Gear Hobbing Research Articles

Mathematical Modeling and Generating Method of Hourglass Worm Gear Hob’s Rake Face Based on a Rotating Paraboloid Surface

The rake angles on both sides of the cutting edges of the hourglass worm gear hob significantly influence its cutting performance, which, in turn, plays a decisive role in the surface quality of the machined worm wheel. To balance the rake angles along the tooth height direction of each hob tooth and enhance the overall cutting performance of the hob, this paper proposes a method that utilizes a rotating paraboloid surface to generate the helical rake face of the hourglass worm gear hob. First, the conjugate condition equations for the rake face generated by the rotating paraboloid surface are derived. A mathematical model for the helical rake face of planar double-enveloping hourglass worm gear hob is established. This study explores the influence of two machining parameters on the rake angle, specifically the milling drive ratio coefficient k and the geometric parameter of a parabolic milling cutter p. Through a systematic analysis of the variations in rake angle at the dividing toroidal surface and along the tooth height direction, the optimal parameter values were identified as k = 0.9115 and p = 0.6834. The results show that, after optimization, the hob rake angle range is around ±4.7°, with a maximum rake angle difference of 6.3072° along the tooth height direction, and the rake angles on both sides of the teeth are more balanced. The structure of the rake face is more reasonable, reflecting the feasibility of rotating paraboloid tools for forming tools in the machining of complex surfaces.

Intelligent improvement of gear hobbing process based on the TRIZ method

Intelligent improvement of gear hobbing process based on the TRIZ method

Evaluation of machine tool dynamics in dry gear hobbing considering time-varying thermal effects

Effective stability analysis strongly depends on accurately predicting machine tool dynamics. However, the nonlinear thermal effects during the machining operations present a significant challenge to accurately modeling the machine tool dynamics. To this end, the evolution of the machine tool dynamics under the thermal growth during the dry gear hobbing process is investigated, and a rapid evaluation model of the temperature-dependent dynamics is developed. Firstly, a preliminary test was conducted to explore thermal effects on the machine tool dynamics. Then, the free vibrations at the spindle nose during the hobbing operations were filtered, and the corresponding modal parameters were estimated. Subsequently, the influence of temperature rise on the modal parameters is analyzed. The results show that the first- and third-order natural frequencies increase by 142 and 95 Hz, respectively, and the damping ratios for all modes are reduced with the machine tool temperature rise. Finally, the relationship between the feature temperatures and modal parameters is described using the multi-output Gaussian Process regression (MOGPR) model. The overall prediction accuracy is 95.6 %, and the relative errors in the test data set are within 10 %. The findings can provide an essential basis for the machining stability analysis of dry gear hobbing.

Gear Hobs-Cutting Tools and Manufacturing Technologies for Spur Gears: The State of the Art.

The present work aims to provide the readers with a bird's-eye view of the general domain of cylindrical gear manufacturing technologies, including the cutting tools used, and related topics. The main scientific sources are explored to collect data about the subject. A systematization of the scientific works is completed, to emphasize the main issues the researchers have focused on in the past years in the domain. Several specific aspects are investigated: chip-forming process, cutting tool lifetime, the materials used to produce gear hobs, temperature and lubrication, the cutting tool geometry, cutting parameters, design methods, and optimization. Some gaps in the research have been identified, which are mainly related to the gear hob's design. These gaps, the organization of knowledge, the current requirements of the industry, and the actual socio-economic priorities form the basis for identifying new scientific research directions for the future in the area of spur gears manufacturing technologies and cutting tools. The main output of this work is a frame to guide the development of scientific research in the domain of spur gear production.

Chatter and Surface Waviness Analysis in Oerlikon Face Hobbing of Spiral Bevel Gears

A vectorized analytical model for the cutting dynamics in the spiral bevel gear face hobbing process has been developed, which is based on machine tool kinematics and vibration vectorization. The structural modal parameters of the cutter head spindle system are obtained through experimental modal analysis with hammer impact testing. The analytical model is utilized to simulate the generation of simulated vibration acceleration signals during spiral bevel gear hobbing. A wavelet threshold denoising method is applied to process the simulated vibration signals of the spiral bevel gear face hobbing with added white noise. Signal processing methods, including short-time Fourier transform are employed for time-domain analysis, frequency-domain analysis, and time–frequency-domain analysis of measured signals and simulated signals, thereby extracting the corresponding statistical features. In addition to the results of the experimental modal analysis, the causes of chatter in spiral bevel gear hobbing are discussed in detail, revealing that the main factor is cutter head vibration in the Y direction of the Hunan ZDCY CNC EQUIPMENT YKA2260 machine tool used in this research. The error in the time-domain characteristic parameters between simulated signals and measured vibration acceleration signals is within 15%, with a difference of 3.5% in spectral peak values. The predicted tooth surface morphology from simulation matches the actual morphology on the workpiece, comprehensively validating the reliability of the cutting dynamics model for the spiral bevel gear face hobbing process. Another conclusion drawn from numerical simulation experiments is that the amount of tooth surface waviness of the spiral bevel gears is the ratio of tool chatter frequency to cutting fundamental frequency.

Experimental Investigation on Surface Characteristics of Finish Hobbed Gear using Grey Relational Analysis

Introduction: Spur gears are important for transferring motion and power among shafts. The surface characteristics of these gears are important for their life and smooth operation. To improve profitability and customer satisfaction, a study was conducted to analyze the surface quality of spur gears produced through CNC hobbing machining. Objectives: The objective this investigation is to conduct experimental trials to estimate the best hobbing parameters to minimize surface roughness and microgeometric deviations. In this investigation, effect of varying cutting speed and feed rate on surface finish have been reported. Methods: An experiment are conducted according to Taguchi L9 experimental design. Grey Relational Analysis is performed to estimate the optimum machining parameters. Results: The experimental finding reveals, at cutting speed 400 rpm, the feed rate 8 mm/min, and depth of cut 3.91 mm gives good quality of surface (Ra 0.5530). The gear hobbing process has increased to a greater level of performance. The roughness of the flank surface and microgeometry deviations decreases with an increase in hob cutter speed. Conclusions: This ultimately reduces the inherent vibrations between the hob cutter and the gear blank, thus minimizing microgeometric deviations. The variation in feed rate was noticed and had a very significant impact on the efficiency and surface quality of the gear. The study recommends that a cutting speed of 400 rpm is the most effective for obtaining the best results.

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.

Prediction of pose- and position-dependent tool-tip dynamics in high-speed dry gear hobbing

High-speed dry gear hobbing is an advanced and efficient machining technology for automotive gears. Frequent changes in the hob mounting angle (tilt angle) and shifting position result in variations in the tool-tip frequency response function (FRF), which inevitably modify the hobbing stability boundary. To construct an accurate stability boundary for high-speed dry gear hobbing, the primary objective is to predict the tool-tip FRF related to different combinations of hob tilt angles and shifting positions, that is, pose- and position-dependent tool-tip FRF. This study proposes a novel tool-tip FRF prediction strategy that combines multi-output Gaussian Process regression (MOGPR) and Receptance Coupling Substructure Analysis (RCSA). First, the FRFs at the tips of the hob-mounting base were estimated through a series of impact tests under a limited combination of hob tilt angles and shifting positions, and the corresponding modal parameters were identified. The MOGPR model was then leveraged to reveal the mapping relationships between the modal parameters, hob tilt angles and shifting positions. Based on this, the hob-mounting base pose- and position-dependent FRFs can be obtained using the modal fitting technique. Subsequently, the pose-and position-dependent tool-tip FRFs were obtained by coupling the receptances of the hob-toolbar assembly with the fitted hob-mounting base FRFs through the RCSA. Finally, a series of impact tests were conducted to verify the effectiveness of the proposed method. The prediction of pose- and position-dependent tool-tip dynamics can provide a foundation for accurately modeling hobbing stability.

Spatial distribution model of thermal load for high-speed dry hobbing tool based on probability density function

High-speed dry hobbing is a clean and environmental-friendly gear machining process, but thermal dissipation inefficiency accelerates tool wear and shorten tool life which is difficult to be effectively inhibited due to its complex distribution characteristics. This paper proposes a thermal load distribution model based on probability density function, describing the spatial distribution of thermal load on tool and providing theoretical support for predicting the distribution of thermal load. Firstly, conducting a finite element simulation analysis based on a mathematical model of high-speed dry gear hobbing process; Secondly, the influence of various parameters on the constructed model is analyzed, and the Bayesian optimization algorithm is utilized to optimize the model parameters. Finally, the model is validated at the micro and macro level. The results show that the average coefficient of determination of the model is greater than 0.86 in micro level. And the average fitting error is less than 6 °C in macro level, besides, the average relative error is less than 15%. The description of the uneven thermal distribution on tool is obtained with probability density function, it provides a theoretical support for the prediction and further optimization of thermal load on tool under multiple parameters in the future.

A Study on the Effect of Gear Hobbing Process Parameters on the Residual Stress of the Tooth Root

The root residual stress during gear machining has a significant impact on the bending fatigue performance of the gear. The process parameters of gear hobbing (hob speed, axial feed speed, and radial cutting depth) directly affect the residual stress of the tooth root. To investigate the relationship between the process parameters of hobbing and the residual stress of the tooth root respectively, an analysis of an orthogonal and single factor was conducted in the hobbing experiment, taking into account the interactions among factors, which revealed the influence rule and primary–secondary relationship of the process parameters on the residual stress of the tooth root. The importance coefficients of the process parameters on the residual stress of the tooth root were calculated using the Least Absolute Shrinkage and Selection Operator (LASSO) method. The results indicate that the residual tensile stress at the tooth root increases with an increase in the hob speed and axial feed speed within the selected range but decreases with an increase in the radial cutting depth. The influence of the process parameters on the residual stress of the tooth root can be ranked as follows: hob speed (importance coefficient 0.460), axial feed speed (importance coefficient 0.278), and radial cutting depth (importance coefficient 0.262). This research provides a basis for improving the residual stress of the tooth root and enhancing the anti-fatigue manufacturing of gears, thus holding significant research value.

Gear Hob Base Worm Modelling from a Straight Toothed Generating Rack

The precision of a gear realized by hobbing is mainly influenced by the precision of the base worm, the adequate form of the rake face and the number of resharpenings. Gearing theory states that the base worm of a gear hob must be of involute type. Despite of this, manufacturing technology often admits a convolute worm as gear hob base worm. Due to the rake face grinding technology, there appears a difference between the theoretical and the real surface. On the other hand, the profile modification of the cutting edges occurs due to the re-sharpening. As a result, the cutting edges cannot reproduce that initial basic worm surface from which the gear hob was derived. In our opinion, the computing of the generating surfaces of the basic worm is still an unsolved problem. This paper deals with the study of a worm derived from a straight toothed generating rack. The incidence of an involute worm and that developed from the generating rack is investigated.

Workpiece Quality Prediction for Gear Hobbing based on Sensor Data

In gear hobbing, as in other soft machining processes, it is essential to maintain the required workpiece quality to avoid rejects or increased rework. To track the workpiece quality, the manufactured gears usually have to be measured on a measuring machine. In order to ensure workpiece quality even with long measuring intervals, process monitoring offers an approach to check the gear quality already during the manufacturing process. In this report, the potential of acceleration data with regard to the assessment of workpiece quality is investigated. In this investigation, both analytical and artificial intelligence based methods are considered.

Research on the deformation characteristics of small module tooth during current-assisted splitting spinning of small module tooth-shaped part

Aiming at the problems such as low material utilization, poor strength and toughness of workpiece during manufacturing of small module tooth-shaped parts (SMTSPs) by traditional gear hobbing and shaping method, a current-assisted splitting spinning forming (CASSF) method was proposed to form SMTSPs with high performance requirements. A coupled electrical-thermal-mechanical finite element (FE) model was established based on the ABAQUS software, and the distribution of equivalent stress and equivalent strain, and deformation characteristics of small module tooth were investigated. The results show that the equivalent stress and equivalent strain decrease from tooth groove arc to the tooth crest arc and centre of the tooth groove at tooth profile surface. The distribution of equivalent stress and equivalent strain in the internal deformation region follows the same trend as the tooth profile surface from the centre of the tooth groove to the tooth groove arc, but increases from the tooth groove arc to the tooth crest. The material of small module tooth experiences three-directional stress state. The material in the gear tooth undergoes radial and axial elongation, and tangential compression, while in the tooth groove it undergoes radial compression, tangential and axial elongation.

Energy Consumption Modeling and Optimization of a Hobbing Machine Tool Considering Multi-Axis Coupling

Energy consumption of machine tools has always been a hot issue in the manufacturing sector due to the concern about climate change. To decrease the energy consumption of machine tools, this paper investigates the multi-axis coupling mechanism of a hobbing machine tool during machining from the design stage, and develops an energy consumption model under multi-axis coupling of the whole machine. Firstly, the multi-axis coupling mechanism in the actual machining process is studied. The hob speed and the feed speed of Z axis moving component will affect the hobbing force, and the component of hobbing force in each direction will affect the load and energy consumption of each axis. Meanwhile, the tracking error of each axis is reduced by a sliding mode controller. Next, a comprehensive energy consumption optimization model of a hobbing machine tool under multi-axis coupling is constructed. Furthermore, three optimization algorithms are implemented to the energy consumption model. Compared with the initial scheme, the simulation experiment results of the case-study indicate that the hobbing machine tool energy consumption is reduced by 1.19%, the steady-state error of each axis is reduced by 35.27%, 21.70%, and 36.34%, respectively, and the maximum deformation of the tool holder is reduced by 10.91%. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is dedicated to dealing with the issue of a hobbing machine tool energy consumption. Based on our previous work, the multi-axis coupling mechanism of the gear hobbing machine tool is investigated, and a comprehensive energy consumption model of the gear hobbing machine tool is proposed. The design variables of the energy consumption optimization model include the structural parameters of the Z axis moving component and the sliding mode controller parameters of the three axes (B, C, and Z axis). Three optimization algorithms are used to drive the optimization model. The simulation results verify the feasibility of the method. The control performance of the system is improved, and the mass of moving component is reduced.

Revolutionizing gear hobbing machine precision: Innovative thermal error compensation and intelligent error control with enhanced crystal structure algorithm and self-attention bidirectional minimal gated unit network

The thermal error stands as a pivotal determinant, significantly impacting both the precision and its stability of gear hobbing processes. Thus far, conspicuous delays in compensation and insufficiencies in precision have been duly noted. To achieve a proficient and exceedingly precise thermal error compensation, an intricate mathematical correlation is expounded, delineating the connection between the spatial pose error of the hob and the inherent thermal error in the gear hobbing machine. In addressing the thermal error linked to the B-axis, a bidirectional-minimal gated unit network is harnessed to characterize long-term memory attributes. An advanced crystal structure algorithm is introduced, encompassing components such as the population initialization mechanism, the nonlinear convergence factor, the Gaussian perturbation mechanism, and an enhanced optimization equation. The weights of the bidirectional-minimal gated unit network are judiciously assigned via the self-attention mechanism. This innovation, recognized as the improved crystal structure algorithm-self-attention-bidirectional-minimal gated unit network, is introduced for the training of the thermal error model for the B-axis. Subsequently, thermal analysis models are formulated, yielding the thermal errors of the X- and Z- axes. An error control model and an error decoupling model are established, employing the thermal errors of the B-, X-, and Z- axes as their input. Ultimately, an intelligent error control system is crafted, in which the error control model, error decoupling model, and thermal error model are seamlessly integrated. The aim is to mitigate tooth flank errors. With the integration of the intelligent error control system, the levels of precision pertaining to gear helix deviation, maximum deviation of a single pitch, and cumulative total pitch deviation are elevated by one, one, and two levels, respectively. More significantly, the geometric error reduction of the tooth flank achieved by the meticulously designed intelligent error control system surpasses that of traditional pitch compensation by a substantial margin. Furthermore, the execution efficiency of the intelligent error control system, when operating within the machine-edge-fog-cloud framework, exhibits a remarkable improvement of 24.18%, 16.20%, and 57.84% when compared to the intelligent error control system operating within the machine-edge-cloud, machine-fog-cloud, and machine-cloud frameworks, respectively.

ANALYTICAL APPROACH FOR PREDICTING THE STATE OF STRENGTH PARAMETERS OF ASSYMETRIC GEARS

During the process of high-speed gear hobbing of asymmetrical cylindrical gear gears, the surface layer undergoes repeated plastic deformation and leads, in turn, to a change in the physical and mechanical properties and structure of the metal. In order to increase the importance of teeth in machine drives of important machinery, the use of gears with an asymmetrical shape of the teeth is demonstrated, which reflects the functional difference of gears according to GOST 1643-81 and an asymmetrical profile. In accordance with the changes, occurring in the surface layer, the depth of the hardened layer is determined by the change in microhardness across the cross section of the part and by changing the nature of interference lines on x-ray diffraction patterns during layer-by-layer etching of the surface under study depending on the cutting speed. The cutting speed acts as a factor that determines the rate of plastic deformation of the surface layer. With increasing strain rate, the tensile strength and yield strength of structural materials increase. Increasing the yield strength reduces the plasticity of the processed material and acts in the direction of reducing the degree of hardening. With increasing temperature and degree of deformation, the rate of the softening process, which occurs due to recrystallization, increases. An increase in cutting temperature increases the intensity of the softening process and reduces the degree of hardening.

Scientific Basis for the Substantiation of Process Regulations for the Micro-Cutting of Hardened Gears

Abstract The paper considers scientific principles of technological procedure development for the selection and assignment of parameters of velocity machining by blade tool at gear milling with due regard to the required parameters of the gear surface layer. Optimum micro-cutting conditions are determined when full participation in stock removal of all mill teeth is provided. Technological regulation of selection and setting of machining parameters is spread for gear hobbing of the spur gear wheels with fine-modular and coarse-modular hardness (220...320 HV) and after heat treatment (HRC46...63). Correlation with essential parameters of the surface layer, cutting depth, feed, speed and radius of rounding of the cutting edge of milling cutters’ teeth is established. It is scientifically grounded, tested, and proved at what modes of cutting, the radius of rounding of cutting edge of the cutting tool is made metal removal at oncoming and passing high-speed micro milling. The process of determining of minimal sliding angle, or maximum value (without the use of coolant and with coolant), in which there is no micro-cutting process taking into account variation of variable parameters of cutting conditions and geometrical parameters of hobbing cutters is modelled. For the first time, we ascertained the relation between the sliding angle and the maximum contact angle of the mill tooth with the work surface, which allowed determine the efficiency of the shaping process through coefficient (without coolant and with coolant).

Face gear drive manufacturing: Pinion/cutter design for a crowned contact pattern

Face gear drives are special angular gears in which an involute pinion and face gear wheel mesh. They enable high transmission ratios in small construction spaces. The face gear is typically manufactured by gear hobbing or gear shaping using an involute pinion-type cutter. Face gear drives with identical pinion and cutter parameters form a conjugated pairing. Conjugate pairings tend to have unfavourable edge contact, which is usually counteracted by geometric flank modifications during manufacture. A common modification technique is the crowning of the flanks. This usually requires changes to the machine kinematics. Due to their geometry and manufacturing process, face gear drives offer an easy way to achieve a crowned contact pattern in the facewidth direction without changing the machine kinematics, making them promising for multiple applications. Using a pinion with fewer teeth than the cutter results in a crowned contact pattern (lead crowning). The position of the contact point along the facewidth can be adjusted by varying the profile shift coefficient of the pinion or the cutter. This paper presents a straightforward method for selecting proper design parameters depending on the contact distances. The contact distances can be estimated analytically to evaluate the chosen design parameters. Example calculations are given as proof of the developed method presented in this paper. Overall, this study offers a novel evaluation strategy for an ideal cutter/pinion design for manufacturing durable face gear drives with optimised contact patterns.

Analysis of hob vibration frequency components distribution mechanism of different faults states

The correct understanding of the effective frequency components distribution in different states is essential for high precision hob fault diagnosis and wear identification. To explore the unclear vibration frequencies, a hob dynamic differential equation is established. The frequency components of gear hobbing under healthy states, steady faults, impact faults, and composite faults are summarized theoretically, especially the higher harmonics and the corresponding modulation sidebands, which are mainly the results of the convolution, overlapping, and the nonlinear feedback of the hobbing frequency and its harmonics, meshing frequency and its harmonics, rotating frequency and its harmonics. Moreover, the influence of the hob second response function on the amplitudes of the vibration components are analyzed, which has a relatively negative effect on the amplitudes of the lower frequency vibration components but markedly increases the vibration components near the natural frequency. The above theoretical analysis is verified by the acquired hob vibration signal.

An Intelligent Deep Learning Technique for Predicting Hobbing Tool Wear Based on Gear Hobbing Using Real-Time Monitoring Data

Industry 4.0 has been an impactful and much-needed revolution that has not only influenced different aspects of life but has also changed the course of manufacturing processes. The main purpose of the manufacturing industry is to increase productivity, reduce manufacturing costs, and improve the quality of the product. This has helped to drive economic growth and improve people’s standards. The gear-hobbing industry, being the most efficient one, has not received much attention in terms of Industry 4.0. In prior works, simulation-based approaches with individual parameters, e.g., temperature, current, and vibration, or a few of these parameters, were considered with different approaches, This work presents a real-time experimental approach that involves raw data collection on three different parameters together, i.e., temperature, current, and vibration, using sensors placed on an industrial machine during gear hobbing process manufacturing. The data are preprocessed and then utilised for training an artificial neural network (ANN) to predict the remaininguseful life (RUL) of a tool. It is demonstrated that an ANN with multiple hidden layers can predict the RUL of the tool with high accuracy. The compared results show that tool wear prediction using an ANN with multiple layers has better prediction accuracy during worm gear hobbing.