An Improved Model for Calculating the Mesh Stiffness of Helical Gears

2019 ◽  
Author(s):  
Jing Wei ◽  
Shaoshuai Hou ◽  
Aiqiang Zhang ◽  
Chunpeng Zhang
Keyword(s):  
Analytical Method ◽  
Coupling Effect ◽  
Contact Stiffness ◽  
Helical Gear ◽  
Accurate Solution ◽  
Gear Transmission ◽  
Hertzian Contact ◽  
Mesh Stiffness ◽  
Single Tooth ◽  
Helical Angle

Abstract Time-varying mesh stiffness (TVMS) is one of the important internal excitations of gear transmission systems. Accurate solution of meshing stiffness is the key to research the vibration response of gear transmission system. In the traditional analytical method (TAM), the TVMS of single-teeth engaged region consist of bending, shearing, axial compression deformation stiffness, fillet-foundation stiffness, and Hertzian contact stiffness, the TVMS of double-tooth engaged region is the sum of the single-tooth engaged region, which will lead to repeated calculation of the fillet-foundation stiffness. In order to overcome this shortcoming, considering the coupling effect between two pairs of meshing tooth, an improved method of fillet-foundation is adopted to calculate to TVMS of each slice gear. According to the ‘slicing method’, the helical gear is divided into slice gear. Considering the coupling effect of each slice gear, the TVMS of helical gear can be obtained. The improved analytical method (IAM) is verified by comparing with finite element method (FEM) and TAM. Based on the IAM, the effects of the helical angle, face width, the number of gear, and modification coefficient on the mesh characteristics are analyzed. The results show that the IAM is consistent with the FEM and also consistent with TAM in single-tooth engagement. However, there is obviously error with the TAM in double-tooth or multi-tooth engagement.

scholarly journals A revised method to calculate time-varying mesh stiffness of helical gear

2022 ◽  
Vol 355 ◽  
pp. 01005
Author(s):  
Xiao Wu ◽  
Yang Luo ◽  
Qinmin Li ◽  
Juanjuan Shi
Keyword(s):  
Contact Stiffness ◽  
Helical Gear ◽  
Vital Role ◽  
Hertzian Contact ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Load Dependence ◽  
Tooth Width ◽  
Width Direction ◽  
Slice Method

Time-varying mesh stiffness (TVMS) of gear plays vital role in analysing dynamic characteristic of gear transmission. So accurately evaluating the TVMS is important and essential. In this paper, a revised method to calculate the TVMS of helical gear is proposed. Based on slice method, the helical gear is sliced into pieces along the tooth width direction. The proposed method corrects the fillet foundation stiffness within multi-tooth in contact and considers the non-linearity and load-dependence of the Hertzian contact stiffness. The effect of the axial mesh force is considered. Finally, an equivalent helical gear model is established in ANSYS to study the mesh stiffness. The results show the proposed method has high effectiveness compared with FEM (finite element method).

Analysis of tooth stiffness of nutation face gear

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Guangxin Wang ◽  
Lili Zhu ◽  
Peng Wang
Keyword(s):  
Gear Transmission ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Face Gear ◽  
Content Type ◽  
Gear Teeth ◽  
Meshing Stiffness ◽  
Single Tooth ◽  
Tooth Stiffness ◽  
External Face

Purpose The purpose of this paper is to obtain the single-tooth stiffness, single-tooth time-varying meshing stiffness and comprehensive meshing stiffness of the internal and external face gears and to analyze the influence of the modulus, pressure angle and tooth width of each face gear on the single-tooth stiffness of the gear in nutation face gear transmission. Design/methodology/approach From the point of view of material mechanics, the gear teeth of nutation face gear are simplified as spacial variable cross-section beams. The shear deformation of gear teeth, the bending deformation of tooth root and the additional elastic deformation caused by the base deformation are gotten by simplified trapezoidal section method, thus the stiffness of nutation face gear teeth can be obtained. The comparison with finite element method results verifies the rationality of simplified trapezoidal section method for calculating the tooth stiffness of nutation face gear. Findings The variation of stiffness of internal and external face gears along the meshing line and tooth height in nutation face gear transmission is studied, and the variation laws of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained. Originality/value Nutation face gear transmission is a new type of transmission. The stiffness of face gear teeth is analyzed, and the variation rules of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained, which not only enriches the research of nutation face gear transmission but also has important guiding significance for the application of nutation face gear in engineering practice.

A parameterized numerical model for the evaluation of gear mesh stiffness variation of a helical gear pair

2008 ◽  
Vol 222 (7) ◽  
pp. 1321-1327 ◽  
Author(s):  
J Hedlund ◽  
A Lehtovaara
Keyword(s):  
Numerical Model ◽  
Transmission Error ◽  
Helical Gear ◽  
Hertzian Contact ◽  
Mesh Stiffness ◽  
Fe Method ◽  
Gear Design ◽  
Gear Mesh ◽  
Stiffness Variation ◽  
Gear Mesh Stiffness

One of the most common challenges in gear drive design is to determine the best combination of gear geometry parameters. These parameters should be capable of being varied effectively and related to gear mesh stiffness variation in advanced excitation and vibration analysis. Accurate prediction of gear mesh stiffness and transmission error requires an efficient numerical method. The parameterized numerical model was developed for the evaluation of excitation induced by mesh stiffness variation for helical gear design purposes. The model uses linear finite-element (FE) method to calculate tooth deflections, including tooth foundation flexibility. The model combines Hertzian contact analysis with structural analysis to avoid large FE meshes. Thus, mesh stiffness variation was obtained in the time and frequency domains, which gives flexibility if comparison is made with measured spectrums. Calculations showed that a fairly low number of elements suffice for the estimation of mesh stiffness variation. A reasonable compromise was achieved between design trends and calculation time.

Advancement and Application of the Bezgin Method to Estimate Effects of Stiffness Variations along Railways on Wheel Forces

2019 ◽  
Vol 2673 (7) ◽  
pp. 248-264
Author(s):  
Niyazi Özgür Bezgin ◽  
Mohamed Wehbi
Keyword(s):  
Analytical Method ◽  
Contact Stiffness ◽  
Hertzian Contact ◽  
Dynamic Impact ◽  
Transition Zones ◽  
Railway Tracks ◽  
Impact Forces ◽  
Track Stiffness ◽  
Railway Engineering ◽  
New Equation

The need for an analytical method that one can apply manually to estimate dynamic impact forces on railway tracks that occur because of varying track stiffness or track profile initiated a study to develop an analytical method named as the Bezgin Method. The advancement of this method presented in this paper includes an extension of a set of equations developed and introduced by the first author earlier as the Bezgin Equations using the proposed method and development of a new equation. In addition to track stiffness taken into consideration in the equations introduced earlier, the Extended Bezgin Equations presented in this paper take into account bogie stiffness, wheel spring stiffness, Hertzian contact stiffness, and a factor for damping. The new equation takes into account the effect of vertical wheel acceleration as a train transitions to a stiffer structure or transitions along an ascending track profile. The paper unites and applies these equations to estimate wheel forces that develop along stiffness transition zones by considering an array of train speeds for an array of track stiffness ratios and representative values for track profile deviations along the transitions. Final section of the paper includes elaborate finite element analyses of structural track models that involve transitions of soil supported ballasted railway tracks with concrete based ballasted tracks along various transition lengths and compares their estimates for dynamic impact force factors with those estimated by the Extended Bezgin Equations. The paper concludes with a discussion of the potential uses, benefits, and the value of the Bezgin Method for railway engineering.

scholarly journals Measurement of Helical Gear Transmission Error and Improvement of Analytical Method.

1997 ◽  
Vol 63 (609) ◽  
pp. 1775-1782 ◽  
Author(s):  
Kazuo YOSHIKAWA ◽  
Hirofumi TANI ◽  
Ichiro TARUTANI ◽  
Akira SUZUKI ◽  
Hiroki MAKI ◽  
...  
Keyword(s):  
Analytical Method ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear Transmission

Integrated Excitation Models of the Helical Gear System

2007 ◽  
Author(s):  
Takayuki Nishino
Keyword(s):  
Gear Tooth ◽  
Moving Load ◽  
Helical Gear ◽  
Gear System ◽  
Tooth Surface ◽  
Response Analysis ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Face Width ◽  
Single Tooth

The vibration of the helical gear system is generated by three kinds of excitation. The first cause is a displacement excitation due to the tooth surface error. The second is a parametric excitation by the periodical change of the tooth mesh stiffness. The third is a moving load on the tooth surface during the progress of mesh of the teeth. In mesh of a pair of helical gears, the composite load of the distributed load along a contact line moves its operating location from one end of face width to the other end during the process of mesh progress. This moving load causes fluctuation of bearing load that excites the housing. Therefore, it is important to treat gear mesh excitation as a moving load problem. For this purpose, two kinds of mesh models, in which the three different types of excitations above are incorporated, are proposed. In the first model, a pair of gear tooth is represented by the multiple springs and the moving load can be taken into account by the multiple mesh excitation forces that have the phase differences from each other. The second one incorporates the excitation moment into the single tooth spring model. Then, response analysis is done for a simple gear-shaft model. As the result, the moving load causes vibration with non-coupled or independent modes between the drive and driven shaft. Thus, the effectiveness of the proposed method is established.

Gear transmission error outside the normal path of contact due to corner and top contact

1999 ◽  
Vol 213 (4) ◽  
pp. 389-400 ◽  
Author(s):  
R. G. Munro ◽  
L Morrish ◽  
D Palmer
Keyword(s):  
Dynamic Test ◽  
Theoretical Models ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear Transmission ◽  
The Novel ◽  
Transmission Systems ◽  
Helical Gears ◽  
Tooth Stiffness ◽  
Top Contact

This paper is devoted to a phenomenon known as corner contact, or contact outside the normal path of contact, which can occur in spur and helical gear transmission systems under certain conditions. In this case, a change in position of the driven gear with respect to its theoretical position takes place, thus inducing a transmission error referred to here as the transmission error outside the normal path of contact (TEo.p.c). The paper deals with spur gears only, but the results are directly applicable to helical gears. It systematizes previous knowledge on this subject, suggests some further developments of the theory and introduces the novel phenomenon of top contact. The theoretical results are compared with experimental measurements using a single flank tester and a back-to-back dynamic test rig for spur and helical gears, and they are in good agreement. Convenient approximate equations for calculation of TEo.p.c suggested here are important for analysis of experimental data collected in the form of Harris maps. This will make possible the calculation of tooth stiffness values needed for use in theoretical models for spur and helical gear transmission systems.

The Effect of Thermo-Hydrodynamics on Manual Automotive Transmissions Gear Rattle

2009 ◽  
Author(s):  
Miguel De la Cruz ◽  
Stephanos Theodossiades ◽  
Homer Rahnejat ◽  
Patrick Kelly
Keyword(s):  
Contact Stiffness ◽  
Hertzian Contact ◽  
Transmission Model ◽  
System Response ◽  
Common Denominator ◽  
Gear Teeth ◽  
Lubricated Contacts ◽  
Engine Order ◽  
Dynamic Transmission Model ◽  
Gear Rattle

Manual transmission gear rattle is the result of repetitive impacts of gear meshing teeth within their backlash. This NVH phenomenon is a major industrial concern and can occur under various loaded or unloaded conditions. It fundamentally differs from other transient NVH phenomena, such as clonk or thud, which are due to impulsive actions. However, they all have their lowest common denominator in the action of contact/impact forces through lubricated contacts. Various forms of rattle have, therefore, been defined: idle rattle, drive rattle, creep rattle and over-run rattle. This paper presents a dynamic transmission model for creep rattle conditions (engaged gear at low engine RPM). The model takes into account the lubricated impact force between a gear teeth pair during a meshing cycle as well as the friction between their flanks. Hertzian contact conditions are applied to the gear pair along the torque path. Additionally, isoviscous hydrodynamic regime of lubrication is assumed for unselected (loose gear pairs) with lightly loaded impact conditions. The highly non-linear impacts induce a range of system response frequencies. These include engine order harmonics, harmonics of meshing frequency and natural frequencies related to contact stiffness. The last of these are dependent on the contact geometry and lubricant rheology. The analysis includes lubricant viscosity variation due to generated contact pressures as well as temperature. For loose gears, subject to oscillations on their retaining bearings, bearing friction is also considered.

Vibration-based fault diagnosis of helical gear pair with tooth surface wear considering time-varying friction coefficient under mixed EHL condition

2021 ◽  
pp. 1-16
Author(s):  
Siyu Wang ◽  
Rupeng Zhu
Keyword(s):  
Dynamic Response ◽  
Hydrodynamic Lubrication ◽  
Helical Gear ◽  
Calculation Model ◽  
Tooth Surface ◽  
Time Varying ◽  
Gear Pair ◽  
Surface Wear ◽  
Mesh Stiffness ◽  
Helical Gear Pair

Abstract Based on “slice method”, the improved time-varying mesh stiffness (TVMS) calculation model of helical gear pair with tooth surface wear is proposed, in which the effect of friction force that obtained under mixed elasto-hydrodynamic lubrication (EHL) is considered in the model. Based on the improved TVMS calculation model, the dynamic model of helical gear system is established, then the influence of tooth wear parameters on the dynamic response is studied. The results illustrate that the varying reduction extents of mesh stiffness along tooth profile under tooth surface wear, in addition, the dynamic response in time-domain and frequency-domain present significant decline in amplitude under deteriorating wear condition.

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