Tooth Modification Research Articles

A novel approach based on a mathematical algorithm and measurement of involute flanks for computing spur gear dimensions with unknown parameters

AbstractInvolute gears of all sizes and types are widely utilized in most machinery. Accurate generation of teeth flanks from the nominally required base circle is most vital in gear manufacturing, performance, and inspection. Despite the vital importance of the base circle in actual gear performance, it is not a widely used inspection parameter. Moreover, the size of base circle radius and geometrical center cannot be obtained by direct measurement. In this work, a new mathematical algorithm was developed to evaluate the base circle dimensions by measurement of only the teeth profiles. Measurement of the outer diameter is not required nor is the prior knowledge of any gear dimension such as its module or pressure angle. The evaluated base circle dimensions are then used to compute remaining dominant gear dimensions including its pressure angle. The developed approach was tested on an ideal gear model then applied to the flank points obtained by measurements performed on a Coordinate Measuring Machine (CMM) and by photogrammetry (PG). The experimental results were compared to those measured using a gear roll tester (GRT) and were found to be in very good agreement. The methodology and measurement procedure presented in this work are distinguished by their ability to measure the actual gear dimensions regardless of any tooth modification made to the profile or addendum during manufacturing. This makes the proposed work well-suited for reverse engineering and rapid prototyping reverse calculations.

Numerical Analysis of Tooth Contact and Wear Characteristics of Internal Cylindrical Gears with Curved Meshing Line

In order to improve the contact strength and reduce the sliding friction of the gear pair, an internal cylindrical gear pair with a curved meshing line is studied in this paper. Firstly, a curved meshing line is designed. The tooth profiles of the internal gear pair with the designed meshing line are calculated by using differential geometry and the gear meshing principle. Secondly, a wear model is established by combining the finite element method and the Archard wear formula. Then, a numerical simulation is conducted; the relative curvature, sliding coefficient, sliding distance, maximum contact pressure, transmission error, and wear depth are calculated. Ultimately, the variation law of tooth surface wear of new gear with and without installation errors is observed under different stress cycles. On this basis, the influence of tooth modification on tooth surface wear is further researched. Through the results, the advantages of the introduced novel internal cylindrical gears in wear resistance are further demonstrated. The study in this paper provides new research ideas and methods for gear wear research and gear design.

Vibration Analysis of the Double Row Planetary Gear System for an Electromechanical Energy Conversion System

Electromechanical energy conversion systems (EECSs) are widely used in vehicles to combine the double-row planetary gear system (DRPGS) with high transmission efficiency and high-performance motors. The integrated structure of the ring gear and motor rotor have put forward higher demands for the vibration performance of the DRPGS. This paper establishes a multibody dynamic model of the DRPGS for an EECS. Based on the kinetic relationship between the gear pairs and bearing components, the dynamic equations of the DRPGS are derived. The DRPGS model is simulated under different operating conditions. The results are compared to reveal the relationships between the system vibration and the operating speed and load torque. The typical conditions are selected to study the effectiveness of the structural parameters in reducing the DRPGS vibrations. The structural parameters, including the bearing clearance, the ball numbers, the gear tooth modification amount, and length, are comprehensively discussed. Several suggestions for the low-vibration design of the DRPGS for the EECS are provided.

FE-analytical slice model and verification test for load distribution analysis and optimization of planetary gear train in wind turbine

Load distribution behavior of planetary gear train (PGT) is crucial for the contact and bending fatigue failure of wind turbine transmission system. With the increasing power of wind turbines, the load and failure rate of wind turbine become larger, which leads to the demand of accurate and efficient modeling, analysis and optimization for load distribution of PGT. In this paper, a new efficient and accurate FE-analytical slice model for load distribution analysis and optimization of PGT in wind turbine is proposed, which is explicitly formulated by the geometry slice model of external/internal gear contact, original FE-analytical slice model for local contact deformation, and efficient finite element (FE) model for global structural deformation. In the FE-analytical slice model, geometry errors are effectively descripted by discretizing gears into a series of slices, while gear tooth contact elasticity and structural elasticity are addressed by the FE-analytical method accurately and efficiently. Upon the proposed model, the load distribution behaviors of PGT with coupling effects of elasticity and errors are revealed and optimized by tooth modification and in-phase eccentricity arrangement strategy. The load distribution tests of PGT in wind turbine are conducted, verifying the proposed FE-analytical slice model which is significant to improve the load-bearing capacity and avoid the fatigue failure of wind turbine transmission system.

Dynamic characteristics analysis of gear tooth modification in a three-stage gear system

Gears serve as vital elements in high-efficiency mechanical transmissions, playing a pivotal role in vehicles. Employing gear modification has the capacity to significantly enhance the dynamic properties of the Planetary Gear Transmission (PGT) systems. In this study, the investigation has been directed toward a three-stage PGT model system with a comprehensive consideration of various vibration-related factors that affect the dynamic behavior of the system. These factors are encompassed by Time Varying Mesh Stiffness (TVMS), torsion and bending forces experienced by connecting shafts, dynamic Transmission Error (TE), impact of gear meshing eccentric load forces, inherent flexibility in the supporting shaft structure, and influence of torque and power fluctuations originating from a multi-cylinder engine. The estimation of TVMS is carried out for both external-external and external-internal teeth meshing pairs, utilizing the Potential Energy Method (PEM). Subsequently, this study employs the lumped parameter method to establish a model with a specific objective of investigating the lateral-torsional-coupling behavior within adopted PGT model system. The lateral vibration displacement characteristics of the PGT model system is deeply analyzed, revealing the influence of speed on lateral vibration and displacement frequency domain characteristics through a 3D waterfall diagram. Furthermore, a Tooth Profile Modification (TPM) method is applied utilizing two distinct parameters namely [Formula: see text] TPM parameter and [Formula: see text] TPM parameter. The objective is to mitigate vibrations and evaluate the performance of the adopted PGT model after employing each TPM parameter through both TVMS and Root Mean Square (RMS).

A Novel Tooth Modification Methodology for Improving the Load-Bearing Capacity of Non-Orthogonal Helical Face Gears

This study proposes a double-crown tooth surface modification technology that improves the load-carrying capacity of non-orthogonal helical tooth surface gears. The tooth modification is determined by a modified rack-cutter, and its feed motion is related to an intentionally designed transmission error. The novelty of the tooth modification design is that the transmission error can be pre-designed. First, changing the tooth profile of the tool enables preliminary modification along the tooth profile direction; second, by modifying the interaction between the tool and the machined gear, subsequent fine adjustments are made to the contact path. This two-stage tooth modification strategy not only retains the advantages of the traditional method but also significantly improves the balance of the load distribution on the tooth surface through an original contact path modification strategy. Through systematic tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA), it was verified that the new method reduces contact stress and tooth root bending stress and improves the gear’s resistance to misalignment errors. This research provides the basis and motivation for further exploring and improving this tooth profile modification technology to solve the challenges faced by more complex gear systems.

Dynamic characteristics of a spur gear pair under the coupled effects of angular misalignment fault and tooth modification

Angular misalignment is a common fault in gearbox manufacturing and installation, which directly affects the meshing characteristics of the gear pair. Tooth axial modification is considered to be a useful way to suppress angular misalignment. However, accurate determination of contact characteristics, e.g., contact stiffness and friction, caused by the coupled effects of angular misalignment and tooth modification is difficult. To settle this problem, this article put forward a method on the strength of the slice coupling and nonlinear Hertzian contact calculation. With the proposed model, the meshing errors caused by angular misalignment and tooth axial modification are derived. Then the influence of nonlinear Hertzian contact and friction on time-varying mesh stiffness (TVMS) is considered in each sliced tooth. In addition, an iterative computation method is proposed to calculate the proposed analytical model. Further, a dynamic model is developed to study the influences of angular misalignment and tooth axial modification on gear dynamic characteristics. Finally, the analytic model is validated by an experimental setup for a spur gear pair with ideal installation, misalignment and tooth axial modification. Results show that the proposed model is effective and efficient for predicting the dynamic response of the spur gear pair under the coupled effects of angular misalignment and tooth modification.

Closed-loop topology modification of gear tooth flanks considering both dressing and honing processes for internal-meshing gear honing

Gear machining accuracy is significantly affected by the precise motion and geometry of honing wheels in the gear honing process, wherein dressing is critical to ensure the proper profile of honing wheels. Although dressing constitutes an essential process that has long been utilized to finalize work gear, it has rarely been investigated in prior research. This study proposes a closed-loop topology modification method for gear honing, considering both dressing and honing processes. A dressing gear is utilized to re-shape the honing wheel profile, which is then applied to finalize the work gear. Mathematical models of the dressing and the honing are established for a CNC internal-meshing gear honing machine. The model also applies additional motion functions of dressing and honing axes. The sensitivity matrix method combined with the Levenberg-Marquardt algorithm determines the additional motions according to the expected tooth modification. The effectiveness and practicability of the proposed method are verified by carrying out double-crowning as the gear tooth modification in numerical instances.

A new method for calculating time‐varying torsional stiffness of RV reducers with variable loads and tooth modifications

AbstractRotate vector (RV) reducers have advantages of high torque ratio, and extremely reliable functioning under dynamic load conditions, and so forth, and they are extensively used in precision transmissions, such as industrial robots. The torsional stiffness of RV reducers is a main parameter affecting the meshing vibration and transmission performance. In addition, the variable loads and tooth modifications have significant influence on the torsional stiffness of RV reducers. In this paper, a new method of calculating torsional stiffness for RV reducers considering variable loads and tooth modifications is presented. The dynamic stress and deformation of meshing teeth are calculated based on Hertz formulation, and the number of meshing teeth is determined by analyzing the dynamic stress of meshing teeth. Then, the torsional stiffness of RV reducers is obtained. Finite element method is applied to calculate the deformation of cycloidal‐pin gear in the maximum force position δmax. The influence of variable applied loads and different tooth modifications of cycloidal‐pin gear transmission on torsional stiffness are also studied. The results show that variable applied loads and different tooth modifications influence the torsional stiffness of RV reducers by changing teeth deformation and clearance, respectively.

An analytical method for the meshing characteristics of asymmetric helical gears with tooth modifications

This paper establishes a time-varying meshing stiffness (TVMS) analytical method for asymmetric helical gear pairs based on the potential energy principle and slice method. The method considers the adjacent teeth' influence on the deformation of the gear body part. The proposed method is verified the reasonableness by finite element (FE) analysis. The basic parameters of asymmetric helical gear such as helical angle, pressure angle and tooth width are estimated for the meshing characteristics. The results show that the increase of helix angle, pressure angle of the driving side, normal modulus and tooth width will affect the contact ratio and maximum meshing stiffness of helical gears. The variation of these parameters can minimize the fluctuation of the TVMS curve when the overlap contact ratio reaches an integer. The variation trend of the loaded-static transmission error (LSTE) is opposite to that of the TVMS curve. The load share ratio (LSR) on a pair of gear pairs will decrease with the increase of the degree of reattachment. Furthermore, the influence of tooth modifications on TVMS is estimated by using the proposed method. The mean value of stiffness is reduced after the tooth modifications. The TVMS curve changes more gently after the tooth tip modification.

파라메트릭 스터디를 통한 전동식 기어시스템의 소음 및 PPTE 분석

The gear overlap ratio shows the characteristics of the spur gear and the helical gear and varies according to the torsional angle. The gear ratio, tooth width, and center distance, which are restricted in a space of performance and manufacturing and design in the gearbox, are fixed. A parametric study on modules, the number of teeth, and torsion angles was conducted to analyze the relationship between the overlap ratio and PPTE. Then, contact analysis was performed by correcting the tooth profile to improve the transmission error. Contact analysis was performed through correction of the tooth modification to improve transmission error, and the noise was analyzed according to the overlap ratio by applying a noise prediction equation.

Effects of Tooth Modification in the Involute Helical Gear Form-Grinding Process on Loaded Transmission Character with Consideration of Tooth Axial Inclination Error

Due to the existence of machining and installation errors, axis parallelism error of gear pairs occurs, which causes eccentric load and mesh in-out impact, thus weakening loaded transmission character. To solve this problem, the axis parallelism error of gear pairs was equated with tooth axial inclination error based on the gear-meshing principle. On this basis, we established the tooth modification model with tooth axial inclination error as the variable according to involute helical gear form-grinding process. Then, the degradation of loaded transmission character caused by axis parallelism error of gear pairs was quantitatively analyzed. The gear grinding, gear measuring, and gearbox vibration measuring were, respectively, performed on high-precision CNC horizontal gear form-grinding machine tool L300G, Gleason 350 GMS, and JWY-II multifunctional gearbox loading test bench. The results show that the proposed method can effectively reduce eccentric load and mesh in-out impact and significantly improve loaded transmission character. Therefore, it can provide a theoretical and experimental basis for the research of high-performance gear-grinding technology of gear-grinder machines.

Meshing characteristics of spur gear pairs with tooth modification under different assembly errors and sensitivity analysis for impact factors

Meshing characteristics of spur gear pairs with tooth modification under different assembly errors and sensitivity analysis for impact factors

Mesh stiffness and dynamic response analysis of modified gear system with thin web and weight reduction holes

Though the special gear foundation structure and tooth modification are effectively applied to weight optimization and vibration control, the lack of an effective mathematical model limits the investigation of their effects. The present work develops a general polygonal approximation method for weight reduction holes, which is introduced into an analytical-finite element (AFE) method along with the decomposition method to calculate the time-varying mesh stiffness (TVMS) of modified spur gear pairs with complex foundation (thin webs and weight reduction holes). The comparisons with the traditional finite element (FE) method show the superiority of the model in calculation accuracy and efficiency. Furthermore, the actual TVMS is introduced into the dynamics model of a high-speed gear-rotor-bearing system to analyze the dynamic responses, and the effectiveness of the model is verified by experiments. The results indicate that the thin web has a greater influence on the reduction of average amplitude in stiffness than holes. The thin web significantly controls the system vibration, while the tooth modification reduces the vibration fluctuation caused by holes at medium and high speeds. The analysis and experimental results provide an important reference for gear weight optimization and vibration reduction.

Phylogeny of the amphibamiform temnospondyls: the relationship of taxa known by adults, larvae and neotenes

The Amphibamiformes, small temnospondyls from late Palaeozoic rocks, have been increasingly considered as the stem-group of some or all extant amphibians (Lissamphibia). Their relationships have become intensely studied after the discovery of new taxa and the revision of poorly known ones, but understanding is hampered by the fact that amphibamiforms fall into two very distinct groups: (a) terrestrial taxa known by adults only (Amphibamidae, Micropholidae) and (b) aquatic taxa known by larvae and neotenic adults (Branchiosauridae). The Branchiosauridae were recognized as a clade supported by a suite of larval synapomorphies, but the unknown larval morphology of the terrestrial clades leaves the question open to whether some branchiosaurid apomorphies might have been more widely distributed. Recently, some branchiosaurid specimens from Nýřany (Czech Republic) were proposed to be larvae of olsoniforms and amphibamids, and together with a revision of ancient branchiosaurid-like taxa from the United States and France prompt a re-analysis of this issue. In a phylogenetic analysis of 48 taxa and 113 characters, the Branchiosauridae were found to be monophyletic and nest in an unresolved trichotomy with Amphibamidae and the putative relatives of Lissamphibia. The present analysis finds the hypothesized olsoniform larvae from Nýřany to be adults of Branchiosaurus salamandroides, whereas some of the larvae from Mazon Creek (Illinois, USA) are not branchiosaurids, but immature specimens of the amphibamid Amphibamus grandiceps. Within branchiosaurids, four clades have been identified: (a) the Carboniferous Anthracobamus clade (Anthracobamus, Montceaubatrachus), (b) the mostly Carboniferous Branchiosaurinae (Branchiosaurus, Milnererpeton) and two largely Permian clades, the newly defined Apateoninae (genus Apateon) and Leptorophinae (Melanerpeton, Leptorophus, Schoenfelderpeton) clade. Branchiosaurid evolution involved a trend towards an enhanced paedomorphosis, a modification of branchial teeth, and successive reduction of bone in the scales and pectoral girdle.

Towards general performance diagrams to define optimum profile and lead modifications with regard to transmission error in spur and helical gears

Some theoretical results on mesh elasticity and contact patterns in narrow-faced spur and helical gears are presented, which lead to original semi-analytical definitions of optimum combinations of profile relief and lead crown minimising the time-variation amplitudes of transmission error. Extensive comparisons with results from a benchmark code prove that the proposed methodology is sound and can be used to define optimum modifications with minimum effort and computational time. Dimensionless performance diagrams are derived from systematic simulations over a broad range of gear macro- and micro-geometries. Although no closed-form solutions can be found, general trends are clearly identified, making it possible to define optimum tooth modifications with reasonable precision. The importance of face contact ratio is highlighted as it can lead to highly contrasted results with either one or two solutions minimising the time-variations of transmission error. For a given gear geometry and set tooth profile and lead modifications, it is shown that the specific influence of loading can also be derived from the proposed performance diagrams.

Charecterization of A Complete Denture :- A Case Report

Characterization is a process in which the character or collective qualities of a person are introduced in complete denture either by modification of teeth or by modification of denture bases ,to make it more natural for that person , characterization of complete denture is necessary to give the denture a leaf like appearance , to make it appear more natural this case report reviews various principles in an effort to produce a natural appearing denture.

Evaluating bond strength of acrylic teeth to conventional and high impact denture base resin incorporating various groove designs

Purpose: In spite of chemical union between acrylic resin teeth and acrylic denture base material, detachment of teeth particularly anterior teeth is a frequent observation. The purpose of this study was to evaluate shear bond strength between denture base resin and acrylic resin denture teeth after incorporating various grooves on the ridge lap area. Materials & Methods: A total of 60 samples were prepared and divided into two groups with 30 samples each. Sample in group I were processed with conventional resin whereas in group II with high impact resin. The teeth in each group were subjected to no treatment, vertical groove & Horizontal retentive goove placement on the ridge lap area. In each group unmodified teeth served as control. A shear force was applied at an angle of 130 degrees to the lingual surface of teeth using instron universal testing machine until fracture occurred. Data obtained was statistically analysed using Post hoc and Mann-Whitney Test. Results: Unmodified resin teeth showed the least bond strength. Modification of teeth with vertical and horizontal groove significantly improves the bond strength with denture resin. A significantly greater force was required to fracture teeth from high impact resin and with vertical groove.

Recent Progress and Prospect on Tooth Modification of Involute Cylindrical Gear

Background: Recent reviews on tooth modification of involute cylindrical gear are presented. Gear pairs are widely employed in motion and power transmission systems. Manufacturing and assembling errors of gear parts, time-varying mesh stiffness, and transmission error of gear pair usually induce vibration, noise, non-uniformly load distribution, and stress concentration, resulting in earlier failure of gear. Tooth modification is regarded as one of the most popular ways to suppress vibration, reduce the noise level, and improve the load distribution of gear pairs. Objective: The objective of this study was to provide an overview of recent research and patents on tooth modification methods and technology. Methods: This article reviews related research and patents on tooth modification. The modification method, evaluation, optimization, and machining technology are introduced. Results: Three types of modifications are compared and analyzed, and influences of each on both static and dynamic performances of gear pair are concluded. By summarizing a number of patents and research about tooth modification of cylindrical gears, the current and future development of research and patent are also discussed. Conclusion: Tooth modification is classified into the tip or root relief along with tooth profile, lead crown modification along tooth width, and compound modification. Each could be applied in different ways. In view of design, optimization under the given working condition to obtain optimal modification parameters is more practical. Machining technology and device for modified gear is a key to get high-quality performance of the geared transmission. More patents on tooth modification should be invented in the future.

Longitudinal Tooth Modification to Improve the Load Capacity of Misaligned Gear Systems

Longitudinal Tooth Modification to Improve the Load Capacity of Misaligned Gear Systems