On the Dynamic Gear Tooth Loading as Affected by Bearing Clearances in High Speed Machinery

1982 ◽  
Vol 104 (4) ◽  
pp. 724-730 ◽  
Author(s):  
B. M. Bahgat ◽  
M. O. M. Osman ◽  
T. S. Sankar
Keyword(s):  
High Speed ◽  
Design Method ◽  
Gear Tooth ◽  
Contact Point ◽  
Velocity Ratio ◽  
Spur Gears ◽  
Governing Equations ◽  
Contact Mode ◽  
Gear Teeth ◽  
Geometrical Constraints

The paper studies the effect of bearing clearances in the dynamic analysis of gear mechanisms in high speed machinery. For this purpose, an analytical model is developed based on the interdependence between kinematics and kinetic relationships that must be satisfied when contact is maintained between the journal and its bearing. The contact modes are formulated such that the bearing eccentricity vector must align itself with bearing normal force at the point of contact. The analysis mainly relies on determining the direction of the bearing eccentricity vector defined as the clearance angles βi at the bearing revolutes for each contact mode of the gear teeth. The governing equations of the clearance angles are developed using the geometrical constraints of the contact point location and the velocity ratio. The clearance angles and their derivatives are subsequently used to systematically evaluate kinematic and dynamic quantities of each gear as well as the dynamic tooth load. A pair of rigid tooth spur gears with two revolute clearances is analyzed to illustrate the procedure. The model presented in the paper provides a design method for investigating the effect of bearing tolerances and wear on the evaluation of dynamic tooth load in high speed gearing systems.

On the Dynamic Gear Tooth Loading of Planetary Gearing as Affected by Bearing Clearances in High-Speed Machinery

1985 ◽  
Vol 107 (3) ◽  
pp. 430-436 ◽  
Author(s):  
B. M. Bahgat ◽  
M. O. M. Osman ◽  
R. V. Dukkipati
Keyword(s):  
High Speed ◽  
Gear Tooth ◽  
Contact Point ◽  
Velocity Ratio ◽  
Planetary Gear ◽  
Spur Gears ◽  
Governing Equations ◽  
Contact Mode ◽  
Gear Teeth ◽  
Geometrical Constraints

The paper studies the effect of bearing clearances in the dynamic analysis of planetary gear mechanisms in high-speed machinery. For this purpose, an analytical model is developed based on the interdependence between kinematics and kinetic relationships that must be satisfied when contact is maintained between the journal and its bearing. The contact mode is formulated such that the bearing eccentricity vector must align itself with bearing normal force at the point of contact. The analysis mainly relies on determining the direction of the bearing eccentricity vector defined as the clearance angles βi at the bearing revolutes for each contact mode of the gear teeth. The governing equations of the clearance angles are developed using the geometrical constraints of the contact point location and the velocity ratio. The clearance angles and their derivatives are used to systematically evaluate kinematic and dynamic quantities. A rigid planetary spur gears with two revolute clearances is analyzed to illustrate the procedure.

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 Study of Lubricant Jet Flow Phenomena in Spur Gears—Out of Mesh Condition

1978 ◽  
Vol 100 (1) ◽  
pp. 61-68 ◽  
Author(s):  
D. P. Townsend ◽  
L. S. Akin
Keyword(s):  
High Speed ◽  
Gear Tooth ◽  
Velocity Ratio ◽  
Jet Impingement ◽  
Gear Ratio ◽  
Experimental Program ◽  
High Speed Photography ◽  
Gear Mesh ◽  
Mesh Condition ◽  
Oil Jet

An analysis was conducted for oil jet lubrication on the disengaging side of a gear mesh. Results of the analysis were computerized and used to determine the oil jet impingement depth for several gear ratios and oil jet to pitch line velocity ratios. An experimental program was conducted on the NASA gear test rig using high-speed photography to experimentally determine the oil jet impingement depth on the disengaging side of mesh. Impingement depth reaches a maximum at gear ratio near 1.5 where chopping by the leading gear tooth limits the impingement depth. The pinion impingement depth is zero above a gear ratio of 1.172 for a jet velocity to pitch time velocity ratio of 1.0 and is similar for other velocity ratios. The impingement depth for gear and pinion are equal and approximately one-half the maximum at a gear ratio of 1.0. Impingement depth on either the gear or pinion may be improved by relocation of the jet from the pitch line or by changing the jet angle. Results of the analysis were verified by experimental results using a high-speed camera and a well lighted oil jet.

Gear-Tooth Stresses at High Speed

1950 ◽  
Vol 163 (1) ◽  
pp. 162-175 ◽  
Author(s):  
W. A. Tuplin
Keyword(s):  
Fatigue Limit ◽  
High Speed ◽  
Gear Tooth ◽  
Permissible Stress ◽  
Usual Practice ◽  
Gear Teeth ◽  
Speed Up ◽  
The Mean ◽  
Stress Cycles ◽  
The Difference

If the maximum stress in a gear tooth is less than the fatigue limit for the material, the tooth should not fail even after indefinitely prolonged running. Fatigue data collected in the conventional way suggest that the number of stress cycles required to cause failure of a given material under any particular stress is independent of the time-rate of repetition of stress. It should therefore be permissible to stress any gear, regardless of its speed, up to the fatigue limit for its material, although this suggestion may need modification because of the difference between the impulsive nature of the application of load to a gear, and the more gradual fluctuation of stress in a fatigue-test specimen of the Wöhler type. Where high-speed gears have failed under stresses apparently lower than the fatigue limit, it becomes necessary to consider whether the actual stress was as low as had been supposed. Errors of pitch and profile in gear teeth may cause actual stresses to be higher than nominal stresses by an amount that increases with speed in any particular installation, up to a limit that would not be exceeded even at infinite speed. The nominal permissible stress (corresponding to the mean transmitted torque) should therefore take account of probable errors in the teeth. High tooth-loads may also be induced by running a geared system in a condition approaching that of resonance with some type of vibration. In general, this danger is more likely in high-speed installations than in others, and it is not always wise to follow the usual practice of ignoring its possibility.

Analysis of the dynamic contact between rotating spur gears by finite element and multi-body dynamics techniques

2001 ◽  
Vol 215 (4) ◽  
pp. 423-435 ◽  
Author(s):  
K Lee
Keyword(s):  
Finite Element ◽  
Contact Point ◽  
Equations Of Motion ◽  
Mass Effect ◽  
Dynamic Contact ◽  
Spur Gears ◽  
Gear Teeth ◽  
Body Dynamics ◽  
Tooth Surfaces ◽  
Multi Body

A numerical method is presented for the dynamic contact analysis of spur gears rotating with very high angular speeds. For each gear an elastic tooth of distributed mass is connected to a rigid disc with kinematic constraints, and finite element formulations are used for the equations of motion of the teeth. The velocity and acceleration as well as the position of the contact point sliding on the mating gear teeth are precisely computed by simultaneously using the motions of a pair of rotating tooth surfaces. The equations of motion subjected to the kinematic constraint and contact condition are solved by enforcing the velocity and acceleration constraints as well as the displacement constraint. In the numerical simulation the importance of the mass effect of gear teeth is demonstrated, and it is shown that the solution is obtained even if gears repeat contact and separation.

Calculation of Spur Gear Tooth Flexibility by the Complex Potential Method

1985 ◽  
Vol 107 (1) ◽  
pp. 38-42 ◽  
Author(s):  
A. Cardou ◽  
G. V. Tordion
Keyword(s):  
Singular Point ◽  
Complex Potential ◽  
Gear Tooth ◽  
Contact Point ◽  
Spur Gear ◽  
Potential Method ◽  
Complex Potentials ◽  
Spur Gears ◽  
Tooth Contact ◽  
Complex Potential Method

Complex potentials have already been used to calculate analytically spur gear stresses. However, their application to the calculation of tooth flexibility is not so straightforward since displacements of interest are at the tooth contact point, which is a singular point for the equations being used. A method has been devised to circumvent this difficulty and to obtain the value of the displacement at each point of the line of action, and thus, the flexibility of a given pair of spur gears.

A Virtual Tool for Wear Simulation of Standard and Non-Standard Spur Gears

2012 ◽  
Author(s):  
F. Karpat ◽  
S. Ekwaro-Osire ◽  
E. Karpat
Keyword(s):  
High Speed ◽  
High Performance ◽  
Failure Modes ◽  
Power Transmission ◽  
Wear Behavior ◽  
Gear Tooth ◽  
Load Capacity ◽  
High Load ◽  
Wear Depth ◽  
Spur Gears

There is an industrial demand for the increased performance of mechanical power transmission devices. This need in high performance is driven by high load capacity, high endurance, low cost, long life, and high speed. New designs and modifications in gears have been investigated to obtain high load carrying capacity and increased life with less volume and weight. Tooth wear is one of the major failure modes in gears. Although there are different classifications of wear mechanisms, wear on gears can be simply classified as mild wear, pitting, and severe wear, depending on the wear rate. These types of wear may lead to power transmission losses, decreased efficiency, increased vibration and noise, and gear tooth failure. This paper deals with the simulation of wear for standard and non-standard gears using an analytical approach. A numerical model for wear prediction of gear pair is developed. A wear model based on Archard’s equation is employed to predict wear depth. A MATLAB-based virtual tool is developed to analyze wear behavior of standard and non-standard spur gears with various gear parameters. In this paper, this virtual tool is introduced by using many numerical examples.

Development of a Dynamometer to Study the Performance of Plastic Gears

2007 ◽  
Author(s):  
Mike Cassata ◽  
Martin Morris ◽  
Jorge Abanto-Bueno
Keyword(s):  
High Speed ◽  
Failure Modes ◽  
Gear Tooth ◽  
Digital Camera ◽  
Operating Conditions ◽  
Spur Gears ◽  
Camera System ◽  
Dupont Company ◽  
Plastic Gears ◽  
Flank Surface

A testing facility has been developed to explore the failure modes of plastic gears. The overall goal is the prediction of gear tooth failure for a given set of operating conditions and to classify failure modes of plastic gears. The initial investigation is centered on the testing of plastic spur gears placed on a parallel-shaft drive train between a variable-speed, reversible DC motor and an eddy current dynamometer. The testing apparatus has been designed, fabricated, and refined to deliver consistent results. The dynamometer places two plastic spur gears in mesh, one being the drive gear and the other the driven. Most of the test gear pairs were injection molded, 40-tooth, 0.8 module gears. These gears were molded using Delrin™ 311DP, a polyoxymethylene polymer which is made by the DuPont Company. Optical encoders were attached to the input and output shafts to sense the shaft position providing a measurement of the deflection and wear of the gear teeth. In addition, an infrared temperature sensor was retrofitted to the dynamometer apparatus to measure the tooth-flank surface temperature. All of the tests where the gear flank temperature reached 250°F resulted in a catastrophic failure. The apparatus was also fitted with a high-speed digital camera system capable of sampling 1000 frames per second. The camera recorded the failure of the plastic gears.

Analytical Reconstruction of the Running Surfaces of Gear Teeth Using Standard Profile and Lead Measurements

1983 ◽  
Vol 105 (4) ◽  
pp. 725-735 ◽  
Author(s):  
W. D. Mark
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Spur Gears ◽  
Gear Teeth ◽  
Tooth Width ◽  
Least Squares Fit ◽  
Geometric Deviations ◽  
Standard Profile ◽  
Involute Surface ◽  
Class Of Functions

A method is developed for analytically reconstructing the geometric deviations of the running surface of a gear tooth from a perfect involute surface. The method uses standard profile and lead deviation measurements and is applicable to both helical and spur gears. The reconstruction is carried out by using normalized Legendre polynomials. For this class of functions, it is shown that the optimum locations of the profile and lead deviation measurements are the locations of the zeros of the Legendre polynomial of degree equal to the number of profile or lead deviation measurements taken–after appropriate normalization of the tooth width or depth, as appropriate. A least squares fit procedure for establishing a common origin of ordinates for sets of profile and lead deviation measurements is formulated, and its solution is carried out in closed form. Account is taken of the noninsignificant errors that typically arise in profile and lead deviation measurements so that the final analytically reconstructed tooth surface is free of inconsistencies.

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