Dynamic characteristics of the planetary gear train excited by time-varying meshing stiffness in the wind turbine

Wind power has attracted increasing attention as a renewable and clean energy. Gear fault frequently occurs under extreme environment and complex loads. The time-varying meshing stiffness is one of the main excitations. This study proposes a 5 degree-of-freedom torsional vibration model for the planetary gear system. The influence of some parameters(e.g., contact ratio and phase difference) is discussed under different conditions of a single teeth pair and double pairs of teeth. The impact load caused by the teeth face fault, ramped load induced by the complex wind conditions, and the harmonic excitation are investigated. The analysis of the time-varying meshing stiffness and the dynamic meshing force shows that the dynamic design under different loads can be made to avoid resonance, can provide the basis for the gear fault location of a wind turbine, and distinguish the fault characteristics from the vibration signals.

Dynamic Characteristics of Double-Helical Planetary Gear Sets Under Time-Varying Mesh Stiffness

Internal and external meshes are two of primary excitation sources which induce vibration while double-helical planetary gear sets are in transmission. Based on the analysis of tooth movement principle,three cases of mesh stiffness are derived via investigating the length of action lines,and catalogued in terms of β < β0,β = β0and β > β_0. The simulation demonstrates mesh stiffness between gear pairs performs as a trapezoid waveform( TW) and changes along with the line of action simultaneously,total mesh stiffness comes from the superposition of each engaged gear. While governing equations of motion contained 16 DOFs( degree of freedom) are constructed and effectively solved through the combination of numerical approaches. Comparing with sinusoidal waveform mesh stiffness( SW),the results show that dynamical factors and perturbation under the excitation of TW( β < β_0) are greater and remarkable than that from SW,with respect to the mean dynamic factors about 1. 51 and 1. 28,respectively. The fluctuation response between ring- planet( R- P) is stronger than sun-planet( S-P) which is also validated by both approach studies,frequency spectra analyses identifies larger distinct rotational resonance and more frequencies under TW excitation.

Effect analysis of friction and damping on anti-backlash gear based on dynamics model with time-varying mesh stiffness

A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.

Influence Predictions of Contact Effects on Mesh Stiffness of Face Gear Drives with Spur Gear

Mesh stiffness is one of important base parameters of face gear dynamic studies.However,a calculation solution of mesh stiffness of face gear drives is not to be constructed due to complex geometric flakes of face gear teeth.Thus,a calculation solution of mesh stiffness of face gear drives with a spur gear,which is based on the proposed equivalent face gear teeth and Ishikawa model,is constructed,and the influence of contact effects on mesh stiffness of face gear drives is investigated.The results indicate the mesh stiffness of face gear drives is sensitive to contact effects under heavy loaded operating conditions,specially.These contributions will benefit to improve dynamic studies of face gear drives.

Simulation study on dynamics of cylindrical gear meshing with the evolution meshing stiffness

Simulation study on the cylindrical gear meshing with the evolution gear meshing stiffness is being done for better understanding the dynamic characteristics of the kinematics.With consideration of damping,bearing clearance and gear backlash nonlinearity,the dynamic model is set up and computed in MATLAB.The analysis about the relationship between the kinematic responses and the meshing stiffness are carried out.And the results showed that as the gear mesh stiffness is changed from small to large,the performance of the system is changed from the harmonic stable periodic motion to with one times,two times,four times,ending chaos of the stability of the bifurcation.The research results would have theoretical guidance value for the fault diagnosis in engineering.

Nonlinear parametrically excited vibration and active control of gear pair system with time-varying characteristic

In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.

Improved analytical model for mesh stiffness calculation of cracked helical gear considering interactions between neighboring teeth

As one of the most typical fault forms of the helical gear,the crack will change the dynamic excitation and further affect the dynamic behaviors of the transmission systems.Due to the complicated structure of the helical gears,the coupling effect between the neighboring loaded teeth is usually ignored in the mesh stiffness calculation,making it considerably overestimated especially in the case of the crack fault.An improved mesh stiffness calculation method of helical gear with spatial crack is proposed to make up this gap.The interactions between the loaded neighboring teeth induced by the gear body flexibility were considered to improve the calculation accuracy and applicability.Besides,the load distribution law for the engaged cracked tooth along the tooth width and profile can be obtained.The results indicated that the mesh stiffness of the multi-tooth engagement calculation using this model could be further improved compared with the traditional methods.Finally,the effects of the helix angle,crack depth,and crack propagation length on the mesh stiffness and load distribution were investigated using the proposed method.

非对称齿轮啮合刚度精确求解及齿廓参数分析

非对称齿轮是一种轮齿两侧采用不同压力角的新型渐开线齿轮,其齿廓参数对齿轮齿廓形状、运动特性、承载能力、传动效率和动力学特性等有至关重要的影响。基于齿轮啮合原理,运用李特文矢量法,根据加工刀具齿廓参数方程推导了非对称齿轮全齿廓方程;应用材料力学理论,建立非对称齿轮时变啮合刚度的数值求解模型,并通过有限元方法验证了该模型的有效性。基于所建立数值分析模型进行算例研究,总结了刀具圆角、压力角和变位系数对齿轮啮合刚度和重合度的影响规律。结果表明,随着轮齿工作侧压力角的增大,齿轮齿根厚度增加,单齿对的啮合刚度加大,齿轮的承载能力得到有效提高。加工工作侧轮齿齿廓刀具圆角的增大,也有利于提高齿轮的啮合刚度;同时,工作侧齿廓压力角的增大会使齿轮的齿顶厚度降低、啮合重合度减小,会导致齿轮的齿顶强度和冲击韧性降低。非对称齿轮齿廓设计时,应根据实际工况合理设置压力角参数。

双曲型法向圆弧齿轮传动的动力学分析

为探究啮合刚度、传动误差及侧隙对双曲型法向圆弧齿轮传动动态响应的影响,建立齿轮副的动力学方程,并在数值计算的基础上进行仿真分析。运用有限元方法,计算接触位置处的载荷及变形,并对时变啮合刚度、静态传动误差和侧隙进行量化分析。仿真结果表明:对振动位移响应影响最大的是侧隙,其次是时变啮合刚度;对动态啮合力影响最大的则是时变啮合刚度和侧隙。

基于动态啮合刚度的直齿圆柱齿轮动态特性研究

齿轮系统转速直接影响齿轮系统的动态特性,然而在啮合刚度的计算中该因素却被许多学者们忽略。为了研究转速对啮合刚度的影响,基于有限元框架使用平均加速度法提出了一种计算与转速相关的动态啮合刚度的算法,同时对不同转速下的动态啮合刚度进行仿真计算与分析,最后进一步探究了受动态啮合刚度影响后的齿轮系统所具有的相关动态特性。分析表明,动态啮合刚度始终围绕着静态啮合刚度上下波动;随着转速的增加,其波动幅度增加,振荡次数减少;随着转速的变化,动态啮合刚度计算的动态传动误差振幅相对于静态啮合刚度而言大小关系不一致,且计算的齿轮系统共振转速区间或超前或滞后于静态啮合刚度模型;动态啮合刚度影响特定转速区间的齿轮系统的振动周期。对与转速相关的动态啮合刚度的研究可为直齿圆柱齿轮传动性能的改善及减振降噪提供参考。

小模数齿轮传动的时变啮合刚度计算方法

小模数齿轮传动中心距较小,其动态性能对中心距误差非常敏感,且中间级齿轮常被设计在固定轴上高速旋转,齿轮中心孔与轴之间存在间隙,考虑这些特征,建立了中心距误差与轴孔配合间隙影响下的齿轮啮合特性参数与时变啮合刚度计算模型,研究了二者对啮合刚度的影响规律。研究结果表明:中心距误差会改变齿轮副的重合度与啮合刚度;轴孔配合间隙使实际中心距围绕理论中心距上下周期性波动,导致整个周期内啮合刚度强化区域与弱化区域共存;中心距误差与轴孔配合间隙的影响在不同的转角范围内存在既有相互叠加又有相互削弱的现象,这一现象使得各轮齿的啮合刚度有差异,存在诱发更大振动与不同噪声的风险。

基于时变啮合刚度的多剥落齿轮振动响应分析

为了探究多剥落齿轮系统中振动响应的演变规律,融合时变啮合刚度构建了多剥落齿轮动力学模型。首先,融合修正的能量法和单/双齿对啮合角位移计算方法,建立多剥落齿轮啮合刚度模型;其次,考虑时变啮合刚度、齿侧间隙和初始压力角等因素,构建6自由度多剥落齿轮动力学模型,并从仿真、理论和实验维度开展模型有效性分析;最后,基于所构建的模型,研究齿根、节线和齿顶位置同时发生剥落时,剥落尺寸变化对啮合刚度影响,获得多剥落齿轮振动响应的演变过程。研究结果表明,所构建模型与理论及实验误差小于0.5%,并得到了齿根、节线和齿顶位置剥落的啮合刚度及振动响应的演变规律,随着剥落宽度的扩展,节线附近振动幅值增大显著;随着剥落深度的增加,齿顶位置受到的振动冲击更为强烈;而随着剥落长度的增加,剥落的波及范围扩大。所得结论为齿轮系统的健康监测和早期故障诊断提供了理论指导。

蜗杆斜齿轮传动副时变啮合刚度计算及非线性动力学特性分析

蜗杆斜齿轮传动副作为一种交错轴点接触传动形式,掌握其时变啮合刚度及啮合侧隙与误差等引起的非线性动力学行为是减振降噪的核心。文中基于势能法修正并求解蜗杆斜齿轮传动副理论时变啮合刚度,建立考虑齿侧间隙-综合误差及时变啮合刚度的动力学模型,采用4~5阶Runge⁃Kutta法对系统动力学方程进行数值求解,得到蜗杆斜齿轮传动副动力学特性曲线。结合时域图、Poincaré图及FFT频谱图,分析齿侧间隙、阻尼比及载荷等因素对传动副振动和冲击状态的影响,结果表明:较小的误差幅值及较大的阻尼比可使系统处于稳定的周期运动状态。研究结果对优化蜗杆斜齿轮传动系统的振动噪声有指导意义。

面向齿廓变位的圆柱直齿轮啮合动态特性研究

为研究齿廓变位的直齿轮传动系统啮合特性,建立了变位直齿圆柱齿轮传动分析模型。该模型考虑了赫兹接触刚度、弯曲刚度、剪切刚度、轴压刚度和圆角基础刚度,给出了两种不同的齿廓变位的几何设计。在此基础上采用数值模拟方法研究了齿廓变位对时变啮合刚度(TVMS)和动态特性的影响。对于单个齿廓变位,正变位虽然增加了齿轮的厚度,但降低了齿轮的轮齿刚度以及齿轮副的接触比,从而加剧齿轮系统的振动。相反,负变位可以提高齿轮的轮齿刚度,增加齿轮的接触比,使得齿轮系统的传动更平稳。对于复合变位,负复合变位的S齿轮传动会导致TVMS升高,并显著降低振动,而s_(0)齿轮变位对时变啮合刚度(TVMS)影响较小,但对动态特性影响较大。

考虑齿圈柔性的内啮合齿轮时变啮合刚度计算分析

当前大多数内齿轮啮合刚度都是基于忽略齿圈基体变形的假设计算的,文中应用Weber能量法基于精确的齿廓曲线方程建立内齿轮悬臂梁等效模型,同时基于铁木辛柯(Timoshenko)曲梁理论计算齿圈基体的变形量,并将齿圈变形耦合到齿轮啮合刚度计算中。通过MATLAB GUI编程进行内啮合齿轮时变啮合刚度数值计算,分析了齿圈柔性对啮合变形的影响,研究了齿圈厚度、支撑数量及啮合力位置对啮合刚度的影响。结果表明:齿圈厚度和支撑数量的增加均有利于齿轮副啮合刚度的增大;啮合齿中线位于固定支撑点时,齿圈啮合刚度最大,在靠近支撑中间位置时,啮合刚度最小,齿圈啮合刚度对应于螺栓支撑呈周期性波动。

斜齿轮时变啮合刚度改进算法及影响因素分析

在势能法基础上,基于切片积分原理,考虑齿根过渡曲线方程,提出一种改进的斜齿时变啮合刚度计算方法。该方法考虑了真实齿根过渡曲线参数方程,修正了渐开线齿廓的积分区间,与有限元方法的对比结果验证了算法的有效性,减小了时变啮合刚度的计算误差。在此方法基础上,分析了齿宽、螺旋角、齿数和模数对时变啮合刚度的影响。结果表明,时变啮合刚度均值受齿宽影响较大,近似成线性关系;受螺旋角、齿数影响较小;螺旋角增大,均值以较小幅度波动性变化;中心距一定时,齿数增大,时变啮合刚度缓慢增大;齿轮参数改变会影响重合度;轴向重合度为整数时,时变啮合刚度波动值较小。

考虑点蚀情况的双渐开线齿轮动态特性研究

齿轮是机械传动系统的核心部件,点蚀与磨损是其主要失效的形式。为解决齿轮发生点蚀失效时双渐开线齿轮的时变啮合刚度与动态特性不明这一问题,采用接触线百分比法求解了发生点蚀时双渐开线齿轮的啮合刚度,并利用有限元法验证了算法的正确性。首先,对不同点蚀情况进行了分类,分析了不同点蚀数量对双渐开线齿轮接触线长度的影响;然后,基于接触线百分比法,利用轮齿载荷与轮齿变形的比值关系求解了不同点蚀情况下齿轮的啮合刚度,采用有限元法验证了算法的正确性,并对比分析了点蚀对双渐开线与普通渐开线齿轮啮合刚度的影响;最后,建立了两种齿轮的柔性多体动力学模型,基于冲激函数法分析了两种齿轮在不同点蚀情况下的动力学特性。研究结果表明:相同工况条件下,随着点蚀程度的加深,两种类型齿轮啮合刚度均不断减小,动态啮合力及振动角加速度幅值增加,其中双渐开线齿轮啮合力最大值为1.24×10^(5)N,角加速度最大值为2.66×10^(6)°/s^(2);相比于普通渐开线齿轮,双渐开线齿轮在点蚀影响下的啮合刚度变化更稳定,加速度幅值波动更平缓,具有更好的抵抗冲击能力和动力传递稳定性。

考虑磨损故障的双渐开线齿轮传动系统动态特性研究

针对目前双渐开线齿轮(DIG)研究过程中齿廓磨损对双渐开线齿轮动态特性的影响问题,对考虑磨损故障的双渐开线齿轮传动系统动态特性进行了研究。首先,进行了双渐开线齿轮接触线长度与齿面载荷计算,考虑相对滑移距离,建立了等效接触模型;然后,进行了双渐开线齿轮齿面累积磨损量、齿轮齿面累积磨损深度的计算,建立了双渐开线齿轮啮合刚度计算模型,进行了磨损故障的双渐开线齿轮刚度的计算;最后,以一对双渐开线齿轮为研究对象,采用集中质量法建立了6自由度动力学模型,研究了齿面磨损对双渐开线齿轮动力学特性的影响。研究结果表明:在运行1×104次载荷循环后,混合弹流润滑状态下,双渐开线齿轮与普通渐开线齿轮(CIG)在节线附近齿根位置的最大累计磨损量差值为0.00207μm,且双渐开线齿轮节线靠近齿顶位置的磨损小于普通渐开线齿轮的磨损;双渐开线齿轮系统在磨损后振动加速度幅值小于普通渐开线斜齿轮的幅值。通过对不同磨损情况下的时域响应进行研究,发现磨损导致双渐开线齿轮传动系统的振动幅值增大。

裂纹工况下斜齿轮系统啮合刚度计算模型研究

当斜齿轮副产生裂纹时,会影响齿轮副的啮合刚度。为了获得更准确的裂纹斜齿轮副的啮合刚度,提出一种改进的裂纹斜齿轮啮合刚度计算模型,综合考虑轮齿刚度、齿轮基础刚度在横向和轴向的影响,研究了齿顶扩展裂纹和端面扩展裂纹两种典型裂纹工况下的齿轮系统啮合刚度,并将啮合刚度解析计算结果与有限元模拟结果进行了对比。结果表明:啮合刚度的降低程度主要与裂纹区域有关,裂纹区域越大,啮合刚度降低越大;在裂缝长度和深度相同的情况下,端面扩展裂纹对啮合刚度的影响比顶部扩展裂纹更显著。仿真结果与计算结果吻合较好,验证了所提方法的准确性和有效性。

含角度不对中误差的斜齿轮啮合刚度分析

角度不对中误差是齿轮箱中一种常见的安装误差,它将导致轮齿间出现局部应力过大、振动噪声过高等不良现象。然而,如何准确的预测角度不对中误差对斜齿轮啮合传动的影响是一大难题。针对此问题,本文基于“切片法”提出了斜齿轮角度不对中误差啮合刚度迭代模型,该模型综合考虑了角度不对中误差引起的轴向弯曲刚度和扭转刚度。通过有限元方法验证了所提模型的正确性。基于此模型研究了不同角度不对中误差参数及载荷对啮合刚度的影响。结果表明,随着角度不对中的增大,啮合刚度逐渐降低;随着载荷的增大,啮合刚度逐渐增大。该研究可为角度不对中误差的刚度计算提供理论支撑。