A face-gear drive system has been extensively used in important transmission devices with strict requirements for size and weight such as helicopter reducer and so on. Its dynamic characteristics ...directly affect the stability and reliability of the equipment. A piecewise torsional-bending-pendular nonlinear dynamics model of the face-gear drive system is established to study its nonlinear dynamics and dynamic characteristics. The multi-state engagements including drive-side teeth engaging, teeth disengagement, back-side teeth engaging, and alternate engaging between single-teeth pair and double-teeth pairs caused by the couple of the backlash and the contact ratio being greater than 1.0 is considered. The change of the dynamic engaging force and load distribution ratio for the system is analyzed by numerical results under three different states engagement. The effects of the load coefficient, meshing frequency and the comprehensive transmission error on the dynamic characteristics and nonlinear dynamics of the system are studied based on three different Poincaré mappings defined by bifurcation diagrams, top Lyapunov exponent diagrams, phase portraits and variation curve of the dynamic engaging force. Results show that the complex phenomena such as teeth disengagement, drive-side and back-side impact occur with alternating meshing of the single and double pair teeth via the change of studied parameters. The research is helpful for the optimization of the face-gear drives.
Adhesive wear in mixed elastohydrodynamic lubrication (EHL) has been one of the most prominent problems for heavy-loaded helical gears. However, this issue was rarely investigated in previous ...researches. In this work, an adhesive wear model for helical gears is established in line-contact mixed EHL. The contact parameters of the pinion and gear are derived according to the equivalent tapered roller contact model, and the load is attained in consideration of the varying contact line ratio. Then the asperity contact pressure is calculated according to Hertz's elastic contact theory and load sharing. Moreover, the sliding distances of the points on tooth surface of driving pinion and driven gear are achieved by a single point observation method, and Archard theory in dry contact is extended to the mixed lubrication to estimate the wear rate in mixed EHL by using fractional film defect. The modified Archard's wear model is then employed in formulating and accounting for the gear tooth wear. Effects of surface roughness, geometrical parameters and working parameters on wear depth of the driving pinion are furtherly investigated. The results show that the wear depth in mixed EHL is lower than that under dry contact, which indicates that tooth wear can be reduced with the reasonable lubricants. As the surface roughness becomes large, the asperity contact pressure, the tooth surface temperature and wear depth are increased. Additionally, the wear depths decrease with the increase in module, helix angle, pressure angle, tooth width or rotation speed but increase with input torque.
•An adhesive wear prediction method is developed for helical gears in mixed EHL.•Effects of tooth surface roughness on the wear of helical gear are investigated.•Efficient lubrication can greatly reduce the wear depth of tooth surface.•Geometrical and working parameters optimization is beneficial for wear resistance.
•It is the first time to study the vibration characteristics of worm helical gear.•The influence of different errors on vibration characteristics is considered.•An experimental platform is built to ...test the vibration with different errors.•The experimental results verify the accuracy of theoretical analysis.
The application of worm helical gear in smart car, smart home and other fields can significantly reduce the weight of products. Accordingly, the requirements for vibration and noise are also increased. In this paper, the lumped mass method is used to establish the dynamic model of point contact bending-twisting shaft meshing coupling worm helical gear drive. In this model, the contact ellipse is transformed into an equivalent rectangle, and the nonlinear factors such as time-varying meshing stiffness, tooth meshing error and meshing damping are considered. The vibration characteristics of worm helical gear drive in three directions and at meshing point are obtained for the first time. Machining accuracy, tooth surface modification and assembly errors are transformed into the error in the dynamic model respectively, and their effects on the vibration characteristics are analyzed. The closed vibration and noise performance test bench of worm helical gear drive is built, and the influence of three kind of errors on the vibration characteristics of worm helical gear drive are tested to verify the correctness of the dynamic model and its numerical analysis results. Both the theoretical analysis and the experimental results show that machining accuracy, tooth surface modification and the assembly error have a great influence on the vibration characteristics.
•A multiple degrees of freedom nonlinear dynamic model of a gear pair in coal is presented.•The gear meshing features and bearing coupling effect are taken into account.•A chaos control method is ...proposed.•The control method is simple and feasible to implement.
Under the nonlinear influence, the nonlinear oscillation of the semi-direct gear drive system (SDGDS) in coal cutters will happen, which will cause the system unstable. To solve this unstable problem, a multiple degrees of freedom (MDOF) nonlinear dynamic model of a gear pair is set up using mass centralized method, with both gear meshing features including time-varying mesh stiffness, mesh damping, backlash and dynamic transmission errors and nonlinear coupling effect such as radial clearance of ball bearing being taken into account. After the application of dimensionless treatment, the system is calculated using Runge-Kutta method. Meanwhile, the main parameters which may cause chaos and bifurcation are studied, for example, exciting frequency, radial clearance of ball bearing and mesh stiffness ratio. Then, the kinematic phase diagram, the Poincare map, the largest Lyapunov exponent chart as well as the bifurcation diagram are presented with different parameters. Furthermore, a chaos control method by means of proportion integral (PI) is proposed within a selected reasonable range. The results demonstrate that different parameters can lead to the occurrence of different chaotic behavior. It is also found that the chaotic control method suggested in this paper may not only reduce the area of chaos sufficiently but also suppress the chaotic phenomenon effectively. Besides, as there exists many nonlinear parameters, the study of parameters will lay a profound theoretical basis and practical significance for the improvement of the system stability and the optimization of the system parameters.
•Meshing point track and contact line range on tooth surface are rigidly divided.•Modeling approaches of tooth stiffness under line and point contact are proposed.•Models of load distribution ratio ...and meshing stiffness are established.•Effect of force on load distribution ratio and meshing stiffness is analyzed.•Coupling relationship among force, distribution ratio and stiffness is revealed.
Analytical models of load distribution ratio (LDR) and meshing stiffness for orthogonal spur-face gear drive under point contact are established to provide the parameter basis for dynamics studies in this paper. Meshing point tracks and contact line ranges on tooth surfaces are strictly divided according to the point contact ratio. Local contact stiffness at meshing point is calculated based on Hertz contact theory and calculation approaches of global tooth stiffness under line and point contact are proposed and compared. Then, models of LDR and meshing stiffness are constructed and analyzed. The results show that the global tooth stiffness decreases after considering point contact on the basis of line contact. LDR is significantly affected by the error on tooth surface. The meshing stiffness increases with the increase in meshing force. The contact deformation accounts for a high proportion in the total deformation. It expands the existing modeling methods to cover line and point contact, and lays the foundation of studies for orthogonal spur-face gear drive.
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•Entire tooth surface precise modeling method of face-gear drive is investigated.•A modified imaginary shaper is modeled mathematically as the geometric design tool.•A method for determining minimum ...and maximum radii of face gear is developed.•Tooth modification and optimization of face-gear drive are investigated.•Systematic analysis method for basic characteristics of face-gear drive is developed.
Entire tooth surface precise modeling and systematic analysis method for face-gear drives with an involute helical pinion are investigated. A modified imaginary shaper is mathematically modeled as the geometric design tool. The entire tooth surface of the face gear is determined analytically as the envelope to the family of imaginary shaper tooth surface. A practical method to determine the minimum and maximum radii of the face gear is developed. Addendum modification of the face gear is implemented mathematically based on the modified imaginary shaper to improve face-gear tooth-top thickness. Conical modification of the pinion is proposed to avoid contact between face-gear tooth-root fillet and the pinion tooth. Transverse pressure angle modification of the pinion is also proposed to avoid edge contact arising at inner-end and outer-end edges of face-gear tooth. Finite element models with nine pairs of teeth are employed for 3D contact finite element analysis to investigate the basic characteristics of face-gear drives, including meshing and tooth contact analysis, contact and bending stress analysis, contact ratio, transmission error, mesh stiffness, and sensitivity test. The helical face-gear drive is sensitive to rotation direction and shaft angle error. The presented geometric design method is illustrated and validated by numerical examples and trial manufacture.
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•Developed a set of space curve meshing equations for ZC1 worm drives based on the meshing theory.•Presented an approach of employing five-axis machining to fabricate a worm pair.•Developed an FE ...model for a ZC1 worm drive and investigated the contact behavior of the worm drive.•Confirmed the machining efficiency and precision of the five-axis machining approach.
ZC1 worm drives are traditionally machined by grinding with grinding wheels. However, the process efficiency and machining precision of the grinding method are low and cannot meet the design requirements of worm/worm gear transmissions. In order to overcome those shortcomings, we propose a methodology of using five-axis machining to machine the ZC1 worm drives to attain higher efficiency and precision. A ZC1 worm gear drive model with was first created using MATLAB based on the gear meshing theory. Meshing analysis of the ZC1 worm drive was then performed using ANSYS to obtain equivalent stress and contact patterns under different operation conditions. Finally, ZC1 worm drives were machined via five-axis machining and grinding separately. The prototyped ZC1 worm drives were compared through experiments. Experimental data indicated that the distributions of surface wear and contact patterns of the five-axis machined worm drive are more uniform. Moreover, the application of the five-axis machining dramatically enhanced the machining efficiency and precision by significantly reducing the manufacturing time from 30 days to two days and minimizing the influence of human factor on the product properties.
•New stiffness and damping models are developed for oil film in normal and tangential directions.•Smaller lubricant stiffness is beneficial for alleviating gear meshing impact and shear ...vibration.•Meshing impact and friction heat is suppressed by either larger normal lubricant damping or smaller tangential lubricant damping.•Better combined stiffness and damping can be achieved by optimizing gear geometric parameters and operating conditions.
Innovative stiffness and damping models for oil films are developed to account for the impacts in both normal and tangential directions. Given that these models are applied to a gear drive in line contact elastohydrodynamic lubrication (EHL), the combined stiffness is derived from the stiffness of both the oil film and gear tooth while the combined damping is established from the damping of these parts. The effects of three fundamental parameters (contact force, rotation speed, and tooth numbers) of the gear drive in line contact EHL on the combined stiffness and damping are then investigated. The results reveal that the small normal and tangential stiffness of the lubricant can alleviate meshing impact and shear vibration, while the impact and friction heat can be reduced by using an oil film with either a large normal damping or small tangential damping. Given that its amplitude and fluctuation are closely related to shear rate, effective viscosity, entrainment velocity, and curvature radii, the improved combined stiffness and damping can be obtained by rationally matching the geometric and operating parameters.
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