Comparisons of gear dynamic responses with rectangular mesh stiffness and its approximate form

Chen Siyu,Tang Jinyuan,Hu Zehua 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.9

The mesh stiffness is close to rectangular stiffness, and the first harmonic approximate term of rectangular stiffness is generally adoptedin the nonlinear gear dynamic analysis. The differences between the rectangular stiffness and its approximate form are analyzed indetail. The frequency response and dynamic factor are calculated by a numerical method, to illustrate the dynamic characteristics of thegear nonlinear system with different mesh stiffness forms. The results show that: The trends of frequency response of gear dynamic systemwith rectangular stiffness and its approximate form are identical. The jump phenomena are detected in both cases. Without the effectof static transmission error, the dynamic factor with rectangular mesh stiffness is larger than that with approximate mesh stiffness. Underdesign power and speed condition, the result with approximate mesh stiffness function may deduce reasonless suggestions for a designer. The static transmission error will enlarge the vibration amplitude and dynamic factor when the approximate mesh stiffness is adopted, butthe effects on the response of gear system with rectangular mesh stiffness are fractional. The mesh stiffness may excite the odd subharmonicresonance, and the static transmission error may excite the even sub-harmonic resonance respectively.

Mesh stiffness analysis of beveloid gears for the rotating vector transmission

Yucheng Huang,Xuesong Du,Caichao Zhu,Gaoxiang Ni,Najeeb Ullah,Hao Liu 대한기계학회 2019 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.33 No.8

This paper investigates the meshing stiffness of beveloid gears in the beveloid rotate vector (BRV) transmission. It is a new kind of transmission evolved from rotate vector (RV) reducer. In the BRV transmission, the beveloid gear is a kind of involute gear with a bevel angle. The BRV transmission have high power density, large transmission ratio and high precision in geared coupled systems. However, there is rare systematic research conducted on the meshing stiffness analysis of the BRV transmission at present. Based on the loaded contact finite element analysis principle, a meshing stiffness analysis model for beveloid gears is established. The influence of different factors such as pitch cone angle, addendum coefficient, load and rim structure parameters of external gear on meshing stiffness are studied. The results show that the pitch cone angle and addendum coefficient have little effect on the shape of the meshing stiffness curve, but they have a significant influence on the amplitude of meshing stiffness. In contrast, the load can affect both the shape and the amplitude of the meshing stiffness curve obviously. Also, the size of scallop-hole and rim thickness have a great impact on the amplitude of the meshing stiffness. The prescribed piece of study can provide a better understanding for gear researchers in order to understand the influence of different parameters on dynamic characteristics analysis of the BRV transmission systems.

Dynamic characteristics of a planetary gear system based on contact status of the tooth surface

Ruibo Chen,Jianxing Zhou,Wenlei Sun 대한기계학회 2018 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.32 No.1

Studies on the planetary gear have attracted considerable attention because of its advantages, such as compactness, large torque-toweight ratio, vibrations, and high efficiency, which have resulted in its wide applications in industry, wind turbine, national defense, and aerospace fields. We have established a novel dynamic model of the planetary gear transmission by using Newton’s theory, in which some key factors such as time-variant meshing stiffness, phase relationships, and tooth contact characteristics are considered. The influences of gear axial tipping, operating conditions, and the meshing phase on the contact characteristics and the dynamic characteristics were researched systematically. It was found that the contact area of the tooth surface was moved due to the axial gear tipping, which obviously affected the meshing stiffness. With the increase in the inclination angle of the sun gear, the meshing stiffness decreases, which produces an evident influence on the high natural frequency in the planetary transmission system. In terms of the dynamic characteristics of the system, the component of rotating frequency appeared in the dynamic meshing force of the sun gear and the planetary gear. Moreover, the floating track of the center wheel varied significantly and exhibited an oval distribution as the inclination angle of the sun gear changed. When the inclination angle of the sun gear increased, the rotating frequency component increased significantly, but the other meshing frequency components remained unchanged; meanwhile, the deformation of the floating track also increased. If the inclination angle of the sun gear changes, the vibration state of the system and the collision impact could become more serious, and the lifetime of the planetary transmission system will reduce. Furthermore, when the load was increased, we found that the gear-tooth contact zone transformed from line contact to surface contact, the meshing stiffness increased, the effect of high natural frequency on the planetary transmission system became more evident, but its low-order natural frequency remained stable. With regard to the dynamic characteristics of the system, the components of the major frequency at the external gearing remained unchanged, but the rotation frequency of the sun gear and the meshing frequency amplitude increased linearly with the increase in load. In conclusion, the variation in the meshing stiffness of the planetary gear system had minor impact on the low-order natural frequency, but had a significant impact on the high natural frequency of the planetary transmission system due to the phase variation of the gear.

Effects of gear eccentricity on time-varying mesh stiffness and dynamic behavior of a two-stage gear system

Xiuzhi He,Xiaoqin Zhou,Zhen Xue,Yixuan Hou,Qiang Liu,Rongqi Wang 대한기계학회 2019 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.33 No.3

Gear eccentricity, one of the most common defects of gear systems, affects not only dynamic behavior but also mesh stiffness. Accurate mesh stiffness under defect conditions is vital for the dynamic simulation and fault diagnosis of gear systems. Hence, the timevarying mesh stiffness affected by gear eccentricity, which is commonly neglected in most studies, is incorporated in the proposed twostage spur gear dynamic model and calculated by a novel gear mesh model with an improved potential energy method. The effects of mesh stiffness with and without gear eccentricity on the gear system are compared on the basis of the constructed dynamic model. The influences of gear eccentricity on dynamic transverse and torsional responses, as well as dynamic transmission errors, are also quantitatively studied. Some helpful analytical results are then presented.

용접철망을 배근한 거푸집 데크플레이트 슬래브의 휨거동

정상근(Jung Sang-Keun),최준형(Choi Joon-Hyung),양일승(Yang Il-Seung),문연준(Moon Youn-Joon),김순철(Kim Soon-Chul) 대한건축학회 2008 대한건축학회 학술발표대회 논문집 - 계획계/구조계 Vol.28 No.1(구조계)

The object of this study is investigated to flexural behaviors of deck-plate slabs using wire mesh. The wire mesh instead of deformed bars are used to improve convenience of construction. Test variables are concrete topping thicknesa(75㎜, 100㎜), types of main bars(1-D6, 2-D6, 3-D6) in compression and tension regions, and width in bottom face of deck plate(58㎜, 68㎜). The vertical loading by monotonic are applied to investigate the yielding strength, maximum strength, initial stiffness and failure modes. Test results are follows ; (1) Higher stiffness and strength was shown that more the wire mesh was, the thicker the slab was. (2) In specimens using wire mesh instead of reinforced bars, experiment results is 1.13~1.83 times that those of calculated results.

Gear dynamic modelling based on the concept of dynamic mesh stiffness: theoretical study and experimental verification

Chongyang Xie,Wei Yu 대한기계학회 2022 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.36 No.10

Gear mesh stiffness (GMS) is considered as one of the most important internal excitations affecting the dynamic response of the gear transmission system. In most gear dynamic model established by the lumped parameter method, the GMS is pre-calculated under static condition, and treated as a kind of known input of the gear dynamic model. However, the actual tooth contact state under dynamic operation condition is rather different from that under static condition, which means the variation of GMS should also be evaluated dynamically. In this paper, a new gear dynamic model is established based on the lumped parameter method, where the real-time GMS is used. To validate the proposed gear dynamic model, simulated result has been compared with the experiment result that reported in the literature, and it shows that the proposed gear dynamic model is more reasonable for gear dynamic response prediction.

Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach

Mohsen Rezaei,Mehrdad Poursina,Shahram Hadian Jazi,Farhad Haji Aboutalebi 대한기계학회 2018 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.32 No.8

Time-dependent mesh stiffness is a most important reason of vibration and dynamic excitation in gear sets. In this research, analytical formulas of the helical gear set and the planetary gear system are combined to calculate the time-dependent mesh stiffness of the helical planetary gear system. For this purpose, at the first step, the analytical equations are derived for the spur gear pair. Then by dividing a helical tooth into the several independent thin spur tooth slices, the helical gear pair mesh stiffness is extracted. Finally, these equations are extended to the helical planetary gear system. The suggested analytical results and those which obtained by the finite element method (FEM) are compared and are in good agreement when the helix angle is less than 15 degrees. Also, the helical planetary gear system mesh stiffness in different cases such as fixed carrier, fixed sun gear and fixed ring gears is calculated. These results show that the value of mesh frequency ratio in each case scales the mesh stiffness shapes in the rotation angle direction. In other words, mesh frequency ratio parameter determines the number of meshing period in each rotation of planets.

Influences of friction and mesh misalignment on time-varying mesh stiffness of helical gears

Lin Han,Lixin Xu,Houjun Qi 대한기계학회 2017 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.31 No.7

As one of the most important excitation sources of vibration, time-varying mesh stiffness of helical gear pairs need accurately calculated. Compared with spur gears, friction in helical gears is significant. This work for the first time presents an improved calculation method for the mesh stiffness of helical gears with effect of friction incorporated. Firstly, helical gear is sliced into number of pieces along its axis direction and each piece could be regarded as spur gear. Then forces applied to each piece including friction force are analyzed. Potential energy method is employed to develop time-varying mesh stiffness of each piece pair of both kinds of helical gears with different transverse and axial contact ratios. Furthermore, influences of various working conditions and misalignment on mesh stiffness are also investigated. Results indicate that effect brought by friction on total mesh stiffness should be not neglected. The reduction amount of stiffness increases with lower speed, heavier load and rougher surface. The stiffness difference between cases with and without friction is affected by gear geometry and mounting parameters like module, helix angle and mounting misalignment. This work provides an essential tool for comprehensive dynamics analysis with consideration of the relationship between stiffness and working conditions.

Contact finite element method for dynamic meshing characteristics analysis of continuous engaged gear drives

Yong-jun Wu,Jian-jun Wang,Qin-kai Han 대한기계학회 2012 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.26 No.6

The dynamic meshing characteristics of gear drives have been a major concern in the design of power transmission systems as they affect vibration, acoustic noise, durability and efficiency. Gaining a more comprehensive understanding of the dynamic meshing characteristics of continuous engaged gear drives is a key to the development of power transmission systems. In this paper, a dynamic contact finite element analysis method, considering the variation of the engaged teeth pairs, the loaded elastic and contact deformations, and the sliding friction, is presented for the dynamic meshing characteristics analysis of continuous and elastic engaged gear drives. Various kinds of continuous engaged gear models under low and high speed condition are simulated and compared using the presented method. The tooth profile modification was designed based on the simulation results. Moreover, the effects of the tooth profile modification, the sliding friction and the time-varying meshing stiffness upon the dynamic meshing characteristics of continuous engaged gear drives are discussed in detail. The results show that the method is not only effective in designing and evaluating the tooth profile modification, but also in studying the dynamic meshing characteristics of continuous engaged gear drives with realistic time-varying meshing stiffness and tooth sliding friction. The present method could provide an effective tool for vibration mechanism study and dynamic design of the continuous engaged gear drives considering more influence factors.

A hybrid finite element and analytical model for determining the mesh stiffness of internal gear pairs

Shuo Feng,Lehao Chang,Zhaoxia He 대한기계학회 2020 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.34 No.6

This work developed an efficient model for calculating the mesh stiffness of spur/helical internal gear pairs by combining the finite element method (FEM) and analytical formula. The tooth global deformation is obtained by separation of the deformation of a full finite element model and a partial model, and the local contact deformation is derived by an analytical line contact formula based on Hertz contact theory. The transmission error and mesh stiffness of the gear pair can be acquired after solving the nonlinear contact equilibrium equations. Compared with the conventional FEM, the proposed method has much smaller computational consumption. Furthermore, it also overcomes the disadvantage that the analytical method is difficult to consider different ring gear structures. Then the influences of ring thicknesses and the number of support pins of the ring gear on the mesh stiffness are discussed. The results show that the ring flexibility will change the amplitude-frequency components of the mesh stiffness a lot.