3. •Gearbox power loss. Part II: Friction losses in gears
Carlos M.C.G. Fernandes, Pedro M.T. Marques, Ramiro C. Martins, Jorge H.O. Seabra
Pages 309-316
Abstract
The second part of the study presents an extensive campaign of experimental tests in an
FZG test rig. An average coefficient of friction between meshing gears was devised from the
experimental results. Several aspects regarding the meshing gears power loss are discussed
such as gear loss factor, coefficient of friction and the influence of gear oil formulation
(wind turbine gear oils).
•Tooth stress calculation of metal spur and helical gears
Toni Jabbour, Ghazi Asmar
Abstract
A method for the calculation of the root and contact stresses for metal, spur and helical gears
is presented in this work. The results of this method are verified by finite element
calculations. This method enables the modeling of a pair of meshed gears during an interval
of rotation by considering, for helical gears, a non-uniform load distribution along the lines of
contact. Consequently, we were able to determine the parameters as well as the gear
configurations for which the bending and contact stresses are maximum, in addition to
relations directly yielding the critical bending and contact stress for a pair of mating spur and
helical gears
Pages 375-390
4. Mesh stiffness calculation using an accumulated integral potential
energy method and dynamic analysis of helical
• Pages 447-463
•Zhiguo Wan, Hongrui Cao, Yanyang Zi, Wangpeng He, Yimin Chen
Abstract
As one of the most important dynamic excitation sources, the gear time-varying mesh
stiffness is the key parameter of gear system dynamic model. So how to calculate the
gear mesh stiffness accurately is of great importance. In this paper, an accumulated
integral potential energy method is proposed to calculate the mesh stiffness of helical
gears. Compared with the finite element model (FEM) and the ISO standard, the
proposed analytical method is verified as its results agree well with the others'.
Meanwhile the effects of different helical gears parameters (e.g., helix angle, normal
module) on mesh stiffness are studied. The results show that the fluctuation degree of
mesh stiffness becomes smaller as helix angle or face width increases, by contrast the
influence of normal module on the mesh stiffness shows an opposite trend. Furthermore,
the mesh stiffness reduction of helical gears due to the tooth crack is quantified. Finally, a
dynamic model of helical gear transmission is established to study the vibration
characteristics of helical gears. The results show that the mesh stiffness plays a vital role
in controlling the vibration of helical gears and has a significant effect on the vibration
characteristic of helical gears with tooth crack
5. •Method for remanufacturing large-sized skew bevel gears
using CNC machining center
•Pages 213-229
•Kazumasa Kawasaki, Isamu Tsuji, Hiroshi Gunbara, Haruo Houjoh
Abstract
A method for remanufacturing pinion member of large-sized skew bevel gears using a CNC
machining center and respecting an existing gear member is proposed. For this study, first
the tooth surface forms of skew bevel gears are modeled mathematically. Next, the real
tooth surfaces of the existing gear member are measured using a coordinate measuring
machine and the deviations between the real and theoretical tooth surface forms are
formalized using polynomial expression. Moreover, the tooth contact pattern and
transmission errors reflecting the deviations of the tooth surface forms of the gear member
are analyzed, and the tooth surface form of the pinion member that has good performance
mating with the existing gear member is designed. The pinion member was
remanufactured by swarf cutting using a CNC machining center. The gear member is also
remanufactured using this method in order to apply to the case where pinion member
exists in reverse or both gear and pinion members do not exist. The tooth surface form
deviations were detected, and the experimental tooth contact pattern of the pinion and
gear members was compared with analytical one. The results showed good agreement.
6. Dynamic analysis and experimental study of a marine gearbox with
crossed beveloid gears
•Pages 17-28
•Chaosheng Song, Caichao Zhu, Huaiju Liu, Gaoxiang Ni
Abstract
Dynamic modeling of beveloid gears is less developed than that of conventional involute
gears with parallel axis because of their complicated mesh mechanism and 3-dimensional
dynamic coupling. For evaluating the dynamic characteristics of a marine gearbox with
crossed beveloid gears more realistically, a systematic dynamic modeling approach was
proposed based on the lumped parameter and the finite element method. Considering the
time-varying mesh stiffness excitation, time-varying loaded translational transmission error
excitation, sliding friction excitation and backlash nonlinearity, a coupled gear–shaft–
bearing–housing dynamic model for a marine gearbox with crossed beveloid gears was
developed based on the proposed modeling method. Then, numerical integrations
applying the explicit Runge–Kutta formula and the implicit direct integration were used to
solve the nonlinear dynamic model. The dynamic transmission error, dynamic mesh force,
and dynamic equivalent shaft-bearing supporting force were obtained as well as the
dynamic response of the housing. Finally, a test rig was established for the marine gearbox
with crossed beveloid gears and vibration tests were performed to investigate the dynamic
responses. Through analyzing the responses in time domain and frequency domain, the
experimental results compared well with the theoretical dynamic results.
7. •The wear and thermal mechanical contact behaviour of
machine cut polymer gears
•Pages 822-826
•K. Mao, P. Langlois, Z. Hu, K. Alharbi, X. Xu, M. Milson, W. Li, C.J. Hooke, D. Chetwynd
The present paper will concentrate on an extensive investigation of machine cut acetal gear
wear and thermal mechanical contact behaviour. The results for machine cut acetal gears
will be compared to previously published results obtained for polymer gears manufactured
through injection moulding. The machine cutting manufacturing process can be economical
for small batch runs due to the expense of the mould for injection moulding. Injection
moulding becomes economical for larger batches. A new and unique polymer gear test rig
has been employed to investigate the polymer gear wear behaviour. The unique test rig
design allows the effect of misalignment on polymer gear engagement to be considered
and the gear surface wear to be recorded continuously. Extensive experimental tests have
been carried out to investigate machine cut acetal gear wear performance. Further
examinations have been carried out using a scanning electron microscope to understand
the gear wear mechanisms. An equation has been presented to predict polymer gear flank
temperature and correlated well with the tests.
Abstract
8. Study on spatial curve meshing and its application for logarithmic
spiral bevel gears
•Pages 172-190
•Rulong Tan, Bingkui Chen, Changyan Peng, Xuan Li
ABSTRACT
The goal of the paper is to develop the theory of curving meshing and apply it in high
performance gear transmission. With this aim, this study investigates the gear geometry
and kinematics of space curve meshing in gear design field. Here, definition of conjugate
curves and the method of obtaining them are described. What's more, an extended
method to get tooth surfaces from a space curve and its conjugate curve is proposed and
the meshing characteristics of these tooth surfaces are argued. Then, based on arguments
for conjugate curve theorem, this paper proposes the mathematical model of conical-helix
bevel gears from the idea of logarithmic spiral bevel gears. To validate this model and
investigate the tooth contact characteristics of conical-helix bevel gears, the numerical
example of a pair of these gears with specific profiles is represented by applying the
general computer program, ANSYS 14.0. Results show that the main characteristics of
these gears include loads in the same direction, pure rolling contact and low bending
stresses. The results also agree with the theoretical derivations for conjugate curves and
conical-helix bevel gears
9. •Torque loss and wear of FZG gears lubricated with wind
turbine gear oils using an ionic liquid as additive
•Pages 306-314
•Carlos M.C.G. Fernandes, A. Hernandez Battez, R. González, R. Monge, J.L. Viesca,
A. García, Ramiro C. Martins, Jorge H.O. Seabra
Abstract
This work presents a study of the tribological behavior of a mineral fully-formulated wind
turbine gear oil additised with [BMP][NTf2] ionic liquid. The target application is the wind
turbine gearboxes, thus the fully formulated oil with and without ionic liquid additive was
tested in a rolling bearings test rig to measure the thrust rolling bearing torque loss and
was also tested in a FZG gear test rig to measure the gears torque loss at operating
conditions similar to the observed in a wind turbine gearbox.
The results show that a wind turbine gear oil additised with ionic liquid can reduce the
torque loss and improve the gearbox efficiency while producing less wear particles as
observed in the oil analysis.
10. Improved time-varying mesh stiffness model of cracked spur
gears
•Pages 271-287
•Hui Ma, Xu Pang, Ranjiao Feng, Jin Zeng, Bangchun Wen
ABSTRACT
Based on our previous work (Ma et al., 2014, Engineering Failure Analysis, 44, 179–194),
this paper presents an improved analytical model (IAM) for the time-varying mesh
stiffness (TVMS) calculation of cracked spur gears. In the improved analytical model, the
calculation error of TVMS under double-tooth engagement due to repeatedly
considering the stiffness of the fillet-foundation is revised, and the effects of reduction
of fillet-foundation stiffness of cracked gears and extended tooth contact (ETC) are also
considered, which have a great influence on TVMS, especially under the condition of
large torques and crack levels. Moreover, the comparisons among the IAM, traditional
analytical model (TAM) and finite element (FE) model are also carried out under
different torques and crack depths. IAM is also verified by comparing TVMS and
vibration responses obtained by FE model, which can be considered as a gauge to
evaluate the calculation error. The results show that the maximum error of IAM is about
12.04%, however, that of TAM can be up to 32.73%
11. In situ surface characterization of running-in of involute gears
Mario Sosa, Stefan Björklund, Ulf Sellgren, Ulf Olofsson
Abstract
Gear life and operation are largely determined by the properties of the contacting
surfaces, which inevitably change over the gear life. The initial topography transformation,
a characteristic effect of running-in, is very important. This paper focuses on how the
running-in of the surface topography can be characterized and what methodology can be
used for this purpose. To characterize running-in, gears were run in an FZG back-to-back
test rig and the changes in surface topography were measured in situ using a Form Talysurf
Intra. This enables the same gear tooth surface to be measured with enough precision to
follow its development through the different stages of running-in. Gear tooth surfaces as
manufactured were measured on three occasions: in initial manufactured condition, after
a standard running-in procedure, and after an efficiency test. Running-in was characterized
both qualitatively by plotting roughness profiles and quantitatively by analyzing a selected
set of roughness parameters. This paper demonstrates that: the asperity peaks were worn
off in the initial running-in stage; roughness, waviness, and form can be separated using a
carefully chosen polynomial fit and the Gaussian filter; surface topography can be
examined initially, after running-in, and after operation in situ; and complete wear of the
initial surface can be observed in specific circumstances
13. Gearbox power loss. Part I: Losses in rolling bearings
•Pages 298-308
•Carlos M.C.G. Fernandes, Pedro M.T. Marques, Ramiro C. Martins, Jorge H.O. Seabra
ABSTRACT
This work is devoted to the analysis, modeling and validation of gearbox power loss,
considering the influence of the gears, rolling bearings and seals, the influence of the
operating conditions, lubricant formulation and the lubrication method.
The first part of this work a rolling bearing torque loss model is calibrated for several wind
turbine gear oils and for ball and roller contacts. The results achieved clarify the importance
of a rolling bearing in a gearbox power loss.
In the second part of this work will be presented the same approach for gears. The final
part will converge in the application of findings in two full gearboxes, a planetary and a
parallel axis gearbox, both in multiplying configuration
Properties comparison of rubber and three layer PTFE-NBR-bronze
water lubricated bearings with lubricating grooves along entire
bush circumference based on experimental tests
•Pages 404-411
•Wojciech Litwin
14. Abstract
Water lubricated bearings have been in industrial use for well over a century. During the
last decade their traditional range has been expanded with new, modern products. Despite
that fact, certain solutions continue to employ the standard rubber bearing with lubricating
grooves located along entire bush circumference.
The work presents experimental research conducted on comparable sliding bearings with
lubrication grooves along entire bush circumference, assessing them against a different,
modern solution. Movement resistance, pressures in bearing interspace and shaft orbits
were measured and analyzed. It was proved that classic bush geometry is not appropriate
for hydrodynamic lubrication.
•A summary of fault modelling and predictive health
monitoring of rolling element bearings
•Pages 252-272
•Idriss El-Thalji, Erkki Jantunen
The rolling element bearing is one of the most critical components that determine the
machinery health and its remaining lifetime in modern production machinery. Robust
Predictive Health Monitoring tools are needed to guarantee the healthy state of rolling
element bearing s during the operation. A Predictive Health Monitoring tool indicates
the upcoming failures which provide sufficient lead time for maintenance planning. The
Predictive Health Monitoring tool aims to monitor the deterioration i.e. wear evolution
rather than just detecting the defects.
15. A numerical investigation of both thermal and texturing surface effects
on the journal bearings static characteristics
•Pages 228-239
•Nacer Tala-Ighil, Michel Fillon
Abstract
Journal bearing characteristics modellization has been investigated in this paper for both
cases of texture presence or absence onto the bearing surface. The thermal effect has been
studied. The used numerical approach in this analysis is finite difference method. The
textured bearing performance enhancement passes essentially by a minimum film thickness
and a friction torque improvement through an appropriate surface texture geometry and right
texture distribution on the bearing surface.
•A novel view on lubricant flow undergoing cavitation in sintered
journal bearings
•Pages 189-208
•Bernhard Scheichl, Ioana Adina Neacşu, Alfred Kluwick
Abstract
A new rational formulation of the cavitation phenomenon occurring in porous journal bearings
in the regime of fully hydrodynamic lubrication is presented. The suitably extended form of the
Reynolds equation is coupled with the semi-phenomenological Darcy׳s law so as to yield a
proper description of the combined flow through the lubrication gap and the porous (sintered)
seat, respectively.
16. Characterisation of white etching crack damage in wind turbine
gearbox bearings
•Pages 164-177
•T. Bruce, E. Rounding, H. Long, R.S. Dwyer-Joyce
Abstract
White etching cracks (WECs) have been identified as a main failure mode of wind turbine
gearbox bearings (WTGBs). This study reports an investigation of the destructive sectioning of a
failed low speed planetary stage WTGB and the damage found at manganese sulphide (MnS)
inclusions. The bearing inner raceway was sectioned through its circumferential and axial
directions in order to compare the damage around inclusions in different directions. 112
damage initiating inclusions were catalogued and their properties were investigated.
Ultrasonic measurement of lubricant film thickness in sliding Bearings
with overlapped echoes
•Pages 89-94
•Kai Zhang, Qingfeng Meng, Tao Geng, Nan Wang
Abstract
The lubricant film thickness in sliding bearings with a thin liner have previously been
immeasurable due to the overlapping of ultrasonic signals making the use of the ultrasonic
spring model impossible. In this paper, we firstly modeled the overlapped echoes in terms of
superimposed Gaussian echoes corrupted by noise and used the EM algorithms to extract the
interested echo. Then the extracted echo was used to obtain the lubricant film thickness by an
ultrasonic spring model. A high precision calibrated rig which could form a series of known film
thicknesses was set up and the performance of the method was shown to work well.
17. •Maximum margin classification based on flexible convex hulls for fault
diagnosis of roller bearings
Ming Zeng, Yu Yang, Jinde Zheng, Junsheng Cheng
ABSTRACT
A maximum margin classification based on flexible convex hulls (MMC-FCH) is proposed and
applied to fault diagnosis of roller bearings. In this method, the class region of each sample set
is approximated by a flexible convex hull of its training samples, and then an optimal separating
hyper-plane that maximizes the geometric margin between flexible convex hulls is constructed
by solving a closest pair of points problem. By using the kernel trick, MMC-FCH can be extended
to nonlinear cases. In addition, multi-class classification problems can be processed by
constructing binary pairwise classifiers as in support vector machine (SVM). Actually, the
classical SVM also can be regarded as a maximum margin classification based on convex hulls
(MMC-CH), which approximates each class region with a convex hull.
Fault detection and isolation of bearings in a drive reducer of a hot
steel rolling mill
•Pages 35-44
•Marcello Farina, Emanuele Osto, Andrea Perizzato, Luigi Piroddi, Riccardo Scattolini
Abstract
Defective bearings are a major concern in rotating machinery. In this work we propose a two-
step scheme, relying on two complementary data-driven techniques, for fault detection and
isolation for a drive reducer in a hot steel rolling mill. A preliminary fault detection phase is
based on a computationally lightweight time-domain multivariate statistical technique.
18. •Dynamic modelling of wear evolution in rolling bearings
•Pages 90-99
•Idriss El-Thalji, Erkki Jantunen
Abstract
Condition monitoring tools aim to monitor the deterioration process i.e. wear evolution
of defects. The wear evolution is quite complex process due to the involvement of
several wear and stress concentration mechanisms. Therefore, the purpose of this paper
is to provide a dynamic model of wear evolution that considers the topographical and
tribological changes over the lifetime. The model suggests the use of multiple force
diagrams to simulate the dynamic impact and utilises several models of contact
mechanics to estimate the transition points between the wear evolution stages. The
simulated results of the developed evolution model are in principal agreement with the
experimental results.
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