Gear Model Research Articles

Study on the Influence of Gear Spoke Hole Numbers on Meshing Noise

Gear meshing stiffness is one of the important causes of noise, and the structure optimization of gears, such as spoke hole structures, has been proven to be an effective method to reduce gear meshing noise. In this paper, the meshing dynamics model of spur gears with spoke structures was established, and the quasi-static dynamics simulation of the meshing process was carried out by ANSYS. The results show that more spoke holes lead to less meshing stiffness and less stiffness fluctuation. The BEM (boundary element method) acoustic simulation of spur gears meshing was accomplished by the LMS Virtual.Lab. It shows that meshing stiffness is the dominate factor for noise and less meshing stiffness will result in louder noise. In summary, having fewer spoke holes causes less noise, and the experiment shows the same trend. This has certain reference significance for gear structure design considering NVH (noise vibration harshness) performance.

OBJECTIVE FUNCTION OF PARAMETRIC OPTIMIZATION OF THE SPEED OF A CLOSED PLANETARY MECHANISM FORMED BY TWO SIMPLE JAMES PLANETARY MECHANISMS

The results of building а mathematical model of estimation the speed of the designed construction of the closed planetary mechanism formed from two simple planetary mechanisms of James are presented. The speed of the designed construction of the mechanism is estimated by the value of the equivalent moment of inertia of the mechanism links reduced to its input shaft. A model is a dimensionless function (analogue the equivalent moment of inertia) of two variables - transmission relations of simple planetary mechanisms, and set of numerical parameters. The parameters take into account the values of the coefficients that characterize the mass inertia models of gears and planet carriers, the design and strength limitations of external gears of simple planetary mechanisms of James, as well as the structure of these mechanisms. Set of values of parameters and range of varying of possible values of transmission relations of simple planetary mechanisms influence on position of a minimum of the analogue the equivalent moment of inertia. The influence of the number of planetary gears of simple planetary mechanisms and the moment of inertia of the planet carrier of the differential mechanism on the positions of the minima of the analogues of the reduced moment of inertia of a closed planetary gear was analyzed in calculations for contact strength and bending strength. Based on the function of the analogue of the equivalent moment of inertia, the objective function of parametric optimization of the project fast-acting of the design of a closed planetary mechanism is built. Keywords: simple James planetary mechanism (mechanisms type ); closed planetary mechanism; moment of inertia of gear-wheel; moment of inertia of the planet carrier; moment of inertia of the planetary mechanism; contact strength of the gearing; bending strength of the gearing; parametric optimization; parametric optimization of the equivalent moment of inertia of the planetary mechanism

Effect of Machined Tooth Surface Mixed Lubrication Sliding Wear on Gear Dynamic Characteristics

Tooth surface wear causes variation in meshing stiffness and transmission error of the gear system and further causes the fluctuation of dynamic characteristics. In this study, a dynamic behavior prediction model of the gear transmission system was established, which considered the machined tooth surface wear based on the mixed lubrication sliding wear model and the gear tribology-dynamic model. The gear pair wear characteristics along the meshing line were analyzed through simulations, and the impacts of wear conditions, operating torque, and speed on the dynamic characteristics of the gear transmission system with tooth surface wear were discussed. The results demonstrated that the transmission error and the vibration displacement amplitude of the gear system had increased gradually with the increase of the wear degree and that the fluctuation intensified. The fluctuation of gear dynamic characteristics increased with the increase in torque, and the fluctuation of gear dynamic characteristics initially increases and then decreases with the increase in rotating speed.

Design and Investigation of an Asymmetric Logarithmic Spiral Gear Drive

Sliding on gear teeth working surfaces has negative effects on the performances of gears, such as tooth surface wear, pitting, etc. In order to reduce the gear sliding during high speed and heavy load, a new type of pure rolling gear, named as an asymmetric logarithmic spiral gear, is designed referring to the characteristics of the Issus planthopper gear. To explore the meshing principle of this kind of gear, the equations of the teeth surfaces, their working lines, and contact lines are all derived. Then, the tooth profile parameters and slip rate are calculated. To ensure accurate gear engagement, the gear interferences are analyzed to build the gear models. Subsequently, the gear is performed to simulate its working condition by the finite element method. Furthermore, the results are compared with that of the pure rolling single arc gear. As a result, the asymmetric logarithmic spiral gear behaviors less contact and bending stresses than the pure rolling single arc gear under the same work condition.

A Hybrid Multistep Procedure for the Vibroacoustic Simulation of Noise Emission from Wind Turbines

This paper proposes an efficient hybrid analytical-computational approach for the simulation of mechanical vibrations and sound radiation in wind turbine drive trains.The computational procedure encompasses the detailed modeling of vibrational sources and structural sound paths as well as the major panels of airborne noise radiation. The angle-varying mesh stiffness is obtained from a series of quasi-static finite element simulations. A novel procedure is proposed to obtain the time-varying mesh stiffness at fluctuating speed. The varying mesh stiffness is introduced as a parametric excitation in an analytical gear model, and the Fourier-transformed results are used as vibrational sources in a finite-element-based harmonic response analysis of the drive train. The present paper focuses on the modeling of gear contact and gearbox vibrations. The models and procedures are outlined, and computational results are compared to physical measurements on a 2.5 MW wind turbine. The results are in good qualitative agreement at tonal frequencies. This is particularly the case at fluctuating speed, where both the simulation and the measurement show the characteristic effect of frequency modulation. The computational procedure has been expanded to the whole drive train and is effectively applied in the conception and evaluation of design measures for the reduction of tonal amplitudes.

Load Distribution and Dynamic Response in Torque Split Applications

This study consists of constructing and analyzing gear mathematical models of torque split systems for contact pressure distribution and dynamic transmission error at different gear positions concerning phase angles. According to the method specified in the AGMA 927 standard, load distribution is calculated by considering shaft torsion and bending deformations. Partial contact loss may occur as a result of shaft bending with asymmetric gear positioning on a long shaft. The contact separation can be decreased by reaction force balancing if the driven gears are in the opposite position with respect to the drive gear. In the calculation of the dynamic transmission error of the torque split model, a parametric phase difference for the gear positions is proposed using gear geometry parameters. The variation of the dynamic response according to the change in the parametric phase angle in the torque split system is analyzed for the same values of each gear. Small changes in the phase values change the system response significantly. To obtain lower dynamic transmission error amplitude, the phase difference and gear positions are examined. The contact pressure distribution is validated by the finite element method, and the dynamic transmission error is compared with the experimental study in the literature.

Wear analysis and simulation of small module gear based on Archard model

With the development of micro machining technology, small module gears are widely used in the field of high precision technology. In view of the failure problems such as tooth fracture and fatigue pitting caused by dynamic wear in the process of small module gear transmission, this paper takes a micro planetary gear reducer as the research object and establishes the analysis framework of small module gear wear calculation model based on Archard wear model and Hertz contact theory. Considering the influence of installation error and position tolerance, tooth contact analysis (TCA) model of small module gear is established based on the theory of small displacement torsor (SDT) and space coordinate transformation, and the impact of these errors on the dynamic contact trajectory, contact stress, and tooth surface wear is analyzed based on the numerical simulation. The numerical simulation results show that with the increase of the installation error, the contact trajectory will deviate significantly, which will finally result in increased contact stress and wear. Moreover, with the decrease of tolerance level, the service life of the device increases under the same reliability level. The above analysis of tooth surface wear can provide references for the design and installation of a small module gear transmission.

Development of the fatigue life model for plastic gears of automotive actuators under vibration

In this research, a series of analysis and validation were conducted for estimating the fatigue life of plastic gears. A jig for depicting assembly state in vehicle actuators was made based on failure mechanism analysis. A vibration test for detecting the resonance frequency was performed using a frequency range specified in the ISO standard and it is confirmed that a resonance point occurs within a range generated by an engine operation. Finite element analysis was conducted to obtain the maximum stress in the vibration test applied with a sinusoidal sweep signal and the cycles to failure were calculated through the accelerated testing. The fatigue life model for plastic gears was established by deriving an S-N curve on the relation between stress and cycles to failure. The purpose of this study is to propose a design guideline for improving the reliability of vehicle actuators through the establishment of a fatigue life model for the elemental components.

Study of Brake Disc Friction Characteristics Effect on Low Frequency Brake Induced Vibration of Aircraft Landing Gear

During aircraft braking, the change of ground adhesion forces can cause forward and backward vibration of the landing gear, and the performance of the brake disc may exacerbate this vibration. In order to solve this problem, a rigid–flexible coupling dynamic model of a two-wheel strut landing gear considering the friction characters of brake discs with different materials and a hydraulic brake system model is established in this paper. The brake disc friction characteristics effect on the low-frequency brake-induced vibration of the landing gear given different brake disc materials and ambient temperatures is studied. It is shown that the C/SiC brake disc has a “negative slope” phenomenon between the friction coefficient of the brake disc and the wheel speed, and this variable friction characteristic has a great effect on the low-frequency braking-induced vibration of the landing gear. In addition, the variable friction characteristics of the C/SiC brake disc are easily affected by ambient temperature, while the friction coefficient of the C/C brake disc changes stably.

Wear prediction considering dynamic load for spur gear in mixed elastohydrodynamic lubrication

In this work, a wear prediction model considering the dynamic load is proposed for spur gears in mixed elastohydrodynamic lubrication (EHL). The dynamic load is calculated by gear dynamic model. Combining gear wear model and dynamic model, the wear depth under the dynamic load is determined and compared with that under quasi-static load. The comparative results show that the maximum wear depth under dynamic load is significantly larger than that under quasi-static load near engaging-in point. The effects of fractional film defect coefficient on wear depth are considerable under dynamic load, which is closely related to gear contact temperature. Furthermore, the effects of surface roughness and gear geometrical parameters on wear depth are studied. The investigation reveals that the wear depth decreases with the increased tooth width, module and pressure angle, but increases with the surface roughness. It illustrates that gear wear depth under the dynamic load can be reduced by optimizing gear geometrical parameters.

Carburizing effect-inspired bending fatigue forecasting model for spiral bevel gears

Collaborative optimization considering complex meshing interface physical performance evolution is always an important challenge for designer in recent field of spiral bevel gears. Where, an innovative root bending fatigue life forecasting model is established by considering the root flank carburizing effect for spiral bevel gears. First, root flank carburizing simulation is performed to output carburizing effect evaluations, namely the root flank hardness gradient at different carburizing layers and residual stress distribution. Then, carburizing effect-inspired root bending fatigue life forecasting model was established. Where, finite element method (FEM) based bending stress considering residual stress is determined, and root flank hardness gradient is used to compute S-N curve. Considering tooth flank carburizing effect, root bending fatigue life forecasting is performed by correlating with multiaxial fatigue criterion. Finally, the proposed forecasting model is exercised with an instance aerospace spiral bevel gears to verify the impact of key machine settings on the result root bending fatigue life.

Dynamic modeling and vibration analysis of spur gear system considering thin-walled gear and hollow shaft

This paper proposes a gear dynamic model considering the thin-walled gear and hollow shaft. The shell element is adopted to establish the gear-shaft finite element model instead of using the beam element and lumped mass element. The shortcomings of the traditional dynamic model and the influences of thin-walled hollow shafts are analyzed. Numerical results show that the simplification strategy of the traditional dynamic model will lose several vital modal information and evaluate excessive critical speeds. The proposed model obtains the extra resonant frequency in the high-speed region. However, the traditional model loses this phenomenon due to the simplified thin-walled structural features. The equivalence of the hollow shaft to a beam model requires the condition of a small radius-thickness ratio. Otherwise, it will lead to deviations in the predicted vibration characteristics. The proposed model helps to provide a theoretical basis for high-performance design and vibration and noise reduction of high-speed and lightweight gear transmission systems.

Study on multi-clearance nonlinear dynamic characteristics of herringbone gear transmission system under optimal 3d modification

The tooth surface 3d modification technology is the most effective method to realize the reduction of vibration and noise of gear system (GS) by comprehensively considering tooth profile modification and axial modification. Moreover, the system nonlinear factors such as backlash and bearing clearance will make the motion of GS have complex variability. Therefore, we will combine 3d modification technology with contact performance and dynamic characteristics to optimize the meshing characteristics of herringbone gear pair through tooth contact analysis technology, loaded tooth contact analysis technology and antlion optimizer with error minimum amplitude as optimization objective, determine three nonlinear dynamic model of herringbone gear for numerical solution. Finally, this paper studies the influence of different system parameters on the system nonlinear dynamic characteristics under 3d modification and non-modification from both local vibration characteristics on the diagrams of time history, phase, spectrum and Poincare map and global vibration characteristics on the diagrams of system bifurcation and maximum Lyapunov exponent. The results show: After optimizing modification, the system vibration is obviously reduced. With the increase of input power, input speed, backlash and static transmission error (STE), the system has jump, while there is no jump with the change of bearing clearance and damping ratio. Compared with other parameters, the changes of input speed and STE make system have complex bifurcation characteristics. The 3d modification can eliminate the jump and make system motion more regular.

Convective heat transfer modelling in dry-running polymer spur gears

Heat convection is an important phenomenon in the process of cooling polymer spur gears running in dry conditions, which ultimately affects the strength of the gears. In order to gain some insight into this phenomenon, a numerical heat convection model for polymer spur gears is proposed in this work, which is based on a detailed CFD simulation of the gears in operating conditions and it allows us to investigate the heat convection through their external surfaces.The performance of this numerical model is illustrated with several examples, in which a parametric study has been conducted to observe the variation of the heat transfer coefficients with the face width and the angular speed of the gears. The results obtained from this parametric study are compared to those obtained from a representative classical heat convection model, observing that the relative differences between them in terms of heat transfer coefficients can be as high as 125%.Finally, a new optimized heat convection model for polymer spur gears running in dry conditions is proposed, in which the convective heat transfer coefficients for the external surfaces of the gears are calculated from empirical equations based on the Newton’s law of cooling. This optimized model has lower computational cost than the numerical one, while it provides an important increase of the accuracy of the classical heat convection models, reducing the maximum relative differences to 10%.

Design and Analysis of Novel Non-Involute Cylindrical Gears with a Curved Path of Contact

In this paper, novel non-involute cylindrical gears are designed based on a curved path of contact. Firstly, a parabolic curve is predesigned as the contact path of novel gears. Then, the tooth profiles of the novel gears are calculated using differential geometry and spatial meshing theory. Secondly, the three-dimensional tooth models of the novel non-involute gears are established according to a machining simulation. Thirdly, a simulation model (including misalignment error and longitudinal modification) is established to analyze the performance of the novel non-involute gears. Finally, an example is given, and the results show that the presented novel non-involute gears have greater load-carrying capacity compared with the involute gears. Moreover, whether modified or not, with or without misalignment error, the stresses of the presented novel gears are lower than those of involute gears.

Computerized analysis of traveling wave vibration characteristics of aviation thin-walled spiral bevel gears

Aviation thin-walled spiral bevel gears are prone to traveling wave vibration. This study proposes an efficient traveling wave vibration analysis method based on the contact finite element model of the spiral bevel gears. The excitation vibration modes under the typical working condition is obtained through comparison to the modal analysis and harmonic response analysis. The resonance modes and frequencies are determined by Campbell diagram. The effect of thin-walled structure parameters on the traveling wave vibration of aviation spiral bevel gears is investigated. The results show that the traveling wave vibration of the gear is easily excited by the forward traveling wave and backward traveling wave resonance of 2nd nodal diameter/1st nodal circle, forward traveling wave resonance of the 6th nodal diameter, backward traveling wave resonance of 7th nodal diameter. The increase of gear blank web thickness will decrease peak stresses. The increase of conical web thickness and angle will decrease the peak stresses of compound vibration. The adjacent modals will aggravate the vibration. The decrease of the modal frequency spacing will increase the peak stresses.

Comparative study about dimensional accuracy and form errors of FFF printed spur gears using PLA and Nylon

In the present paper the comparison of dimensional accuracy and form errors of FFF (Fused Filament Fabrication) 3D printed spur gears obtained in two different polymeric materials (PLA and Nylon-PA6) is presented. Two types of gears were designed and printed, having different module and teeth number. First, the gear modelling process is presented. The printing parameters were defined for both materials. Then, the measuring processes were described. Using the method of the sector span, the base circular thickness and the base pitch of the gears were determined. Additionally, the root and tip diameters were measured, and their roundness and concentricity errors were determined. The analysis of the results shows that, in general, PLA allows obtaining better dimensional accuracy than Nylon. Nylon parts, which were obtained with lower infill ratio than PLA parts showed lower from errors.

Chaos Analysis of Single-Stage Spur Gear System Considering Backlash Fractal

PurposeConsidering the time-varying pressure angle and dynamic clearance, the effects of rotational speed, tooth surface friction, and tooth surface morphology on the system’s dynamic response are studied.MethodAn improved gear nonlinear model is proposed, which considered nonlinear factors such as time-varying pressure angle, position angle, tooth surface morphology, and tooth surface friction. The time-varying dynamic backlash is deduced, and the nonlinear dynamic equation of the gear is established. The nonlinear dynamic response of the gear system is obtained based on Runge–Kutta method.ResultsThe influence of the rotational speed and tooth surface friction on single-stage spur gear system response is analyzed through the analysis of the bifurcation diagram, the three-dimensional spectrum diagram, the proportion of the meshing state, and the largest dynamic meshing force (LDMF). Dynamic response differences between the three different model are compared. In addition, by changing the tooth surface roughness and fractal dimension, the influence of tooth surface morphology on the dynamic response of the system is studied.ConclusionCompared with the traditional model, when the dynamic center distance and dynamic pressure angle are considered, the system response may enter a chaotic state earlier. When the tooth surface friction is further considered, the chaotic state of the system response is suppressed. At the same time, the velocity of the dynamic transmission error is significantly reduced, and the fluctuation amplitude of the dynamic pressure angle is increased. The value of LDMF rose overall. The stability of the system response decreases with the increase of tooth surface roughness and fractal dimension. Compared with the fractal dimension, the tooth surface roughness has a more obvious effect on the dynamic response of the system.

Scaling up breastfeeding in England through the Becoming Breastfeeding Friendly initiative (BBF).

Breastfeeding is the most accessible and cost-effective activity available to public health and has been shown to be one of the most effective preventive measures mothers can take to protect their children's health. Despite the well-documented benefits, the UK has one of the lowest breastfeeding rates in the world. The Becoming Breastfeeding Friendly (BBF) toolkit was developed through highly structured technical and academic collaboration, led by Yale University. It provides an evidence-based process to help countries assess their breastfeeding status and readiness to scale up, and identifies concrete measures countries can take to sustainably increase breastfeeding rates, based on data-driven recommendations. BBF is grounded in the Breastfeeding Gear Model complex adaptive systems framework which is made up of eight simultaneous conditions that sustain breastfeeding. In 2018, a committee of multi-agency stakeholders implemented the BBF process in England, collecting evidence to score the 'gear' components of England's breastfeeding environment against 54 benchmarks. The Training and Programme Delivery gear received the highest score, attributable to existing learning outcomes for health professionals and practitioners, peer supporters and specialist services, although there is a need for greater coordination and integration. The lowest scores were given for Promotion and Coordination, Goals and Monitoring due to the lack of a dedicated national strategy for breastfeeding and poor sharing of localised strategies and programmes. The process generated clear recommendations highlighting the need for more robust routine infant feeding data collection and reporting, and the necessity for strengthening leadership, monitoring and oversight to scale up and sustain breastfeeding.

Influence of brake-disc friction characteristics on anti-skid braking control system of aircraft

The low-frequency landing gear walk of aircraft during braking processis studied. Firstly, by virtual of LMS Virtual.Lab motion software, the multi-body dynamic model of the landing gear is established, the motion pair and internal and external loads are applied, and the torsion spring is set at the connection between the landing gear and the fuselage to simulate the flexibility of the landing gear. Then, the variation of friction coefficient of brake discis considered in the model of braking pressure and torque. When the braking control system works, if the braking pressure is less than the limit value, the gear walk is less affected by the friction characteristics of the brake disc. If the braking pressure reaches the limit value, the law of gear walk is the same as that of the pilot's manual control of the braking pressure. At this time, the gear walk is only affected by the positive and negative slope of the friction coefficient of the brake disc. If the friction coefficient curve of the brake disc presents a negative slope, it may cause gear walk, and the greater the absolute value of the slope, the more obvious the gear walk is. Improving the friction characteristics of brake discs can provide a new strategy forgear walk control.