失效相关的齿轮一次四阶矩可靠性分析

齿轮是机械传动的关键零件之一,为了分析其可靠性,在改进的验算点一次二阶矩可靠性方法基础上,应用Taylor级数展开和Hermite多项式近似等方法,推导了齿轮功能函数的验算点前四阶矩,分析了具有齿根断裂和齿面点蚀两种主要相关失效模式的齿轮传动可靠性,给出了其相关系数和齿轮的可靠度。另一方面,因影响齿轮失效的因素繁杂众多,计算齿轮的可靠度时,不管是用一次二阶矩可靠性方法还是四阶矩可靠性方法,其计算量均偏大,且容易出错。针对该问题,提出了一种分类变差系数验算点一次四阶矩可靠性分析方法,该方法对齿轮功能函数的不同基本随机变量进行分类综合,减少了设计变量,使计算量明显减小,解决了用矩方法分析结构可靠性时计算量偏大且易出错的难题。最后应用所提分类变差系数验算点一次四阶矩可靠性分析法估计了某车床主轴箱一对传动齿轮的可靠性,计算结果显示该对齿轮齿根弯曲疲劳强度和齿面接触疲劳强度有一定的相关性,所用一次四阶矩方法因包含偏度、峰度等更高阶的统计信息可进一步提高估计精度。     

正交面齿轮传动系统非线性振动特性研究

作为一种新型传动形式,面齿轮传动在高速大功率场合的应用越来越多,其非线性振动特性分析对提高其工作可靠性具有重要意义。为研究正交面齿轮传动系统的非线性动力学特性,建立了包含支承、齿侧间隙、时变啮合刚度、综合传动误差、阻尼和外激励等参数的系统弯-扭耦合动力学模型,并使用PNF(Poincaré-Newton-Floquet)方法对系统的动力学微分方程进行求解。计算结果表明：随着转速增大,系统呈现混沌-周期-混沌的运动特征,不同的混沌区域间存在周期窗口;在不同的参数条件下系统会出现4种动态响应,即简谐响应、次谐波响应、拟周期响应及混沌响应;不同的响应特性对应的动载系数幅值差别非常大,应尽量调节系统转速,使系统的动态响应保持在周期窗口内。     

基于有限单元法的多间隙耦合齿轮传动系统非线性动态特性分析

针对齿轮传动系统的动态传递误差、单双边冲击状态、脱齿、拍击及混沌现象等复杂非线性动力学问题,在同时考虑齿侧间隙、轴承间隙、时变啮合刚度及齿面摩擦等非线性特性的基础上,首次提出一种基于有限单元法的多间隙耦合齿轮传动系统的非线性动态特性分析方法。以某单级斜齿轮传动系统为例,利用大型通用有限元分析软件AN-SYS/LS-DYNA建立耦合系统动力学模型,分析支撑状态下耦合系统的非线性动态特性,研究了不同转速及负载力矩对耦合系统非线性动态特性的影响规律。结果表明有限单元法能在满足高精度分析的条件下求解各种复杂工况的齿轮系统非线性动力学问题,为进一步研究齿轮传动系统非线性动力学问题提供有力工具。     

Reliability analysis of chatter stability for milling process system with uncertainties based on neural network and fourth moment method

A reliability analysis of the milling system with uncertainties is developed in this paper to predict reliable chatter-free machining parameters. The chatter reliability refers to the probability of no chatter for the dynamic milling system. Then a reliability model is established to predict the chatter vibration, in which the dominant modal parameters of the dynamic milling system are defined as random variables. To solve the reliable model with the second-order fourth-moment (SOFM) method, the limiting axial cutting depth is substituted by an explicit expression obtained using a neural network. Therefore, after distributions of the random parameters are experimentally determined, the reliability of the given machining parameters can be computed with the SOFM method. Furthermore, a reliable stability lobe diagram (RSLD) can be plotted to obtain more reliable and accurate stable region instead of the conventional SLD. A case study is performed to validate the feasibility of the proposed method. The reliability of the milling system was calculated with the SOFM method, the first-order second-moment (FOSM) method and the Monte Carlo simulation (MCS) method. The results from the SOFM method and MCS method were found to be more consistent. Moreover, a RSLD with the reliability level 0.99 was compared with a conventional SLD plotted using the mean values of the random parameters. Chatter tests shown that the RSLD with the higher reliability level was more accurate for predicting the chatter-free machining parameters.     

基于齿轮传动系统横-扭-摆耦合非线性动力学模型的齿廓修形优化设计

基于齿轮传动系统动力学模型的齿廓修形优化设计可真实地反映修形参数对齿轮动态特性的影响。考虑几何偏心、陀螺力矩和齿向偏载力矩,建立了单级齿轮传动系统10自由度横-扭-摆耦合非线性动力学模型。提出了考虑齿轮实际运动状态并可适用于齿廓修形齿轮的啮合刚度模型,并采用解析法计算啮合刚度。为了降低齿轮传动系统的振动和噪声,以减小齿轮传动系统的动载系数为目标,建立了基于齿轮传动系统横-扭-摆耦合非线性动力学模型的齿廓修形优化模型。对某重载车辆齿轮传动系统进行了齿廓修形优化设计,优化结果有效的降低了齿轮的动载荷,可为设计低振动和低噪声的齿轮传动系统提供依据。     

考虑摆线轮磨损的RV减速器传动精度可靠性分析与参数优化

针对RV （rotate vector）减速器在工作过程中存在的零件磨损导致传动精度下降的问题,建立了考虑摆线轮磨损的RV减速器传动精度动态可靠性模型,进行传动精度可靠性分析,并对关键零件的公差以及摆线轮的修形参数进行优化设计。以某重载RV减速器为研究对象,利用Archard磨损公式对摆线轮的磨损深度进行计算,分析轮齿齿廓磨损的分布情况,并基于数值仿真数据利用高斯过程回归模型预测磨损量;建立了含动态磨损的RV减速器传动精度可靠性模型,用蒙特卡洛法求解其动态可靠度;建立了以传动精度动态可靠度为约束条件,以加工成本最低、额定寿命周期内最大磨损量最小为优化目标的优化模型,采用多目标遗传算法求得最优解。结果表明;优化后摆线轮的磨损量略微增大,而减速器的加工成本明显降低;优化后减速器传动精度可靠度得到明显提高,在额定寿命6 000 h内的可靠度满足预期要求。研究结果可以为高精度RV减速器的设计提供参考。     

Copula‐function‐based analysis model and dynamic reliability of a gear transmission system considering failure correlations

In this study, an improved prediction model is introduced to assess the residual strength of gear transmission systems. The residual strength and stress‐strength interference theories are then combined to facilitate the study of the reliability of the gears and bearings in these systems. Based on the copula function, the correlation between the gear contact and bending failure is determined. The relationship between the copula function and reliability is used to determine the dynamic reliability of the gears while considering multiple correlated failure modes. In this manner, more accurate and dynamic reliability attenuation characteristics are obtained for the gear transmission system.     

基于贝叶斯理论的非线性结构模型修正及其动力可靠度分析EI北大核心CSCD

提出一种基于贝叶斯推理的非线性结构模型修正方法,同时考虑激励的随机性,建立了复合随机振动系统的动力可靠度分析方法。利用实测结构动力响应主分量的瞬时特征参数作为非线性指标构建似然函数,结合拒绝延缓自适应(Delayed Rejection and Adaptive Metropolis,DRAM)算法和高斯过程替代模型实现了非线性结构模型修正及其参数的不确定性量化。根据首次超越破坏准则,利用广义概率密度演化方法,分别对仅考虑激励随机性的确定性模型和同时考虑结构参数与激励不确定性的复合随机振动模型进行动力可靠度分析,并利用蒙特卡洛随机抽样方法验证了计算结果的准确性。研究结果表明:基于振动响应瞬时特征参数的贝叶斯推理方法能够快速、准确地实现结构的非线性模型修正及其参数的不确定性量化。与具有初始设计参数名义值的确定性模型相比,考虑参数不确定性的复合随机模型的动力可靠度总体偏低,因此,在结构安全评估中应考虑非线性模型参数不确定性的影响,使评估结果更加安全、可靠。     

齿面摩擦对面齿轮传动系统振动特性的影响分析

为研究齿面摩擦力对正交面齿轮传动系统动态特性的影响,基于集中参数理论,建立了考虑齿面摩擦、齿侧间隙、传动误差、时变啮合刚度、啮合阻尼、支撑刚度和阻尼等参数的正交面齿轮多自由度耦合振动模型,采用龙格库塔数值积分法对系统的动力学方程求解,得到随摩擦系统变换的系统动态响应分岔特性。结果表明,随齿面摩擦系数的变化,面齿轮传动系统的动力学特性有周期响应和混沌响应,动态特性比较复杂。     

Analysis of complex system reliability with correlated random vectors

The analysis of reliability of complex engineering systems remains a challenge in the field of reliability. It will be even more difficult if correlated random vectors are involved, which is generally the case as practical engineering systems invariably contain parameters that are mutually correlated. A new method for transforming correlated distributions, involving the Nataf transformation, is proposed that avoids the solution of integral equations; the method is based on the Taylor series expansion of the probability density function (PDF) of a bivariate normal distribution resulting in an explicit polynomial equation of the equivalent correlation coefficient. The required numerical results can be obtained efficiently and accurately.The proposed method for transformation of correlated random vectors is useful for developing a method for system reliability including complex systems with correlated random vectors. Based on the complete system failure process (originally defined as the development process of nonlinearity) and the fourth-moment method, the analysis of system reliability for elastic-plastic material avoids the identification of the potential failure modes of the system and their mutual correlations which are required in the traditional methods. Finally, four examples are presented – two examples to illustrate the potential of the new method for transformation of correlated random vectors, and two examples to illustrate the application of the proposed more effective method for system reliability.     

等高齿锥齿轮非线性振动特性的联合求解方法

齿轮重载啮合中发生的轮齿接触损失会引起齿轮传动中的动态传递误差,动态传递误差的存在是等高齿锥齿轮非线性振动的重要原因,准确预测和计算等高齿锥齿轮传动中的动态传递误差是进一步改善这类齿轮系统振动特性的有效手段。针对某重载等高齿锥齿轮,研究了其在一定运行速度和扭矩范围内的频率响应特性;运用一种新的曲面积分与局部有限元联合求解方法求解了等高齿锥齿轮传动中的动态传递误差,从而揭示出此类传动系统振动的强非线性特性。这种方法无需将时变拟合刚度和啮合频率变量等非线性因素作为外部的激励进行求解,而是从齿轮啮合的每一时步,计算动态啮合力以及动态传递误差,最终得出等高齿锥齿轮的非线性振动特性。该方法可以精确表达轮齿几何及轮齿接触力等因素对齿轮动力学性能的影响,为等高齿锥齿轮这类复杂振动特性的传动系统提供了一种行之有效的分析方法。     

裂纹故障对行星齿轮传动系统动力学特性的影响

针对行星传动装置动态特性复杂、故障率高的问题,拟从动力学角度探索行星传动系统的故障机理。采用改进能量法,仿真分析正常与含裂纹齿轮时变啮合刚度,考虑时变啮合参数影响,运用集中参数法建立了行星齿轮传动系统动力学模型;求解得到了正常与含故障齿轮传动系统动态响应,并对比分析了裂纹故障对动力学特性的影响;通过台架实验,分析了裂纹故障对齿轮动态响应的影响,结合小波分析与EEMD方法对齿轮振动信号进行频谱分析,并对比分析了正常与故障齿轮的频域特性差异,揭示了行星齿轮传动系统的故障机理。研究表明:所建立的动力学模型精度较高,能够很好地描述含故障齿轮传动系统的动力学特性;由于裂纹故障引起传动系统振动的调制效应,导致在齿轮啮合频率附近出现明显边频带,故障齿轮箱的振动能量主要集中在高频段。     

随机参数齿轮系统的非线性动力响应分析

建立了物理参数和几何参数均为随机变量,并考虑具有齿轮侧隙、轴承间隙、时变刚度、齿间摩擦力和静态传递误差的齿轮-转子系统非线性振动的动力学方程。利用Newmark-β逐步积分法将此随机参数时变刚度系统的非线性动力学方程转换为随机参数的拟静力学控制方程,利用求解随机变量函数数字特征的代数综合法和矩法,导出了系统动态位移响应的均值和均方差计算公式。算例结果表明:齿轮模数的随机性对系统响应的随机性影响较大,摩擦系数对系统振幅的影响不可忽视,特别当齿轮的间隙大于10?5m时,系统的振幅受其影响增大。关键词:随机参数;齿轮-转子系统;非线性动力学;Newmark-β法;时变刚度     

多轴系耦合作用下齿轮系统转子裂纹故障的振动特性研究

为了探究多轴系耦合齿轮系统中的转子裂纹故障与单轴系转子裂纹故障振动响应特性的异同点,基于Jones轴承建模理论,建立滚动轴承的拟静力学模型;利用Timoshenko梁单元建立传动轴的有限元模型;考虑时变啮合刚度、齿轮传递误差、陀螺效应等因素,利用集中参数法建立齿轮副的动力学模型。将轴承、传动轴与齿轮副模型进行集成,建立齿轮系统非线性动力学模型;利用能量释放率理论与应力强度因子为零法分析裂纹转子单元的呼吸效应,利用Newmark-?数值积分法对转子裂纹故障进行动力学仿真,研究转子裂纹故障的振动响应特征。结果表明：与单轴系转子裂纹故障不同,当齿轮系统发生转子裂纹故障时,由于齿轮啮合的引起的耦合效应及转子裂纹引起的呼吸效应,时域响应表现出明显的幅值调制现象,频域中转频及其2倍频幅值增加明显,在啮合频率处伴有明显的边频带。研究结果为齿轮系统转子裂纹故障的监测与诊断提供了理论基础。     

汇流传动齿轮-转子-轴承系统非线性动力学分析

考虑齿侧间隙、传动误差和时变啮合刚度等非线性因素,并同时考虑滑动轴承非线性油膜力和齿轮啮合力的耦合影响,建立了汇流传动齿轮-转子-轴承系统的动力学模型。从转速方面出发,研究了齿轮系统的非线性动态响应,分析了齿轮啮合力和非线性油膜力之间的耦合作用,判断了转速变化下的油膜稳定性。结果表明：随着转速变化,系统表现出周期一运动、周期二运动、拟周期运动,混沌等丰富的动力学特性,并发现了拟周期分岔通向混沌的道路;随着转速升高,非线性啮合力和非线性油膜力先后对系统振动起到主要作用;油膜振动通过半频涡动失去了稳定性。     

二级圆柱斜齿轮系统耦合动态响应分析

应用集中参数法建立了一种计及时变啮合刚度、齿侧间隙、传动误差的二级圆柱斜齿轮传动系统弯－扭－轴－摆耦合动力学模型,推导并求解了传动系统的动力学微分方程组,得到了二级圆柱斜齿轮传动系统的动力响应。基于有限元法建立了箱体的动力学分析模型,在得到传动系统动态响应及轴承结合部动力学参数数值基础上,对箱体进行了动力响应分析。在将齿轮系统划分为传动系统与箱体两个子系统的基础上,实现了对整个齿轮系统的动力学分析。     

Reliability-based design of automotive transmission systems

A reliability-based approach is presented for the design of three-speed automotive transmission systems. The design of an automotive transmission system involves the design of the gear train, shafts (input, connecting, and output), bearings, keys, and splines. The gear train is idealized as a weakest-link kinematic chain, and the design is conducted with respect to failure due to bending and surface wear. The shafts are designed with respect to fatigue failure due to bending and torsion. The design of bearings (cylindrical roller bearings), keys, and splines are based on the maximum allowable stress in the components. The failure of the system is assumed to correspond to zero output power from the transmission system based on a series-parallel model. The reliability-based design is conducted for a specified value of the reliability of the system. The structural and kinematic designs of the transmission system (i.e. the gear train) are assumed to be known. The design parameters such as power transmitted, gear face widths, dimensions of roller bearing, length of splines, length of keys, and material properties are considered as random variables. The reliability-based design results are compared with those obtained by a deterministic design procedure. The effects of variation of design parameters, such as the reliability of the system and coefficient of variation of the input speed are also studied. In addition, a comparison of the designs obtained with different distributions of the random variables is also made and conclusions drawn.     

小角度空间交错轴变厚齿轮传动的啮合动态特性研究

为揭示小角度空间交错轴变厚齿轮副的时变啮合特性与非线性动态特性,在精确几何建模的基础上,建立了空间小角度交错轴变厚齿轮传动时变啮合模型,获取其时变啮合刚度与时变传动误差;考虑外部载荷与侧隙变化的影响,采用集中参数法建立了齿轮传动非线性动力学模型,对其系统非线性特征进行了仿真。结果表明外部载荷的增加直接导致了齿轮副啮合刚度、传动误差、动态传动误差和动态啮合力的增加,同时啮合刚度的增加使得系统共振频率增加;侧隙的增加使得系统在轻载下出现与单边、双边冲击耦合的突跳现象,在重载下双边冲击区域变大,动态啮合力增加。     

Analytical model for mesh stiffness calculation of spur gear pair with non-uniformly distributed tooth root crack

Gear tooth crack is likely to happen when a gear transmission train is working under excessive and/or long-term dynamic loads. Its appearance will reduce the effective tooth thickness for load carrying, and thus cause a reduction in mesh stiffness and influence the dynamic responses of the gear transmission system, which enables the possibility for gear fault detection from variations of the dynamic features. Accurate mesh stiffness calculation is required for improving the prediction accuracy of the dynamic features with respect to the tooth crack fault. In this paper, an analytical mesh stiffness calculation model for non-uniformly distributed tooth root crack along tooth width is proposed based on previous studies. It enables a good prediction on the mesh stiffness for a spur gear pair with both incipient and larger tooth cracks. This method is verified by comparisons with other analytical models and finite element model (FEM) in previous papers. Finally, a dynamic model of a gear transmission train is developed to simulate the dynamic responses when cracks with different dimensions are seeded in a gear tooth, which could reveal the effect of the tooth root crack on the dynamic responses of the gear transmission system. The results indicate that both the mesh stiffness and the dynamic response results show that the proposed analytical model is an alternative method for mesh stiffness calculation of cracked spur gear pairs with a good accuracy for both small and large cracks.     

基于刚柔耦合建模的齿轮箱动力学仿真与实验研究

运用LMS Virtual.Lab建立了齿轮传动系统多刚体模型,通过仿真计算获得了齿轮副的时变啮合刚度,并与运用有限元法仿真计算得到的齿轮副时变啮合刚度进行了对比。考虑齿轮箱体柔性化,通过对刚柔耦合模型进行动力学仿真分析,在获取箱体Craig-Bampton模态的基础上,建立了箱体-轴承-齿轮耦合动力学模型。计算获取了齿轮副动态啮合力、齿轮箱体表面振动响应云图以及关键点的振动加速度、速度和位移,并开展了台架试验和验证分析。结果表明,运用刚柔耦合法仿真得到的齿轮啮合力以及齿轮箱体动态响应,其能量主要集中在齿轮啮合频率及其倍频处,运用刚柔耦合法仿真结果与实验结果在振动加速度以及振动位移方面有良好的一致性,验证了齿轮系统刚柔耦合模型的正确性。