Gear Model Research Articles

Cylindrical gear transmission errors influenced by temperature based on thermal network

Cylindrical gear transmission errors influenced by temperature based on thermal network

New deterministic model for calculating mesh stiffness and damping of rough-surface gears considering elastic–plastic contact and energy-dissipation mechanism

For a long time, meshing parameter calculations and dynamic modeling of gear systems have assumed smooth tooth surfaces, disregarding the impact of actual three-dimensional (3D) microscopic topography. Based on elastic–plastic contact and energy-dissipation mechanisms, this work developed a comprehensive deterministic model that integrates 3D rough surface modeling, reconstruction, and contact analysis, for calculating the time-varying mesh stiffness (TVMS) and mesh damping (TVMD) of deterministic rough-surface gears. Distinct from fractal and statistical models, the deterministic model analyzes deterministic, real 3D rough surfaces rather than simple surfaces defined by a few parameters. Utilizing stochastic process theory, different-topography surfaces are obtained using height and spatial features and reconstructed employing watershed algorithm and ellipsoidal asperity fitting. Subsequently, a deterministic elastic–plastic contact model based on equivalent rough curved-surface contact is constructed, emphasizing local contact states and energy dissipation for calculating contact stiffness (CS) and damping (CD) of gears. Accordingly, a meshing characteristics analysis model is established for calculating TVMS, TVMD, and load sharing ratio (LSR). Experimental validation and comparisons with several statistical and gear contact models demonstrate the effectiveness, reliability, and superiority of the proposed deterministic model. Multi-parameter impact analysis reveals small Sq (meaning low roughness Sa) and Ssk and high load correlate with increased CS and TVMS, while CD and TVMD depend on their interaction and hardness. Overall, by bridging the micro-surface topography and macro-meshing parameters, our model provides essential insights for the design and manufacturing of high-performance gear to reduce vibration and noise.

Study on the contact performance of the variable hyperbolic circular arc tooth trace cylindrical gear with installation errors

Abstract. Installation errors are important factor for the contact performance of the variable hyperbolic circular arc tooth trace (VH-CATT) cylindrical gear; the study of the relationship between installation errors and contact performances is beneficial for gear vibration and noise reduction. Firstly, based on the meshing theory, the tooth surface equation and contact ellipse of the VH-CATT cylindrical gear were deduced, and the tooth surface imprinting experiment was realized. Next, the tooth contact analysis model of the VH-CATT cylindrical gear was developed to investigate the influence of the installation errors on the elliptical contact area. Then, the calculation formulas of the tooth surface gap and contact point flexibility matrix were carried out to develop the load tooth contact analysis model of the VH-CATT cylindrical gear. Finally, the influence of the installation errors on the load distribution was investigated. Research shows that the elliptical contact area of the VH-CATT cylindrical gear is a line contact within a certain range and is located in the middle section of the tooth width. The elliptical contact area of the VH-CATT cylindrical gear increases or decreases rapidly when meshing in and out, and all the installation errors have a certain influence on the elliptical contact area, except for the center distance error. The single-tooth meshing area with the installation errors is greater than that of the ideal gear pair. The load distribution area with the installation errors deviates from the middle section, except for the center distance error. The installation rotation errors around the x and y axis have a certain influence on the maximum load of the single-tooth meshing area. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimizing the design.

A two-stage flank correction method for the continuous generation of face gears

Face gear pairs are particularly suitable for application in advanced equipment drivetrains with intersecting shafts. The continuous generation process of face gear tooth flanks using worms offers high machining efficiency, but achieving high accuracy in this process remains a considerable challenge. A two-stage flank correction method for face gears ground by worms on a computer numerical control (CNC) generator is proposed. This method comprehensively involves both the worm dressing and face gear grinding stages, considering the actual machine tool structure and constant offsets among its axes. Firstly, the machining kinematics for both stages are derived and the high-order tooth flank model of the face gears is developed. Secondly, the sensitivity of tooth flank deviations to variations in the kinematic coefficients is analyzed, and the deviations on both flanks of the tooth space generated with initial kinematics are measured. Finally, three cases of correction for the measured deviations are compared using the proposed method. Correcting only the grinding stage is effective and computationally inexpensive, and employing this case for manufacturing face gear tooth flank significantly reduces deviations.

Study on the Parameter Influences of Gear Tooth Profile Modification and Transmission Error Analysis

Gear transmission systems are widely used to transfer energy and motion and to guarantee the accuracy of the entire machine system. The modification technique is a common method that improves the gear profile and reduces the transmission error. Based on the parametric model, a modified gear can be established for the evaluation of static and dynamic characteristics. The influences of profile modification parameters and gear parameters are investigated while changing the rules of different kinds of factors. Based on sensitive parameters, a two-stage profile modification curve is proposed to improve the performance of gear pairs. Thus, considering the time-varying mesh stiffness and backlash, a novel, dynamic modified gear model is established to analyze the dynamic performance, such as the dynamic transmission error. Based on the proposed curve, the range and amplitude of the transmission error can be decreased. Additionally, the vibration displacement and noise can be reduced to improve the running characteristics.

Comparative analysis of dynamic load characteristics of artillery steering gear based on different MBD methods

The multi-body dynamics analysis model of the steering gear of a certain type of artillery was established. The dynamic load characteristics of the output gear of the steering gear motor and its driven gear under the given speed and load conditions were calculated based on the three different MBD analysis methods, such as the speed, meshing force, and contact stress. Through the comparative analysis, it was concluded that the calculation results of rigid-flexible coupling analysis were closer to the theoretical value and the fluctuation range was smaller, which provides reference and basis for the prediction of gear fatigue life and the optimization design under dynamic load conditions.

Analysis of landing gear simplified modeling and simulation based on amesim

Aiming at the theoretical research of aircraft take-off and landing taxiing control characteristics and real-time interactive application scenarios, the simplified model modeling method of landing gear is studied. Through the reasonable simplification hypothesis of the landing gear pillar, a benchmarked, general, and pillar-type simplified model of the landing gear is formed. In the process of ground motion, based on the force analysis of aircraft taxiing, a six-degree-of-freedom mathematical model of ground taxiing is established. Based on the Amesim six-degree-of-freedom model, the aircraft is built, and the simulation test of aircraft taxiing turning and landing brake is carried out in combination with the simplified take-off and landing model. The results show that the general benchmarked pillar landing gear model formed in this paper is reasonable and feasible, and can quickly construct the aircraft landing gear model, which is convenient for subsequent optimization and design.

ANALYSIS OF THE MIXED ELASTOHYDRODYNAMIC LUBRICATION CHARACTERISTICS OF DOUBLE CIRCULAR ARC GEARS CONSIDERING MICRO-MORPHOLOGY

Different machining methods result in diverse morphologies on the surface of gears. Under mixed lubrication, the friction and contact behavior of the real morphology interface becomes more complex. This study aims to analyze the influence of different process tooth surface micro-morphologies on the lubrication performance of the meshing area of double circular arc gears. Focusing on elastohydrodynamic lubrication (EHL) characteristics of the double circular arc gears as the research object, the study involved measuring the three-dimensional morphology of the meshing position of the double circular arc gears. Non-Gaussian simulation technology was then used to characterize the micromorphology of the tooth surface resulting from different processes (i.e. hobbing process and skiving process). The tooth surface suction speed was determined based on the meshing characteristics of double circular arc gears. Based on the theory of point contact EHL, Reynolds equation and film thickness equation considering micromorphology were derived, and numerical solutions were obtained using the multi-grid method. A point contact EHL model for double circular arc gears was established considering the micromorphology of tooth surfaces in different processes. Results show that, the oil film pressure is positively correlated with rotational speed and torque. The oil film thickness is positively correlated with rotational speed, and negatively correlated with input torque. The negative of micro-morphology on the tooth surface on the lubrication performance could lead to an increase in pressure fluctuations and the absence of the second pressure peak. The uneven distribution of oil film and the lager roughness value could result in obvious fluctuations. The lubrication performance of the contact area in the gear hobbing process is superior to that in the gear skiving process. This study lays the foundation for further exploring the coupling characteristics between the double circular arc gear transmission system and elastic fluid dynamic lubrication. Keywords: Double circular arc gears, Point contact, Mixed EHL, Lubrication characteristics, Micro- morphology.

Dynamic Simulation Analysis of Aviation Gear Transmission Based on Rough Tooth Surface

In order to explore the influence of tooth surface microstructure on the dynamics of aviation gear transmission, this paper describes the profile of aviation gear considering rough surface based on fractal theory. With the help of the established gear fractal contact model, the dynamic parameters such as time-varying friction coefficient, time-varying meshing stiffness and transmission error of rough tooth surface are characterized. The nonlinear dynamic model of aviation gear is established to solve the dynamic response of smooth and rough tooth surface. The dynamic meshing force, dynamic friction force, vibration time domain and frequency domain diagram are obtained, and the corresponding experiments are carried out. The simulation and experimental results show that the fluctuation range of the dynamic simulation results of aviation gear transmission based on rough tooth surface will be larger, and it has a certain degree of disorder, which is closer to the experimental results.

Mathematical Model and Analysis of Novel Bevel Gear with High Load-Capacity Based on the Geometric Elements

Load-capacity has always been one of the performances that is paid much attention to in the development of bevel gear transmission applications. Consequently, the mathematical model of novel bevel gear with high load-capacity based on geometric elements is proposed in this paper, which could be applied to the aviation, aerospace and other fields. In parallel, the design principle and design method of the novel bevel gear are introduced in detail. Subsequently, the conditions for tooth surface continuity and non-interference are derived. Furthermore, the model of novel bevel gear is established. Finally, the load-bearing characteristics are analyzed, revealing that an increase in the number of contact points could significantly enhance the load capacity of the bevel gear pairs. When the load torque applied to bevel gear II is 100 Nm, the contact pressure endured by the bevel gear pair with five-point contact is decreased by 41.37% compared to the bevel gear pair with single-point contact. When the number of contact points is the same, increasing the distance between the contact points could also reduce the contact stress. This provides strong theoretical support for the application of the bevel gear based on the geometric elements.

Mathematical modeling of a magnetic gear for an autonomous wind turbine

Mathematical modeling of a magnetic gear for an autonomous wind turbine

Analysis of the Synchronized Locking Dynamic Characteristics of a Dual-Sidestay Main Landing Gear Retraction Mechanism

As an advanced design technology for large wide-body airliners, the three-dimensional (3D) dual-sidestay (DSS) landing gear retraction mechanism can share the ground loads transferred by the landing gear, reducing the load on the wings. However, the addition of a strut system may significantly impact the synchronous locking performance of the landing gear with extremely high sensitivity. To study this impact pattern, both a rigid–flexible-coupling dynamic model of DSS landing gear considering joint clearance and node deviation and a synchronous locking test platform are established in this paper, and the simulation model is validated through the experimental results. Based on the simulation model, this paper conducts a detailed study on the influence of different node deviations and joint clearance on the synchronous locking dynamic characteristics of the DSS landing gear. The results show that, as the node deviation increases, the locking of the lock link gradually lags until one side cannot be fully locked; the structural clearance has a smaller impact on the synchronous locking of the landing gear. The feasible region of parameters satisfying the synchronous locking condition is given, which provides a basis and support for the parameter design of dual-sidestay retraction mechanisms.

Mathematical model of non-generated straight bevel gears based on a four-axis CNC machine

Mathematical model of non-generated straight bevel gears based on a four-axis CNC machine

Structure of Molecular Water and the 3D Pythagoras Theorem

Water ice crystals inherently embed in their shape complex hexagonal structures, emerging mostly due to the O-H bond angle 104.5 degrees being close to the 120 degrees found in hexagons. This article explores the possible integration of water molecules into a recently published mathematical architecture called the Universal Gear model. Already published in a mathematics peer-reviewed journal, the Universal Gear is an orthogonally-intertwined construct of Pythagoras theorem driven planes, that all together provide a perfect balance in terms of the three main equations governing three-dimensional existence: zero net sum of lengths, zero net sum of areas and zero net sum of volumes. Computer-aided Design shows how a group of (simplified and realistic) water molecules successfully integrate into the (regular and irregular) version of the Universal Gear. Interestingly the geometric pattern that emerges from the projected field of water molecules integrated into the Universal Gear is a structure already observed in monuments of ancient civilizations. The ambient conditions, in terms of pressure and temperature, where such a structure could appear is not yet known, requiring further research preferably using computational molecular dynamics.

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.

Research on the model of staggered tooth phase to reduce vibration of single-stage gear transmission system: Theoretical analysis and experiments.

Aiming at the problems of high vibration and high noise in gear transmission systems, a model of gear with staggered tooth phase structure(GSTPS) for reducing vibration is proposed. Without changing the overall structure of the gear transmission system, the purpose of reducing mesh stiffness fluctuations is achieved by staggering adjacent gears at a certain angle along the axis, thereby the vibration of the gear transmission system could be reduced. The characterization method of time-varying mesh stiffness of the GSTPS is studied. Then, the impact of different staggered tooth phases(STP) on reducing vibration of the transmission system are researched, and the basis for selecting the optimal STP are obtained. The experimental platform for reducing vibration with STP is established. And some experimental studies were conducted to validate the theoretical model.

Forecasting model for hypoid gear elastohydrodynamic lubrication considering entrainment effect

In full consideration of time-varying meshing performance and oil film characteristics, entrainment effect on elastohydrodynamic lubrication (EHL) is developed for establishing accurate forecasting model of the complex hypoid gears. Firstly, dynamic loaded tooth contact analysis (DLTCA) is employed to determine the meshing interface kinematics, load distribution and entrainment speed under dynamic load condition. Then, entrainment speed is introduced into the EHL governing equation and accurate forecasting model is established. With accurate discretization of EHL governing equation, discrete convolution and fast Fourier transformation (DC-FFT) method is employed to compute the flank elastic deformation. Finally, a hypoid gear set in automotive industrial application is exercised to verify entrainment effect on EHL assessment in the proposed model.

Determining the Gear Design Parameters Which Have Strong Correlation with Gear Volume and Contact Ratio for Helical Gear Design Optimization

The market has a significant demand for low-cost, compact size, extended fatigue life and high load-carrying capacity helical gears. One way to manufacture such gears is by minimizing gear volume and maximizing contact ratio. Most researchers focus on gear design optimization, but minimal study has been conducted to identify design variables that significantly impact gear volume and contact ratio. Hence, it is crucial to determine gear design parameters that strongly correlate with gear volume and contact ratio beforehand. A single-stage helical gear train of local electric multiple units (EMU) is used as the gear model, and the calculations are done based on ISO 6336. Seven parameters have been chosen as independent variables; module, number of teeth of pinion, gear ratio, helix angle, tooth thickness factor, normal pressure angle and addendum factor. Graphs of total gear volume and contact ratio against independent variables are plotted to examine their relationship. The results indicate that normal module, number of teeth of the pinion, and gear ratio strongly correlate with the total gear volume. Meanwhile, the number of teeth of pinion, helix angle, tooth thickness factor, normal pressure angle and addendum factor strongly correlate with contact ratio. Therefore, these design parameters must be considered to improve the accuracy of the gear design optimization model, which aims to optimize gear volume and contact ratio.

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.

A novel method for helical gear modeling with an experimental validation

Dynamic models are important for developing gear diagnostics methods since they allow physical phenomena occurring during operation to be studied in a relatively simple environment. The main challenge in gear modeling is the calculation of the time-variant gear mesh stiffness, and this challenge is even greater in helical gears. The mechanism of helical gears is more complex than in spur gears; the helix angle both adds an axial component to the contact force and also makes the contact line three-dimensional. This study suggests a novel dynamic model for helical gear vibrations that combines an existing validated dynamic model for spur gears with a unique extension for helical gears. The extension is based on a common method called “multi-slice”, according to which the helical tooth width is divided into infinitesimal slices, and each slice is treated as spur tooth. The suggested model introduces a novel implementation of the multi-slice method that overcomes the aforementioned challenges with only few parameters and calculations, depends on the tooth geometry. Furthermore, for the first time in helical gear modeling, the manufacturing profile errors are integrated to the model to generate scatter in the data that can better reflect the reality. The model is validated experimentally and for two different test-rigs by a qualitative comparison of the RMS of the vibration signal. The simulations and the measured data show similar behavior at different ranges of rotational speed and applied load, emphasizing the potential inherent in the model for future work on gear fault diagnosis.