Gear Geometry Research Articles

Computerized Generation of Nonstandard and Asymmetric Involute Spur Gears Based on Rack Cutter Parametric Tracing

In the field of gear design, to apply any form of analysis (such as FEA, dynamic, and stress analyses), a delicate and accurate representation of the gear geometry is essential. It is the foundation for any design modification attempts, and any approximation of the tooth profile must be avoided. In the literature, many approximations were held to the involute tooth geometry, particularly in the filet region, where it was simply represented by a straight line or circular arc instead of a true trochoidal arc from a generation process. This approach might lead to inaccurate bending stress results, as it fails to detect the impact of the undercut or the profile correction process. Other common approximations have been widely observed in the literature, such as utilizing an asymmetric cutter to simultaneously generate the two sides of the asymmetric gear. Moreover, the graphical rack-cutter generation technique was widely used to generate involute gears. This technique, although shown to be accurate in generating a 2D standard tooth, is time-consuming as it necessitates the use of source code, a programming language, a graphic processor for displaying computer graphs, a post-graphic processor for eliminating unrelated lines, and a post-process for exporting the tooth geometry to CAD software. This research presents an alternative direct computerized generation method that is shown to be accurate, generate both 2D and 3D gears, and be significantly more time-efficient. Moreover, a novel technique to generate a fully asymmetric nonstandard tooth (pressure angle, trochoidal fillet, and shifting factor) is proposed using two half-cutters.

Possibilities of creating spur gear geometry

The swift advancement of science in computer technology enables the resolution of increasingly intricate engineering challenges through contemporary calculation techniques. Numerical methods employed in mathematics are among these. The finite element method, also known as FEM, is widely recognized as a prevalent numerical technique. The Finite Element Method (FEM) is a versatile technique employed to tackle diverse engineering challenges. These may include problems related to flexibility, strength, heat transfer, and a variety of gear solutions. The Finite Element Method is primarily employed in this domain to address deformation and stress analyses pertaining to the gears under examination. Numerous programs are available for addressing issues through the Finite Element Method. However, a crucial prerequisite for effectively analyzing deformation and stress in gearing is the precise definition of the computer model representing the gear system under investigation. The focus of the article is on discussing the process of designing gear geometry within CAD software systems.

Experimental investigation of the load-carrying capacity of machine-hammered surfaces with variation of the process parameters

If the load exceeds the load carrying capacity of the tooth on the gear, tooth flanks or tooth root damage occurs. The resilience of gears can be increased with various manufacturing and finishing processes. Machine Hammer Peening (MHP) is currently being researched as an alternative to shot peening to increase the load carrying capacity of gears. Due to adjacent teeth, the machining of the tooth root and tooth flank is only possible with an impact angle β > 0 ° between the hammer head and the normal of the machining surface, depending on the gear geometry. The aim of this work is to gain knowledge about the rolling sliding resistance of hammered contact surfaces under the influence of different impact angles and machining directions. For this purpose, three impact angles and two machining directions are varied during the machining of the analog specimens by the MHP. In fatigue strength tests, the hammered test specimens are compared with a ground and a shot-peened variant. The fatigue strength tests show that the hammered test specimens with an impact angle β ≤ 30 ° achieve a higher number of load cycles on average than the ground reference variant (increase of up to 100 %). For the transfer of the results to the process for hammered tooth flanks, it can be hypothesized that for impact angles β ≤ 30 °, the machining direction locally on the flank in the opposite direction to the sliding speed leads to a higher rolling sliding strength in the range of short time fatigue strength.

Investigation of tooth thickness faults in small plastic gears

In this article we investigated the tooth thickness faults of small plastic gears. Faults in tooth thickness can lead to excessive heating and failure of the gears. It is therefore worth investigating how these can be detected. For the measurements, we used an equipment that is capable of measuring the recirculation torque to investigate the effects of faults on the teeth of small plastic gears. For the analyses, gear geometries were created using 3D CAD software that included a tooth that was different from the standard tooth thickness. The other teeth of the gears were the standard size. The thickness of the faulty tooth was either 0.1 or 0.2 mm less or more than the standard. These gears were analysed by pairing them with gears that did not contain faulty teeth.

Reverse engineering of a toothed gear

With the rapid development of modern industry, the need for spare parts has increased. Most mechanical systems have transmission components which are composed of toothed gears. In most cases, the manufacturer of the spare part does not exist on the market and the need to reproduce the failed part needs to be met. Usually, toothed gears are obtained using special cutting machines, like Gleason, Lees-Bradner, and Pfauter. To be able to reproduce the part by using a common manufacturing process, the current paper presents a RE method for obtaining the 3D geometry of a toothed gear in the scope of machining the part using a CNC 3-axis mill. CAD software and 3D scanning technology is used to recreate the gear’s 3D model and ensure accurate dimensions for the gear teeth, including tooth spacing, depth, and angle.

Parameters impact analysis on contact characteristics of intersected beveloid gear and involute cylindrical gear

According to gear geometry and tooth contact analysis (TCA) theory, the TCA model of intersected beveloid gear and involute cylindrical gear pair is built. The formulas for calculating curvature and contact ellipse at contact points are derived, and the shape and region of contact ellipse are determined. Then, the impacts of cone angle, helix angle and installation errors on contact characteristics are studied by numerical examples. The finite element model of gear pair is established to carry out the loaded tooth contact analysis (LTCA) and verify the accuracy of theoretical TCA model. The results show that gear pair with small cone angle or big helix angle has wide contact area, large carrying capacity and high transmission quality. The shaft angle error may cause the edge contact of gear pair, while the axial position error has limited effect. The research can provide input parameters for the study of tooth surface wear mechanism and dynamics in the future work.

An Advanced DEM-FEM Method for Herringbone Gear in Shot Peening

Introduction: The complex geometry of herringbone gear can lead to uneven surface strengthening, which affects the overall effect of treatment. Methods: A discrete element model (DEM) of shot peening for herringbone gears was developed, incorporating accurate gear surface parameters to study impact characteristics along the tooth profile. A finite element model (FEM) was created for small local units of the gear surface to calculate the residual stress and roughness. Results: There are a large number of low-velocity shots at the root of the gear, and the closer to the top of the gear, the higher the impact velocity of the shots, but the number of impacts also decreases. The surface roughness Sa near the root of the tooth is the smallest, the Sa at the pitch circle is the largest, and the Sa at the top of the tooth is intermediate. However, the residual stress levels at different positions of the tooth surface are not significantly different. Conclusion: The difference in tooth surface roughness of herringbone gear is the synergistic effect of shot impact velocity and shot frequency, but this synergistic effect has no significant effect on the stress after shot peening.

Geometric synthesis in the profile of the involute tooth for improving the performance of bending in the material of the spur gear

Abstract Transferring power from one rotational axis to another in numbers of axes requires portable equipment such as gear. In operation, involuted teeth were reported as bending and pitting failures. Bending fatigue causes gear tooth cracks at the root, and pitting causes more wear. This bending failure was reduced with the help of material selection, geometric modifications like changes in profile shape, transmission error, module, tip relief, pressure angles, and the application of forces. A normal force acting on a gear tooth gets resolved into three components, like tangential, radial, and axial. When it comes to enhancing bending strength, the geometric forms of profiles have a significant impact. A variety of tools and techniques, including hobbing, shaping, grinding, etc., are available at the fingertips for altering gearing tooth. Changing the borders of gear tooth profiles with hobbing tools is becoming more popular among the authors as a means for altering gear tooth. There are four distinct geometric profiles that may be used to change gear geometries and enhance bending strength by reducing stress on the tooth. These profiles include trochoidal, circular, bezier, and cubic spines, and they are implemented using a hob cutter. It is noteworthy to note that these designs boost strength by integrating the shape of number of teeth on the spur gear. This study compares the number of teeth on the gear’s pinion with other geometric characteristics, including pressure angle, module, etc., in order to discover the optimal way for modifying the involute tooth of the gear in order to increase the bending resistance effectively of the spur gear. For the purpose of boosting the strength of gear material, a number of research endeavours have utilized circular profiles; nonetheless, this profile is older than the Bezier curve profile. Here, Bezier curves with a three-and five-point profile give better results than other profiles with significant reductions in bending stress for the same quantity of tooth on the gear.

Tooth friction in spur gear transmission. From local to mean tooth friction loss

In a gear transmission, power losses come from a variety of sources, classified as load-dependent and no-load-dependent losses. No-load-dependent losses are the ones that remain constant regardless of the applied load, such as losses due to drag in rolling element bearings, seals, churning and/or windage for gears. Load-dependent losses include friction losses due to sliding and rolling between gear teeth. These losses are particularly important in some gear transmissions because of their direct impact on overall efficiency and thermal behaviour. Consequently, knowledge of the friction coefficient associated to this loss is of major interest for optimising gears (geometry, surface finish, lubrication, etc.). In this article, a new method is proposed for predicting the mechanical efficiency losses associated with the mean coefficient of friction for pairs of cylindrical gears. It is based on a model developed previously to estimate the instantaneous tooth friction along the plane of action in gears. This model takes into account the lubricant shear and the friction on contacting asperities. The proposed mean friction coefficient is deduced from the instantaneous friction coefficient using specific calculations, particularly at the pitch point. To verify the method, the estimated results are compared with those in the literature calculated for gears and operating conditions common on FZG test rigs.

High-ratio planetary gearbox with EC gearing for robot applications

The drive system of robots and robot-like systems (RLS) is often designed with a combination of an e-motor and a gearbox with a high transmission ratio to optimize performance. The various types of possible robot gearboxes can be selected based on their characteristics, which strongly influence the performance of the entire robotic system. Planetary gear drives have advantages due to their high efficiency and low design complexity. Disadvantageous is the low transmission ratio per stage and the resulting large design space required with the currently predominant involute gearing. Using special tooth profile shapes, such as the eccentric cycloid (EC) gearing, enables a high transmission ratio per stage to be achieved, thus reducing the design space required. In order to evaluate the design, a description of the geometry and characteristics of the EC gearing is necessary. The application-optimized design can be made accessible on an interdisciplinary basis using a suitable description language for the product development of the complete robotic system. The paper shows the design and analysis of a planetary gearbox with a high transmission ratio for applications in robotics. The planetary gear stage is designed with the EC gearing, which offers advantages compared to the involute gearing. The performance of the selected gearing is evaluated based on various characteristics. This allows advantages to be identified compared to the established types of transmission for robots and RLS. Overall, the paper presents a new robot gearbox with a comprehensive description and analysis directly accessible for simulation or production using additive manufacturing.

Evaluating the Accuracy of the Reverse Engineering Process of Worn, Non-Standard Spur Gears—Pilot Studies

For years, gears have been self-made by many industrial plants as substitutes (custom spare parts) for original parts from the manufacturer. This common practice uses a process called reverse engineering (RE). However, in the available scientific database, it is difficult to find articles about the accuracy of such a process. And while it is obvious that in order to obtain the most accurate quality of such a process, modern measurement techniques (coordinate, optical) should be used, most companies cannot afford to purchase such equipment. Reproducing gear geometry is difficult. But the issue of RE of non-standard gears seems to be even more difficult. This is why the authors undertook pilot studies to assess the accuracy of the RE process of worn, non-standard spur gears using conventional techniques and measuring instruments. Eight gears were tested, the module of which ranges from 1.020 to 4.98 mm. The key parameter was selected to estimate the accuracy of the process—the base pitch. The goal is to determine the value of the profile angle. Eleven models were proposed to estimate the nominal tolerance field, using various types of random data distribution. The tested gears were made in IT grade: 6, 7, 8, and 9 according to DIN 3961. Vernier disk micrometers were used for research. It has been shown that the nominal module does not have to be treated as a random variable in the population. Equation of identity was developed, allowing conversion of any gear with specific values of geometric parameters into an identical gear with alternative values of these parameters. The most effective estimating model was selected taking into account the symmetric Student–Fisher distribution with a confidence level of 60%. However, it is not possible to correctly reproduce the geometry of the gear wheel in that way. The following aspects should be taken into account: type and degree of mode of failure, number of load cycles, rotational speed, direction of rotation, material, type of thermochemical treatment, and torque. A simulation using FEM should be performed to determine the fatigue plastic deformations and diagnose their impact on the geometric dimensions of the gear wheel.

Анализ контакта конических зубьев шестерен на основе машинного обучения

In this paper, we study the analysis of the contact of bevel gear teeth based on machine learning methods. Bevel gear teeth are widely used in various industrial and mechanical systems to transmit rotational motion with high precision and reliability. Traditional methods of gear contact analysis are based on mathematical models and empirical formulas, which may be limited in accuracy and applicability. In recent years, machine learning has become a powerful tool in the field of engineering and mechanics to more accurately model and predict the contact behavior of bevel gear teeth. The paper proposes the use of machine learning methods, such as neural networks or deep learning algorithms, to train models capable of analyzing the contact of bevel gear teeth. Wear, load, and gear geometry data can be used to train models, which can then predict contact parameters and evaluate contact performance.

Flank fractures on spiral bevel gears—transfer of analytical methods for the estimation of residual stresses from cylindrical gears to bevel gears

The classic flank and root load capacity calculation on the component surface forms the basis for the design of power gears today. However, flank fractures also occur in practice, particularly with large-module gears and/or low case-hardening depths. It is a fatigue damage with crack initiation in the tooth interior, its prevention requires the calculation of the stresses below the surface. In addition to understanding the load stresses, the inhomogeneous load bearing capacity and the residual stress profile in case-hardened gears are also of great importance. There are various calculation approaches for this in the area of cylindrical gears, but these have not yet been transferred to the complex geometry of spiral bevel gears. The focus of this publication is on estimating the residual stresses in the tooth volume by generating a three-dimensional residual stress tensor field in the bevel gear tooth based on the two-dimensional calculation approaches used to date on cylindrical gears. In combination with the stress tensor-time curves from a tooth contact simulation with the LTCA tool BECAL, this can be fed into different failure hypotheses, which is illustrated using an example.

THE DRIVE OF THE MOLDING MACHINE: THE POWER PARAMETERS OF THE SHAFTS AND THE CALCULATION OF GEARS

The drive of the technological machine is considered. This is a cutlet forming machine. The drive of the machine has two stages. The power on the drive shafts is given as a function of the power on the motor shaft. The torques on the intermediate and slow-speed drive shafts are analyzed. They are represented as a function of power, speed and gear ratio. Examples of calculating the geometry of gears are given. These gears are included in the drive. The material is used in practical classes.

Investigation of the Influence of Contact Patterns of Worm-Gear Sets on Friction Heat Generation during Meshing

Friction losses and scuffing failures are interesting research topics for worm gears. One of the factors leading to scuffing is the heat generated in the contact of gear teeth. The contact geometry of worm gears is complex, leading to high friction between contact surfaces. High friction between contact surfaces during operation generates heat friction that causes the occurrence of scuffing, which in turn determines the scuffing load capacity. To analyse the thermal characteristics of a worm-gear pair and the thermal behaviour of contact teeth, a direct-coupled thermal–structural 3D finite element model was applied. The heat flux due to friction-generated heat was determined on the gear tooth to investigate thermal characteristics and predict transient temperature fields. This study permits an in-depth understanding of the temperature fields and the friction heat generation process. Also, better control of the contact pattern between worm-gear teeth would decrease friction heat and increase scuffing load capacity. This paper investigates the transient thermal behaviour among different pinion machine setting parameters that can result in an optimal tooth-contact pattern that produces a lower temperature field, thus achieving higher transmission efficiency.

Mathematical modeling and simulation of generation milling process to manufacture complex face gear surface through multi-axis machine kinematics

Manufacturing of face gear is a complex process, due to its varying geometry, hence the application is not wide as conventional gear geometry. The developments in analytical tools and kinematics of the CNC machine tools motivate researchers to explore the manufacturing process and associated applications. This article presents an efficient method for the generation milling of spur face gear utilizing a nutating head multi-axis CNC machine tool where the tool swings about an arbitrary axis in an inclined plane. The mathematical model of the disk milling cutter and face gear geometry were derived from the shaper geometry by applying the theory of gearing, equation of meshing and coordinate transformation. The cutter location (CL) data was evaluated by aligning the tool orthogonal unit vector and the tooth surface normal vector at the contact point by calculating the appropriate transformation matrices. The evaluation of machine coordinates on a multi-axis CNC milling machine was analyzed with respect to the machine pivot point and the axes movement during generation milling for the face gear drive was studied on the nutating head machine. The NC data is derived from the CL data using the inverse kinematics and the machining simulation was carried out using suitable software. The tooth surface deviation of a maximum of 43.5 μm was observed between the simulated model and the theoretical model, which is well within the requirement of roughing. The generation milling process with the proposed machine configuration is concluded as a profound face gear manufacturing technique.

Assessing the impact of manufacturing uncertainties on the static and dynamic response of spur gear pairs

The present research activity aims to bridge the gap between gear geometry tolerances, eventual test rig uncertainties, and the resulting gear excitations represented by the static transmission error (STE) as the main source of whining noise. This article offers a detailed experimental investigation addressing the impact of manufacturing errors in the form of lead slope and profile slope errors. One of the major contributions of this article is related to the number of carried measurements, including six spur gear pair configurations. While most literature focuses on gear defects related to wear, cracks, or pitting, this study emphasizes the need to consider gear micro geometry tolerances to minimize vibroacoustic response at the source. The experiments under static conditions are conducted for various operating conditions and compared with numerical computational schemes. Latin Hypercube sampling is selected to compute the peak-to-peak static transmission error bounds. Results yield reliable prediction of the gear STE response even in the presence of deviations. The manufacturing errors cause different trends of STE response, with up to 8 μm difference at low torque. The robustness of the predictive numerical tool is validated, which enables further confident parametric studies. Finally, the dynamic behavior is investigated. Important differences are detected for gears having the same macro geometry and different manufacturing errors. The meshing excitations resulting from gear uncertainties lead to notable fluctuations in the dynamic responses.

Development of analytical models for tip, root, and end relieving of spur gears by pulsed electrochemical finishing process

This paper describes analytical modelling for the non-contact tip, root, and end relieving of spur gears and their associated volumetric material removal rate (MRR) by the pulsed electrochemical finishing (PECF) process. The models were developed using Faraday’s law of electrolysis and involute geometry of spur gears. The developed models are validated experimentally using the innovatively designed and developed cathode gears and experimental apparatus by varying voltage, pulse-on time, and pulse-off time at four levels each. It found that minimum prediction errors for the developed models for the amount of tip, root, and end relief are 0.8%, 0.3%, and 1.3%, respectively, and minimum prediction error for models of volumetric MRR of tip, root, and end relief are 6.9%, 0.6%, and 9.8% respectively. A study of microgeometry along the profile and lead direction of spur gear confirmed that the PECF process not only successfully imparted tip, root, and end relief but also reduced their arithmetical average roughness and maximum height by 61.1% and 62.5% for tip relief, 67.7% and 67.8% for root relief, and 63.8% and 66.6% for end relief respectively. It also removed hob cutter marks and cracks revealed from the comparison of surface morphology of spur gear flank surfaces before and after tip, root, and end relieving. Maximum values of % reductions in maximum height and arithmetical average roughness occurred for pulse-on and pulse-off times as 3 and 4 ms (i.e., 43% duty cycle). The developed models will be very useful in designing or predicting the amount of tip, root, and end relief that can be imparted for a given modification duration. Conversely, they can be used for parametric optimization of the PECF process and to compute the required duration for the PECF process to impart the desired amount of tip/root/end relief to spur gears.

A non-restrictive approach of gear geometry calculation for plastic gears

AbstractFor the unrestricted calculation of gearboxes with a constant transmission ratio, a parameter radius ratio is developed. For this purpose, a parameter radius ratio is introduced that has a piecewise continuous and differentiable domain of definition. Thus, the parameter can be used efficiently in the algorithmic implementation for the optimisation of a contact point of two gears. Furthermore, the data processing of the surface intersection is shown. Through direct surface conjugation, two paired gears can always achieve a line contact, therefore an optimal power transmission can be achieved regarding the technical properties. The procedure is demonstrated with a practical example of a planetary gear with skewed planet.

A New Experimental Methodology to Study Convective Heat Transfer in Oil Jet Lubricated Gear Units

The purpose of this study is to generate some experimental data associated with the thermal heat exchange between an oil jet flow and a rotating gear. To this end, a specific test bench was designed. The principle of this test bench is to inject oil heated to a temperature of about 80 °C onto a rotating test sample at ambient temperature. Temperature measurements of the oil via injection nozzles and the rotating component allow the determination of the heat flow between these elements using a numerical method developed to this end. This test rig enables the study of the parameters that may affect heat exchange, such as oil flow rate and injection temperature, nozzle geometry and position, gear rotational speed and tooth geometry, or oil characteristics. In this study, three of these parameters were investigated, namely the test sample rotational speed, the oil flow rate, and the oil jet velocity. The experiments were conducted on an aluminum disc and spur gear. Subsequently, the experimental results were compared with existing models that represent the convective exchanges between oil and a gear. Some discrepancies between existing models and experimental results appear at high rotational speeds, underlining that the convective heat transfer does not always increase with this parameter.