•Analytic-iterative method for calculating the actual contact ratio.•Finite element simulations of exemplary tooth geometries as a reference.•Contact ratio factor to correlate actual contact ratio ...with tooth root stress.•Method for calculating the tooth root stress of steel-plastic spur gear pairs.•Comparison of calculation results of the proposed method and existing approaches.
The operational behavior and, in particular, the bending strength of thermoplastic gears are substantially influenced by the significant increase in contact ratio under load. According to current analytic calculation standards and guidelines, this effect is neglected when tooth root stress is calculated. Using numerical methods, such as the finite element method (FEM), a consideration of deflections is possible but the usage is complex and extensive in engineering practice compared to recomputing guidelines or standards like VDI 2736 or ISO 6336. In this work, a method is presented for calculating the nominal tooth root stress based on existing analytic guidelines, taking the actual contact ratio into account. Based on the example of three test gear geometries, the results are compared to existing guidelines, as well as numerical computations, showing that the presented method correlates well with the latter.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
•A mesh stiffness analytical model of helical gears with spalling is established.•Mesh stiffness is compared with that using finite element (FE) method.•Contact stress and tooth root stress are ...compared using analytical and FE methods.•Mesh characteristics under different spalling parameters are analyzed.
This paper investigates the effect of a gear tooth spalling in a helical gear. An analytical model was developed to study the effect of the damage to the time-varying mesh stiffness, contact stress and tooth root fillet stress. In order to validate the efficiency and the accuracy of the proposed method, a finite element method is presented for simulation, such to compare the mesh stiffness and stresses obtained from the analytical method under different spalling variables, including the spalling lengths, widths, axial positions (in the direction of face width) and tooth orientation positions (from dedendum to addendum). The results show that the proposed analytical method has higher computation efficiency than the finite element method, and the mesh stiffness obtained from two methods shows a good agreement. However, some errors exist between the time-varying mesh stiffness and stresses obtained by the two methods, but change laws of the tooth root stress and contact stress obtained from the two methods are similar. This is because the effects of flank-tip contact and spalling edge contact are considered in the finite element method, which makes the results more accurate than the results obtained by the proposed analytical method.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•A new analytical model is established to calculate the maximum tooth root stress and critical section location of gear based on mechanics theory.•The new model can determine the critical section ...location accurately and quickly by solving the extreme value.•Both bending moment stress and compressive axial stress are taken into account in the model with the accurate profile equation.•The result of the new model is consistent with that of finite element method and more reliable than international standards.
An accurate calculation of the maximum tooth root stress (TRS) and critical section location (CSL) provides a basis for predicting and improving gear performance. The irregular profile represented by the implicit function may cause the calculation to be more complex. In current research, finite element methods (FEM model) and experimental test methods (ET model) can obtain accurate results but need large computational resources and time. The results from ISO 6336:2006 (ISO model) and AGMA 2101-D04 (AGMA model) are obtained conveniently but sometimes not reliable. Therefore, a new analytical model based on the mechanics theory with an accurate profile equation is established to calculate the maximum TRS and corresponding CSL quickly and accurately by solving the extreme value. Finally, the results of the spur gear in five cases with different parameters are obtained and compared to those of the FEM, ISO and AGMA models. It is shown that the results of the new model are in agreement with those of the FEM model, even under different parametric conditions.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
A model is introduced for analyzing the influence of tooth shape deviations and assembly errors on the helical gear mesh stiffness, loaded transmission error, tooth contact stress and tooth root ...stress. The helical gear is approximated as a series of independent spur gear slices along axial direction whose face-width is relatively small. The relative position relationships among those sliced teeth in mesh are developed with tooth profile errors and the stiffness of the sliced tooth is calculated by the potential energy method. From the equilibriums of the forces, gear mesh stiffness, loaded transmission error, tooth contact stress and tooth root stress are calculated. Then two cases are presented for validation of the model. It is demonstrated that the model is effective for calculating the stiffness of helical gear pairs. Finally, the effects of the tooth tip reliefs, lead crown reliefs and misalignments on the gear mesh stiffness, transmission error, tooth contact stress and tooth root stress are analyzed. The results show that mesh stiffness decreases, loaded transmission error, the maximum tooth contact stress and the maximum tooth root stress grow with the increasing tooth tip relief, lead crown relief and misalignment. And tooth edge has concentrated tooth contact stresses with a gear misalignment.
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NUK, OILJ, SAZU, UKNU, UL, UM, UPUK
•Spur gears are designed for different rim thickness and pressure angles.•Static stress analysis is performed and crack initiation points are defined.•The fatigue propagation analyses are conducted ...in ANSYS smart crack growth.•The effect of rim thickness and pressure angle on crack propagation is investigated.
Gears are the most significant machine elements in power transmission systems. They are used in almost every area of the industry, such as small watches to wind turbines. During the power transmission, gears are subjected to high loads, even unstable conditions, high impact force can be seen. Due to these unexpected conditions, cracks can be seen on the gear surfaces. Moreover, these cracks can propagate, and tooth or body failures can be seen. The fatigue propagation life is related to the gear tooth root stress. If the root stresses decrease, the fatigue life of the gears will increase. In this study, standard and non-standard (asymmetric) gear geometries are formed for four different rim thicknesses and four different pressure angles to examine fatigue crack propagation life. Moreover, the effects of the rim thickness and drive side pressure angle on the root stress are investigated. The static stress analyses are carried out to determine the starting points of the cracks, and the maximum point of the stress is defined as the starting point of the cracks. Fatigue crack propagation analyzes are performed for gears whose crack starting points are determined. The static stress analyses are conducted in ANSYS Workbench; similarly, the fatigue propagation analysis is performed in ANSYS smart crack growth. In this way, the directions of the cracks are determined for different rim thicknesses and drive side pressure angles. Besides, the number of cycles and da/dN graphs is obtained for all cases depending on crack propagation. As a result of the study, maximum stress values were decreased by 66%. The fatigue propagation life was increased approximately fifteen times by using the maximum drive side pressure angle and optimum rim thickness.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Misalignment errors (MEs) cause uneven load distribution across the faces of the gear teeth that increase contact and tooth root stress (TRS), moving the peak TRS to the edge of the face width, ...seriously affecting the gear system transmission performance. This article employs the finite element method (FEM) to calculate the TRS of helical gear pairs under different MEs. The effect of MEs on the distribution of TRS is analyzed, and the characteristics of TRS distribution under different types of MEs are determined. Subsequently, a TRS testing platform is established, and the accuracy of the finite element model is validated through strain tests by introducing MEs through changes in the position of journal bearings. Finally, based on the particle swarm optimization-improved backpropagation (PSO-BP) neural network, a correlation model between MEs and the distribution characteristics of TRS along the tooth width is established. Utilizing this model, it is possible to calculate the maximum TRS at different positions of the helical gear tooth root under any MEs.
•Semi-analytical approach for determination of load sharing of a face-gear drive.•Assessment of static transmission error, flank contact pressure and tooth root stress.•Comparison of semi-analytical ...approach with FEM contact analysis.
The present manuscript expands on a procedure developed to calculate load sharing, transmission characteristics, tooth root stress and the flank contact pressure in face-gear drives. On the one hand the procedure uses the analytical determination of the contact path for meshing of rigid gears including the dimensions, and directions of the contact ellipses based on Hertzian theory of elastic contact. On the other hand it uses the determination of the load-dependant compliance of a pair of teeth by finite element analysis. The combination of these two calculation methods / approaches renders the finite element contact analysis unnecessary thus significantly shortening the required computation time. The exact geometric representation of the tooth flanks for the finite element analysis is also not required. This not only avoids a greater preprocessing effort but also enables an efficient automation of the procedure. All steps of this procedure are described in depth in this manuscript. The accuracy of the proposed semi-analytical approach is validated through a direct comparison with an FEM contact analysis carried out as an example for a face-gear drive.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The determination of tooth bending strength is a basic issue in gear design. This work presents the change of nominal tooth root stress of external toothed, cylindrical gears depending on the ...geometry used. The nominal tooth root stress is analyzed with using finite element simulations. The numerical calculations are executed in Abaqus. The imported geometries are produced by our own program in MATLAB. The boundary conditions to the models are defined accordance with the most significant analytical methods used in practice. This approach allows mapping direct correlation analysis by these calculations. The optimization of computational capacity used is also considered. In addition to the examination of the significant tooth stress value of symmetrical element pairs, the position of the critical cross-section is also analyzed. The effect of the asymmetric design of the tooth profile on the nominal tooth root stress is also presented in our investigations. The purpose of the numerical simulations carried out here is to determine the effect of the coast side angle on the magnitude of the significant tooth root stress and the position of the critical cross-section.
For the problem of bending fatigue strength test of involute helical gear, the change regulations of bending stress and load distribution relation of helical gears with different tooth width and ...helical angle are researched by using RomaxDesigner. The contact line positions and the maximum stress are got, and it can be used to determine the loading position and load of helical gear in single tooth bending fatigue test. The simulation values of bending stress of different helical angle gears and the calculated values obtained by a series of correction coefficients in GB/T 3480—1997 are compared and analyzed. It is found that there is a big difference between them, which proves the necessity of bending fatigue test of helical gear. The test scheme of helical gear bending fatigue strength is raised. The results of helical gear bending fatigue test according to the method can be transformed into the national standard, which can be used in future to improve the accuracy of evaluating helical gear bending strength.
This study investigated the impact of spur gear rim and web thickness on root stress. A finite-element analysis model (FEM) was utilized and validated through a gear-bending test. Four gears with ...different rim and web specifications, including a solid gear, were designed and tested using strain gages to measure their root stress. The 3D FEM was validated by comparing the measured root stresses with that analyzed by the developed FEM. Using this model, a parametric study was conducted by varying the web position, pressure angle, and module to investigate the effect of the backup ratio on the root stress ratio of the gear. A stress-ratio map was generated based on the results. This stress-ratio map was compared with the rim thickness factor (
Y
B
) for external spur gears specified in ISO 6336-3. The comparison reveals that the rim thickness factor specified in ISO 6336 is overly conservative compared to values obtained in this study. Our results suggest that the thickness of both the rim and web should be considered to reduce the weight of spur gears. These findings can be applied to the design of lightweight spur gears.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
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