线绳驱动转速提升式低频俘能器的设计与研究

俘获周围环境中丰富的低频机械能对减少废旧电池数量、实现自维持传感器、降低传感器网络的使用和维护成本等具有重要意义, 但传统的振动型俘能器对低频机械能的俘获效果不佳. 为了有效收集周围环境中的低频机械能, 本文提出一种线绳驱动、具备转速提升功能的电磁式俘能器, 首先借助线绳驱动转轴结构将低频振动转换为双向旋转运动, 再通过刚度自动改变的拨片和磁齿轮将双向旋转运动转换为转速更高的单向旋转运动, 从而提高输出功率. 对所提出的俘能器建立了机电耦合动力学模型, 并通过样机制作和实验测试证实了理论模型的正确性. 实验研究表明, 在激励幅值40 mm和激励频率2 Hz的条件下, 通过本文设计制作的2.5倍转速提升功能的磁齿轮, 可将线绳驱动电磁式俘能器的最大输出功率增加至7.82 mW, 比对应的无磁齿轮提升转速的线绳驱动电磁式俘能器的最大输出功率(3.22 mW)高约143%. 在相同的激励条件下, 制作的俘能器的交流电能经过桥式整流器转换为直流后, 可在1.2 s内将220 μF储能电容器的电压从0 V提升至1.5 V. 在低频、不规则的振动激励下, 所制作的俘能器仍可提供0.35 mW的输出功率, 为设计高性能低频俘能器提供一条可行的解决方案.      

An enhanced multi-term harmonic balance solution for nonlinear period-one dynamic motions in right-angle gear pairs

A nonlinear time-varying dynamic model for right-angle gear pair systems, considering both backlash and asymmetric mesh effects, is formulated. The mesh parameters that are characteristically time-varying and asymmetric include mesh stiffness, directional rotation radius and mesh damping. The period-one dynamic motions are obtained by solving the dimensionless equation of gear motion using an enhanced multi-term harmonic balance method (HBM) with a modified discrete Fourier Transform process and the numerical continuation method. The accuracy of the enhanced HBM solution is verified by comparison of its results to the more computational intensive, direct numerical integration calculations. Also, the Floquet theory is applied to determine the stability of the steady-state harmonic balance solutions. Finally, a set of parametric studies are performed to determine quantitatively the effects of the variation and asymmetry in mesh stiffness and directional rotation radius on the gear dynamic responses.     

Dynamic behavior of gear pumps: effect of variations in operational and design parameters

This work presents a wide number of results about the influence that variations in terms of operational and design parameters play on the dynamic behavior of external gear pumps. These results are obtained by using a non-linear lumped-parameter kineto-elastodynamic model developed and experimentally assessed with the aim of including all the important dynamic effects. On the one hand, the effects of variations in the operational parameters—namely output pressure, rotational speed and oil viscosity—are analysed; on the other hand, the effects of modifications of some design parameters are shown: clearances and relief groove dimension. The results in terms of gear eccentricity, pressure evolution, pressure forces, gear accelerations and variable forces exciting the pump casing enlighten the dynamic behavior of gear pumps and give useful indications for design improvements and vibration and noise reduction. As regards specifically gear accelerations as well as forces exciting the casing, they strongly increase with both output pressure and rotational speed, but variations in rotational speed in the operational range give lower effects. Conversely, the modifications of the clearances give negligible effects, while the relief groove dimension is very important: the larger the relief grooves are, the higher the gear accelerations and forces exciting the casing become.     

Dynamic behavior of an agricultural power take-off driveline for rattle noise reduction: Part 1. Effect of spline tolerance on the power take-off rattle noise

An agricultural tractor has a power take-off (PTO) driveline that is directly connected to the engine to improve its power transmission efficiency. The PTO driveline comprises various mechanical components coupled by a spline joint. The spline coupling tolerance causes collisions between various mechanical parts of the PTO driveline and affects gear collision, thereby causing rattle noise. Therefore, the aim of this study is to conduct a dynamic behavior analysis to predict the gear rattle noise level of a PTO driveline. The dynamic behavior of the PTO driveline was analyzed through 1D simulations, and the results confirmed that the dynamic behavior changes according to rotation speed. Experimental verification of the dynamic behavior analysis results confirmed that the dynamic behavior changes as the main engine excitation-component amplification changes and then decreases at a relatively high rotation speed. Additionally, the dynamic behavior changes of the PTO driveline resulted in a jumping phenomenon that occurs rapidly at a specific rotation speed. The amplification of the engine’s main components was reduced from 3 to 4 times to 1.2 times owing to the jumping phenomenon; the noise level of the gear rattle was also reduced by approximately 10.9 dB(A).     

Energy dissipation mechanism and experiment of particle dampers for gear transmission under centrifugal loads

As a passive means of vibration reduction, particle damping is mainly applied to the horizontal or vertical steady field. However, it is seldom applied to centrifugal fields. Under high speed and heavy loading, the vibration of tooth surfaces of gear transmissions becomes more severe shortening gear service life and augmenting noise. Under centrifugal loading, the particle system exhibits different characteristics, for example, particles are extruded at the end farthest from the center. We investigated gears with drilled via holes filled with damping particles. Using the discrete-element method, we developed an energy dissipation model for the particle system accounting for friction and inelastic collisions. Energy dissipation and damping characteristics of this system were analyzed. Experiments were also conducted with the gear system having different particle filling rates. The results show that this filling rate is an important parameter associated with particle damping in a centrifugal field. An unsuitable filling rate would significantly reduce damping effectiveness. With changes in rotation speed and load, the gear transmission system has different optimal filling rates. The results provide guidelines for the application of particle damping in centrifugal fields of gear transmissions.     

磁力耦合道路能量收集设计与动力学分析

通过在交通环境布置无线传感器等小型机电系统, 实现交通状况监测、交通系统管控、交通设施健康状态监测等, 可以使交通系统更加安全、有序、高效地运行. 但是, 如何为这些广泛分布的小型机电系统供能？本文提出了一种磁力耦合道路能量收集设计, 用以收集车辆滚压能量并转换成电能. 通过磁力耦合进行无接触能量传递, 减小了装置受到的冲击并使得装置具有良好密封性, 从而提升装置的鲁棒性. 通过升频齿轮机构、棘轮机构将车辆滚压激励转换为高速单向旋转, 并且通过换向齿轮机构能够继续收集复位弹性势能, 提高了收集装置的输出功率. 基于磁力耦合道路能量收集系统的工作原理建立了机电耦合动力学模型. 数值仿真探究了减速带限位距离和复位弹簧刚度等关键设计参数对能量采集系统动力学和电学性能的影响. 能量采集系统在车速为50 km/h时最大输出电压为76.28 V, 最大功率为59.94 W. 磁力耦合道路能量收集装置可以成为未来智慧交通系统的重要组成部分, 俘获交通环境能量为交通环境中小型机电系统提供可持续的绿色无碳电力.      

Stochastic Vibration Model of Gear Transmission Systems Considering Speed-Dependent Random Errors

A dynamic and stochastic simulation model is developed for analyzing the vibration of gear transmission systems with consideration of the influence of the time-variant stiffness, loads, and gear transmission errors. The gear transmission system is viewed as a non-linear, time-correlated and stationary stochastic system. The transmission errors of gears are decomposed into harmonic and random components based on the spectral analysis. To simulate the random component, a second order Markov process with time-variant parameters considering influence of rotational speed is proposed and the method to determine the model parameters based on the random error of measured gear transmission error is developed. A simulation system is developed. The input to the simulation system is a white Gaussian noise process and harmonic errors, and the output is the rotational vibration acceleration of gears. Experiments are carried out to verify the proposed model. The influences of the random error on vibration acceleration are examined using the developed simulation system.     

Passive control of vibration of thin-walled gears: advanced modelling of ring dampers

Vibrations on gears are mainly induced by the gear mesh contact. Resonance conditions of the gear may occur during service if the mesh frequency is close to the natural frequencies of the system at the designed speed of the shaft. Since detuning is not always possible in gears, the response level must be reduced by increasing the damping of the system. In this paper, a passive approach based on the application of a ring damper to reduce the vibration level is presented. The ring damper is placed in a groove underneath the outer rim of the gear. The contact is guaranteed by the preload due to the elasticity of the ring damper itself and above all by the centrifugal force that presses the damper against the groove during rotation. The relative motion of the two components at the contact interface dissipates energy by friction, and hence damping is generated. The vibration amplitude is reduced by optimizing the material and geometrical properties of the ring damper. One of the most important parameters in the determination of the amount of damping due to friction phenomena is the static normal load at the contact, which depends on the mass, the shape, and the material of the ring damper. A numerical method is presented, which couples the static and dynamic equilibrium equations of the assembly. The core of the proposed method is the contact element that takes into account local stick–slip–lift off of the contact and determines the contact forces in terms of static and dynamic loads, which are then used to solve the coupled static and dynamic equilibrium. Since the ring damper has a cut that breaks its continuous circular shape in order to be fitted on the groove, the hypothesis of cyclic symmetry for the gear/ring–damper assembly fails. As a consequence, an appropriate reduced-order modeling is presented to allow the forced response calculations. The algorithm is applied to a dummy bevel gear and to a ring damper having a flat punch contact area. The forced response calculations are performed to highlight the nonlinear interaction between the gear and damper by varying the parameters that mainly affect the amount and distribution of the contact forces and therefore the response level.     

Motion generation of RCCC mechanism using numerical atlas

This article presents a synthesis method for the motion generation of RCCC mechanism using the numerical atlas. Based on the Fourier series theory, the geometrical model of the rigid body rotation angle of RCCC mechanism is established. Through harmonic analysis, the rotation angle output characteristics were observed to be dependent on the rigid body rotation angle operator. Subsequently, two numerical atlas databases are constructed. The theoretical formulas to calculate the real size and installing dimensions were proposed. On the basis of the theoretical formulas and two numerical atlas databases, the problem of rigid body guided synthesis of RCCC is solved.     

A review of space tether in new applications

Gear eccentricities are one of the practical types of the manufacturing errors that affect the dynamic performance of a planetary gear train (PGT). Previous research about the effects of the gear eccentricities is abundant, and many of them focus on the parallel shaft gear set. However, almost none of them have considered the influence of the gear eccentricities on the mesh stiffness. In fact, the existence of the gear eccentricities can change the center distance and the mesh positions of a meshing gear pair, which will directly affect the mesh stiffness. Situation can be even more complex for the PGT with either sun gear eccentricities or planet gear eccentricities or both of them. Based on that, a new dynamic model of a PGT with gear eccentricities is established. The planar motions of the PGT and the mesh stiffness are integrated and solved simultaneously where the mesh stiffness is determined by the actual mesh positions of the meshing gear pair. The mesh stiffness is calculated by the energy potential method. The time-varying center distance caused by the gear eccentricities is also considered, which can result in the change of line of action, pressure angle, contact ratio and mesh positions. The influence of gear eccentricities on the dynamic performance of a 4-planet PGT is studied. Some useful results are derived at last.     

不等间隔角速率输出的捷联航姿算法研究

结合实际系统陀螺输出为不等间隔角速率信号且时间间隔已知的特点，将陀螺输出数据的时间间隔引入定时增量算法，提出了一种梯形积分增量算法。为补偿圆锥运动误差，推导了不等间隔角速率输出时的旋转矢量二子样算法，并在典型圆锥运动条件下，将本算法与甚童的捷联姿态算法进行比较。结果表明：在陀螺输出为不等间隔的角速率信号时，不等间隔的等效旋转矢量算法具有一定的优越性。     

Identification of resonant frequencies of rotating beams with the use of PZT crystals

An instrumentation system using piezoelectric crystals to excite and sense resonant frequencies of rotating blades is described. The output signals from sensors are transmitted through slip rings, processed through a specially designed differential amplifier to reject noise and cross-talk and analyzed. Effect of speeds of rotation on flexural frequencies is experimentally investigated.     

The analysis of power circulation and the simplified expression of the transmission efficiency of 2K-H closed epicyclic gear trains

Transmission efficiency is a principal index for estimating the performance of 2K-H closed epicyclical gear trains. To calculate transmission efficiency, it must confirm the power flow direction in transformation gear train and verify if there is power circulation in closed epicyclical gear train firstly. In this paper, a simple algorithm is proposed to confirm the power flow direction and estimate if there exist the power circulation based on transmission ratio of basic links in differential gear train and transformation gear train. The simplified equations are deduced to calculate the transmission efficiency and some examples are given finally.     

一种适合工程实用的捷联航姿算法

从工程实用的角度出发，针对惯性元件输出中存在干扰这一问题对四元数的三子样旋转矢量算法和四阶龙格－库塔法进行了分析和比较，指出四阶龙格－库塔法是一种具有工程实用价值的捷联航姿算法，并给出了在理想情况和有干扰的情况下算法的仿真结果。     

Comparison of spur,helical and curvilinear gear drives by means of stress and tooth contact analyses

Involute tooth surfaces are a successful technical solution for both spur and helical gear drives since they provide linear contact and a low-level function of transmission errors under good conditions of meshing. Tip relief is usually required to improve contact conditions during the transfer of meshing between adjacent pairs of teeth. Yet, unfavorable conditions of contact appear when shaft deflections and misalignments are present. Localization of contact through lead crowning is a solution that increases the cost of machining in both spur and helical gear drives. In this sense, the generation process of curvilinear gear drives provides localization of contact with no additional cost. Comparison of stresses and transmission error functions in spur, helical and curvilinear gear drives is investigated to show if the application of curvilinear gear drives yields some advantages respect to spur and helical gear drives. The three mentioned types of cylindrical parallel-axis gear drives are provided, firstly, with linear contact, and, secondly, with localized contact, for the purpose of comparison. Different misalignments conditions are taken into account by means of several numerical examples.     

磨损与动力学耦合的行星传动齿轮动力学研究

行星齿轮磨损会导致齿轮齿侧间隙非线性增大、传动精度下降、齿面冲击力增大, 进而会导致齿轮传动系统振动加剧, 因此需要对行星齿轮的齿面磨损与动力学耦合特性进行研究. 本文构建了齿轮非线性磨损与考虑齿轮齿侧间隙的非线性动力学耦合计算模型, 对行星传动齿轮磨损动力学特性进行了研究. 首先建立齿轮啮合非线性动力学模型, 获得齿轮运行过程中的非线性啮合力; 进一步将非线性啮合力与齿轮齿面磨损模型相结合, 研究齿轮齿面磨损分布规律; 并根据齿轮磨损后的齿侧间隙对齿面重构, 同时对齿轮动力学模型进行更新; 进而得到行星齿轮传动中动态啮合力和磨损特性的变化趋势, 并获得齿轮传动系统齿轮齿向振动响应. 数值计算结果表明, 行星齿轮磨损导致齿轮在单?双齿交替啮合时产生的冲击增大, 同时太阳轮?行星轮啮合齿对对磨损较为敏感, 齿面啮合条件剧烈恶化, 是造成行星齿轮传动性能退化的主要原因, 本文研究结果为行星齿轮传动系统运行状态评估与可靠性预测提供了理论基础.      

惯性-视觉-磁场传感器组合的低成本标定方法

针对一种融合了惯性-视觉-磁场信息的传感器组合,给出了一套低成本的标定和建模方法.对于传感器模型中的确定性项和非确定性项参数,分别采用了基于输入指令向量模匹配的方法和基于时间序列分析的方法来进行标定和建模,利用所得到的模型补偿之后的传感器输出误差的方差降为原来的1/3以下;对于摄像机坐标系和加速度计坐标系之间的相对旋转矩阵,提出了一种基于重力向量和铅垂线的标定方法,仿真结果表明,标定结果的相对误差小于7%.     

Nomographs for synthesis of epicyclic-type automatic transmissions

This paper presents a MATLAB optimization technique for the determination of the gear ratios of epicyclic-type transmission mechanisms for a given set of velocity ratios. First, all of the feasible clutching sequences are enumerated directly without using complicated techniques. Then, for the transmission mechanism with the associated clutching sequence graph, the overall velocity ratios are derived and expressed in terms of the gear ratios of all the mating gears. Next, following the general trend of increased shift stages and a wider range of velocity ratios, the numbers of teeth of all gears are estimated by MATLAB optimization technique in a single run. Ravigneaux gear mechanisms are used as design examples. The methodology can be applied to any transmission mechanism depending on its kinematic and geometric constraints. New five- and six-velocity automatic transmissions are enumerated from the Ravigneaux gear mechanism. It is a major breakthrough to design a completely satisfactory six-speed automatic transmission from the Ravigneaux gear mechanism since it has only eight links. The new design makes use of the benefits of the Ravigneaux gear train and overcomes the previous art difficulties. This structural design has realized a six-speed automatic transmission, while having minimal number of clutches, and brakes. It is also low cost due to adoption of the conventional available Ravigneaux gear train.     

Nonlinear dynamics of a spur gear pair with force-dependent mesh stiffness

Time-varying mesh stiffness is one of the main excitation sources of a gear system, and it is also considered as an important factor for the vibration and noise of gears. Thus, this excitation is usually taken as an input into the gear dynamic model to obtain the system dynamic responses. However, the mesh stiffness of a gear pair is actually nonlinear with respect to the dynamic mesh force (DMF) that fluctuates during the operation of gears. Therefore, the dynamic model of gears with the quasi-static mesh stiffness calculated under a constant load is not accurate sufficiently. In this paper, a dynamic model of spur gear is established with considering the effect of the force-dependent time-varying mesh stiffness, backlash and profile deviation. Due to the nonlinear relationship between the mesh stiffness and the load for each tooth pair, it needs first to determine the load sharing among tooth pairs and then calculate the overall mesh stiffness of the gear pair. As the mesh stiffness and DMF are related, the mesh stiffness is no longer directly taken into the gear dynamic model as an input, but is jointly solved with the numerical integration process using the gear dynamic model. Finally, the dynamic responses predicted from the established gear dynamic model are compared with the experimental results for validation and compared with the traditional models to reveal their differences. The results indicate that the established dynamic model of spur gear transmission has a wider application range than the traditional models.     

Dynamic characteristic analysis of spur gear system considering tooth contact state caused by shaft misalignment

The effect of gear contact state change due to shaft misalignment on meshing stiffness is usually neglected in the traditional stiffness calculation model with misalignment error, the further influence mechanism of shaft misalignment on gear dynamic characteristics is also unclear. To address these shortcomings, a new mesh stiffness calculation model with misaligned gear considering the effects of tooth contact state is proposed by combining the improved loaded tooth contact analysis (LTCA) model. Then the effects of tooth contact state changes aroused by shaft misalignment on the meshing stiffness excitation are investigated. Moreover, a dynamic model of the misaligned gear system with 8 degrees of freedom (DOF) is established, and based on which the dynamic characteristics of the gear system are investigated and verified by experiment. The study results indicate that the proposed model can be used to evaluate the stiffness excitation and dynamic characteristics of the misaligned gear system with the tooth contact state taken into consideration. This study can provide a theoretical method for evaluating and identifying shaft misalignment errors.