Internal Gear Pair Research Articles

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.

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.

Calculation of Time-Varying Mesh Stiffness of Internal Gears based on Precise Tooth Profile and Dynamic Analysis of Planetary Systems with Root Cracks

The internal meshing spur gear pair is the research object, and the potential energy method is applied to calculate the time-varying meshing stiffness of the internal gear. The internal gear tooth profile is divided into two parts: involute and transition curves, and the gear tooth stiffness is calculated by numerical integration based on accurate tooth profile, which improves the calculation accuracy. Analyzed the influence of different crack size parameters on the stiffness of internal meshing gears. A coupled dynamic model of a planetary system with internal gear crack faults was established, and the influence of cracks on the dynamic response of the planetary system was studied using Zoom-FFT spectrum and cepstrum analysis methods. The simulation results show that as the crack parameter size increases, the mesh stiffness of the internal gear pair gradually weakens, and the periodic vibration impact of the planetary-internal gear pair is also more severe. Cepstrum analysis can easily capture weak fault characteristic frequency information in the system and discover their variation patterns. The research results can provide a theoretical basis for the state monitoring and fault diagnosis of gear systems with crack defects.

Theoretical derivation and analysis of strength calculation formulas of internal gear pair with double contact points

To describing the strength conditions of tooth surfaces of internal gear pair with double contact points (IGPDCP) accurately, theoretical calculation method of the strength of tooth surfaces is proposed in this paper. Theoretical derivation and analysis of strength calculation formulas of the IGPDCP drive are carried out. For contact strength analysis, based on Hertz point contact theory, general calculation idea of contact strength is provided. The main curvature of the active contact line on tooth surfaces of the pinion and internal gear are derived, respectively. Furtherly, according to theoretical calculation and derivation, the formula for calculating the contact strength of the IGPDCP drive is obtained. Orthogonal test method is used to derive the calculation formula of bending strength of the IGPDCP drive, considering test factors include the modulus, tooth number of gear, transmission ratio, helix angle, contact angle, pressure angle, and torque. Nonlinear regression equations of bending stress of the pinion and internal gear are derived, respectively. The discussion of results of contact and bending strength between formula calculation and finite element analysis are present. The conclusions show that the proposed formulas can satisfy theoretical analysis and engineering application.

Three-Dimensional Conjugate Tooth Surface Design and Contact Analysis of Harmonic Drive with Double-Circular-Arc Tooth Profile

A three-dimensional conjugate tooth surface design method for Harmonic Drive with a double-circular-arc tooth profile is proposed. The radial deformation function of the flexspline (FS), obtained through Finite Element (FE) analysis, is incorporated into the kinematics model. By analyzing the FS tooth enveloping process, the optimization of the overlapping conjugate tooth profile is achieved. By utilizing the hobbing process, the three-dimensional machinable tooth surface of FS can be acquired. Utilizing the coning deformation of the FS, simulations are conducted to analyze the multi-section assembly and meshing motion of the machinable tooth surface. The FE method is utilized to analyze and compare the loaded contact characteristics. Results demonstrate that the proposed design method can achieve an internal gear pair consisting of a circular spline with a spur gear tooth surface and the FS with a machinable tooth surface. With the rated torque, approximately 24% of the FS teeth are engaged in meshing, and more than 4/5 of the tooth surface in the axial direction carries the load. The contact patterns, maximum contact pressure, and transmission error of the machinable tooth surface are 227.2%, 40.67%, and 71.24% of those on the spur gear tooth surface, respectively. It clearly demonstrates exceptional transmission performance.

Initial impact force analysis and simulation of planetary helical gear transmission

The planetary gear transmission is widely used because of its advantages such as large transmission ratio and high transmission efficiency. But at the moment of starting, there is a speed difference between driving gear and driven wheel due to the backlash between the teeth, this will easily cause the initial collision and impact force, which seriously affect the life of gear transmission, even lead to tooth surface pitting and root fracture failure, therefore, it is necessary to conduct a quantitative analysis of the initial collision. Based on the gear meshing principle and the system dynamics theory, the analytical calculation formula of initial impact force for the internal and external meshing gear pair was derived. The impact simulation analysis model of planetary helical gear transmission was established based on the finite element LS-DYNA, and the simulation analysis results were compared with the analytical calculation results, which verified the correctness of the analytical calculation model. This paper reveals the impact collision mechanism and studies the influence law of the speed and temperature on the impact force, thus laying a good theoretical foundation for the dynamic modification design of the planetary gear transmission and preventing the failure of the gear teeth from impact collision.

Optimization design and analysis of internal gear transmission with double contact points

Internal gear transmission with double contact points is consist of the pinion having circular-arc tooth profile and the internal gear having parabola tooth profile. To further improve load capacity and reduce total volume of internal gear drive with double contact points, a multi-objective and multi-parameter optimization mathematical model is established based on genetic algorithm. Through the comparison analysis, contact stress of tooth surfaces after optimization design is reduced by 21.9% and the volume of gear after optimization design is reduced by 3.93%. Furthermore, contact characteristics of tooth surfaces are discussed considering the parameters optimization of contact angles and pressure angles. Based on Hertz contact theory, theoretical calculations of contact stresses under different contact angles and pressure angles are provided. And finite element method is used to analyze the contact conditions of tooth surfaces to verify theoretical calculation results. Research results show that contact angle of the internal gear pair with double contact points should less than 12.5° and pressure angle of the internal gear pair with double contact points should be 20°–30°.

Study on Design Constraints of Conjugated Straight-Line Internal Gear Pair

In order to solve the problem that the design constraints of the conjugated straight-line internal gear pair are unclear, the designing and checking of gear pairs requires repeated trial and error. By analogy with the design of the involute gear pair, the basic design parameters of the conjugated straight-line internal gear pair were clarified. Based on the mathematical model of the gear pair, the constraints on basic design parameters were given according to gear engagement theory and the geometrical relations of the tooth profile. The calculation formula and the constraint of the contact ratio were deduced according to the kinematic relations. Based on Litvin’s undercutting theory, the constraints on avoiding undercutting and end cutting were deduced and their correctness was verified by examples. The judgment method of tooth-overlapping interference and its corresponding numerical calculation flow were presented. The constraint on avoiding radial interference was deduced and analyzed. Based on the above content, the influence laws of design parameters on the design constraints were studied. Last, design examples were given and the effective design flow diagram of the conjugated straight-line internal gear pair was summarized. These research results provide a theoretical basis for the parameter design of conjugated straight-line internal gear pairs, provide guidance to avoid the interference of the gear pair, and promote the design system of the gear pair.

Evaluating the Time-Varying Mesh Stiffness of Planetary Gear Set With Gear Crack Considering the Friction Force Under Mixed Elastohydrodynamic Lubrication Condition

Abstract The mesh stiffness calculation of the planetary gear system with gear crack is investigated, and gear crack is modeled into end-face and addendum extended crack. Furthermore, the mesh stiffnesses are calculated under the effect of friction force obtained under the mixed elastohydrodynamic lubrication (EHL) condition. The nonuniformly distributed gear cracks on external and internal gear pairs are comprehensively modeled and analyzed, which is rarely investigated in previous studies. Moreover, the influence of crack propagation conditions on the meshing stiffness of the planetary gear system is analyzed. The obtained results show that the mesh stiffnesses experience abrupt variation in the pitch area during meshing, the extent of change is determined by the amplitude of the friction coefficient; in addition, gear crack position and extent could cause mesh stiffness reduction at varying levels at different stages of gear meshing.

Mathematical model and deviation analysis of machining cutters for internal gears with double contact points

An internal meshing gear pair that includes double contact points is proposed by the authors. For further performance evaluation and engineering application, special machining cutters for generating tooth surfaces are studied in this paper. General formulas and mathematical models of tooth surfaces of the hobbing cutter for the pinion are derived based on the actual tooth profile. Solid models of the three-dimensional hobbing cutter are established and calculation formulas of deviation conditions between the ideal tooth surface and the generated tooth surface are deduced. Deviation analysis considering the parameters of helical angle and pitch circle radius is discussed. Numerical simulations of the hobbing process are also carried out. While for the internal gear, tooth profile of skiving cutter is designed and forming formulas of tooth surfaces of the skiving cutter are derived. Solid models of the three-dimensional cutter are established, and the deviation calculation method of tooth surfaces is also provided. The research results lay the essential theoretical foundations and engineering analysis for practical applications of the new internal gears.

Calculation and influence analysis of tooth surface friction coefficient of planetary gear system in mixed lubrication condition

Based on the gearing theory, the calculation formulas of comprehensive curvature radius, relative sliding speed and tooth surface contact stress of internal and external meshing gear pair of the planetary gear system are deduced in this paper. Combined with load sharing theory and thermal elastohydrodynamic lubrication analysis method, the oil film thickness, film bearing ratio and friction coefficient are solved and the effects of roughness and input power on the friction coefficient are studied. The results show that with the increase of tooth surface roughness, the film bearing ratio decreases and friction coefficient increases; As the input power increases, the film temperature increases, the oil viscosity and film thickness decreases, which causes the tooth surface friction coefficient increases.

Optimal design of transplanting mechanism with differential internal engagement non-circular gear trains

This study aimed at the problems of unequal speed transmission ratio mutual restriction and side gap accumulation of the transplanting mechanism with single-degree-of-freedom K-H-V non-circular planetary gear train, which leads to poor trajectory and attitude, and poor precision of movement. This study has proposed a simple structure of transplanting mechanism with differential internal engagement non-circular planetary gear trains, which reconstructs the complex transplanting trajectory and attitude of the planting arm through single-stage unequal speed transmission. The working principle of the transplanting mechanism was analysed, and the kinematic theoretical model of the transplanting mechanism was established. The optimal design software for the transplanting mechanism was developed based on the visual platform. The dimensions optimisation on the transplanting mechanism was completed considering the requirements with strong coupling, and multi-objective and a set of superior mechanism parameters were obtained. The design theory and method of the internal engagement non-circular gear pair were proposed based on the generating principle. The correctness and accuracy of the trajectory and attitude of the transplanting mechanism were verified through virtual simulation experiments. The experiments show that the designed transplanting mechanism with internal engagement non-circular planetary gear trains was compact in structure, the trajectory meets the requirements of multi-objective transplanting, and the trajectory and attitude can be accurately reproduced, which provides a new feasible solution for the innovative design of the transplanting mechanism.

Geometry design, meshing analysis and error influences of face-hobbed cycloidal bevel gears with double circular-arc profile for a nutation drive

As the core components of nutation drive, the internal meshing pair of bevel gear must be delicately designed to achieve desirable operational performances for the transmission device. For this purpose, this paper designs a face-hobbed internal meshing pair of cycloidal bevel gears with double circular-arc profile (DCAP). First, a cutter head with DCAP cutting edges is designed to generate the tooth surface of internal gear pair. Then, the tooth geometry of the external and internal bevel gears are derived according to the meshing theory. Finally, a finite element model is developed to simulate the meshing characteristics of the gear pair. The simulation results reveal that the proposed face-hobbed cycloidal bevel gear pair with DCAP has higher contact/bending strength, better load sharing and smaller transmission error compared with the logarithmic spiral bevel gear pair with DCAP. The effects of four typical manufacturing errors on meshing characteristics of the proposed bevel gear pair are investigated to provide fundamental references for the tolerance design of cycloidal bevel gears.

Research on methods of tooth contact analysis and modification optimization for internal spur gear pair

Internal spur gear pair is widely used in industry. There is little current research on how to analyze and modify internal spur gear pairs that affect design and transmission performance. In this paper, a modeling method and an improved tooth contact analysis (TCA) method for internal spur gear pair are presented. The comparison between the improved TCA method and conventional TCA method is done, and the correctness and advantage of the improved TCA method are proved. The loaded tooth contact analysis (LTCA) method for spur gear pair is studied, and its feasibility is verified by Romax. Based on the method of penalty function, a modification optimization method of internal spur gear pair is proposed. Compared with the conventional particle swarm modification optimization, the proposed modification optimization method of internal spur gear pair is suitable for engineering application from the view of time-consuming and result. In order to facilitate modification, a modification parameter conversion method is proposed, and the conversion formulas from the modification length on tooth root of pinion to that on tooth tip of ring gear is derived. A dynamic model for internal spur gear pair is built, and dynamic simulation is carried out. The analysis results show that the optimization of the correction can significantly reduce the mean square value of the vibration acceleration. The research results supply a basis for the analysis and the modification optimization of internal spur gear pair.

TAGUCHI AND RSM BASED OPTIMIATION OF ENERGY CONSUMPTION ON INTERNAL GEAR PUMPS

Internal gear pumps are used in a variety of applications for the transfer of many different types of liquids like fuel, oil and food in both the industry and daily life. Power transfer is provided in the applications of those pumps in the transfer sets, especially through the induction motor and the coupling connection. The R & D studies for the efficiency of pumps carried out worldwide account for 6% of the total, and thus energy savings of 303 trillion BTU can be achieved annually. With minimum energy consumption, high rates of energy savings will be ensured by transferring maximum amount of fuel. For this purpose, firstly a detailed literature review was made, and then industrial pump manufacturers and scientific studies were investigated. As a result of that, a new type of internal gear pair design ,which has not been manufactured so far in the industry, has been proposed. In the new pump, the effects of tooth length and the changes in the number of revolutions on flow, power and SEC results were studied. Thus, it will be possible to compare energy expenditure and flow rate with the other pumps developed. By using Response Surface Method (RSM), Taguchi Method and Anova Variance Analysis, optimum speed and tooth length were determined as 700 RPM for speed and 85 mm for tooth length by taking SEC S/N graph into account. In this way, pump production with optimum flow rate and energy consumption amount in the industry was produced, and the energy consumption value was decreased during the fuel transfer from 156,1 Wh/m3 to 92,0 Wh/m3.In addition, the change in the flow rate was found to be the most effective parameter in the 83% rate change. As for the calculation of the Ptotal results, it was determined that a 50% shaft speed and a 45% inner gear were effective.

Investigation of Load Capacity of High-Contact-Ratio Internal Spur Gear Drive with Arc Path of Contact

Tooth root bending stress and surface contact stress are two major determinants of the load carrying capacity of gear drives. Generally, a high contact ratio has the potential to enhance the gear strength. In this paper, the basic procedures and methods for constructing a high-contact-ratio (HCR) internal spur gear pair with the arc path of the contact are presented. The effects of design and modification parameters such as deflection angle, modification angle, and addendum coefficient on gear drive are analyzed in detail based on 2D finite-element models (FEMs). A comparison of experimental and finite-element analyses (FEA) of the bending stress, contact stress, and contact ratio between HCR and involute internal spur gear drives was conducted to demonstrate the advantages of the HCR gear drive in terms of load capacity. The results show that appropriately increasing the deflection angle and addendum coefficient is beneficial for reducing bending and contact stresses. It was also observed that the bending and contact stresses of a HCR pinion are lower than those of an involute one. Moreover, the contact ratio increases with input torque.

Design principle and meshing analysis of internal gear drive with three contact points

A kind of internal gear drive with three contact points is presented in the article. Firstly, the pinion with circular-arc form and the internal gear with parabola-circular form are proposed, respectively. General equations of tooth profiles are provided. Furthermore, according to gear geometry, mathematical model of the pinion and the internal gear are generated and their tooth surfaces equations are derived. Meanwhile, based on design parameters, 3D solid models of the new gear pair with three contact points are developed utilizing modeling software. Finally, meshing characteristics of generated new gear pair are analyzed, such as sliding ratios and contact stress conditions. General corresponding comparisons with other internal gear drive are also discussed. Research conclusions show that the new internal gear pair with three contact points has low sliding ratios and high contact strength.

Time-varying meshing stiffness calculation of an internal gear pair with small tooth number difference by considering the multi-tooth contact problem

Time-varying meshing stiffness calculation of an internal gear pair with small tooth number difference by considering the multi-tooth contact problem

Design and Analysis of Conjugated Straight-Line Internal Gear Pairs

Design and Analysis of Conjugated Straight-Line Internal Gear Pairs