scholarly journals Gear Teeth Deflection Model for Spur Gears: Proposal of a 3D Nonlinear and Non-Hertzian Approach

Machines ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 223
Author(s):  
Fabio Bruzzone ◽  
Tommaso Maggi ◽  
Claudio Marcellini ◽  
Carlo Rosso
Keyword(s):  
A Priori ◽  
Three Dimensional ◽  
Spur Gear ◽  
Test Case ◽  
Spur Gears ◽  
Three Dimensional Model ◽  
Gear Teeth ◽  
Face Width ◽  
Mechanics Model ◽  
Pressure Distributions

In this paper, a three-dimensional model for the estimation of the deflections, load sharing attributes, and contact conditions will be presented for pairs of meshing teeth in a spur gear transmission. A nonlinear iterative approach based on a semi-analytical formulation for the deformation of the teeth under load will be employed to accurately determine the point of application of the load, its intensity, and the number of contacting pairs without a priori assumptions. At the end of this iterative cycle the obtained deflected shapes are then employed to compute the pressure distributions through a contact mechanics model with non-Hertzian features and a technique capable of obtaining correct results even at the free edges of the finite length contacting bodies. This approach is then applied to a test case with excellent agreement with its finite element counterpart. Finally, several results are shown to highlight the influence on the quasi-static behavior of spur gears of different kinds and amounts of flank and face-width profile modifications.

Tooth Influence on Flexural and Torsional Flexibility, and Model Tooth Number Prediction for Optimum Dynamic Simulation of Wide-Faced Spur Gears

2005 ◽  
Vol 128 (3) ◽  
pp. 626-633 ◽  
Author(s):  
Raynald Guilbault
Keyword(s):  
Dynamic Simulation ◽  
Three Dimensional ◽  
Spur Gear ◽  
Spur Gears ◽  
Acceptable Error ◽  
Face Width ◽  
Dynamic Analyses ◽  
Tooth Number ◽  
The Common ◽  
Common Face

Refined dynamic analyses of gear pairs, including precise tooth contact description, often lead to unreasonable simulation requirements. Therefore, numerous models employ simplifications, such as two-dimensional deflection of the engaged gear set, which is inappropriate for wide-faced wheels. Other models propose three-dimensional (3D) representation of one tooth on a complete hub. This approach introduces the torsional and flexural deflection of the gear body, but underestimates the corresponding stiffness. Since forthcoming improvements of gear analysis should offer efficient 3D dynamic simulation of wide-faced gear sets, this paper primarily quantifies the flexibility error levels implied with 3D one tooth full hub spur gear models. Subsequently, a procedure is developed to determine the number of teeth required for a 3D model so that it will include the torsional and flexural flexibility of the spur gear body, within acceptable error levels. This procedure offers an efficient approach to optimize the (precision)/(simulation time) ratio. The method deals with gears of any diametral pitch, and covers the common face width and tooth number ranges.

The Compliance of Solid, Wide-Faced Spur Gears

1990 ◽  
Vol 112 (4) ◽  
pp. 590-595 ◽  
Author(s):  
J. H. Steward
Keyword(s):  
Experimental Data ◽  
Contact Line ◽  
Load Distribution ◽  
3D Model ◽  
Spur Gear ◽  
Point Load ◽  
Spur Gears ◽  
Line Load ◽  
Gear Teeth ◽  
Theoretical Results

In this paper, the requirements for an accurate 3D model of the tooth contact-line load distribution in real spur gears are summarized. The theoretical results (obtained by F.E.M.) for the point load compliance of wide-faced spur gear teeth are set out. These values compare well with experimental data obtained from tests on a large spur gear (18 mm module, 18 teeth).

Investigation of the Hertzian Stress Distribution on the Surface of the Straight Bevel Gear

2013 ◽  
Vol 307 ◽  
pp. 304-307 ◽  
Author(s):  
Aref Bahramighahnavieh ◽  
Peiman Mosaddegh ◽  
Saleh Akbarzadeh
Keyword(s):  
Stress Distribution ◽  
Spur Gear ◽  
Bevel Gear ◽  
Gear Teeth ◽  
Straight Bevel Gear ◽  
Face Width ◽  
The Face ◽  
Simulation Results ◽  
Abaqus Software ◽  
Good Agreement

In this paper, a model has been developed for calculating the Hertzian stress distribution of straight bevel gear. One pair of straight bevel gear teeth replaced with multiple pairs of spur gear teeth by using Tredgold approximation. The transmitted load and radii of curvature are evaluated and used to determine the stress distribution. The results show that these stresses are constant along the face width of tooth. Moreover, the magnitude of theses stresses are in good agreement with the simulation results using commercial ABAQUS software

scholarly journals Study of Lubricant Jet Flow Phenomena in Spur Gears

1975 ◽  
Vol 97 (2) ◽  
pp. 283-288 ◽  
Author(s):  
L. S. Akin ◽  
J. J. Mross ◽  
D. P. Townsend
Keyword(s):  
Motion Picture ◽  
High Speed ◽  
Drop Size ◽  
Gear Tooth ◽  
Jet Flow ◽  
Spur Gear ◽  
Spur Gears ◽  
Gear Teeth ◽  
Flow Phenomena ◽  
Oil Jet

Lubricant jet flow impingement and penetration depth into a gear tooth space were measured at 4920 and 2560 using a 8.89-cm- (3.5-in.) pitch dia 8 pitch spur gear at oil pressures from 7 × 104 to 41 × 104 N/m2 (10 psi to 60 psi). A high speed motion picture camera was used with xenon and high speed stroboscopic lights to slow down and stop the motion of the oil jet so that the impingement depth could be determined. An analytical model was developed for the vectorial impingement depth and for the impingement depth with tooth space windage effects included. The windage effects on the oil jet were small for oil drop size greater than 0.0076 cm (0.003 in.). The analytical impingement depth compared favorably with experimental results above an oil jet pressure of 7 × 104 N/m2 (10 psi). Some of this oil jet penetrates further into the tooth space after impingement. Much of this post impingement oil is thrown out of the tooth space without further contacting the gear teeth.

scholarly journals Baseline Experimental Results on the Effect of Oil Temperature on Shrouded Meshed Spur Gear Windage Power Loss

2017 ◽  
Author(s):  
Irebert R. Delgado ◽  
Michael J. Hurrell
Keyword(s):  
Experimental Test ◽  
Power Loss ◽  
Spur Gear ◽  
Spur Gears ◽  
Test Results ◽  
Oil Viscosity ◽  
Gear Teeth ◽  
Temperature Load ◽  
Loss Efficiency

Rotorcraft gearbox efficiencies are reduced at increased surface speeds due to viscous and impingement drag on the gear teeth. This windage power loss can affect overall mission range, payload, and frequency of transmission maintenance. Experimental and analytical studies on shrouding for single gears have shown it to be potentially effective in mitigating windage power loss. Efficiency studies on unshrouded meshed gears have shown the effect of speed, oil viscosity, temperature, load, lubrication scheme, etc. on gear windage power loss. The open literature does not contain experimental test data on shrouded meshed spur gears. Gear windage power loss test results are presented on shrouded meshed spur gears at elevated oil inlet temperatures and constant oil pressure both with and without shrouding. Shroud effectiveness is compared at four oil inlet temperatures. The results are compared to the available literature and follow-up work is outlined.

Determining the Lewis Factor for Plastic Spur Gears With Asymmetric Teeth

2009 ◽  
Author(s):  
J. L. Moya ◽  
A. S. Machado ◽  
A. M. Becerra ◽  
J. A. Vela´zquez ◽  
R. Goytisolo
Keyword(s):  
Theoretical Analysis ◽  
Direct Effect ◽  
Spur Gear ◽  
Spur Gears ◽  
Gear Teeth ◽  
Tooth Fracture ◽  
Tooth Width

The basic weakness of plastic spur gear teeth is tooth fracture brought on by the accumulation of stress at the root of the tooth and by the geometry of the tooth. Tooth width and height play a major role in failure, as does the Lewis factor, which has a direct effect on the expression to calculate tooth strength. This study describes a theoretical analysis of a procedure to determine the Lewis factor for asymmetric teeth.

An obstacle problem for Koiter’s shells

2019 ◽  
Vol 24 (10) ◽  
pp. 3061-3079 ◽  
Author(s):  
Philippe G Ciarlet ◽  
Paolo Piersanti
Keyword(s):  
Asymptotic Analysis ◽  
A Priori ◽  
Elastic Shell ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Model ◽  
Limit Model ◽  
Membrane Shells ◽  
Point Of Departure ◽  
Confinement Condition

In this paper, we define, a priori, a natural two-dimensional Koiter’s model of a ‘general’ linearly elastic shell subject to a confinement condition. As expected, this model takes the form of variational inequalities posed over a non-empty closed convex subset of the function space used for the ‘unconstrained’ Koiter’s model. We then perform a rigorous asymptotic analysis as the thickness of the shell, considered a ‘small’ parameter, approaches zero, when the shell belongs to one of the three main classes of linearly elastic shells, namely elliptic membrane shells, generalized membrane shells and flexural shells. To illustrate the soundness of this model, we consider elliptic membrane shells to fix ideas. We then show that, in this case, the ‘limit’ model obtained in this fashion coincides with the two-dimensional ‘limit’ model obtained by means of another rigorous asymptotic analysis, but this time with the three-dimensional model of a ‘general’ linearly elastic shell subject to a confinement condition as a point of departure. In this fashion, our proposed Koiter’s model of a linearly elastic shell subject to a confinement condition is fully justified in this case, even though it is not itself a ‘limit’ model.

Studies on the Dynamic Performance of a Spur Gear With Hollow Teeth

1992 ◽  
Author(s):  
A. Ramamohana Rao ◽  
B. Srinivasulu
Keyword(s):  
Damping Ratio ◽  
Dynamic Performance ◽  
Spur Gear ◽  
Dynamic Loads ◽  
Response Analysis ◽  
Spur Gears ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Direction Parallel ◽  
Gear Teeth

Abstract Performance of spur gears largely depends on the magnitude and nature of variation of dynamic loads occuring between mating teeth. Variable tooth mesh stiffness is one of the primary sources causing parametric excitations resulting in dynamic loads. The usual method of varying the mesh stiffness to reduce dynamic loads is to use high contact ratio and profile modified gears. In this paper, a new type of tooth design to improve the dynamic performance of spur gears is presented. In this, a through hole is drilled in each tooth in a direction parallel to the gear axis. The diameter of the hole and its position on the tooth centre line are variable. Such a gear is called a hollow gear. Dynamic analysis is carried out for the mesh of hollow pinions mating with solid gears. The results are compared with solid pinions (no holes in teeth) meshing with solid gears. Finite element method is used for the analysis. For estimation of the dynamic load variation in hollow-solid and solid-solid gear meshes, a model incorporating the varying mesh stiffness and damping of gear teeth is used. Governing differential equations are solved using unconditionally stable Newmark-beta algorithm. The dynamic loads obtained are used as an input time varying loads for the determination of dynamic fillet and hole stress response of solid and hollow gear teeth whichever is applicable. Modal superposition technique is used for transient response analysis. The study shows that for the same damping ratio, dynamic loads in hollow-solid meshes are nearly the same as in a solid-solid mesh. In reality, the dynamic loads in a hollow-solid mesh are less than a solid-solid mesh due to its inherent higher material damping.

Calculation of Wobble From Lead Inspection Data of Gear Teeth With Modifications

1998 ◽  
Author(s):  
Xiaogen Su ◽  
Donald R. Houser
Keyword(s):  
Satisfactory Result ◽  
Spur Gear ◽  
Helical Gear ◽  
Spur Gears ◽  
Helical Gears ◽  
Gear Teeth ◽  
Inspection Data

Abstract The effect of the reference misalignment including eccentricity and wobble on profile and lead inspection traces is discussed. The relative slopes of the lead traces induced by wobble are used to calculate the magnitude of the wobble. The deviation caused by the wobble is removed from the lead inspection results. This method is theoretically ‘exact’ for spur gears and is approximate for helical gears. Real measurement examples show this method produces a good result with a spur gear and a satisfactory result with a helical gear.

scholarly journals Compliance and Stress Sensitivity of Spur Gear Teeth

1981 ◽  
Vol 103 (2) ◽  
pp. 447-459 ◽  
Author(s):  
R. W. Cornell
Keyword(s):  
Closed Form Solution ◽  
Time History ◽  
Peak Stress ◽  
Spur Gear ◽  
Stress Sensitivity ◽  
Form Solution ◽  
Sensitivity Analyses ◽  
Spur Gears ◽  
Contact Ratio ◽  
Gear Teeth

The magnitude and variation of tooth pair compliance with load position affects the dynamics and loading significantly, and the tooth root stressing per load varies significantly with load position. Therefore, the recently developed time history, interactive, closed form solution for the dynamic tooth loads for both low and high contact ratio spur gears [1] was expanded to include improved and simplified methods for calculating the compliance and stress sensitivity for three involute tooth forms as a function of load position. The compliance analysis is based on Weber [2] and O’Donnell [3] but with an improved fillet/foundation compliance analysis. The stress sensitivity analysis is a modified version of the Heywood method [4] but with an improvement in the magnitude and location of the peak stress in the fillet. These improved compliance and stress sensitivity analyses are presented along with their evaluation using test, finite element, and analytic transformation results, which showed good agreement.

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