Life Distribution Transformation Model of Planetary Gear System

Planetary gear systems have been widely used in transportation, construction, metallurgy, petroleum, aviation and other industrial fields. Under the same condition of power transmission, they have a more compact structure than ordinary gear train. However, some critical parts, such as sun gear, planet gear and ring gear often suffer from fatigue and wear under the conditions of high speed and heavy load. For reliability research, in order to predict the fatigue probability life of planetary gear system, detailed kinematic and mechanical analysis for a planetary gear system is firstly completed. Meanwhile, a gear bending fatigue test is carried out at a stress level to obtain the strength information of specific gears. Then, a life distribution transformation model is established according to the order statistics theory. Transformation process is that, the life distribution of test gear is transformed to that of single tooth, and then the life distribution of single tooth can be effectively transformed to that of the planetary gear system. In addition, the effectiveness of the transformation model is finally verified by a processing method with random censoring data.

PERIODIC WINDOWS OF NONLINEAR GEAR SYSTEM BASED ON SYMBOLIC DYNAMICS

The periodic window is researched by means of the symbolic dynamics and formal language. Firstly, the proper sampling period is taken and the orbital points of periodic motion are obtained through Poincar6 mapping. Secondly, according to the method of symbolic dynamics of one-dimensional discrete mapping, the symbolic sequence describing the periodic orbit is obtained. Finally, based on the symbolic sequence, the corresponding model of minimal finite automation is constructed and the entropy is obtained by calculating the maximal eigenvalue of Stefan matrix. The results show that the orbits in periodic windows can be strictly marked by using the method of symbolic dynamics, thus a foundation for control of switching between target orbits is provided.

Bifurcation of multi-freedom gear system with spalling defect

This study focuses on the bifurcation characteristics of the four degree-of- freedom gear system with local spalling defect to explore the spalling nonlinear dynamic mechanism. The dynamic model of the gear system with spalling defect, time-variant mesh stiffness, and nonlinear clearance is established to investigate the effect of spaUing defect on mesh stiffness and dynamic bifurcation. The primary resonance and internal resonance responses of the spalling model are analyzed by the averaging method, and the bifurcation characteristics with the evolvement of spall and internal excitation are studied by employing the singularity theory for the two-state variable system, which reveal the different bifurcation characteristics caused by the spalling defect. The results obtained herein can provide a theoretical basis to spalling fault diagnosis of gearbox.

Chaos control of gear system with elastomeric web based on multi-parameter multi-step method

This paper employs a multi-parameter multi-step chaos control method, which is built up on the OGY method, to stabilize desirable UPOs of a gear system with elastomeric web as a high-dimensional and non-hyperbolic chaotic system, and the analyses are carried out. Three types of relations between components of a certain control parameter combination are defined in a certain control process. Special emphasis is put on the comparison of control efficiencies of the multi-parameter multi-step method and single-parameter multi-step method. The numerical experiments show the ability to switch between different orbits and the method can be a good chaos control alternative since it provides a more effective UPOs stabilization of high-dimensional and non-hyperbolic chaotic systems than the single-parameter chaos control, and according to the relation between components of each parameter combination, the best combination for chaos control in a certain UPO stabilization process are obtained.

A Contact Force Model Considering Meshing and Collision States for Dynamic Analysisin Helical Gear System

The current research on gear system dynamics mainly utilizes linear spring damping model to calculate the contact force between gears. However, this linear model cannot correctly describe the energy transfer process of collision that often occurs in gear system. Focus on the contact-impact events, this paper proposes an improved gear contact force model for dynamic analysis in helical gear transmission system. In this model, a new factor associated with hysteresis damping is developed for contact-impact state, whereas the traditional linear damping factor is utilized for normal meshing state. For determining the selection strategy of these two damping factors, the fundamental contact mechanics of contact-impact event affected by supporting forces are analyzed. During this analysis, an effect factor is proposed for evaluating the influence of supporting forces on collision. Meanwhile, a new restitution of coefficient is deduced for calculating hysteresis damping factor, which suitable for both separation and non-separation states at the end of collision. In addition, the time-varying meshing stiffness (TVMS) is obtained based on the potential energy approach and the slice theory. Finally, a dynamic analysis of a helical gear system is carried out to better understand the contact force model proposed in this paper. The analysis results show that the contribution of supporting forces to the dynamic response of contact-impact event within gear pair is important. The supporting forces and dissipative energy are the main reasons for gear system to enter a steady contact state from repeated contact-impact state. This research proposes an improved contact force model which distinguishes meshing and collision states in gear system.

INVESTIGATION OF RATTLING THRESHOLD IN GEAR SYSTEM

A lumped mass gear-rattling model with backlash is established by considering the time varying mesh stiffness, composite transmission error and the torque fluctuation. Based on the principle that no separation will occur if the response amplitude is not larger than the static response, the threshold is obtained by theoretical derivation. The validity of the theoretical derivation is verified by the numerical method. The results show that the time-varying mesh stiffness has little effect on the threshold. When the exciting frequency is less than the system natural frequency, the theoretical agrees well with the numerical one. The higher the exciting frequency or the smaller the average input torque is, the easier the separation will occur. When the exciting frequency is larger than the natural frequency by a certain value, the theoretical threshold does not agree with the numerical results. The numerical results show that the motion state will change from the meshing state to the separating state directly. The phenomenon that the gear pair sometimes separates and sometimes meshes occurs only when the exciting frequency is smaller.

Analysis of Helical Gear System Dynamic Response Based on Fuzzy Numbers

A non-linear dynamic model with the single degree of freedom of a helical gear pair introducing frzzy numbers is developed. In this proposed model, time-variant mesh stiffness, which is a non-linear parameter, mesh damping and composite error of a pair of meshing tooth of the gear pair are all included. Mesh stiffness is calculated by expressing Bo (r) as a Fourier series. Ⅱshape function is introduced as the membership function to characterize the fuzziness of the error. Fuzzy displacement dynamic response of the geared system at A- level, which is a closed interval, is ohtained by removing the fuzziness of the fuzzy differential equations and using Runge-Kutta numerical method. In fact, the fuzzy dynamic response and dynamic loading factor are aH the interval functions related λ. The result obtained here can be used to the fuzzy dynamic optimization design course of the helical gear system. The main advantage of this method is to introduce the concept of fuzzy number for the first time to the analysis of the gear system dynamics.

A review on design and testing methodologies of modern freight train draft gear system

Rolling stock connection systems are key to running longer and heavier trains as they provide both the connections of vehicles and the damping,providing the longitudinal suspension of the train.This paper focuses on the evolution of both connection and stiffness damping systems.Focus is on freight rolling stock,but passenger draw gears are also examined.It was found that connection systems have evolved from the buff and chain system used in the pioneer railways of the 1800s to the modern auto-coupler connection systems that are in-service worldwide today.Refined versions of the buff and chain coupling are,however,still in use in the EU,UK,South America and India.A wide range of auto-coupler systems are currently utilised,but the AAR coupler(Janney coupler)remains the most popular.A further variation that persists is the SA3 coupler(improved Wilson coupler)which is an alternative auto-coupler design used mainly throughout the former Soviet Union.Restricting the review to auto-coupler systems allowed the paper to focus on draft gears which revealed polymer,polymer-friction,steel spring-friction,hydraulic draft gears and sliding sill cushioning systems.Along with the single compressive draft gear units balanced and floating plate configurations are also presented.Typical draft gear acceptance standards are presented along with modelling that was included to aid in presentation of the functional characteristics of draft gears.

The effect of the planet's number on dynamic characteristics of planetary gear systems

Considering the effect of planet's number on the dynamic characteristics of the planetary gear system, a translationtorsion lumped-parameter model of 2K-H spur planetary gear system was established. Through the analysis of numerical solution, the results show that 1) When the planet's number is more than 3, the order of the natural frequency will become the same; 2) When the planet's number increases, the natural frequencies of planet mode remain invariant, but when it comes to rotational mode and translational mode, the higher order natural frequencies increase and the lower order natural frequencies decrease; 3) The planet's number has a great impact on the higher order natural frequencies and a little impact on the lower order natural frequencies; and 4) To avoid the resonance, we can appropriately increase or decrease the number of the planet.

Forced oscillations with time-varying mesh stiffness and backlash in gear systems

A dynamic model to describe the torsional vibration behaviors of a spur gear system is presented in this paper.Differential equations of nonlinear dynamics for the gear system exhibiting combined nonlinearity influence such as time-varying mesh stiffness,backlash and dynamic transmission error(DTE) were obtained.The method of multiple scales was employed to solve the nonlinear differential equations with parametric excitation in gear systems,by which both the frequency-response curves of the primary resonance caused by internal excitation and the analytical periodic solutions of nonlinear differential equations were obtained.The nonlinear influence of stiffness variation,the damping and the internal excitation on the system response was shown by frequency-response curves.Compared with numerical examples,the approximate analytical solutions are in good agreement with exact solutions,which proves that the method of multiple scales is effective for solving nonlinear problems in gear systems.

Effect of Supported Bearing Clearance on Load-Sharing Characteristics of a Double-Row Planetary Gear System

Few studies were focused on the load-sharing characteristics of double-row planetary gear(DRPG)systems with bearings.Meanwhile,the supported bearing has an important influence on the transmission characteristics of the entire system.To overcome this problem,a multi-body dynamic(MBD)model of the DRPG system fully considering the influences of bearing parameters is established.Dynamic loads among contacting gear pairs have been obtained to calculate the load-sharing coefficient(LSC)of the system.The LSC of each gear tooth pair has been compared to study the effect of the supported bearing clearance on the load-sharing characteristics.These methods are based on Hertz contact theory.The liner stiffness and damping are used in the model.The results show that the supported bearing clearance has a greatly effect on the LSC of the DRPG system.Choosing appropriate clearance parameters of supported bearing can help suppress the uneven load distribution of the DRPG system.The results can provide some guidance to find new method to study the LSC and increase the service life of planetary gear systems.

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.

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.

Design and Analysis of Power and Transmission System of Downhole Pure Electric Command Vehicle

Electric vehicles use electric motors, which turn electrical energy into mechanical energy. As electric motors are conventionally used in all the industry, it is an established development site. It’s a mature technology with ideal power and torque curves for vehicular operation. Conventional vehicles use oil and gas as fuel or energy storage. Although they also have an excellent economic impact, the continuous use of oil and gas threatened the world’s reservation of total oil and gas. Also, they emit carbon dioxide and some toxic ingredients through the vehicle’s tailpipe, which causes the greenhouse effect and seriously impacts the environment. So, as an alternative, electric car refers to a green technology of decarbonization with zero emission of greenhouse gases through the tailpipe. So, they can remove the problem of greenhouse gas emissions and solve the world’s remaining non-renewable energy storage problem. Pure electric vehicles (PEV) can be applied in all spheres, but their special implementation can only be seen in downhole operations. They are used for low noise and less pollution in the downhole process. In this study, the basic structure of the pure electric command vehicle is studied, the main components of the command vehicle power system, namely the selection of the drive motor and the power battery, are analyzed, and the main parameters of the drive motor and the power battery are designed and calculated. The checking calculation results show that the power and transmission system developed in this paper meets the design requirements, and the design scheme is feasible and reasonable.

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 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.

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.

Dynamical load sharing behaviors of heavy load planetary gear system with multi-floating components

To investigate the dynamical load sharing behaviors of multi-floating components in the heavy load planetary gear system,a multi-floating planetary gear system that includes a floating central component and a quasi-floating planet flexible supporting pin is employed.Then a 21 degree of freedom lumped parameters dynamical model of this system is presented to study the dynamical load sharing behaviors.Some influencing factors,such as supporting stiffness,positions error of sun or carrier,and external input load are analyzed on the dynamical load sharing of the planetary gear system with multi-floating components.The results demonstrate that the load sharing condition of the system is best when both the sun gear and planet gears are multi-floating at the same time.When the planet gear position errors remain constant,reducing the flexible pin stiffness of planet gear or increasing external input load can effectively improve the load sharing.These conclusions are verified by the relevant experiments.

Design System of the Two-step Gear Reducer on Case-based Reasoning

The design of the two-step gear reducer is a tedious and time-consuming process. For the purpose of improving the efficiency and intelligence of design process, case-based reasoning（CBR） technology was applied to the design of the two-step gear reducer. Firstly, the current design method for the two-step gear reducer was analyzed and the principle of CBR was described. Secondly, according to the characteristics of the reducer, three key technologies of CBR were studied and the corresponding methods were provided, which are as follows： （a） an object-oriented knowledge representation method, （b） a retrieval method combining the nearest neighbor with the induction indexing, and （c） a case adaptation algorithm combining the revision based on rule with artificial revision. Also, for the purpose of improving the credibility of case retrieval, a new method for determining the weights of characteristics and a similarity formula were presented, which is a combinatorial weighting method with the analytic hierarchy process（AHP） and roughness set theory. Lastly, according to the above analytic results, a design system of the two-step gear reducer on CBR was developed by VC＋＋, UG and Access 2003. A new method for the design of the two-step gear reducer is provided in this study. If the foregoing developed system is applied to design the two-step gear reducer, design efficiency is improved, which enables the designer to release from the tedious design process of the gear reducer so as to put more efforts on innovative design. The study result fully reflects the feasibility and validity of CBR technology in the process of the design of the mechanical parts.