Modeling and Analysis of Sliding Friction in Gear Dynamics

2000 ◽  
Author(s):  
Manish Vaishya ◽  
Donald R. Houser
Keyword(s):  
Sliding Friction ◽  
Transmission Error ◽  
Spur Gear ◽  
Spur Gears ◽  
Parameter System ◽  
Modeling And Analysis ◽  
Gear Teeth ◽  
Lumped Parameter ◽  
Force Transmissibility ◽  
Vibration Coupling

Abstract Sliding resistance on gear teeth can have a dominant effect on housing vibration and noise, due to fluctuating excitation and high force transmissibility in the off-line of action direction. Hence reliable modeling of friction from tribological considerations, supported by experimental data, is of utmost importance. This paper examines some lubrication theories and validates them with 2-disk tests and quasi-static loaded gear tests. From the knowledge of friction characteristics, a lumped parameter system is synthesized for a pair of spur gears. This model includes sliding friction, mounting compliances and lateral-torsional vibration coupling. A different formulation has been applied, which unlike most current models, accounts for energy dissipation in the system due to friction. The influence of various excitations like transmission error, friction and parametric variations, on dynamic response of gears is investigated. Finally, the model is evaluated with dynamic tests carried out on a spur gear set, under varying conditions of torque, speed and lubricant.

Design of High Speed Gears, Low Load Gears for Minimizing Gear Whine Noise

2013 ◽  
Author(s):  
Rodney Glover
Keyword(s):  
High Speed ◽  
Sliding Friction ◽  
Transmission Error ◽  
Spur Gear ◽  
Low Noise ◽  
Spur Gears ◽  
Contact Ratio ◽  
Low Load ◽  
Gear Manufacturing ◽  
The Cost

The main purpose of the supercharger timing gears is to keep the rotors from contacting each other. They are often lightly loaded and designed for low noise. As timing gears, they have by definition a ratio of 1.0. Furthermore, the timing gears are presently spur gears due to the cost of assembling helical gears onto the rotor shafts without allowing timing errors between the rotors. The original timing gear designs were spur gears with contact ratios slightly above 2.0. A major NVH issue has been gear whine noise, because most applications are in luxury vehicles and are evaluated with the hood open and the engine at idle. In this operating condition, the background noise is very low and any tonal gear whine noise is audible. The first effort was to push the gear manufacturing quality to the limits of modern grinding capability. In order to further reduce gear whine noise, the designs have evolved to finer pitch gearing with a contact ratio over 3.0 to reduce transmission error. Micro-geometries were optimized for low transmission error (TE) at low load. OSU Gear Lab’s RMC and LDP became primary tools in optimizing the gear designs for minimum TE. An important factor when increasing the contact ratio is to not increase the sliding friction significantly to keep the fixed oil sump temperature from increasing too much and cause wear issues in operation. Typically, the new high contact ratio spur gear designs in production have reduced the gear whine levels by more than 6 dB and have had very few noise complaints.

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).

Low excitation spur gears with variable tip diameter

2021 ◽  
Vol 263 (5) ◽  
pp. 1275-1285
Author(s):  
Joshua Götz ◽  
Sebastian Sepp ◽  
Michael Otto ◽  
Karsten Stahl
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Low Noise ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Axial Forces ◽  
Tooth Width ◽  
Drive Trains ◽  
Static Transmission Error

One important source of noise in drive trains are transmissions. In numerous applications, it is necessary to use helical instead of spur gear stages due to increased noise requirements. Besides a superior excitation behaviour, helical gears also show additional disadvantageous effects (e.g. axial forces and tilting moments), which have to be taken into account in the design process. Thus, a low noise spur gear stage could simplify design and meet the requirements of modern mechanical drive trains. The authors explore the possibility of combining the low noise properties of helical gears with the advantageous mechanical properties of spur gears by using spur gears with variable tip diameter along the tooth width. This allows the adjustment of the total length of active lines of action at the beginning and end of contact and acts as a mesh stiffness modification. For this reason, several spur gear designs are experimentally investigated and compared with regard to their excitation behaviour. The experiments are performed on a back-to-back test rig and include quasi-static transmission error measurements under load as well as dynamic torsional vibration measurements. The results show a significant improvement of the excitation behaviour for spur gears with variable tip diameter.

scholarly journals Research on the Design and Modification of Asymmetric Spur Gear

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaohe Deng ◽  
Lin Hua ◽  
Xinghui Han
Keyword(s):  
Computer Aided Design ◽  
Design Method ◽  
Geometric Model ◽  
Simulation Method ◽  
Transmission Error ◽  
Spur Gear ◽  
Geometric Shape ◽  
Spur Gears ◽  
Gear Design ◽  
Aided Design

A design method for the geometric shape and modification of asymmetric spur gear was proposed, in which the geometric shape and modification of the gear can be obtained directly according to the rack-cutter profile. In the geometric design process of the gear, a rack-cutter with different pressure angles and fillet radius in the driving side and coast side was selected, and the generated asymmetric spur gear profiles also had different pressure angles and fillets accordingly. In the modification design of the gear, the pressure angle modification of rack-cutter was conducted firstly and then the corresponding modified involute gear profile was obtained. The geometric model of spur gears was developed using computer-aided design, and the meshing process was analyzed using finite element simulation method. Furthermore, the transmission error and load sharing ratio of unmodified and modified asymmetric spur gears were investigated. Research results showed that the proposed gear design method was feasible and desired spur gear can be obtained through one time rapid machining by the method. Asymmetric spur gear with better transmission characteristic can be obtained via involute modification.

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.

Dynamic Transmission Error Measurements From Spur Gear Pairs Having Tooth Indexing Errors

2017 ◽  
Author(s):  
Brian Anichowski ◽  
Ahmet Kahraman ◽  
David Talbot
Keyword(s):  
High Speed ◽  
Transient Behavior ◽  
Transmission Error ◽  
Spur Gear ◽  
Spur Gears ◽  
Transient Effects ◽  
Dynamic Factors ◽  
Frequency Domains ◽  
Error Dynamic ◽  
Dynamic Transmission Error

This paper complements recent investigations [Handschuh et al (2014), Talbot et al (2016)] of the influences of tooth indexing errors on dynamic factors of spur gears by presenting data on changes to the dynamic transmission error. An experimental study is performed using an accelerometer-based dynamic transmission error measurement system incorporated into a high-speed gear tester to establish baseline dynamic behavior of gears having negligible indexing errors, and to characterize changes to this baseline due to application of tightly-controlled intentional indexing errors. Spur test gears having different forms of indexing errors are paired with a gear having negligible indexing error. Dynamic transmission error of gear pairs under these error conditions is measured and examined in both time and frequency domains to quantify the transient effects induced by these indexing errors. Both measurements indicate clearly that the baseline dynamic response, dominated by well-defined resonance peaks and mesh harmonics, are complemented by non-mesh orders of transmission error due the transient behavior induced by indexing errors.

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.

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.

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.

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