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.

Effect of moisture absorption on damping and dynamic stiffness of carbon fiber/epoxy composites

Behzad Ahmed Zai,박명균,H. S. Choi,Hassan Mehboob,Rashid Ali 대한기계학회 2009 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.23 No.11

In this paper, the damping and dynamic stiffness of UHN125C carbon fiber/epoxy composite beam was experimentally measured. The effect of fiber orientation angle and stacking sequences on damping, resonance frequency, and dynamic stiffness was discussed with a focus on the effect of moisture absorption. Dried specimens were immersed in distilled water for a certain period to absorb water for 8, 16, and 24 d, respectively, and the moisture content absorbed in the specimen was measured. Furthermore, using the impact hammer technique, the measurements of dynamic responses were conducted on a cantilever beam specimen with one end clamped by bolts and metal plates. The damping properties in terms of loss factor were approximated by half-power bandwidth technique. The dynamic stiffness was evaluated using resonance frequency as a function of moisture content. The damping increased with the increase of moisture content; however, the dynamic stiffness reduced with the reduction of resonance frequency. The results of the dynamic stiffness were aided by measuring the dynamic strain using DBU-120A strain-indicating software. The increment in the dynamic strain strengthened the results obtained for dynamic stiffness.

A hybrid method for dynamic stiffness identification of bearing joint of high speed spindles

Yongsheng Zhao,Bingbing Zhang,Guoping An,Zhifeng Liu,Ligang Cai 국제구조공학회 2016 Structural Engineering and Mechanics, An Int'l Jou Vol.57 No.1

Bearing joint dynamic parameter identification is crucial in modeling the high speed spindles for machining centers used to predict the stability and natural frequencies of high speed spindles. In this paper, a hybrid method is proposed to identify the dynamic stiffness of bearing joint for the high speed spindles. The hybrid method refers to the analytical approach and experimental method. The support stiffness of spindle shaft can be obtained by adopting receptance coupling substructure analysis method, which consists of series connected bearing and joint stiffness. The bearing stiffness is calculated based on the Hertz contact theory. According to the proposed series stiffness equation, the stiffness of bearing joint can be separated from the composite stiffness. Then, one can obtain the bearing joint stiffness fitting formulas and its variation law under different preload. An experimental set-up with variable preload spindle is developed and the experiment is provided for the validation of presented bearing joint stiffness identification method. The results show that the bearing joint significantly cuts down the support stiffness of the spindles, which can seriously affects the dynamic characteristic of the high speed spindles.

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.

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.

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.

궤도구조를 고려한 철도교량의 동적거동 분석

강덕만(Kang Duck-Man),안해영(An Hea-Young),성덕룡(Sung Deok-Yong),김성일(Kim Sung-Il),박용걸(Park Yong-Gul) 한국철도학회 2009 한국철도학회 학술발표대회논문집 Vol.2009 No.5월

This study is objected by analyzing whether it is applied to the analysis model considering the track stiffness or not when the railway bridge is designed or reviewed for the dynamic stability. It is performed that the analysis model is verified by comparing the field test result with the analysis result. Also, The dynamic response of railway bridge through the existing analysis model is compared with the analysis model considered the track stiffness. In addition, it is performed by analyzing the model considering the stiffness of concrete track. Therefore, this study is suggested that the design of railway bridge apply to the existing analysis model considering the mass of track and the dynamic stability review of railway bridge apply to it considered the stiffness & mass of track. Also, it is suggested that the stiffness of concrete slab on the bridge must consider when it is designed or checked over the dynamic stability.

CORNERING STIFFNESS AND SIDESLIP ANGLE ESTIMATION BASED ON SIMPLIFIED LATERAL DYNAMIC MODELS FOR FOUR-IN-WHEEL-MOTOR-DRIVEN ELECTRIC VEHICLES WITH LATERAL TIRE FORCE INFORMATION

Y. F. LIAN,Y. ZHAO,L. L. HU,Y. T. TIAN 한국자동차공학회 2015 International journal of automotive technology Vol.16 No.4

The simplified lateral dynamic models of front and rear tires are proposed with lateral tire force information in this paper. The regression models of the recursive least squares (RLS) with forgetting factors and constraints are constructed based on simplified lateral dynamic models for estimating tire cornering stiffness. In addition, a nonlinear observer of sideslip angle is designed for four-in-wheel-motor-driven electric vehicles (FIWMD-EVs) with the estimated information on tire cornering stiffness. Sideslip angle can be estimated through a first-order Stirling’s interpolation filter (DD1-filter) and a firstorder low-pass filter. The reliability, feasibility, effectiveness, and practicality of simplified lateral dynamic models are verified by contrast simulation experiments. The simplified lateral dynamic models of front and rear tires are not influenced on the change of sideslip angle, nor influenced by each other. Moreover, it can result in improving computation speed that computational burden is reduced after simplifying lateral dynamic models. With the estimated information above mentioned, sideslip angle is also estimated well. The estimated information on tire cornering stiffness and sideslip angle is benefit to the design of lateral stability control system, which can make vehicle adapt to different road conditions and control the steering motion attitude of vehicle in future works.

A Parameter Study for Static and Dynamic Denting

Jung, Dong-Won,Worswick, M.J. The Korean Society of Mechanical Engineers 2004 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.18 No.11

A parametric study of the factors controlling static and dynamic denting, as well as local stiffness, has been made on simplified panels of different sizes, curvatures, thicknesses and strengths. Analyses have been performed using the finite element method to predict dent resistance and panel stiffness. A parametric approach is used with finite element models of simplified panels. Two sizes of panels with square plan dimensions and a wide range of curvatures are analysed for several combinations of material thickness and strength, all representative of auto-motive closure panels. Analysis was performed using the implicit finite element code, LS-NIKE, and the explicit dynamic code, LS-DYNA for the static and dynamic cases, respectively. Panel dent resistance and stiffness behaviour are shown to be complex phenomena and strongly interrelated. Factors favouring improved dent resistance include increased yield strength and panel thickness. Panel stiffness also increases with thickness and with higher curvatures but decreases with size and very low curvatures. Conditions for best dynamic and static dent performance are shown to be inherently in conflict ; that is, panels with low stiffness tend to perform well under impact loading but demonstrate inferior static dent performance. Stiffer panels are prone to larger dynamic dents due to higher contact forces but exhibit good static performance through increased resistance to oil canning.

위상 최적화 및 두께 최적화를 적용한 차체 동강성 개선에 관한 연구

김지언(Jieon Kim),김정호(Jungho Kim),이창건(Changkun Lee),김용석(Yongsuk Kim) 한국자동차공학회 2014 한국자동차공학회 부문종합 학술대회 Vol.2014 No.5

In all vehicle driving situations, some vibration level that is perceived by passengers is a criteria for determining the vehicle’s quality and ride comfort. The main excitations are from road, engine and wind. They can be classified as ‘Structural born vibration’ or ‘Air born vibration’ according to the load path. Among them, the most sensitive vibration paths from road and engine excitation that interface to body directly. Their performance level of vibration is dependent on a interface part’s stiffness, so generally we can improve it by increasing dynamic stiffness on this part at each frequency range. For this reason, in this study, we calculated dynamic stiffness at each frequency on interface parts with FRF(Frequency Response Function) based on CAE. Also we considered Topology optimization and size optimization process for an improved design in terms of vibration performance. The process is as follows; First of all, we identified the weak points as factors in the need to develop with FRF analysis on important interface parts. Secondly, we did topology optimization on areas that have weak dynamic stiffness which were identified in the first step. This result tells us that the load path is critical factor to improve stiffness. Thirdly, we re-organized some structure shapes based on the load path identified in the second step. In this step, we used ‘Morphing’ technology method for changing shape. Finally, we conducted size optimization for getting a final design that is optimized for dynamic stiffness improvement and mass reduction. In this study, we propose a useful method that can draw efficient solution of vehicle body’s dynamic stiffness improvement using an optimization process that sequentially covers shape change and thickness change.