A Wolfrom transmission without carrier Höhn, B.-R.; Zhang, Y.; Geitner, M. ...
MATEC Web of Conferences,
2020, Letnik:
317
Journal Article, Conference Proceeding
Recenzirano
Odprti dostop
Wolfrom-transmission are well known planetary transmission with low number of gears and used for very high transmission - ratio for example : i=100 or more. With the book of Mueller “Die ...Umlaufgetriebe” they are a type of reduced planetary transmission containing two simple transmission one a minus-type and one a plus-type for the two transmission inside. With a common carrier for both transmission and only one sun and two inner gears it is very compact but known for bad efficiency. Firms who produces such transmission are talking about a lot of problems, but no details are published so long. The Author will show that a calculation with low-loss-gears will improve the efficiency very much and that we can produce this type without a carrier. The forces which are active at the planet should be go direct to the housing and not about bearings in a carrier. Details and a modelling of such type will be presented in the conference.
•A new approach is proposed to identify the two faults: spall and crack.•The method is based on the transmission error measurement.•Ensemble empirical mode decomposition is applied to extract ...features from the measured signals.•Fault type is identified via the FEA and virtual signal processing.•The method is useful since the TE gives faulty signal more directly and FEA is used for the fault identification.
Classification of spall and crack faults of gear teeth is studied by applying the ensemble empirical mode decomposition (EEMD) to the transmission error (TE) measured by the encoders of the input and output shafts. Finite element models of the gears with the two faults are built, and TE’s are obtained by simulation of the faulty gears under loaded contact to identify the different characteristics. A simple test bed for a pair of spur gears is prepared to illustrate the approach, in which the TE’s are measured for the gears with seeded spall and crack, respectively. EEMD is applied to extract fault features under the noise from the measured TE. The differences of the spall and crack are clearly identified by the selected features of the intrinsic mode functions based on the class separability criterion. The k-nearest neighbor method is applied for the classification of the faults and normal gears using the features. The proposed method is advantageous over the existing practices in the sense that the TE signal measures the gear faults more directly with less noise, enabling successful diagnosis.
Planetary gear has a broad application in industry due to its advantages. However, most of the mesh stiffness calculation for the planetary gears is based on the assumption that the effect of the ...ring flexibility is ignored. In this paper, the ring deformation based on the uniformly distributed Timoshenko beam theory is coupled into the gear mesh stiffness model of the internal gear pair. Based on this model, the effect of the ring deformation on the internal gear mesh stiffness can be carried on. In this paper, the effect of the support type (fixed support and pin support), ring thickness and number of supports on the mesh stiffness are investigated. It is demonstrated that the ring thickness and the number of supports have a great impact on the mesh stiffness of the internal gear pair while the influence of the support type is little. In addition, the mesh stiffness appears to be periodic with the number of the periodicities exactly equal to the number of the supports.
•A model indicating the effect of gear ring flexibility on mesh stiffness is proposed.•Effect of support type and number of supports are investigated.•Influence of the amplitudes of the applied forces is studied.•Ring thickness effect on the mesh stiffness of internal gear pair is explored.
•An improved time-varying mesh stiffness model for a helical gear pair considering axial mesh force component is proposed.•The axial tooth bending stiffness, axial tooth torsional shear stiffness and ...axial gear foundation stiffness models are proposed.•A rapid time-varying mesh stiffness calculation method is established, in which each stiffness components can be obtained by the integration along the gear width.
An improved time-varying mesh stiffness (TVMS) model of a helical gear pair is proposed, in which the total mesh stiffness contains not only the common transverse tooth bending stiffness, transverse tooth shear stiffness, transverse tooth radial compressive stiffness, transverse gear foundation stiffness and Hertzian contact stiffness, but also the axial tooth bending stiffness, axial tooth torsional stiffness and axial gear foundation stiffness proposed in this paper. In addition, a rapid TVMS calculation method is proposed. Considering each stiffness component, the TVMS can be calculated by the integration along the tooth width direction. Then, three cases are applied to validate the developed model. The results demonstrate that the proposed analytical method is accurate, effective and efficient for helical gear pairs and the axial mesh stiffness should be taken into consideration in the TVMS of a helical gear pair. Finally, influences of the helix angle on TVMS are studied. The results show that the improved TVMS model is effective for any helix angle and the traditional TVMS model is only effective under a small helix angle.
•A probability distribution model describing tooth pitting of spur gears is proposed.•The locations of pits are modeled as a two-dimensional random variable.•Pits are modeled with gradually increased ...sizes instead of fixed ones.•Mesh stiffness under four pitting degrees from no pitting to severe pitting is evaluated.
Tooth damage often causes a reduction in gear mesh stiffness. Thus time-varying mesh stiffness (TVMS) can be treated as an indication of gear health conditions. This study is devoted to investigating the mesh stiffness variations of a pair of external spur gears with tooth pitting, and proposes a new model for describing tooth pitting based on probability distribution. In the model, considering the appearance and development process of tooth pitting, we model the pitting on the surface of spur gear teeth as a series of pits with a uniform distribution in the direction of tooth width and a normal distribution in the direction of tooth height, respectively. In addition, four pitting degrees, from no pitting to severe pitting, are modeled. Finally, influences of tooth pitting on TVMS are analyzed in details and the proposed model is validated by comparing with a finite element model. The comparison results show that the proposed model is effective for the TVMS evaluations of pitting gears.
•An overall gear transmission model which incorporates with gearbox casing is proposed.•Introduced a new way to model gear tooth pitting and spalling.•The proposed model in simulating tooth pitting ...and spalling is validated by experimental tests.•The vibration fault features of tooth pitting and spalling are discussed.
Dynamical modeling of a gear system with faults has been an important research topic for understanding fault features and their associated fault vibration mechanisms. Due to the complicated structures and intricate interactions between the components of the gear system, the fault vibration features and corresponding vibration mechanisms due to tooth pitting and spalling remain mostly unknown. This paper proposes a novel spur gear dynamical model, validated by various experimental tests, to analytically investigate the effects of tooth pitting and spalling on the vibration responses of a gear transmission. The proposed dynamical model considers the effects of tooth surface roughness changes and geometric deviations due to pitting and spalling, and also incorporates Time Varying Mesh Stiffness (TVMS), a time-varying load sharing ratio, as well as dynamic tooth contact friction forces, friction moments and dynamic mesh damping ratios. The proposed gear dynamical model is validated by comparison with responses obtained from experimental test rig under different conditions. Comparisons indicate that the responses of the proposed dynamical model are consistent with experimental results, in both time and frequency domains under different rotation speeds and fault severity conditions.
•A flexible-rigid coupling dynamic (FMBD) model for a planetary gear is presented.•Both flexible ring gear, flexible supports of ring and sun gears, and planet bearing fault are formulated.•Effects ...of the fault width, moment, and input speed on the vibrations of planetary gear are analyzed.•Results from FMBD model are compared with those from experiment in the listed work.
Vibration performances of planetary gears are greatly affected by the flexible ring gear and planet bearing faults. However, the previous works only considered single flexible ring gear, rigid planetary gear system or planet bearing fault in their models. To overcome this problem, a flexible-rigid coupling dynamic (FMBD) model for a planetary gear is presented. Both the flexible ring gear, flexible supports of the ring gear and sun gear, and a rectangular local fault in the planet bearing are formulated in the presented FMBD model. The time-varying impulse force caused by the fault is described by a half-sine profile. Effects of the fault width, moment, and input speed on the time- and frequency-domain responses of the planetary gear are analyzed. To validate the presented FMBD model, the results from the FMBD model are compared with those from the experiment in the listed work. Note that the time- and frequency-domain responses from the flexible-rigid and rigid models are very different. Thus, the flexible ring gear should be formulated in the dynamic models of planetary gear, as well as the flexible supports of the ring gear and sun gear. The presented results can give some guidance for fault detection methods of planet bearings.
The purpose of this study was to simplify the design of the tooth surface of face gear and to clarify the optimization method of the specification setting. Face gears have long been used in fishing ...spinning reels as a speed-increasing gear. Recently, face gears have also been adapted to geared motors for orthogonal reduction gears. However, the design method of the face gear is not supported by a standard theory, and its application is not common. This paper reports the study of face gear that meshes with involute helical gear with offset. The curved surfaces of the face gear tooth can be generated using the involute helical gear surface, which is mesh constant rotation speed. To clarify the meshing of the face gear, the author introduced the idea that the meshing contact progresses along a straight line of action. The meshing point between the involute helical and face gear proceeds at a constant speed along the straight line of action. The straight line of action is continuous and exists as a curved surface. In this method, the meshing contact is always made in the direction normal to the tooth surface of the involute pinion. This method is based on a simple theory and can be used to obtain the tooth surface coordinates of a face gear without complicated repetitive calculations. The tooth profile of the face gear calculated by the conventional generation method using a numerical analysis and calculated by the proposed meshing contact method were compared and, except for the interference area, they were the same. Using this method, design of the tooth surface of a face gear can be simplified.
The need of fine finishing of gears with high shape accuracy increases in various industrial, military and scientific instruments applications for enhancing the working performance, power ...transmission capability, service life, reliability as well as decreasing noise and vibrations at high speed. The surface asperities, dimensional inaccuracy, rough surface and shape inaccuracy of a gear tooth profile occur because of the high speed of material removal mechanism which leads to undesirable effect such as noise and vibration in the gearbox. Therefore, utilizing the conventional tool for finishing of gears at high material removal rates may increase inaccuracy in gear teeth profile shape due to the transverse grinding lines, burns, fine cracks, uneven stress, and thermal distortion. This paper reports on a novel design of a magnetorheological gear profile finishing (MRGPF) tool and its performance analysis to finish the gear teeth profile with more precisely and accurately. The MRGPF tool is made likely similar to the gear grinding profile wheel tool. To analyze the uniform finishing at the gear tooth profile, the magnetostatic finite element analysis (FEA) is performed to predict the uniform magnetic flux density at the proposed tool surface using Maxwell Ansoft. On the basis of the result obtained of magnetic flux density distribution on its finishing surface, the MRGPF tool is designed and fabricated. Further, the experiments are performed to examine the finishing performance of the newly designed tool on the EN-24 steel spur gear teeth profile. The results attest the significant improvement in finishing of gear teeth profile surface with high shape accuracy (DIN standard). This may result in improvement in scuffing performance, reducing noise and vibrations at high speed, reducing wear rate on gear teeth profile and also provides lower friction and temperature during its functional operation.
•Designed a new magnetorheological gear profile finishing tool for fine finishing of gears with high shape accuracy.•Uniform distribution of magnetic flux density with significant magnitude on gear tool profile helps in uniform finishing.•Experimentally demonstrated effectiveness of new tool for fine finishing of gear teeth profile with high shape accuracy.•Magnetorheological finished gears can reduce noise and vibrations during its functional application at high rpm.
•We present a method for analyzing the transmission error of gear system with errors.•The STE considering machining errors, assembly errors, modifications is obtained.
We present a method for ...analyzing the transmission error of helical gear system with errors. First a finite element method is used for modeling gear transmission system with machining errors, assembly errors, modifications and the static transmission error is obtained. Then the bending-torsional-axial coupling dynamic model of the transmission system based on the lumped mass method is established and the dynamic transmission error of gear transmission system is calculated, which provides error excitation data for the analysis and control of vibration and noise of gear system.
PDF
