precision forging of noncircular bevel gears. The precise design method of SFFM proposed in this paper is not only applicable to the precise design of the high-strength gear mold for noncircular bevel gears, but can also provide a valid reference for the precise design of the high-strength mold for other complicated asymmetric parts.

Multi-objective Optimization of Non-circular Gear Through Orthogonal Array and Fuzzy Comprehensive Evaluation Method in WEDM

Multi-objective Optimization of Non-circular Gear Through Orthogonal Array and Fuzzy Comprehensive Evaluation Method in WEDM

Geometric calculation of non-circular gear segments of the planetary mechanism in rotary hydraulic machines

The article discusses the improvement of the methods of geometric design of positive-displacement hydraulic machines with floating satellites. At the first stage, based on standard methods, an “average” round-link planetary mechanism, having the number of teeth as in the designed hydraulic machine, is calculated. At the second stage, the same-type cyclic functions characterizing the paths of the center of the satellite in the coordinates associated with each of the central gearwheels are specified. At the third stage, the coordinate arrays of the satellite in a variety of its positions are calculated. The angular position of the satellite relative to one of the profiled gearwheels (for example, the sun gearwheel) provides equidistance of the centroid of this gearwheel to the path of the center of the satellite. The angular position of the satellite relative to the other profiled wheel is determined by its running around the first wheel. At the final stage of the design, the satellite is constructed in a variety of positions, and the profile of the corresponding non-circular gear rim is obtained as an envelope of the family of satellite curves-profiles.

Reverse design and tests of vegetable plug seedling pick-up mechanism of planetary gear train with non-circular gears

Reverse design and tests of vegetable plug seedling pick-up mechanism of planetary gear train with non-circular gears

Kinematic synthesis and simulation of a vegetable pot seedling transplanting mechanism with four exact task poses

To obtain a picking and planting integrated transplanting mechanism (PITM) with ideal trajectory shape, reasonable operating attitude, and compact structure for vegetable pot seedling transplanting, a symmetrical structural PITM composed of two planetary carriers and driven by a cam–noncircular gear combination mechanism was proposed in this paper. In accordance with the requirements of transplanting agronomy, the shape of the motion trajectory and the attitude of the end tip of the clamping claw at several specific positions (the starting and end points of picking seedling, the starting point of pushing seedling, and a special point on the return segment) were planned. To make the clamping claws of PITM pass through a set of prescribed positions, the mechanism was simplified to an open-chain 3R mechanism. An accurate four-position-based method for solving the open-chain mechanism model was adopted to obtain the curves of its fixed hinge point (central point) and dynamic hinge point (circle point). The ratio of adjacent bars’ lengths was analyzed to determine the feasible interval of the central and circle point curves and the reasonable link length. A desired closed transplanting trajectory that goes through the given points and the corresponding transmission ratio model of the open-chain mechanism was established. After the transmission ratio of each stage of gear and cam pairs was calculated and distributed, the prototype of PITM was designed and manufactured. Lastly, the effectiveness and feasibility of the design were verified through a preliminary experiment of the prototype. Keywords: kinematic synthesis, transmission ratio, non-circular gear, planetary carrier DOI: 10.25165/j.ijabe.20231602.6739 Citation: Sun L, Xu H C, Zhou Y Z, Shen J H, Yu G H, Hu H F, et al. Kinematic synthesis and simulation of a vegetable pot seedling transplanting mechanism with four exact task poses. Int J Agric & Biol Eng, 2023; 16(2): 85-95.

Research on the Tooth Surface Integrity of Non-Circular Gear WEDM Based on HPSO Optimization SVR

Non-circular gears have the characteristics of gear ratio accuracy, good dynamic performance, and wide application prospects but are difficult to manufacture. Wire electrical discharge machining (WEDM) can process almost all kinds of non-circular gear. In order to solve the problem that the process parameters are mainly adjusted using the operator’s experience and to improve the surface quality of non-circular gears machined using WEDM, this research took Pascal gears processed with a fast-walking WEDM machine as the object, conducted orthogonal tests, and used hybrid particle swarm optimization (HPSO) to optimize support vector regression (SVR) with different kernel functions, to predict various surface integrity indicators. The results showed that the rbf kernel function had a better performance in the prediction model of surface integrity indicators, which can provide a reference for the parameter selection of non-circular gear machining using WEDM. The final predicted results were R2 = 0.9978, MAPE = 0.4534 for surface roughness, R2 = 0.9483, MAPE = 3.1673 for surface residual stress, and R2 = 0.9786, MAPE = 0.4779 for surface microhardness.