Gear Tooth Flank Research Articles

Influence of Housing Stiffness of the Slewing Reducer of a Tower Crane on the Load Distribution Pattern over the Gear Tooth Flank

To increase the life of slewing reducers, the reliability of their gearboxes is essential. They should be designed, simulated, and tested considering the installation environment and actual load conditions. Many studies have been conducted on the reliability improvement of gearboxes for reducers; however, a few studies have considered actual input load conditions. Furthermore, there is insufficient research on the effects of housing stiffness on gear misalignment, gear life, and load distribution and maximum contact load of the gear tooth flank. In this study, the effects of housing stiffness were analyzed using input torque measurements to investigate the causes of ring gear damage during durability tests on a slewing reducer. The contact pattern of the gear tooth flank was analyzed by applying dyes to all gears inside the reducer, and the results were compared with simulation results. A large edge contact in the first-stage ring gear of conventional slewing reducers was suggested as the cause of the ring gear damage. A new simulation model using a gearbox housing with an increased stiffness showed that edge contact was improved by the decreased gear misalignment. No abnormal wear and/or partial fracture of the ring gear occurred during the durability test on the improved model under the same conditions as those of the initial model. These results indicate that an increase in the stiffness of the housing reduced the gear misalignment, improved the load distribution, decreased the maximum load of the tooth flank, and increased the gear life.

Effect of friction on nominal stress results in a single tooth bending fatigue test

One of the main reasons for gear failure is bending fatigue, which occurs due to cyclic stresses at the tooth root region. Bending fatigue can cause crack initiation which, in turn, may propagate and result in catastrophic tooth breakage. Single tooth bending fatigue tests are frequently employed to generate statistically significant fatigue data at relatively low price. Hence, they are often employed as screening tests for bending fatigue behaviour of actual running gear pair. Since relatively small alteration of nominal tooth root stress values can produce significant change in bending fatigue lives, it is important to adequately consider the effect of friction and test fixture deformation when conducting single tooth bending fatigue tests. In this paper, numerical investigation of tooth flank friction effect on spur gear load capacity during single tooth bending fatigue test is carried out. Two different test fixtures are considered. Linear elastic finite element analysis is carried out to obtain nominal tooth root stresses. The results show that friction at gear tooth flank as well as fixture deformation can affect nominal tooth root stress results.

Experimental determination of plastic gear durability

There are many plastic materials (POM, PA66, PEEK, …) and material combinations available. The question is which combination is the correct one. It depends on many factors, like expected durability and price, means of production, e.g. injection moulding or cutting, lubrication, microstructure, fillers, etc. The available data bases and data sheets do not present conclusive results. So, it is of the utmost importance for a company to produce effective tests which could present correct results for each individual case.The gear tooth flank profile could be also optimized. S-gear shape is characterized by a convex concave contact in meshing start and end areas. This implies improved properties in comparison to involute gears, like lower contact pressure, less sliding and lower frictional losses, stronger root and improved oil film when lubricated.The paper presents some material properties for the combinations which were tested on the fatigue test benches, presents testing rigs, refers to experiments and discusses results.

Optimization of asymmetric tooth root generated with protuberance hob

The Direct Gear Design method optimizes various parameters and elements of gear tooth geometry to achieve the required gear drive performance. One such critical element of the tooth profile is the root fillet. Previous publications had considered asymmetric tooth root fillet optimization assuming that the tooth involute flanks and root fillets are processed (machined) simultaneously. However, there are many applications that require high gear tooth flank accuracy and high load capacity in combination with minimized gear production cost. In order to satisfy these requirements, the tooth involute flanks and root fillets are processed separately. A gear blank is machined by a topping protuberance hob that finalizes the root fillet, tooth tip diameter and chamfers, leaving stock for the tooth flank grinding. Then, after the gear’s heat treatment (carburizing + case hardening) and in some cases shot peening of the tooth root, the tooth flanks are processed using highly productive generating grinding, removing the grinding stock. As a result, the full residual stress developed by case hardening is retained. This fabrication sequence is most typical for automotive transmission gears.

Analytical Solution to the Heat Transfer in Fling-Off Cooling of Spur Gears

In this research paper, the cooling process of an impingement cooled spur gear is examined by means of an analytical model. The process is modeled as a coolant film, which is flung off a rotating gear tooth flank by centrifugal forces. During the process, heat is transferred from the isothermal gear tooth flank to the coolant film. With a numerical solution to the analytical model, a formulation for the transient local Nusselt number is derived. The evaluation of the numerical solution revealed that the heat transfer is dominated by heat conduction in the coolant film. The heat transfer process ends when the thermal capacity of the coolant film is reached. The transient Nusselt number is used to derive a time-averaged and a global heat transfer coefficient. Furthermore, the influence of the initial coolant film height is examined by using a modified version of the analytical model. The global heat transfer coefficient decreases toward smaller initial cooling film heights. The analytical model is then extended to include the temperature dependency of the viscosity of the coolant. A viscosity that decreases with increasing temperature yields a moderate decrease in heat transfer. A discussion is presented regarding the applicability of the analytical model toward impingement cooled spur gears. The effect of the simplifications made in the derivation of the analytical model is outlined and assessed with regard to the heat transfer mechanism.

Mathematical approach to evaluate involute gear profile and helix deviations without using special gear software

The paper presents mathematical-geometrical approach to evaluate profile and helix deviations of cylindrical involute gear tooth flank without the usage of any specialised gear measurement software. The input data for the evaluation is represented by a set of Cartesian coordinates of surface points (points of contact between the measuring stylus and the measured surface) measured along the profile and flank curves by CAD based tactile gear measurement on coordinate measuring machine. This approach is based on deep study of ISO standards dealing with gear geometry, gear measurement and gear characteristics evaluation. Here, the development of general mathematical model of both helical and spur involute gear tooth flank surfaces is described and geometrical properties of these surfaces (important for corresponding CAD model generation) are mentioned. For practical application, mathematical formulas for calculation of profile and helix deviations from a set of measured points are derived. Due to the purely mathematical approach, no special gear measurement software is necessary for evaluation of profile and helix deviations. The required characteristics of involute gears can be evaluated by means of any general-purpose spreadsheet software. The presented method can be used not only in case of regular involute gear profile and helix inspection but mainly in case of those gear measurement standards that could not be measured as regular gears by commercial software because of unusual shape and design of the standards.

A model to predict initiation and propagation of micro-pitting on tooth flanks of spur gears

Micro-pitting is an early-stage failure mode commonly found in gears. It leads to macro-pitting, spalling, and even tooth fracture failure, which cause destructive damage to gearboxes. A simulation model to predict the initiation and propagation of micro-pitting on tooth flanks of spur gears is presented. The model simulates the actual gear meshing process, considering the time-varying tooth profile. The contact pressure distribution, sliding velocities, rolling velocities, film thicknesses, and shear stresses along the contact line are accurately calculated. A new crack criterion is proposed to predict the initial crack position. A novel wear rate model was developed by considering the influence of crack density to predict the propagation of micro-pitting and the removal of material from the tooth flank. The results of experiments carried out for gear pairs with different tooth tip reliefs and surface roughness showed good agreement with the simulation results. This verified the model validity.

Derivation of theoretical surface of action and tooth flank of face gear from force equilibrium conditions

Derivation of theoretical surface of action and tooth flank of face gear from force equilibrium conditions

On Dynamic Mesh Force Evaluation of Spiral Bevel Gears

The mesh model and mesh stiffness representation are the two main factors affecting the calculation method and the results of the dynamic mesh force. Comparative studies considering the two factors are performed to explore appropriate approaches to estimate the dynamic meshing load on each contacting tooth flank of spiral bevel gears. First, a tooth pair mesh model is proposed to better describe the mesh characteristics of individual tooth pairs in contact. The mesh parameters including the mesh vector, transmission error, and mesh stiffness are compared with those of the extensively applied single‐point mesh model of a gear pair. Dynamic results from the proposed model indicate that it can reveal a more realistic and pronounced dynamic behavior of each engaged tooth pair. Second, dynamic mesh force calculations from three different approaches are compared to further investigate the effect of mesh stiffness representations. One method uses the mesh stiffness estimated by the commonly used average slope approach, the second method applies the mesh stiffness evaluated by the local slope approach, and the third approach utilizes a quasistatically defined interpolation function indexed by mesh deflection and mesh position.

On the third law of gearing: A study on hypoid gear tooth contact

Presented is a procedure to determine the extreme relative curvatures between conjugate gear flanks. This procedure is a modification of the third law of gearing which establishes the extreme relative curvatures between conjugate tooth flanks in terms of normal pressure angle, spiral angle, and hyperboloidal pitch surfaces. The original formulation for the third law of gearing was based on parabolic contact along a line of contact for the limiting condition of relative curvature between two gear flanks. Penetration or existence of negative Gaussian curvature for the relative flank curvature can occur for skew axis gearing with “conjugate” teeth. In such cases, reciprocity between the tooth normal and the twist defined by the gear rotation axes and instantaneous gear ratio is a necessary condition but not a sufficient condition to ensure suitable gear flanks in skew axis gearing. For cases with penetration, a transverse profile amendment is introduced to achieve parabolic contact (zero Gaussian curvature) for the relative curvature between meshing gear tooth flanks. First and second order reciprocity are applied in the transverse direction to determine profile amendment. Ease-off topography and unloaded transmission error (UTE) are used to assess conjugate action between mating gear flanks in direct contact.

Aspects of the Internal Gear Honing Process

Abstract The paper analyzes the process of internal honing of cylindrical gears, a new and modern method of finishing the gear tooth flanks. At the beginning, the kinematics of the process is being analyzed. By realizing the state of art, we were able to identify the main features of the process, its advantages in terms of surface precision and quality, the residual stresses and the wear of the flanks compared with other finishing processes. An experimental study of the geometric precision, the shape of the flanks and the roughness for honed surfaces compared to the unfinished ones, highlighted the value and the need of this process.

Micro-Magnetic and Microstructural Characterization of Wear Progress on Case-Hardened 16MnCr5 Gear Wheels.

The evaluation of wear progress of gear tooth flanks made of 16MnCr5 was performed using non-destructive micro-magnetic testing, specifically Barkhausen noise (BN) and incremental permeability (IP). Based on the physical interaction of the microstructure with the magnetic field, the micro-magnetic characterization allowed the analysis of changes of microstructure caused by wear, including phase transformation and development of residual stresses. Due to wide parameter variation and application of bandpass filter frequencies of micro-magnetic signals, it was possible to indicate and separate the main damage mechanisms considering the wear development. It could be shown that the maximum amplitude of BN correlates directly with the profile form deviation and increases with the progress of wear. Surface investigations via optical and scanning electron microscopy indicated strong surface fatigue wear with micro-pitting and micro-cracks, evident in cross-section after 3 × 105 cycles. The result of fatigue on the surface layer was the decrease of residual compression stresses, which was indicated by means of coercivity by BN-analysis. The different topographies of the surfaces, characterized via confocal white light microscopy, were also reflected in maximum BN-amplitude. Using complementary microscopic characterization in the cross-section, a strong correlation between micro-magnetic parameters and microstructure was confirmed and wear progress was characterized in dependence of depth under the wear surface. The phase transformation of retained austenite into martensite according to wear development, measured by means of X-ray diffraction (XRD) and electron backscatter diffraction (EBSD) was also detected by micro-magnetic testing by IP-analysis.

Parametric Modeling and Contact Analysis of Skew Spiral Bevel Gears

According to the principle of spherical involute generation, the mathematical model of skew spiral bevel gear tooth flank is derived, according to the mathematical model of the tooth flank, a solid model of the bevel gear is constructed, and then the meshing equation is derived by regulation that the relative motion velocity vector is perpendicular to the common normal line at the meshing point for a pair of gears. Finally, the contact line of skew spiral bevel gears meshing is analyzed, and the relative relationship between the meshing contact line and the tooth flank generation line are derived to provide a theoretical model for design, machining and assembly of gear.

Construction of virtual measurement datum in measuring gear tooth flank by laser interferometry

A measurement datum is crucial in measuring a gear tooth flank by laser interferometry. Manufacturing a physical reference tooth flank as a measurement datum has many drawbacks: many different reference tooth flanks are needed with the changing of the measured gear’s parameters; the reference tooth flank’s manufacturing error lowers the measurement precision; the installation error between the measured and referenced tooth flank lowers the measurement precision also. The drawbacks restrain the practical use of measuring gear by laser interferometry. A construction method of a virtual measurement datum has been proposed to solve the problem. First, a virtual error-free model of the measured tooth flank is built according to its parameters and actual measurement position. Subsequently, the interferogram of the virtual tooth flank is simulated as a measurement datum through the ray tracing. To harvest the actual measurement position of the measured tooth flank, a compensation approach for optical system error and a tracing algorithm for actual installation position are developed. Experimental results prove that a virtual measurement datum can be constructed and used in measuring a gear tooth flank. Furthermore, this research verifies that ray tracing can be used to construct a virtual measurement datum in the relevant comparative measurements processes by laser interferometry.

Моделювання формування гвинтовими співвісними твірними лініями поверхонь зубців циліндричних косозубих зубчастих коліс

Моделювання формування гвинтовими співвісними твірними лініями поверхонь зубців циліндричних косозубих зубчастих коліс

Directional Analysis of Surface Textures of Gear Tooth Flank Using 2D Fourier Transform

Directional Analysis of Surface Textures of Gear Tooth Flank Using 2D Fourier Transform

A Contribution To Study The Tooth Flank Fracture (TFF) In Cylindrical Gears

The Tooth Flank Fracture, TFF, is a failure mode observed in the surface-hardened of gear tooth flanks. There is a fatigue phenomenon which initiates from a subsurface crack that occurs in the transition zone between the hardened layer and the core structure of the tooth. It is substantially initiated close to the mid-height of the tooth in the single pair of contact area from a crack that progresses in a direction normal to the active surface flanks and also spreads in the thickness of the tooth up to the breakage of the non-active flank, slightly above the root fillet.The two main modes of fatigue damages for gears are: (i) contact fatigue and (ii) tooth bending root fatigue, are well established and addressed in the international standards such as ISO 6336 part 2 and 3. However, up to now, there is no detailed calculation method to determine the load capacity related to the Tooth Flank Fracture, TFF.The main objective of this work is to develop an efficient and a standardized methodology to identify the occurrence risk of the Tooth Flank Fracture (TFF) in cylindrical gears. Then, to estimate the risk of appearance of TFF, we have studied two fatigue criteria which are introduced in a developed numerical model. The developed approach, which is based on the Hertz theory with the half-space approach, has been validated by finite elements simulations, revealing a good compliance of the “simplified” criteria proposed initially by Dang Van to characterize this failure mode. Good agreement of this criterion is also observed after a comparative study relative to some experimental tests carried out in literature. An advanced parametric study is carried out to properly identify the real impact of the case hardening depth on this damage mode.

A novel gear flank modification methodology on internal gearing power honing gear machine

In order to reduce the impact of load fluctuation, noise and vibration, the tooth surface of the gear in the high speed transmission gearbox is usually modified along the lead and profile direction. In this paper, a method for lead and profile crowning tooth flank of work gear is proposed by setting the movement of A and B axes as two fourth order polynomial functions of axial feed of work gear in the internal gearing power honing. Diamond dressing gear used for honing stone in dressing process is standard involute, and it is not necessary to design an especial diamond dressing gear for each different modified gear. The sensitivity matrix of polynomial coefficients is calculated by the normal deviation of the gear tooth surface, and the influence of the variation of polynomial coefficients on the tooth surface is studied. The honed tooth surface can be approximated to the given tooth surface by adjusting the polynomial coefficients through least squares estimation with the aim of minimization of the tooth surface errors based on sensitivity matrix. The effectiveness of this crowning tooth flank modification method is confirmed numerically using a helical gear on the internal gearing power honing machine.

A method for grinding face gear of double crowned tooth geometry on a multi-axis CNC machine

The stability requirement of bearing contact and a favorable function of transmission errors motivates the investigation of design and manufacture technology of the face-gear drives. Application of a grinding disc wheel with axial profile modification and a longitudinal ease-off topography design of face gear tooth flanks could be proper utilized to obtain a double crowned tooth geometry, which results in the pre-designed bearing contact and desired transmission errors. With the profile crowned tooth geometry of the gear generated by the modified wheel cutter, finding of the execution motions to generate the tooth geometry with the longitudinal ease-off topography design on a multi-axis Computer Numerical Control (CNC) machine with the same tool is a major issue. Therefore, a universal method on the Design Optimization Techniques is proposed to obtain the execution motions for such problem. The proposed optimization methodology is also applicable for the tooth flank error correction by a worm hob or a grinding cutter on the CNC generator. With the term of additional movement of execution motion is defined, a detailed description of additional movements for the ease-offs of the real crowned tooth geometry is also investigated. The feasibility of proposed method is validated by numerical examples.

Numerical simulation of kink angle prediction for non-lubricated surface crack subjected to Hertzian pressure

Analysis of determining linear fracture mechanics parameters for a surface crack loaded with Hertzian pressure without the presence of a lubricant in the crack is presented. For this purpose, the elements of Williams equation for describing stresses near the crack tip are determined: Stress intensity factors KI and KII, and T-stress, which were taken into account when determing the direction of crack propagation by means of Strain energy density (SED) criterion. The elements are determined based on the case of a gear tooth flank, with various friction coefficients on the free surface and friction in the crack being taken into account. The results show that friction on the free surface and, consequently, tangential forces have an impact on whether the crack will propagate along the free surface or into the depth.