Showing papers on "Pressure angle published in 2021"

Computational Studies on Mesh Stiffness of Paralleled Helical Beveloid Gear Pair

Abstract: Considering the asymmetrical left and right tooth profiles including the transient curve at the tooth root region and the varying thickness along the axial direction due to the cone angle, we build the accurate profile curve model including the transient curve at the tooth root of helical beveloid gear with machining parameters to solve the problem of non-applicability of real digital model. According to the feature of gear shape varying along tooth width direction, we introduced the slicing method and derived its grouping formula. Finally, the efficient and accurate slicing-based mesh stiffness calculation model of paralleled helical beveloid gears was proposed using potential energy theory. Then, mesh stiffness was calculated using finite element contact model for comparison and verification. Finally, the impacts of macro geometry parameters including cone angle, normal pressure angle, helix angle, tooth width and addendum coefficient on single and total mesh stiffness were analyzed. The calculated mesh stiffness correlates well with the results from FEM with the maximum peak error is 4.8%. Results show that the tooth width shows an obvious incremental impact on average total mesh stiffness. When the pressure angle, helix angle, cone angle and addendum coefficient increase, the average total mesh stiffness increases first and then decreases. For the fluctuating value, it increases as the tooth width, helix angle and cone angle increase. However, the pressure angle and addendum coefficient show an opposite impact on the fluctuating value.

Predictions of friction and flash temperature in marine gears based on a 3D line contact mixed lubrication model considering measured surface roughness

Abstract: Wear and scuffing failures often occur in marine transmission gears due to high friction and flash temperature at the interface between the meshing-teeth. In this paper, a numerical solution procedure was developed for the predictions of transient friction and flash temperature in the marine timing gears during one meshing circle based on the 3D line contact mixed lubrication simulation, which had been verified by comparing the flash temperature with those from Blok’s theory. The effect of machined surface roughness on the mixed lubrication characteristics is studied. The obtained results for several typical gear pairs indicate that gear pair 4–6 exhibits the largest friction and the highest interfacial temperature increase due to severe rough surface asperity contacts, while the polished gear surfaces yield the smallest friction and the lowest interfacial temperature. In addition, the influences of the operating conditions and the gear design parameters on the friction-temperature behaviors are discussed. It is observed that the conditions of heavy load and low rotational velocity usually lead to significantly increased friction and temperature. In the meantime, by optimizing the gear design parameters, such as the modulus and the pressure angle, the performance of interfacial friction and temperature can be significantly improved.

Minimum friction losses in wind turbine gearboxes

Abstract: Improving the mechanical efficiency is not the most important objective in the design of wind turbine gearboxes since the available wind energy is abundant and costless. The most important criteria for dimensioning the gearbox are the fatigue strength—bending and pitting—, noise emission, vibrations, and maintenance requirements. Nevertheless, mechanical losses increase the lubricant temperature and induce thermal stresses, which increases wear and cracking risk. This means that friction losses should be reduced as much as possible, but always regarding the contact and tooth-root stress levels, as well as the other operating parameters which should be kept for ensuring the required operating conditions. In this paper, a study on the variation of the friction losses with the tooth shift coefficients is presented. All the other geometrical parameters—number of teeth, tooth height, pressure angle, helix angle, face width, and center distance—are unalterable, since all of them have been chosen according to more important design requirements. In addition, to keep the contact and tooth-root stress levels, the shift coefficients of the sun, planets and ring are calculated in such a way that the transverse contact ratios are kept, and therefore the critical load points for bending and pitting are also unchanged. The radial clearance is also kept in order to allow the proper evacuation of the lubricant. Finally, all the geometrical constraints (undercut, pointing, root interference, secondary interference, backlash) are also imposed. With all these restrictions, the optimal shift coefficients for all the gears are calculated to minimize the friction losses.

Analytical solutions and computational nomograms for maximum pressure angle for cam mechanisms for full and half cycloidal and harmonic motion curves

Abstract: High pressure angles in cams with roller followers still pose as a problem in cam projects. The main objective of this work is to deduce the maximum pressure angle equations for full and half cyclo...

Numerical Calculation Method of Meshing Stiffness for the Beveloid Gear considering the Effect of Surface Topography

Abstract: The tooth surfaces of beveloid gears have different topography features due to machining methods, manufacturing accuracies, and surface wear, which will affect the contact state of the tooth surface, thereby affecting time-varying mesh stiffness between mating gear pairs. Therefore, a slice grouping method was proposed in this paper on the basis of potential energy to calculate the total meshing stiffness of beveloid gears with the surface topography. The method in this paper was verified by finite element method (FEM). Compared with the calculation results of this paper, the relative error is 5.9%, which demonstrated the feasibility and accuracy of the method in this paper. Then, the influence of parameters such as pressure angle, helix angle, pitch angle, tooth width, fractal dimension, and fractal roughness on meshing stiffness was investigated, of which results show that pressure angle, pitch angle, tooth width, and fractal dimension have an incremental impact on the mean value of mesh stiffness. However, the fluctuating value of mesh stiffness has also increased as the pressure angle, tooth width, and pitch cone angle increase. Both the helix angle and the fractal roughness have a depressive impact on the total stiffness. But the difference is that, with the increase of the helix angle, the fluctuation of meshing stiffness has been decreased. Conversely, with the increase of the fractal roughness, the fluctuation of meshing stiffness has been increased.

Analysis of tooth stiffness of nutation face gear

Abstract: The purpose of this paper is to obtain the single-tooth stiffness, single-tooth time-varying meshing stiffness and comprehensive meshing stiffness of the internal and external face gears and to analyze the influence of the modulus, pressure angle and tooth width of each face gear on the single-tooth stiffness of the gear in nutation face gear transmission.,From the point of view of material mechanics, the gear teeth of nutation face gear are simplified as spacial variable cross-section beams. The shear deformation of gear teeth, the bending deformation of tooth root and the additional elastic deformation caused by the base deformation are gotten by simplified trapezoidal section method, thus the stiffness of nutation face gear teeth can be obtained. The comparison with finite element method results verifies the rationality of simplified trapezoidal section method for calculating the tooth stiffness of nutation face gear.,The variation of stiffness of internal and external face gears along the meshing line and tooth height in nutation face gear transmission is studied, and the variation laws of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained.,Nutation face gear transmission is a new type of transmission. The stiffness of face gear teeth is analyzed, and the variation rules of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained, which not only enriches the research of nutation face gear transmission but also has important guiding significance for the application of nutation face gear in engineering practice.

An analysis of the effect of pressure angle change on bending fatigue performance in asymmetrical spur gears

Abstract: In this study, the fatigue performances of symmetrical and asymmetrical spur gears were analyzed by performing single tooth bending fatigue tests. The gears tested were determined to be symmetrical...

Real contact ratio and tooth bending stress calculation for plastic/plastic and plastic/steel spur gears

Abstract: This paper presents an iterative method for calculating the effective contact ratio and the bending tooth stress for a pair of plastic/plastic and plastic/steel spur gears with an involute profile. In this method, the pinion and the gear are modeled, at each moment of the mesh cycle, as equivalent springs in parallel undergoing the same displacement along the line of action. This leads to the calculation of the bending stress by taking into account the number of teeth initially in contact and those which enter in contact prematurely. We also investigate the influence of certain gear parameters, such as, the number of teeth, the pressure angle, and the module on the behavior of a pair of meshed gears. In addition, the variation of the bending stress at the tooth fillet is investigated for a pair of plastic/plastic and a pair of plastic/steel spur gears, in order to determine the critical configurations for which the bending stress is maximum. In general, the results obtained from the present method also show that the stress variation in plastic/plastic gears differs markedly from that in plastic/steel gears.

A hybrid prognosis approach for life prediction of gears subjected to progressive pitting failure mode

Abstract: The surface/subsurface-initiated pitting is one of the most common failure modes in a gear. Although models for predicting the initiation of pitting are available, a model for predicting the growth of an existing pitting is not yet available. The present work proposes a hybrid prognosis approach for estimating the growth of pitting on the gear tooth surface, utilizing both empirical model (i.e., modified Paris law) and measured pitting area. The proposed approach is generic as the pitting growth rate is modelled as a function of gear material properties (such as Poisson’s ratio and modulus of elasticity), oil property (such as dynamic viscosity), gear geometrical parameters (such as pitch circle diameter, module, pressure angle and face width) and operating conditions (such as applied load and speed). The pitting evolution process is likely to be different for similar gear pairs due to inherent variations in material properties, manufacturing process, etc. Hence for a more accurate life prediction, the pit growth model parameters need to be updated, which is done using Bayesian inference.

Influencing factors of effective tooth depth in the cylindrical gear rolling process with axial infeed

Abstract: Working tooth depth is the key factor of affecting the transmission of motion and power for gear pair, which is closely related to the tooth depth of gear. To reveal the growth law of the formed teeth in the cylindrical gear rolling process with axial infeed, a sliding ratio model and contact stress model between tooth profiles of rolling die and workpiece were firstly derived based on the characteristics of the gear pair and rolling process with axial infeed. Rolling of cylindrical gears with module of 1.75 mm and pressure angle of 20° was then taken as an example to verify the above-mentioned models, and the influence of the working pressure angle, number of teeth of workpiece, and rotational speed of rolling dies on the effective tooth depth of the workpiece were analyzed by using finite element simulations (FES) and experiments. The results show that the effective tooth depth of the formed workpiece increases with the increases of the addendum modification coefficient of the rolling dies, number of teeth of the workpiece, and rotational speed of the rolling dies. The sliding ratio and contact stress decrease with the increases of the addendum modification coefficient of the rolling dies and number of teeth of the workpiece. Moreover, the effective tooth depth of the workpiece formed by the rolling dies with addendum modification coefficient of 1 is increased by 7.41% compared to that formed by the rolling dies with addendum modification coefficient of the 0.

Investigation of the effect of pressure angle on gear performance in asymmetric gears

Abstract: In this study, asymmetric gear mechanisms having the same working conditions, material and dimensions as symmetric gears but with different pressure angles were designed and compared with symmetric gear mechanism. The effect of the change in pressure angle and profile crowning has been studied in two spur gear pairs with different tooth numbers. First of all, symmetrical and asymmetrical gear geometries were created to meet the specified boundary conditions. Unlike other studies, contact stress, specific sliding, flash temperature, contact temperature, transmission error and gear mesh efficiency, which affect gear life and performance, have been investigated simultaneously with the change in load bearing capacity. The asymmetric gear design and profile crowning improved the factors effecting performance. Profile crowning has been shown that significantly reduces transmission error at all pressure angles. Furthermore it has been seen that is efective at low pressure angle in reduction of spesific sliding, flash temperature and contact temperature As a result of the change in the tooth profile by increasing the pressure angle, it was observed that the load bearing capacity, performance, life, efficiency and reliability increased in the asymmetric gear mechanisms with the same gear main dimensions as the symmetrical gears.

Meshing efficiency analysis of double helical gears considering tribo-dynamic coupling effect

Abstract: In order to obtain accurate meshing efficiency of double helical gears, a calculation method of sliding friction power loss is proposed considering the tribo-dynamic coupling effect. Based on the mixed elastohydrodynamic lubrication (EHL) theory, the initial friction coefficient of tooth surface is obtained and the friction excitation is calculated. Considering the tribo-dynamic coupling effect, a sixteen-degree-of-freedom tribo-dynamic model of double helical gear pair is established, including time-varying mesh stiffness, friction excitation, backlash and transmission error. The tribo-dynamic behaviours of gear pair are analysed before and after coupling, and then the sliding friction power loss and meshing efficiency of double helical gears are obtained. The research results show that after tribo-dynamic coupling, the friction coefficient and friction excitation of double helical gear pair increase, and the meshing efficiency decreases. The meshing efficiency of gear pair increases with the increase of helix angle and pressure angle, and decreases with the increase of surface roughness.

The Influence of Pressure Angle of Spur Gears on Bending Stress Considering the Effect of Root Fillet Radius

Abstract: Tooth breakage from excessive bending stress and surface pitting from excessive contact stress are the two primary fatigue failure modes for gears. Tooth breakage will end the gear life, so gear bending stress has to be accurately calculated for reliable operation. Many efforts have been made to increase gear bending strength including improving gear material property. With increasing demand for high power density gear applications, the need to optimize gears for minimum stress becomes increasingly important. It is imperative to understand the effect of gear parameters on bending stress in the initial stage of designing gears. Gear pressure angle is an important parameter affecting tooth bending stress. Because the critical section occurs in the gear root fillet, the root fillet radius largely affected by tool (hob) tip radius also has a great significance for improving the bending strength. The maximum tool tip radius will vary with the pressure angle changing due to the geometrical relationship of basic rack. This paper investigates the influence of pressure angle of spur gears on bending stress considering the variation of root fillet radius, and provides a recommendation on how to optimize the pressure angle for high bending strength gears. For analysis and validation of results, three methods of predicting bending stress– ISO standard, 3D-TCA (tooth contact analysis) method and Finite Element Analysis are applied and discussed.

Theory and experimental research on spiral bevel gear by double-side milling method

Abstract: In this paper, a double-side milling method on spiral bevel gear is proposed. First, according to the tooth taper processed by double-side milling method, the influence of dedendum angle on the tooth taper was researched. Taking cut parameters into comprehensive consideration, the geometric parameters were designed through the inclination of root line and modified mean point in which machine setting parameters calculated was selected. Only the modified mean point met the meshing equation, and the error of pressure angle would increase as far away from the modified mean point in tooth line. The error would lead to bias in contact. A helical correction motion was introduced and the influence of helical motion coefficient on tooth surface topology was studied. Based on the meshing performance, a suitable coefficient was calculated. Finally, an example was illustrated. The experimental results were consistent with the theoretical analysis. The validity of the proposed method is verified.

Basic theory and design method of variable shaft angle line gear mechanism

Abstract: In this paper, a novel line gear mechanism is proposed; it is called the variable shaft angle line gear mechanism (VSALGM). VSALGM has two rotational degrees of freedom, one is the rotation of the two gears with a constant transmission ratio, and the other is the relative swing of the two gears shafts. First, a novel contact model of VSALGM composed of one driven contact curve and one driving line teeth working surface (DLTWS) was proposed. With the concept, the basic design equations for VSALGM were derived on the basis of the space curve meshing theory of line gear. Moreover, the design criterion of pressure angle for VSALGM was analysed and proposed on the basis of the contact model. A basic design method for VSALGM was thus developed. A design example was given, and prototypes were manufactured using three-dimensional (3D) printing. Kinematic experiments and gear contact spot testing were carried out on a self-made kinematic test rig by the prototypes. The results show that the VSALGM designed in this paper can achieve a continuous, smooth and stable meshing transmission while the shaft angle is continuously changed within its setting range.

Internally-Balanced Displacement-Force Converter for Stepless Control of Spring Deformation Compensated by Cam With Variable Pressure Angle

Abstract: The force required to drive a mechanism can be compensated by adding an equivalent load in the opposite direction. By reversing the input and output of the load compensation, we proposed the concept of a displacement-force converter that enables the deformation of the elastic element to be controlled steplessly by a minimal external force. Its principle was proved in our previous study, but challenges arose owing to the use of a wire and pulley. Here, we introduce a new compensation method using a noncircular cam that generates a compensation torque due to the contact force from the follower, which is split in the tangential direction of the cam by the pressure angle varying at rotation. Using a prototype for proof of concept, the maximum control force required for the extension of the spring was successfully reduced by 23.2%. Furthermore, uniform forces were obtained between extension and compression so that the difference between them decreased from 543% to 49% relative to compression. Thus, actuators and current supplies requiring less power could be selected. Moreover, the prototype model was incorporated into a variable stiffness mechanism of a soft robotic gripper as a wire tensioner to show the expandability of the displacement-force converter.

Studying the Stress–Strain State of Gear Teeth

Abstract: An analytical method for determining the compliance of gear teeth, the load distribution factors, and the bending stresses is proposed. To solve the problem about the stress–strain state of the gear tooth, the latter is represented as a wedge with the angle of the roll corresponding to the pressure angle of the involute tooth. The mathematical model of the loaded tooth is given in the form of an inhomogeneous Volterra integral equation with the kernel depending on the difference in the arguments solved by the method of operational calculus. Using the results of the study in strength evaluation of gear trains allows more accurate determination of their loading capacity.