Face Hobbing Research Articles

Cutting state recognition of spiral bevel gear face hobbing

Abstract To investigate the issue of chatter vibration during the face hobbing process of spiral bevel gears, this study conducted experiments on the YKA2260 gear hobbing machine, collecting 142 sets of vibration acceleration signals. The optimal combination for wavelet threshold denoising was determined based on the signal-to-noise ratio (SNR), and preprocessing of the raw signals was performed. Utilizing wavelet packet decomposition, the energy entropy of wavelet packet coefficients was extracted as feature values. A recognition model for the cutting state during the face hobbing process of spiral bevel gears was established using a Support Vector Machine, achieving a recognition accuracy of up to 98.0769%. Furthermore, the model’s high recognition accuracy for small training samples in engineering applications was validated.

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.

Model for tool wear prediction in face hobbing plunging of bevel gears

This paper deals with tool wear investigations for face hobbing plunging of bevel gears. Initially, the influence of process parameters and tool geometry on tool wear is analyzed both in cutting trials and with the help of the manufacturing simulation BevelCut. Subsequently, a tool wear model is presented. Input parameters into the model are tool and workpiece data as well as process parameters and chip characteristics. Through the manufacturing simulation BevelCut, which is based on a planar penetration algorithm, chip characteristics such as the maximum chip thickness hcu,max are calculated resolved in time and location along the blade's cutting edge. Combined with the local cutting speed, the chip characteristics are used to determine the thrust force, which is required to calculate the elastic workpiece deformation. The model coefficients are calibrated by multi-variable regression analysis using the results of the cutting trials and simulation results. The quality of the regression is determined with the help of equivalence tests. For verification, the process parameters and tool geometry are varied in series production and the tool wear is assessed. Finally, the modeled tool wear is compared to the measured tool wear.

Correction to: Simulation of spiral bevel gear manufacturing by face hobbing and prediction of the cutting forces using a novel CAD‑based model

Correction to: Simulation of spiral bevel gear manufacturing by face hobbing and prediction of the cutting forces using a novel CAD‑based model

Simulation of spiral bevel gear manufacturing by face hobbing and prediction of the cutting forces using a novel CAD-based model

Simulation of spiral bevel gear manufacturing by face hobbing and prediction of the cutting forces using a novel CAD-based model

Analysis of tool wear in face hobbing plunging manufacturing processes

For soft machining of bevel gears, multi-part tool systems consisting of a cutter head and stick blades are commonly used. In the past, experimental investigations regarding the tool wear in bevel gear milling have been carried out, aiming to optimize the process design and thus the process economic efficiency. However, the existing investigations refer only to face milling processes. In this paper, a tool wear study for an industrial application of the face hobbing plunging process is presented. Additionally an analogy trial of the process is designed. Based on the findings, it is concluded that the designed analogy trial is suitable for analyzing the tool wear development for face hobbing plunging processes.

A novel CAD-based simulation model for manufacturing of spiral bevel gears by face milling

Bevel gears are employed in the transmission of motion and torque via non-parallel shafts. When higher strength and lower noise is the objective, spiral bevel gears are used because of their higher tooth contact ratio. Face milling and face hobbing are among the most significant operations for the machining of hypoid and spiral bevel gears due to their high productivity. Although the optimization of these processes is crucial for the production of high-quality gears and the minimization of the total manufacturing cost, there are not many studies reported in this research area, owing to the high complexity of process kinematics. Furthermore, several kinematic variations of the two methods are applied in industry and their results depend highly on the cutting tool geometry. A novel simulation model integrated into a commercial CAD platform has been developed. The model achieves the 3D kinematic simulation of both face milling and face hobbing processes, generating the undeformed solid chip geometry as well as the simulated tooth solid geometry of a spiral bevel gear pinion and a spiral bevel gear wheel as an output. The simulation approach has two main purposes. First, is the optimization of the process through the investigation of the effect of cutting parameters on the quality of the obtained solid tooth flank geometry and second, is the calculation of cutting forces with the use of the obtained solid chip geometries. Aiming towards the validation of the model, the resulted tooth flank geometry is compared with the theoretical tooth exported from a well-established commercial gear calculation and design software and it is verified by means of a novel validation algorithm, also developed as part of this study. This paper focuses on the presentation of the kinematic simulation methodology and the simulation results for the face milling process. An insight into the validation model is provided and validation results are also presented. Finally, a sample investigation of the effect of generating feed rate on the produced gear geometry is conducted with the use of both algorithms.

Mathematical Model of a Vertical Six-Axis Cartesian Computer Numerical Control Machine for Producing Face-Milled and Face-Hobbed Bevel Gears

Abstract Prior to the development of sophisticated computer numerical control (CNC), both face milling (FM) and face hobbing (FH), the two most popular technologies for bevel gear production, required cradle-type machines with diverse and complicated mechanisms. In the last two decades, however, the gear industry has replaced these traditional machines with six-axis CNC bevel gear cutting machines that have superior efficiency and accuracy. One such machine is a vertical six-axis machine with a vertical spindle arrangement, which offers two industrially proven advantages: compact design and maximum machine stiffness. The technical details of this machine, however, remain undisclosed; so, this paper proposes a mathematical model that uses inverse kinematics to derive the vertical machine's nonlinear six-axis coordinates from those of a traditional machine. The model also reduces manufacturing errors by applying an effective flank correction method based on a sensitivity analysis of how slight variations in the individual machine setting coefficients affect tooth geometry. We prove the model's efficacy by first using the proposed equations to derive the nonlinear coordinates for pinion and gear production and then conducting several cutting experiments on the gear and its correction. Although the numerical illustration used for this verification is based only on FM bevel gears produced by an SGDH cutting system, the model is, in fact, applicable in the production of both FM and FH bevel gears.

A CNC tooth grinding method for formate face hobbed hypoid gears

Face hobbing is an efficient process for hypoid gear cutting. However, the continuous indexing process renders it inapplicable for tooth grinding, which limits the further improvement of gear accuracy and transmission performance. In this paper, a tooth grinding method using large diameter conical grinding wheel for Formate® face hobbed hypoid gears (FFHHG) was proposed. The generator of conical grinding wheel was used to replace the cutter blade of the face hobbing process. By controlling the conical grinding wheel, the generator of the grinding wheel can be tangentially in contact with the tooth profile curve of the FFHHG. The sweeping of the generator of the grinding wheel along the extended epicycloidal tooth curve can grind one tooth surface accurately without theoretical deviation. Firstly, the tooth surface was formulated and the geometric parameters of the working side of the grinding wheel were determined to avoid the curvature interference between the grinding wheel and the ground tooth surface. Then, a five-axis tooth grinding tool location model was established to position the grinding wheel and the tooth surface correctly. The interference of the non-working side of grinding wheel was checked and if necessary the grinding wheel axis can be tilted to avoid interference. Finally, the above processes were verified by case analysis and grinding simulations. This study can be employed to improve the pitch accuracy of FFHHG and reduce the tooth profile deviation.

A Study on the Design and Performance of Epicycloid Bevels of Pure-Rolling Contact

To avoid the negative influence of sliding contact, this paper tries to investigate the spiral bevels of pure-rolling contact that can be manufactured by existing manufacture technology. In this process, spatial conjugate curve meshing theory and conjugate surface theory are both introduced to investigate the geometric principles and face hobbing process of the pure-rolling contact epicycloid bevel (PCEB for short in this paper). The tooth surface models of PCEBs by face hobbing process are obtained. Next, a sample is represented to show an application of this model. Then, finite element analysis (FEA) is applied to investigate the contact mechanics characteristics of these gears. Finally, the performance experiment of a prototype is completed to evaluate the deviations between theoretical expectations and practical results. From the FEA and experimental results, it is concluded that the PCEBs can mesh correctly and achieve a higher transmission efficiency.

A disk tool cutting method for bevel gear manufacture on a five-axis machine

Two main popular cutting methods for bevel gear mass production, face milling and face hobbing, both require dedicated tools and machines available from only a few machine tool companies, which makes production more costly. This paper thus proposes a cheaper, more flexible alternative for producing small or medium batches of large bevel gears, a disk tool cutting method using a five-axis machine. In this method, the machine coordinates are derived based on tooth surfaces. The target’s topographic points of tooth surface are applied to construct a fitted surface which is then used to further refine the cutter-contact points to improve the precision of the gear produced. At the same time, mathematical models are established for both the tool and the machine. A coordinate transformation matrix is then generated by aligning the coordinate system of the tool’s reference point with each of the work gear cutter-contact points. Because different machines employ identical transformation matrices for producing the same workpiece, the machine’s five-axis coordinates can be derived using inverse kinematics. These coordinates are the resource to generate the NC machining data that allows NC verification software to perform cutting simulations. The simulation results verify the correctness of the mathematical models.

A Novel Lengthwise Crowning Method for Face-Hobbed Straight Bevel Gears

A recent addition to the many milling processes used in manufacturing to cut straight bevel gears (SBGs) is a new face-hobbing (FH) method that uses a virtual hypocycloid straight-lined mechanism to produce straight-lined teeth. Despite earning much attention because of its high productivity, however, this method is unable to handle lengthwise crowning on tooth surfaces, which results in poor contact performance. This paper therefore proposes a novel lengthwise crowning method, applicable on a modern six-axis computer numerical control (CNC) bevel gear cutting machine, in which the gear blank performs a swinging motion during machining. This swinging motion is enabled by machine setting modifications, which here are derived from a mathematical model of a double (profile and lengthwise) crowned gear. After the model's correctness is confirmed using ease-off and tooth contact analyses, a final investigation examines the effect of two key parameters related to contact performance indexes whose interrelations are graphed to provide a designer reference.

A motion control method for face hobbing on CNC hypoid generator

In this paper, the relative motion relation was derivated among the virtual cradle, generating gear, cutter and workpiece on the CNC hypoid generator. A directly axis coordinate solving method of CNC hypoid generator was proposed by taking cutter axis vector as control objectives to transform the attitude of whole cradle-type generator. The method didn't solve complex nonlinear equations. We also provide a motion control solution for face-hobbing on the CNC hypoid generator using Siemens 840Dsl NC system.In this method, the online real-time programming is achieved, because of the index motion and generating motion of machining process are separated, and spline interpolation and electronic gearbox function are adopted. The tooth form equation which is determined by the motion control model of CNC hypoid generator is derived. The calculation example of a gear sets shows that the theoretical tooth form of the epicycloid hypoid gear machined by such motion control method is consistent with the standard tooth form computed by Gleason CAGE Software. With NC machining simulation software VERICUT, virtual NC hypoid gear cutting machine is established, which realizes face hobbing simulation of such gear sets. At last, a face hobbing experiment is conducted on YK2235 CNC hypoid generator manufactured by Tianjin No. 1 Machine Tool Works, and such face hobbing motion control model is verified as correct through tooth form measurement and rolling test.

Cutting Performance in Machining of Large-Sized Spiral Bevel Gears Using Multi-Axis Control and Multi-Tasking Machine Tool

Large-sized spiral bevel gears are usually manufactured based on a cyclo-palloid system and have equi-depth teeth as well as a face hobbing system by a continuous cutting procedure using a special generator. It has been possible to machine the complicated shape because of the development of a multi-axis control and multi-tasking machine tool.The manufacturing method of the gears has been proposed using this development process. In this method, the spiral bevel gears are modeled based on a CAD system and are machined based on a CAM system. In this paper, the cutting performance in machining of the large-sized spiral bevel gears using the multi-axis control and multi-tasking machine toolis investigated. As a result, the relationship between the tool life of end mill and gear accuracy were made clear. The surface roughness and tool mark of the machined gears were compared with those using the special generator.

Manufacture of face-hobbed straight bevel gears using a six-axis CNC bevel gear cutting machine

Face hobbing is a continuous indexing and double-flank cutting process whose high productivity and precision has made it one of the leading methods for fabricating spiral bevel and hypoid gears. The current method is inappropriate, however, for cutting straight bevel gears (SBGs) because it generates extended epicycloidal flanks. Nonetheless, a mathematical model of a face-hobbed SBG was successfully established in earlier research that enables straight cutting paths to cut straight tooth spaces based on a hypocycloidal straight-line mechanism in which the rolling circle radius equals half the base circle radius. This mathematical model, however, is based on a virtual universal cradle-type bevel gear cutting machine that has not yet been developed. This paper therefore proposes another mathematical model of face-hobbed SBG based on a modern six-axis computer numerical control (CNC) bevel gear cutting machine. The six-axis nonlinear machine settings are derived through conversion from the cradle-type machine settings. Meanwhile, the usage of electric gearbox (EGB) for bevel gear cutting is not revealed because of commercial consideration. Therefore, we also provide a solution to use EGB of Fanuc 16i CNC controller. A cutting experiment validates the proposed mathematical models using our developed six-axis CNC bevel gear cutting machine to cut the face-hobbed SBGs. Finally, a flank topographic correction is made that, according to postcorrection simulated topographic errors, can effectively reduce manufacturing errors. This paper successfully implements a face-hobbing process for manufacturing SBGs on a modern six-axis CNC bevel gear cutting machine.

Mathematical Model for Face-Hobbed Straight Bevel Gears

Face hobbing, a continuous indexing and double-flank cutting process, has become the leading method for manufacturing spiral bevel gears and hypoid gears because of its ability to support high productivity and precision. The method is unsuitable for cutting straight bevel gears, however, because it generates extended epicycloidal flanks. Instead, this paper proposes a method for fabricating straight bevel gears using a virtual hypocycloidal straight-line mechanism in which setting the radius of the rolling circle to equal half the radius of the base circle yields straight lines. This property can then be exploited to cut straight flanks on bevel gears. The mathematical model of a straight bevel gear is developed based on a universal face-hobbing bevel gear generator comprising three parts: a cutter head, an imaginary generating gear, and the motion of the imaginary generating gear relative to the work gear. The proposed model is validated numerically using the generation of face-hobbed straight bevel gears without cutter tilt. The contact conditions of the designed gear pairs are confirmed using the ease-off topographic method and tooth contact analysis (TCA), whose results can then be used as a foundation for further flank modification.

Mathematical Transformation of Machine Settings from Cradle-Type to Cartesian-Type Hypoid Generator

A mathematical model for translating machine settings from universal Cradle-Type hypoid generator to Cartesian-Type hypoid generator is proposed in this paper. A mathematical model of universal Cradle-Type hypoid generator was proposed by Fong [12] to simulate conventional hypoid generators including face milling and face hobbing machines. A few years ago, the Gleason Works presented the Phoenix hypoid generator, which is a Cartesian-Type machine, and the machine is gaining good commercial success. Therefore, we proposed a mathematical transformation model to translate the machine settings from conventional Cradle-Type hypoid generator to the new Cartesian-Type CNC machine. The proposed mathematical equations can be used to implement the existing cutting method on the six-axis CNC machine

Computerized Modeling and Loaded Tooth Contact Analysis of Hypoid Gears Manufactured by Face Hobbing Process

The face hobbing process has been widely applied in automotive industry. But so far few analytical tools have been developed. This makes it difficult for us to optimize gear design. To settle this situation, this study aims at developing a computerized tool to predict the running performances such as loaded tooth contact pattern, static transmission error and so on. First, based upon kinematical analysis of a cutting machine, a mathematical description of tooth surface generation is given. Second, based upon the theory of gearing and differential geometry, conjugate tooth surfaces are studied. Then contact lines are generated. Third, load distribution along contact lines is formulated. Last, the numerical model is validated by measuring loaded transmission error and loaded tooth contact pattern.

Mathematical Model for a Universal Face Hobbing Hypoid Gear Generator

Based on the theory of gearing and differential geometry, a universal hypoid generator mathematical model for face hobbing spiral bevel and hypoid gears has been developed. This model can be used to simulate existing face hobbing processes, such as Oerlikon’s Spiroflex© and Spirac© methods, Klingelnberg’s Cyclo-Palloid© cutting system, and Gleason’s face hobbing nongenerated and generated cutting systems. The proposed model is divided into three modules: the cutter head, the imaginary generating gear, and the relative motion between the imaginary generating gear and the work gear. With such a modular arrangement, the model is suitable for development of object-oriented programming (OOP) code. In addition, it can be easily simplified to simulate face milling cutting and includes most existing flank modification features. A numerical example for simulation of the Klingelnberg Cyclo-Palloid© hypoid is presented to validate the proposed model, which can be used as a basis for developing a universal cutting simulation OOP engine for both face milling and face hobbing spiral bevel and hypoid gears.

Computerized Modeling and Simulation of Spiral Bevel and Hypoid Gears Manufactured by Gleason Face Hobbing Process

The Gleason face hobbing process has been widely applied by the gear industry. But so far, few papers have been found regarding exact modeling and simulation of the tooth surface generations and tooth contact analysis (TCA) of face hobbed spiral bevel and hypoid gear sets. This paper presents the generalized theory of the face hobbing generation method, mathematic models of tooth surface generations, and the simulation of meshing of face hobbed spiral bevel and hypoid gears. The face hobbing indexing motion is described and visualized. A generalized description of the cutting blades is introduced by considering four sections of the blade edge geometry. A kinematical model is developed and analyzed by breaking down the machine tool settings and the relative motions of the machine elemental units and applying coordinate transformations of the elemental motions. The developed face hobbing generation model is directly related to a physical bevel gear generator. A generalized and enhanced TCA algorithm is proposed. The face hobbing process has two categories, non-generated (Formate®) and generated methods, applied to the tooth surface generation of the gear. In both categories, the pinion is always finished with the generated method. The developed tooth surface generation model covers both categories with left-hand and right-hand members. Based upon the developed theory, an advanced tooth surface generation and TCA program is developed and integrated into Gleason CAGE™for Windows Software. Two numerical examples are provided to illustrate the implementation of the developed mathematic models.