Tooth Root Bending Stress Research Articles

Increasing bending strength in spur gears using shape optimisation of cutting tool profile

The geometrical shape of gear tooth fillet profile, usually cut out by the cutter tip, plays a significant role in the evaluation of the gear bending stress. In order to improve the teeth bending strength, a novel curve (quadratic rational Bezier curve) is introduced to describe the cutter tip. The gear tooth finite element models are founded by APDL in the ANSYS software. With the maximum bending stress (von Mises stress) as the objective function, SUB-PROBLEM and FIRST-ORDER optimisation methods in ANSYS are used to optimise the cutter tip. Single-tooth bending test is also conducted to prove the optimisation result. The study reveals that the relationship between the design variable and tooth root bending stress is non-linear, and the gear cut by the optimised cutter exhibits higher bending strength rather than the gear cut by standard cutting tool.

Gear Application Feasibility Study of Functionally Gradient Material

The problems of the tooth root bending stress increase,distortion, the life of the gear reduction and other issues existing in the gear heat treatment process, In order to solve these problems, functionally gradient material (FGM) was used on gear working surface. the analysis of heat treated gear performance and common gear performance comparison analysis has maded; A functionally gradient material cylindrical involute gear model and a common cylindrical involute gear model were created, Then finite element calculation of bending stress and analysis of the two models has maded. The FGM gear have better performance on the root bending stress and the hardness of the working surface, and also can avoid disadvantages about distortion and uniform carburized layer which might happened in heat treatment process. The experimental results show that FGM can be used on gear.

Stress Analysis of Asymmetric Spur Face-Gear Pair Based on Finite Element Method

According to the theory of gear geometry, the equations of teeth surface of double pressure angles asymmetric face-gear were conducted. Discrete points were generated in MATLAB according to the surface equations, and then the author established contact finite element models of single-tooth pair in ANSYS. The calculated value of contact pressure of the single tooth contact finite element model and the calculated value of contact pressure which given by the point-contact Hertz theory were compared to verify the effectiveness of the contact finite element method. Several groups of parameters were calculated and the results showed that the use of reasonable asymmetric design can effectively reduce the max surface contact pressure and the max tooth root bending stress.

Precise modeling of arc tooth face-gear with transition curve

A fabrication method is adopted for which an imaginary gear simultaneously realizes conjugated meshing with an arc tooth cylindrical gear and an arc tooth face-gear. The cutter fillet and tooth crest edge form the tooth root fillet of the gear, and the linear tooth surface equation of the imaginary gear and the position vector of the curvature center of the cutter fillet are constructed with certain cutter inclination to deduce a working arc tooth surface equation. The tooth root fillet equation of the arc tooth face-gear is derived from the meshing geometry and kinematics. A numerically controlled machining model of the arc tooth face-gear is established through the transformation of adjustment parameters from the cutter-tilt milling machine to a common multi-axis NC machine. Motion parameters of each movement axis of the NC machine are acquired. A processing example is presented to verify the precision of the fabrication method in processing the arc tooth face-gear. The method provides a theoretical and tentative basis for the analysis of tooth surface contact stress, tooth root bending stress and dynamics. A hobbing test is conducted to demonstrate the good meshing condition of the arc tooth face-gear pair.

Multi-Objective Topology Optimization for Bevel Gear and Geometrical Reconstruction

Usually the gear modification is a main measure to reduce the vibration and noise of the gears, but in view of the complexity of the gear modification, topology optimization method was used to optimize the structure of the gear. The minimum volume was set as the direct optimization goal. To achieve the target of reducing contact stress, tooth root bending stress and improving flexibility, the upper bound of the stress and lower bound of the flexibility were set appropriately, thus realizing multi-objective optimization indirectly. A method for converting topology result into parametric CAD model which can be modified was presented, by fitting the topology result with simple straight lines and arcs, the model can be smoothed automatically, after further regulating, the geometry reconstruction was finished. After topology optimization, the resulting structure and properties of the gear are consistent with cavity gear. While reducing the weight of the gear, the noise can be reduced and its life would be extended through increasing flexibility and reducing tooth root stress.

Critical stress and load conditions for bending calculations of involute spur and helical gears

In this paper, a non-uniform model of load distribution along the line of contact of spur and helical gears, obtained from the minimum elastic potential criterion, has been used, combined with the equations of the linear elasticity, to evaluate the fatigue tooth-root stress. The critical value of the stress and the critical load conditions have been obtained and a complete analysis of the tooth bending strength has been carried out. As the load per unit of length at any point of the line of contact and any position of the meshing cycle has been described by a very simple analytic equation, a complete study of the location and the value of the tooth-root bending stress has been carried out. From this study, a recommendation for the calculation of the bending load capacity of spur and helical gears is proposed.

Research on Bending Fatigue of Cylindrical Gear Based on ANSYS Workbench

Based on the bending fatigue properties of cylindrical gear pair, the worst meshing positions on driving and driven gears are respectively determined, the corresponding S-N curve for bending fatigue and loading spectrum of tooth root bending stress are obtained. Then a method for analyzing the bending fatigue of the cylindrical gear by ANSYS Workbench is studied and the simulation is carried out. Different from the traditional methods, the bending fatigue characteristic parameters such as safety coefficients and fatigue sensitive coefficients for every part of the tooth can be precisely calculated by finite element method. It provides an important basis for reliability design and structural optimization of the cylindrical gear pair.

Dynamic Contact Emulate Analysis of Logarithmic Spiral Bevel Gear with ANSYS/LS-DYNA

For a new type of bevel gear-logarithmic spiral bevel gear, which stress mechanical properties are studied during the meshing process. Three-dimensional meshing models of logarithmic spiral bevel gear are established by Pro/ E. Because its tooth trace is conical logarithmic spiral, the paper proposes a new modeling method and successfully constructs the engagement model. Based on this, the gear dynamic contact emulation analysis is operated with ANSYS/LS-DYNA software in order to obtain stress distribution in the process of tooth contact. The tooth contact stress and tooth root bending stress magnitude, stress distribution and variation of cloud are analyzed. Contacting engineering practice, the results are in-depth study. Thus it can provide the theory basis for design and the application of this kind of new bevel gear.

Analysis of Field of Stress and Displacement in Process of Meshing Gears

Base on the successively engaging projection called teeth, gears are direct contact bodies, operating in pair, that transmit motion and force from one rotating shaft to another, it is one of the most important mechanical transmission forms in the field of mechanical engineering, it has various forms and uses widely, but the consequences caused by gear failure are often serious. Loaded contact performance, tooth contact stress and tooth root bending stress of the pair of gears are an important concerned index in the successive process of engagement. The precise modeling of involutes cylindrical gear is obtained by using the large scale CAD software, and using of the data interface of the finite element analysis software, it can import the model in the form of dxf into the finite element analysis software, the model of three dimensional finite element nonlinear contact was established. According to the geometric shape of the tooth, it can divide the model into lattice and impose the appropriate boundary conditions, it can be obtain the quasi static characteristics of the meshing tooth by using the finite element analysis. The results of numerical analysis showed that the model can accurately simulate the distribution of equivalent stress and the changing displacement in the process of tooth meshing gear, which verify the accuracy of the model, and the model can be used to deal with the dynamic meshing problem of gears.

S111032 遠心力の影響を考慮した傾斜ウェブを持つ三次元構造薄肉平歯車の歯面接触応力及び歯元応力の理論解析([S11103]伝動装置の基礎と応用(3))

Deformations of thin-rimmed spur gears with inclined webs are analyzed by finite element method (FEM) when the gears are loaded under centrifugal forces. Then loaded tooth contact analyses of the gears with centrifugal deformations are conducted by mathematical programming method and FEM when the gears contact with a solid mating gear. Tooth contact stress and root bending stress are analyzed by FEM at the same time. It is found that centrifugal load exerts greater effect on tooth root stress when gear speed is over 10000rpm. So, it is necessary to take the effect of centrifugal load into account in tooth root strength calculation when gear speed is over 10000rpm. It is also found that centrifugal deformations of the gears almost have no effect on tooth contact patterns of the gears having inclined webs, though it has been reported that centrifugal deformations of the gears with the straight web have great effect on tooth contact patterns. This is because shape of the inclined web after centrifugal deformation is completely different from the shape of the straight web after centrifugal deformation. This difference results in the difference of tooth attitudes and then the difference of the effects of tooth centrifugal deformations on tooth contact patterns. It can be concluded that the effect of centrifugal deformations of the inclined web gears on tooth contact pattern can be neglected even if the gears have very high speeds.

Effect of addendum on contact strength, bending strength and basic performance parameters of a pair of spur gears

Abstract This paper investigates effect of addendum on tooth contact strength, bending strength and basic performance parameters of spur gears. Face-contact model of teeth, mathematical programming method (MPM) and three-dimensional (3D), finite element method (FEM) are used together to conduct loaded tooth contact analyses (LTCA), deformation and stress calculations of spur gears with different addendums and contact ratios. Tooth load, load-sharing rate, contact stress, root bending stress, transmission error and mesh stiffness of the spur gears are analyzed. Effects of addendum and contact ratio on gear strength and basic performance parameters are also discussed. It is found that contact stress distributed on tooth surface along the profile is asymmetrical around the geometrical contact point of the gears when the geometrical contact point is far away from the pitch point, especially at the tip or root contacts. The maximum contact stress is also not exactly at the geometrical contact point. Hertz formula can only calculate the tooth contact stress approximately. FEM can be used to conduct precise analysis of the tooth contact stress. It is also found that increment of addendum can increase number of contact teeth, then this increment can reduce tooth contact stress and root bending stress, generally speaking. But this increment also makes the tooth depth long and lets the tooth be deformed easily. So, this increment can reduce tooth contact stress, but there is no guarantee that this increment can certainly reduce tooth root bending stress. Also, increment of the addendum makes the values of “T” and “V” in the so-called value of “PVT” great. So, scoring strength calculations of the tooth tip and root becomes more important when to use high contact ratio gears (HCRG) with long addendum. Finally, strength calculations of HCRG with misalignment error, lead crowning and thin-walled thickness are discussed simply in this paper.

Effects of machining errors, assembly errors and tooth modifications on loading capacity, load-sharing ratio and transmission error of a pair of spur gears

Abstract This paper quantitatively investigates effects of machining errors (ME), assembly errors (AE) and tooth modifications (TM) on loading capacity, load-sharing ratio (LSR) and transmission error (TE) of a pair of spur gears by using special-developed finite element method (FEM) software in a personal computer. Tooth surface contact stress (TSCS) and tooth root bending stress (TRBS) of a pair of spur gears with ME, AE and TM are analyzed by the FEM software. Effects of ME, AE and TM on TSCS and TRBS are also defined as “Influence factors” and the influence factors of ME, AE and TM on TSCS and TRBS are calculated quantitatively. It is found that misalignment error of gear shafts on the plane of action of the spur gears exerts great effects on TSCS and TRBS while misalignment error of gear shafts on the vertical plane of the plane of action almost exerts no effects on TSCS and TRBS. It is also found that ME and lead crowning have greater effects on TSCS and TRBS. When the maximum tooth surface machining error is 40 μm, influence factor of ME on TSCS and TRBS are about 2.2 and 1.5. When quantity of lead crowning is 40 μm, influence factor of lead crowning on TSCS and TRBS are about 2.0 and 1.4. These influence factors can be used as references when ISO standards are used for tooth surface contact strength and root bending strength calculations of a pair of spur gears with ME, AE and TM. Methods for LSR calculation of a pair of spur gears with ME, AE and TM are also presented in this paper. Effects of ME, AE and TM on LSR are analyzed quantitatively. It is found that ME has greater effect on LSR. When the maximum tooth surface machining error is greater than 10 μm, double pair tooth-contact shall become single pair tooth-contact for sake of the effect of ME. This means that when ME on tooth surface is large, outer limit of the single pair tooth-contact area can not be used as the so-called “worst load position”. It is safe and reasonable to use tooth tip as the “worst load position” when to perform tooth bending strength calculation. Methods for TE calculation of a pair of spur gears with ME, AE and TM are also presented in this paper. Effects of ME, AE and TM on TE of the gears are analyzed quantitatively. It is found that ME not only changes waveform of TE easily, but also makes TE greater and greater when ME is increased. AE and TM also make TE greater and greater when they are increased, but do not change waveform of TE.

Fatigue Strength of RDK401 Nitrocarburized at Low Temperature

In order to examine the application limit of gears made of RDK401 which has a deep case depth by a low temperature gas nitrocarburizing treatment, the Ono-type rotating beam fatigue test, the Nishihara-type rolling contact fatigue test and gear test were carried out, then the underwritten results were obtained.(1) The rotating beam fatigue strength is 42kgf/mm2, when the stress concentration factor is 1.84.(2) The rolling contact fatigue strength is 180kgf/mm2, when the effective case depth is 0.19mm.(3) According to the gear tests, the allowable tooth root bending stress is 41kgf/mm2 and its value is near to that of the carburized gears. Then the allowable tooth surface stress is over 145kgf/mm2 in Hertz pressure.