Application of Isogeometric Analysis Method in Three-Dimensional Gear Contact Analysis

Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a threedimensional body parametric gear model of IGA is established,and a theoretical formula is derived to realize single-tooth contact analysis.Results were benchmarked against those obtained from commercial software utilizing the finite element analysis(FEA)method to validate the accuracy of our approach.Our findings indicate that the IGA-based contact algorithmsuccessfullymet theHertz contact test.When juxtaposed with the FEA approach,the IGAmethod demonstrated fewer node degrees of freedomand reduced computational units,all whilemaintaining comparable accuracy.Notably,the IGA method appeared to exhibit consistency in analysis accuracy irrespective of computational unit density,and also significantlymitigated non-physical oscillations in contact stress across the tooth width.This underscores the prowess of IGA in contact analysis.In conclusion,IGA emerges as a potent tool for addressing contact analysis challenges and holds significant promise for 3D gear modeling,simulation,and optimization of various mechanical components.

Research on Cavitation Characteristics and Influencing Factors of Herringbone Gear Pump

Cavitation is a common issue in pumps,causing a decrease in pump head,a fall in volumetric efficiency,and an intensification of outlet flow pulsation.It is one of the main hazards that affect the regular operation of the pump.Research on pump cavitation mainly focuses on mixed flow pumps,jet pumps,external spur gear pumps,etc.However,there are few cavitation studies on external herringbone gear pumps.In addition,pumps with different working principles significantly differ in the flow and complexity of the internal flow field.Therefore,it is urgent to study the cavitation characteristics of external herringbone gear pumps.Compared with experimentalmethods,visual research and cavitation area identification are achieved through computation fluid dynamic(CFD),and changing the boundary conditions and shape of the gear rotor is easier.The simulation yields a head error of only 0.003%under different grid numbers,and the deviation between experimental and simulation results is less than 5%.The study revealed that cavitation causes flow pulsation at the outlet,and the cavitation serious area is mainly distributed in the meshing gap and meshing area.Cavitation can be inhibited by reducing the speed,increasing the inlet pressure,and changing the helix angle can be achieved.For example,when the inlet pressure is 5 bar,the maximumgas volume fraction in themeshing area is less than 50%.These results provide a reference for optimizing the design and finding the optimal design parameters to reduce or eliminate cavitation.

Contact Stress Reliability Analysis Model for Cylindrical Gear with Circular Arc Tooth Trace Based on an Improved Metamodel

Although there is currently no unified standard theoretical formula for calculating the contact stress of cylindrical gears with a circular arc tooth trace(referred to as CATT gear),a mathematical model for determining the contact stress of CATT gear is essential for studying how parameters affect its contact stress and building the contact stress limit state equation for contact stress reliability analysis.In this study,a mathematical relationship between design parameters and contact stress is formulated using the KrigingMetamodel.To enhance the model’s accuracy,we propose a new hybrid algorithm that merges the genetic algorithm with the Quantum Particle Swarm optimization algorithm,leveraging the strengths of each.Additionally,the“parental inheritance+self-learning”optimization model is used to fine-tune the KrigingMetamodel’s parameters.Following this,amathematicalmodel for calculating the contact stress of Variable Hyperbolic Circular-Arc-Tooth-Trace(VH-CATT)gears using the optimized Kriging model was developed.We then examined how different gear parameters affect the VH-CATT gears’contact stress.Our simulation results show:(1)Improvements in R2,RMSE,and RMAE.R2 rose from0.9852 to 0.9974(a 1.22%increase),nearing 1,suggesting the optimized Kriging Metamodel’s global error is minimized.Meanwhile,RMSE dropped from3.9210 to 1.6492,a decline of 57.94%.The global error of the GA-IQPSO-Kriging algorithm was also reduced,with RMAE decreasing by 58.69%from 0.1823 to 0.0753,showing the algorithm’s enhanced precision.In a comparison of ten experimental groups selected randomly,the GA-IQPSO-Kriging and FEM-based contact analysis methods were used to measure contact stress.Results revealed a maximum error of 12.11667 MPA,which represents 2.85%of the real value.(2)Several factors,including the pressure angle,tooth width,modulus,and tooth line radius,are inversely related to contact stress.The descending order of their impact on the contact stress is:tooth line radius>modulus>pressure angle>tooth width.(3)Complex interactions are noted among various parameters.Specifically,when the tooth line radius interacts with parameters such as pressure angle,tooth width,and modulus,the resulting stress contour is nonlinear,showcasing amultifaceted contour plane.However,when tooth width,modulus,and pressure angle interact,the stress contour is nearly linear,and the contour plane is simpler,indicating a weaker coupling among these factors.

Stability Analysis of Nonlinear Models of Nose Landing Gear Shimmy

Shimmy can reduce the service life of the nose landing gear, affect ride comfort, and even cause fuselage damage leading to aircraft crashes. Taking a light aircraft as the research object, the torsional freedom of landing gear around strut axis and lateral deformation of tire are considered. Since the landing gear shimmy is a nonlinear system, a nonlinear mechanical model of the front landing gear shimmy is established. Sobol index method is proposed to analyze the influence of structural parameters on the stability region of the nose landing gear, and Routh-Huritz criterion is used to verify the reliability of the analysis results of Sobol index method. We analyse the effect of torsional stiffness of strut, caster length, rated initial tire inflation pressure, rake angle, and vertical force on the stability region of theront landing gear. And the research shows that the optimization of the torsional stiffness of the strut and the caster length of the nose landing gear should be emphasized, and the influence of vertical force on the stability region of the nose landing gear should be paid attention to.

Research on Instantaneous Angular Speed Signal Separation Method for Planetary Gear Fault Diagnosis

Planetary gear train is a critical transmission component in large equipment such as helicopters and wind turbines. Conducting damage perception of planetary gear trains is of great significance for the safe operation of equipment. Existing methods for damage perception of planetary gear trains mainly rely on linear vibration analysis. However, these methods based on linear vibration signal analysis face challenges such as rich vibration sources, complex signal coupling and modulation mechanisms, significant influence of transmission paths, and difficulties in separating damage information. This paper proposes a method for separating instantaneous angular speed (IAS) signals for planetary gear fault diagnosis. Firstly, this method obtains encoder pulse signals through a built-in encoder. Based on this, it calculates the IAS signals using the Hilbert transform, and obtains the time-domain synchronous average signal of the IAS of the planetary gear through time-domain synchronous averaging technology, thus realizing the fault diagnosis of the planetary gear train. Experimental results validate the effectiveness of the calculated IAS signals, demonstrating that the time-domain synchronous averaging technology can highlight impact characteristics, effectively separate and extract fault impacts, greatly reduce the testing cost of experiments, and provide an effective tool for the fault diagnosis of planetary gear trains.

Research on Three-Dimensional Simulation of the Internal Arc Gear Skiving

Aiming at the problems that the simulation accuracy which is reduced due to the simplification of the model,a three-dimensional simulation method based on solid modeling is being proposed.By analyzing the motion relationship and positional relationship between the caries knife and the workpiece,the coordinate system of the caries machining was established.With the MATLAB software,the cutting edge model and the blade sweeping surface model of the boring cutter are sequentially established.Boolean operation is performed on the blade swept surface formed by the tooth cutter teeth with time t and the workpiece tooth geometry as well as the undeformed three-dimensional chip geometry model and the instantaneous cogging geometry model are obtained at different times.Through the compare between gear end face simulation tooth profile and the theoretical inner arc tooth profile,we verified the accuracy and rationality of the proposed method.

基于Gym与Flight Gear的AI模拟飞行训练平台搭建

针对AI模拟飞行研究,提出应用平台Gym与Flightgear模拟飞行软件相结合,构建AI模拟飞行训练平台。通过平台优化,可不断增加飞行动作的难度系数,重新设计奖励机制与神经网络,实现由AI操控模拟飞行软件向AI反馈训练数据的交互闭环。训练结果验证了该训练平台的有效性。

Measured load spectra of the bearing in high-speed train gearbox under different gear meshing conditions

The load spectrum is a crucial factor for assess-ing the fatigue reliability of in-service rolling element bear-ings in transmission systems.For a bearing in a high-speed train gearbox,a measurement technique based on strain detection of bearing outer ring was used to instrument the bearing and determine the time histories of the distributed load in the bearing under different gear meshing conditions.Accordingly,the load spectrum of the total radial load car-ried by the bearing was compiled.The mean value and class interval of the obtained load spectrum were found to vary non-monotonously with the speed and torque of gear mesh-ing,which was considered to be caused by the vibration of the shaft and the bearing cage.As the realistic service load input of bearing life assessment,the measured load spectrum under different gear meshing conditions can be used to pre-dict gearbox bearing life realistically based on the damage-equivalent principle and actual operating conditions.

Model of Surface Texture for Honed Gear Considering Motion Path and Geometrical Shape of Abrasive Particle

Gear power-honing is mainly applied to finish small and medium-sized automotive gears,especially in new energy vehicles.The distinctive curved surface texture greatly improves the noise emission and service life of honed gears.The surface texture for honed gear considering the motion path and geometrical shape of abrasive particles has not been investigated.In this paper,the kinematics of the gear honing process is analyzed,and the machining marks produced by the abrasive particles of honing wheel scratching abrasive particles against the workpiece gear are calculated.The tooth surface roughness is modeled considering abrasive particle shapes and material plastic pile-ups.This results in a mathematical model that characterizes the structure of the tooth surface and the orientation of the machining marks.Experiments were used to verify the model,with a maximum relative error of less than 10%when abrasive particles are spherical.Based on this model,the effects of process parameters on the speeds of discrete points on the tooth flank,orientations of machining marks and roughness are discussed.The results show that the shaft angle between the workpiece gear and the honing wheel and the speed of the honing wheel is the main process parameters affecting the surface texture.This research proposes a surface texture model for honed gear,which can provide a theoretical basis for optimizing process parameters for gear power-honing.

Cutting Force Fluctuation Suppression and Error Homogenization of Noncircular Gear Hobbing Based on the Tool Shifting Method

The current research on noncircular hobbing mainly focuses on the linkage model and motion realization.However,the intermittent cutting characteristics of hobbing would increase uncertainties in the manufacturing process.In this paper,a hobbing machining model with tool-shifting characteristics was proposed to solve the problems of cutting force fluctuation and inconsistency of tooth profile envelope accuracy at different positions of the pitch curve in noncircular gear hobbing.Based on the unit cutting force coefficient method,the undeformed chip volume generated by interrupted cutting was used to characterize the fluctuation trend of the hobbing force.The fluctuation characteristics of the cutting force generated by different hobbing models were compared and analyzed.Using the equivalent gear tooth and hob slotting numbers,an analysis model of the tooth profile envelope error of the noncircular gear was constructed.Subsequently,the tooth profile envelope errors at different positions of the pitch curve were compared and analyzed based on the constructed model.The transmission structure of the electronic gearbox was constructed based on the proposed hobbing model,and the hobbing experiment was conducted based on the selfdeveloped noncircular gear CNC hobbing system.This paper proposes a hobbing method that can effectively suppress the fluctuation of the peak and whole circumference cutting force and reduce the maximum envelope error of the whole circumference gear teeth.

Examining the intrinsic foot muscles'capacity to modulate plantar flexor gearing and ankle joint contributions to propulsion in vertical jumping

Background:During human locomotion,a sufficiently stiff foot allows the ankle plantar flexors to generate large propulsive powers.Increasing foot stiffness(e.g.,via a carbon plate)increases the ankle’s external moment arm in relation to the internal moment arm(i.e.,increasing gear ratio),reduces plantar flexor muscles’shortening velocity,and enhances muscle force production.In contrast,when activation of the foot’s intrinsic muscles is impaired,there is a reduction in foot and ankle work and metatarsophalangeal joint stiffness.We speculated that the reduced capacity to actively control metatarsophalangeal joint stiffness may impair the gearing function of the foot at the ankle.Methods:We used a tibial nerve block to examine the direct effects of the intrinsic foot muscles on ankle joint kinetics,in vivo medial gastrocnemius’musculotendinous dynamics,and ankle gear ratio on 14 participants during maximal vertical jumping.Results:Under the nerve block,the internal ankle plantar flexion moment decreased(p=0.004)alongside a reduction in external moment arm length(p=0.021)and ankle joint gear ratio(p=0.049)when compared to the non-blocked condition.Although medial gastrocnemius muscle-tendon unit and fascicle velocity were not different between conditions,the Achilles tendon was shorter during propulsion in the nerve block condition(p<0.001).Conclusion:In addition to their known role of regulating the energetic function of the foot,our data indicate that the intrinsic foot muscles also act to optimize ankle joint torque production and leverage during the propulsion phase of vertical jumping.

Gear Pitting Measurement by Multi-Scale Splicing Attention U-Net

The judgment of gear failure is based on the pitting area ratio of gear.Traditional gear pitting calculation method mainly rely on manual visual inspection.This method is greatly affected by human factors,and is greatly affected by the working experience,training degree and fatigue degree of the detection personnel,so the detection results may be biased.The non-contact computer vision measurement can carry out non-destructive testing and monitoring under the working condition of the machine,and has high detection accuracy.To improve the measurement accuracy of gear pitting,a novel multi-scale splicing attention U-Net(MSSA U-Net)is explored in this study.An image splicing module is first proposed for concatenating the output feature maps of multiple convolutional layers into a splicing feature map with more semantic information.Then,an attention module is applied to select the key features of the splicing feature map.Given that MSSA U-Net adequately uses multi-scale semantic features,it has better segmentation performance on irregular small objects than U-Net and attention U-Net.On the basis of the designed visual detection platform and MSSA U-Net,a methodology for measuring the area ratio of gear pitting is proposed.With three datasets,experimental results show that MSSA U-Net is superior to existing typical image segmentation methods and can accurately segment different levels of pitting due to its strong segmentation ability.Therefore,the proposed methodology can be effectively applied in measuring the pitting area ratio and determining the level of gear pitting.

Design of Linear Functional Noncircular Gear with High Contact Ratio Used in Continuously Variable Transmission

Continuously variable transmission(CVT)of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency.The key technology of CVT with noncircular gear has been broken through some countries,and is in the stage of deep application research.Although the characteristics and design methods of noncircular gear pairs have been continuously studied in China,the noncircular gear CVT is still in the preliminary exploration and research stage.The linear functional noncircular gear pair,whose transmission ratio is a linear function in the working section,to realize continuously variable transmission was the research object in this paper.According to the required transmission ratio in the working section,the transmission ratio function in the non-working section was constructed by using a polynomial.And then the influence of pitch curve parameters in the working section on which in the non-working section was also analyzed to obtain the pitch curve suitable for transmission of this gear pair.In addition,for improving the stability and bearing capacity of gear transmission,the noncircular gear pair transmission with high contact ratio was designed.Furthermore,the accurate value of the contact tooth length was calculated based on the gear principle and the characteristics of the involute tooth profile,from this the contact tooth length error was calculated by comparing the accurate value with its actual value obtained by the rolling experiment.Finally,an indirect method to verify the contact ratio by detecting the contact length error of the tooth profile was proposed.

Experimental Research on the Surface Quality of Milling Contour Bevel Gears

Contour bevel gears have the advantages of high coincidence,low noise and large bearing capacity,which are widely used in automobile manufacturing,shipbuilding and construction machinery.However,when the surface quality is poor,the effective contact area between the gear mating surfaces decreases,affecting the stability of the fit and thus the transmission accuracy,so it is of great significance to optimize the surface quality of the contour bevel gear.This paper firstly analyzes the formation process of machined surface roughness of contour bevel gears on the basis of generating machining method,and dry milling experiments of contour bevel gears are conducted to analyze the effects of cutting speed and feed rate on the machined surface roughness and surface topography of the workpiece.Then,the surface defects on the machined surface of the workpiece are studied by SEM,and the causes of the surface defects are analyzed by EDS.After that,XRD is used to compare the microscopic grains of the machined surface and the substrate material for diffraction peak analysis,and the effect of cutting parameters on the microhardness of the workpiece machined surface is investigated by work hardening experiment.The research results are of great significance for improving the machining accuracy of contour bevel gears,reducing friction losses and improving transmission efficiency.

Loss Analysis of Magnetic Gear with Slotted in Magnetic Modulation Ring

In order to improve the operation efficiency of coaxial magnetic gear(CMG),in this paper,a CMG model with slotted in magnetic modulation ring is proposed.In this model,the permanent magnets(PMs)of internal and external rotors are distributed in Halbach array,the inner rotor PMs are equally divided into 3 small pieces,and the outer rotor PMs are equally divided into 2 small pieces.At the same time,the static magnetic modulation ring iron blocks are slotted,each iron block has 3 slots,the width of the slot is 0.4°,and the depth of the single side slot is 1mm.Finally,a two-dimensional model is established,and the eddy current loss and iron loss of the model are optimized,compared with the conventional CMG model,it is found that the changed pattern can increase the internal and external output torque by 4%and 4.12%,respectively.The eddy current loss is reduced by 66.57%,and the iron loss is reduced by 8.9%,which significantly improve the operation efficiency of the CMG.

Small Sample Gear Fault Diagnosis Method Based on Transfer Learning

Aiming at the problems of lack of fault diagnosis samples and low model generalization ability of cross-working gear based on deep transfer learning, a fault diagnosis method based on improved deep residual network and transfer learning was proposed. Firstly, one-dimensional signal is transformed into two-dimensional time-frequency image by continuous wavelet transform. Then, a deep learning model based on ResNet50 is constructed. Attention mechanism is introduced into the model to make the model pay more attention to the useful features for the current task. The network parameters trained by ResNet50 network on ImageNet dataset were used to initialize the model and applied to the fault diagnosis field. Finally, to solve the problem of gear fault diagnosis under different working conditions, a small sample training set is proposed for fault diagnosis. The method is applied to gearbox fault diagnosis, and the results show that: The proposed deep model achieves 99.7% accuracy of gear fault diagnosis, which is better than the four models such as VGG19 and MobileNetV2. In the cross-working condition fault diagnosis, only 20% target dataset is used as the training set, and the proposed method achieves 93.5% accuracy.

Multi-objective Optimization of a Two-Stage Helical Gearbox to Improve Efficiency and Reduce Height

The goal of this research is to look at multi-target optimization of a two-stage helical gearbox in order to determine the best key design elements for reducing gearbox height and enhancing gearbox efficiency.To do this,the method known as Taguchi and GRA(Grey Relation Analysis)were used in two stages to address the problem.The single-objective optimization problem was addressed first to close the gap between variable levels,and then the multi-objective optimization problem was solved to determine the best primary design variables.The first and second stage CWFWs(Coefficients of Wheel Face Width),ACS(Permissible Contact Stresses),and first stage gear ratio were also calculated.The study’s findings were utilized to identify the best values for five critical design aspects of a two-stage helical gearbox.

齿轮线激光三维测量仪的研制

快速获取齿轮全部齿面的三维误差信息,是表征复杂齿面质量的关键和前提。本文基于激光三角测量原理,建立了齿轮线激光三维测量模型,研制出齿轮线激光三维测量仪,可用于生产现场快速获取被测齿轮的三维齿面误差信息并进行质量评定。仪器采用立式结构,主要由基座、精密主轴、圆光栅传感器、控制系统、软件系统等部分组成。精密主轴采用密珠轴系实现高精度回转,保证了被测齿轮的高精度定位与回转。在精密主轴周向布置两个高精度线激光传感器,并根据被测齿轮参数调整其位姿状态;圆光栅实时获取精密主轴的回转角度,并触发采集器实时采集并记录被测齿轮左右齿面的几何信息。开发了齿轮线激光三维测量与评价软件,可实现齿轮齿廓偏差、齿距偏差、拓扑偏差等项目的测量与评定,能够满足5级精度齿轮的检测要求。

论齿轮样板

齿轮样板是齿轮参数量值的标准实物载体,用于将齿轮国家测量标准所复现的量值传递到各级齿轮测量仪器上,从而实现齿轮测量的准确性和一致性,保证齿轮产品质量。全面概述了齿轮样板起源及其发展历程;详细论述了齿轮样板的种类、结构及特点、齿轮样板的测量技术及装置、齿轮样板的国际比对、未来的发展与展望。齿轮样板迄今已历经九十多年发展,其种类在不断丰富、尺度不断延伸、复杂度不断简化,作为一种“有形”的实物量具,目前仍不可替代。未来随着“无形”的虚拟仿真测量技术发展,对“有形”实物样板的依赖将可以减弱,“无形”的技术将可能成为量值传递的新模式。

考虑制造误差和油膜作用力的齿轮敲击动力学分析

为准确评估变速器空套齿轮受角加速度激励的敲击表现,采用集中参数法建立了模拟变速器敲击台架试验的10自由度扭转动力学模型;在包含时变啮合刚度、间隙非线性和拖曳力矩的基础上,进一步考虑齿轮制造误差和润滑油膜作用力。敲击台架试验结果表明包含楔入和挤压效应的润滑油膜作用力模型能正确反映变速器的敲击响应;数值分析结果表明润滑油膜可以减少制造误差位移激励和时变啮合刚度参数激励产生的齿面敲击,敲击强度随制造误差幅值的增加呈凹函数变化,当制造误差的幅值增加到某一数值时,齿轮副在无角加速度激励时亦产生敲击现象。润滑油温度对敲击的影响与角加速度激励有关:无角加速度激励时,低温时较低幅值的齿轮低频圆周误差通过改变油膜作用力方向产生敲击;油膜作用力产生的敲击响应频率比齿面接触的敲击响应频率更低;当存在角加速度激励时,敲击强度随温度的升高呈凸函数增加。