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Mathematical model and manufacture programming of loxodromic-type normal circular-arc spiral bevel gear

Zhenyun DUAN, Houjun CHEN, Zhilan JU, Jian LIU

《机械工程前沿（英文）》 2012年第7卷第3期页码 312-321 doi: 10.1007/s11465-012-0308-5

摘要：

In this paper, loxodromic-type normal circular-arc spiral bevel gear is proposed as a novel application of the circular-arc tooth profile at the gear transmission with intersecting axes. Based on the principle of molding-surface conjugation, the study develops a mathematical model for the tooth alignment curve and the computational flow at the design stage to enable the generation of the tooth surface. Machining of the tooth surface is then carried out to determine the interference-free tool path of the numerical control (NC). Moreover, a pair of loxodromic-type normal circular-arc spiral bevel gears is manufactured on computer numerical control (CNC) machine tools. The proposed theory and method are experimentally investigated, and the obtained results primarily reflect the superior performance of the proposed novel gear.

关键词： loxodrome circular-arc tooth profile Wildhaber-Novikov (W-N) gear spiral bevel gear

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泛曲线齿锥齿轮的创新设计与应用的二次开发

梁桂明

《中国工程科学》 2001年第3卷第7期页码 70-78

摘要：

曲线齿锥齿轮和准双曲面齿轮（统称为“泛曲线齿锥齿轮”），是一种十分复杂而应用越来越广泛的传动装置。在设计上为了避免改变轴交角，而采用"零"变位传动（x₁+x₂=0）设计的齿形制，至今已在各国工业上通用近百年。文章介绍一种"非零"变位传动（x₁+x₂≠0）设计而又保持轴交角不变的创新齿形制。为了满足生产提出的要求，进行了二次开发。经过第二次创新，能在普通锥齿轮加工机床和刀具上切齿，故极易推广。近12年来，已成功地在工程机械、军品、立式机床、机车、船艇、油田、采煤、水泥等机械上采用，取得高综合强度、高可靠性、长寿命、小体积、低噪声、广泛适应性等优点，可取代（或覆盖）全部以美国Gleason为代表的零传动齿制设计的产品，还可实现某些Gleason所达不到的技术要求，故有广泛的应用前景。

关键词：曲线齿锥齿轮创新设计二次开发

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弧齿锥齿轮主曲率计算的幺正活动标架法

王裕清,梁剑

《中国工程科学》 2001年第3卷第12期页码 68-70

摘要：

曲面上点的主曲率计算是确定轮齿啮合压痕平面投影形状的关键。文章摈弃通常运用啮合原理和坐标变换计算的思路，从曲面本身的性质出发，把幺正活动标架和外微分引入主曲率计算，得到简明、有效的主曲率计算的新算法，并结合压痕公式给出了一个应用实例。该算法可以推广到任意曲面的主曲率计算。

关键词：弧齿锥齿轮主曲率幺正活动标架

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Contact fatigue life prediction of a bevel gear under spectrum loading

Pan JIA, Huaiju LIU, Caichao ZHU, Wei WU, Guocheng LU

《机械工程前沿（英文）》 2020年第15卷第1期页码 123-132 doi: 10.1007/s11465-019-0556-8

摘要： Rolling contact fatigue (RCF) issues, such as pitting, might occur on bevel gears because load fluctuation induces considerable subsurface stress amplitudes. Such issues can dramatically affect the service life of associated machines. An accurate geometry model of a hypoid gear utilized in the main reducer of a heavy-duty vehicle is developed in this study with the commercial gear design software MASTA. Multiaxial stress–strain states are simulated with the finite element method, and the RCF life is predicted using the Brown–Miller–Morrow fatigue criterion. The patterns of fatigue life on the tooth surface are simulated under various loading levels, and the RCF curve is numerically generated. Moreover, a typical torque–time history on the driven axle is described, followed by the construction of program load spectrum with the rain flow method and the Goodman mean stress equation. The effects of various fatigue damage accumulation rules on fatigue life are compared and discussed in detail. Predicted results reveal that the Miner linear rule provides the most optimistic result among the three selected rules, and the Manson bilinear rule produces the most conservative result.

关键词： bevel gear rolling contact fatigue (RCF) multiaxial fatigue criterion load spectrum damage accumulation rule

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High-precision gyro-stabilized control of a gear-driven platform with a floating gear tension device

《机械工程前沿（英文）》 2021年第16卷第3期页码 487-503 doi: 10.1007/s11465-021-0635-5

摘要： This study presents an improved compound control algorithm that substantially enhances the anti-disturbance performance of a gear-drive gyro-stabilized platform with a floating gear tension device. The tension device can provide a self-adjustable preload to eliminate the gap in the meshing process. However, the weaker gear support stiffness and more complex meshing friction are also induced by the tension device, which deteriorates the control accuracy and the ability to keep the aim point of the optical sensors isolated from the platform motion. The modeling and compensation of the induced complex nonlinearities are technically challenging, especially when base motion exists. The aim of this research is to cope with the unmeasured disturbances as well as the uncertainties caused by the base lateral motion. First, the structural properties of the gear transmission and the friction-generating mechanism are analyzed, which classify the disturbances into two categories: Time-invariant and time-varying parts. Then, a proportional-integral controller is designed to eliminate the steady-state error caused by the time-invariant disturbance. A proportional multiple-integral-based state augmented Kalman filter is proposed to estimate and compensate for the time-varying disturbance that can be approximated as a polynomial function. The effectiveness of the proposed compound algorithm is demonstrated by comparative experiments on a gear-drive pointing system with a floating gear tension device, which shows a maximum 76% improvement in stabilization precision.

关键词： inertially stabilized platform floating gear tension device nonlinear friction disturbance compensation proportional multiple-integral observer

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齿轮测量技术100年——回顾与展望

石照耀,费业泰,谢华锟

《中国工程科学》 2003年第5卷第9期页码 13-17

摘要：

全面概述了过去100年齿轮测量技术的发展历程，给出了6件标志性事情；着重论述了测量原理的演变、实现测量原理技术方式的发展以及测量结果的表述与利用；介绍了当今CNC齿轮测量中心的原理、组成和特点；结合90年代以来齿轮测量技术领域中几股新潮流，展望了未来齿轮测量技术的一些研究方向。

关键词：齿轮齿轮测量齿轮误差齿轮测量仪器

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Processing of high-precision ceramic balls with a spiral V-groove plate

Ming FENG,Yongbo WU,Julong YUAN,Zhao PING

《机械工程前沿（英文）》 2017年第12卷第1期页码 132-142 doi: 10.1007/s11465-017-0436-z

摘要：

As the demand for high-performance bearings gradually increases, ceramic balls with excellent properties, such as high accuracy, high reliability, and high chemical durability used, are extensively used for high-performance bearings. In this study, a spiral V-groove plate method is employed in processing high-precision ceramic balls. After the kinematic analysis of the ball-spin angle and enveloped lapping trajectories, an experimental rig is constructed and experiments are conducted to confirm the feasibility of this method. Kinematic analysis results indicate that the method not only allows for the control of the ball-spin angle but also uniformly distributes the enveloped lapping trajectories over the entire ball surface. Experimental results demonstrate that the novel spiral V-groove plate method performs better than the conventional concentric V-groove plate method in terms of roundness, surface roughness, diameter difference, and diameter decrease rate. Ceramic balls with a G3-level accuracy are achieved, and their typical roundness, minimum surface roughness, and diameter difference are 0.05, 0.0045, and 0.105 mm, respectively. These findings confirm that the proposed method can be applied to high-accuracy and high-consistency ceramic ball processing.

关键词： bearing ceramic ball spiral V-groove kinematic analysis trajectory

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Gear fault diagnosis using gear meshing stiffness identified by gearbox housing vibration signals

《机械工程前沿（英文）》 2022年第17卷第4期 doi: 10.1007/s11465-022-0713-3

摘要： Gearbox fault diagnosis based on vibration sensing has drawn much attention for a long time. For highly integrated complicated mechanical systems, the intercoupling of structure transfer paths results in a great reduction or even change of signal characteristics during the process of original vibration transmission. Therefore, using gearbox housing vibration signal to identify gear meshing excitation signal is of great significance to eliminate the influence of structure transfer paths, but accompanied by huge scientific challenges. This paper establishes an analytical mathematical description of the whole transfer process from gear meshing excitation to housing vibration. The gear meshing stiffness (GMS) identification approach is proposed by using housing vibration signals for two stages of inversion based on the mathematical description. Specifically, the linear system equations of transfer path analysis are first inverted to identify the bearing dynamic forces. Then the dynamic differential equations are inverted to identify the GMS. Numerical simulation and experimental results demonstrate the proposed method can realize gear fault diagnosis better than the original housing vibration signal and has the potential to be generalized to other speeds and loads. Some interesting properties are discovered in the identified GMS spectra, and the results also validate the rationality of using meshing stiffness to describe the actual gear meshing process. The identified GMS has a clear physical meaning and is thus very useful for fault diagnosis of the complicated equipment.

关键词： gearbox fault diagnosis meshing stiffness identification transfer path signal processing

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Russian school of the theory and geometry of gearing: Its origin and golden period (1935 --1975)

Dmitry BABICHEV,Sergey LAGUTIN,Natalya BARMINA

《机械工程前沿（英文）》 2016年第11卷第1期页码 44-59 doi: 10.1007/s11465-015-0360-z

摘要：

During the second half of the twentieth century, Soviet scientists were among the world leaders in the theory and geometry of gearing or the theoretical fundamentals of designing gears and gear-cutting tools. The authors of the current paper review works related to the development of the theory of gearing (TG) written in Russian from the mid-1930s to the present. Overall, the review covers more than 400 publications of nearly 200 authors (among more than 1000 studied works). This review involves some works on gear strength and accuracy to attract more experts.

This paper presents a short list of works from the seventeenth century to the nineteenth century and discusses the basic concepts of the TG. This paper also includes a review of more than 160 papers in Russian for the period of 1935–1975, which is the “golden age” of the TG. The main features and achievements during this period are also considered.

The distinctive feature of this review is the use of diagrams that visually present TG experts and the dates and themes of their published works. The diagrams also show the following aspects: 1) The most popular and important themes in a specific period, 2) the most important publications on the themes of interest to readers, and 3) the direction of the works and scope of interests of every researcher.

关键词： theory of gearing (TG) gear geometry generating surface gear synthesis gear analysis

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Fault feature extraction of planet gear in wind turbine gearbox based on spectral kurtosis and time wavelet

Yun KONG, Tianyang WANG, Zheng LI, Fulei CHU

《机械工程前沿（英文）》 2017年第12卷第3期页码 406-419 doi: 10.1007/s11465-017-0419-0

摘要：

Planetary transmission plays a vital role in wind turbine drivetrains, and its fault diagnosis has been an important and challenging issue. Owing to the complicated and coupled vibration source, time-variant vibration transfer path, and heavy background noise masking effect, the vibration signal of planet gear in wind turbine gearboxes exhibits several unique characteristics: Complex frequency components, low signal-to-noise ratio, and weak fault feature. In this sense, the periodic impulsive components induced by a localized defect are hard to extract, and the fault detection of planet gear in wind turbines remains to be a challenging research work. Aiming to extract the fault feature of planet gear effectively, we propose a novel feature extraction method based on spectral kurtosis and time wavelet energy spectrum (SK-TWES) in the paper. Firstly, the spectral kurtosis (SK) and kurtogram of raw vibration signals are computed and exploited to select the optimal filtering parameter for the subsequent band-pass filtering. Then, the band-pass filtering is applied to extrude periodic transient impulses using the optimal frequency band in which the corresponding SK value is maximal. Finally, the time wavelet energy spectrum analysis is performed on the filtered signal, selecting Morlet wavelet as the mother wavelet which possesses a high similarity to the impulsive components. The experimental signals collected from the wind turbine gearbox test rig demonstrate that the proposed method is effective at the feature extraction and fault diagnosis for the planet gear with a localized defect.

关键词： wind turbine planet gear fault feature extraction spectral kurtosis time wavelet energy spectrum

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三峡工程水电站压力管道和蜗壳技术结构型式的选择及论证

戴会超,彭澎

《中国工程科学》 2004年第6卷第2期页码 33-37

摘要：

长江三峡水利枢纽工程建设中重大技术问题的决策是建立在大量科学试验和专家论证的基础上，三峡工程水电站压力管道和蜗壳技术结构型式的选择不仅是重大的技术经济问题，也是关系水电站长期运行问题，文章介绍了三峡工程水电站压力管道和蜗壳技术型式选择及决策。

关键词：三峡工程压力管道蜗壳

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螺旋结构冷却塔的塔板设计方法

黄锐

《中国工程科学》 2008年第10卷第11期页码 43-46

摘要：

针对冷却塔中螺旋结构类型的气液交换塔，提出其内部螺旋塔板形状的设计方法，包括塔壁上外螺旋线和塔中心轴管上内螺旋线的位置确定，以及两线之间螺旋曲面板在平面上的拓扑尺寸。通过塔的几何参数确定螺旋曲面板设计的关键参数，可实现扭曲状塔板与塔壁及内轴的准确配合。

关键词：冷却塔塔板设计螺旋曲面拓扑

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Experimental investigation of fatigue behavior of spur gear in altered tooth-sum gearing

H. K. SACHIDANANDA, Joseph GONSALVIS, H. R. PRAKASH

《机械工程前沿（英文）》 2012年第7卷第3期页码 268-278 doi: 10.1007/s11465-012-0331-6

摘要：

This paper deals with the contact stress, power loss, and pitting of spur gear tooth in altered tooth-sum gearing for a tooth-sum of 100 teeth when altered by±4% tooth-sum. Analytical and experimental methods were performed to investigate and compare the altered tooth-sum gearing against the standard tooth-sum gearing. The experiments were performed using a power recirculating type test rig. The tooth loads for the experimental investigations were determined considering the surface durability of gears. A clear picture of the surface damage was obtained using a scanning electron microphotograph. The negative alteration in the tooth-sum performed better than the positive alteration in a tooth-sum operating between specified center distances.

关键词： spur gear power recirculating test rig altered tooth-sum gearing scanning electron microscopy (SEM)

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Mesh relationship modeling and dynamic characteristic analysis of external spur gears with gear wear

《机械工程前沿（英文）》 2022年第17卷第1期页码 9-9 doi: 10.1007/s11465-021-0665-z

摘要： Gear wear is one of the most common gear failures, which changes the mesh relationship of normal gear. A new mesh relationship caused by gear wear affects meshing excitations, such as mesh stiffness and transmission error, and further increases vibration and noise level. This paper aims to establish the model of mesh relationship and reveal the vibration characteristics of external spur gears with gear wear. A geometric model for a new mesh relationship with gear wear is proposed, which is utilized to evaluate the influence of gear wear on mesh stiffness and unloaded static transmission error (USTE). Based on the mesh stiffness and USTE considering gear wear, a gear dynamic model is established, and the vibration characteristics of gear wear are numerically studied. Comparison with the experimental results verifies the proposed dynamic model based on the new mesh relationship. The numerical and experimental results indicate that gear wear does not change the structure of the spectrum, but it alters the amplitude of the meshing frequencies and their sidebands. Several condition indicators, such as root-mean-square, kurtosis, and first-order meshing frequency amplitude, can be regarded as important bases for judging gear wear state.

关键词： gear wear mesh relationship mesh stiffness transmission error vibration characteristics

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Design optimization of a wind turbine gear transmission based on fatigue reliability sensitivity

Genshen LIU, Huaiju LIU, Caichao ZHU, Tianyu MAO, Gang HU

《机械工程前沿（英文）》 2021年第16卷第1期页码 61-79 doi: 10.1007/s11465-020-0611-5

摘要： Fatigue failure of gear transmission is one of the key factors that restrict the performance and service life of wind turbines. One of the major concerns in gear transmission under random loading conditions is the disregard of dynamic fatigue reliability in conventional design methods. Various issues, such as overweight structure or insufficient fatigue reliability, require continuous improvements in the reliability-based design optimization (RBDO) methodology. In this work, a novel gear transmission optimization model based on dynamic fatigue reliability sensitivity is developed to predict the optimal structural parameters of a wind turbine gear transmission. In the model, the dynamic fatigue reliability of the gear transmission is evaluated based on stress–strength interference theory. Design variables are determined based on the reliability sensitivity and correlation coefficient of the initial design parameters. The optimal structural parameters with the minimum volume are identified using the genetic algorithm in consideration of the dynamic fatigue reliability constraints. Comparison of the initial and optimized structures shows that the volume decreases by 3.58% while ensuring fatigue reliability. This work provides new insights into the RBDO of transmission systems from the perspective of reliability sensitivity.

关键词： gear transmission fatigue reliability reliabi-lity sensitivity parameter optimization