COMMON DEFINITION FOR END-SURFACE CONTACT RATIO OF GEARS AND ITS APPLICATIONS

Common definition and calculating expressions of end-surface contact ratiofor all type of gears are put forward, and with calculation expressions for involute gears,micro-segments profile gears, and sine-curved profile gears being discussed. The end-surface contactratio of gears is defined as the ratio of the action angle (the rotation angle of gear from gear-into gear-out for one pair of teeth) to the rotation angle per pitch (or central angle per tooth).According to the theory of gearing, equation of the meshing line can be deduced from the toothprofiles of basic rack. Having obtained the equation of the meshing line, and being given theaddendum outline of the gears, the contact ratio can be calculated with the calculation expressions.For the involute gears, this definition has same effect as the well-known definition: ratio of thecontact line to the base pitch. This definition of contact ratio is also suitable to othernon-involute gears, such as micro-segments profile gears, sine-curved profile gears, and can givemore reliable results.

Effect of contact angle and helix angle on slide-roll ratio under the accelerated motion state of ball screw mechanism

To study the effect of the contact angle and helix angle on slide-roll ratio at the ball contact points under the accelerated motion state of ball screw mechanisrm(B S M),the curve theory in differential geometry a d the homogeneous transformation matrix ae used to establish the acceleration kinematics model of BSM.The model can be used to describe the accelerated motion relationships among the screw,balls and nut,calculate the acceleration of relative motion at the contact points between the balls and raceways,and analyze five accelerated motion rules between the balls and raceways.It also conducts a simulation analysis of the slide-roll ratio relationship between the accelerations at the ball center and the contact point of ball under different contact angles and helix angles.As shownby the analysis,with the increase in the BSM’s contact angle,the slide-roll ratio at the contact points decreases,and the contact angle has a relatively significant effect on the slide-roll ratio.However,with the decrease in the BSM’helix angle,the slide-roll ratio at the contact points decreases,and the helix angle has a relatively insignificant effect on the slide-roll ratio.By measuring the accelerations of both the screw and nut under the accelerated motion state,it also verifies the existence of the slide-roll mixed motion at the ball contact point A between the ball and the screw racewayand pure rolling at the ball contact point B between the ball and the nut raceway during the accelerated motion.

EFFECT OF INVOLUTE CONTACT RATIO ON THE DYNAMIC PERFORMANCE OF SPUR GEAR WITH NOTOOTH PROFILE MODIFICATION

The effect of involute contact ratio on the torsional vibration behavior ofspur gear-pair is studied analytically through a mass-spring model. The tooth stiffness in model notonly has a relation with time, as many prior studies presented, but, more important, with involutecontact ratio (ICR) as well. The ICR embodies its impact on the spur gear's dynamic performancethrough changing the proportion of tooth stiffness when there are n+1 teeth in contact to toothstiffness when there are n teeth in contact. A couple of curves about impact of ICR on the gear'sdynamic performance are presented, and they clearly demonstrate that the model can accuratelydescribe the effects of ICR on dynamic transmission error. Finally, some conclusions useful toreduce vibration and noise of gear-pair are proposed.

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.

Effects of Service Condition on Rolling Contact Fatigue Failure Mechanism and Lifetime of Thermal Spray Coatings——A Review

The service condition determines the Roiling Contact Fatigue（RCF） failure mechanism and lifetime under ascertain material structure integrity parameter of thermal spray coating. The available literature on the RCF testing of thermal spray coatings under various condition services is considerable; it is generally difficult to synthesize all of the result to obtain a comprehensive understanding of the parameters which has a great effect on a thermal spray coating＇s resistance of RCF. The effects of service conditions（lubrication states, contact stresses, revolve speed, and slip ratio） on the changing of thermal spray coatings＇ contact fatigue lifetime is introduced systematically. The effects of different service condition on RCF failure mechanism of thermal spray coating from the change of material structure integrity are also summarized. Moreover, In order to enhance the RCF performance, the parameter optimal design formula of service condition and material structure integrity is proposed based on the effect of service condition on thermal spray coatings＇ contact fatigue lifetime and RCF failure mechanism. The shortage of available literature and the forecast focus in future researches are discussed based on available research. The explicit result of RCF lifetime law and parameter optimal design formula in term of lubrication states, contact stresses, revolve speed, and slip ratio, is significant to improve the RCF performance on the engineering application.

A multicomponent multiphase lattice Boltzmann model with large liquid–gas density ratios for simulations of wetting phenomena

A multicomponent multiphase（MCMP） pseudopotential lattice Boltzmann（LB） model with large liquid–gas density ratios is proposed for simulating the wetting phenomena. In the proposed model, two layers of neighboring nodes are adopted to calculate the fluid–fluid cohesion force with higher isotropy order. In addition, the different-time-step method is employed to calculate the processes of particle propagation and collision for the two fluid components with a large pseudoparticle mass contrast. It is found that the spurious current is remarkably reduced by employing the higher isotropy order calculation of the fluid–fluid cohesion force. The maximum spurious current appearing at the phase interfaces is evidently influenced by the magnitudes of fluid–fluid and fluid–solid interaction strengths, but weakly affected by the time step ratio.The density ratio analyses show that the liquid–gas density ratio is dependent on both the fluid–fluid interaction strength and the time step ratio. For the liquid–gas flow simulations without solid phase, the maximum liquid–gas density ratio achieved by the present model is higher than 1000：1. However, the obtainable maximum liquid–gas density ratio in the solid–liquid–gas system is lower. Wetting phenomena of droplets contacting smooth/rough solid surfaces and the dynamic process of liquid movement in a capillary tube are simulated to validate the proposed model in different solid–liquid–gas coexisting systems. It is shown that the simulated intrinsic contact angles of droplets on smooth surfaces are in good agreement with those predicted by the constructed LB formula that is related to Young＇s equation. The apparent contact angles of droplets on rough surfaces compare reasonably well with the predictions of Cassie＇s law. For the simulation of liquid movement in a capillary tube, the linear relation between the liquid–gas interface position and simulation time is observed, which is identical to the analytical prediction. The simulation results regarding the wetting phenomena of droplets on smooth/rough surfaces and the dynamic process of liquid movement in the capillary tube demonstrate the quantitative capability of the proposed model.

Non-Contact Method of Heart Rate Measurement Based on Facial Tracking

Image photoplethysmography can realize low-cost and easy-to-operate non-contact heart rate detection from the facial video, and effectively overcome the limitations of traditional contact method in daily vital sign monitoring. However, it is hard to obtain more accurate heart rate detection values under the conditions of subject’s facial movement, weak ambient light intensity and long detection distance, etc. In this article, a non-contact heart rate detection method based on face tracking is proposed, which can effectively improve the accuracy of non-contact heart rate detection method in practical application. The corner tracker algorithm is used to track the human face to reduce the motion artifact caused by the movement of the subject’s face and enhance the use value of the signal. And the maximum ratio combining algorithm is used to weight the pixel space pulse wave signal in the facial region of interest to improve the pulse wave extraction accuracy. We analyzed the facial images collected under different experimental distances and action states. This proposed method significantly reduces the error rate compared with the independent component analysis method. After theoretical analysis and experimental verification, this method effectively reduces the error rate under different experimental variables and has good consistency with the heart rate value collected by the medical physiological vest. This method will help to improve the accuracy of non-contact heart rate detection in complex environments.

Sensitivity analyses of random cave groups on karst tunnel stability based on water–rock interaction using a novel contact dynamic method

This paper concentrates on the sensitivity and dynamic simulation of randomly distributed karst cave groups on tunnel stability and connectivity extended ratio based on water–rock interaction using a novel contact dynamic method(CDM).The concept of karst cave group connectivity extended ratio during tunneling and water inrush is proposed.The effects of cave shape and spatial distribution on Qiyueshan tunnel are investigated.Tunnel deformation and damage index,and connectivity extended ratio with uniform random karst cave groups are evaluated.The results demonstrate that the connectivity extended ratio is verified as a crucial judgment in predicting the safe distance and assessing the stability of the tunnel with the karst cave group.CDM model captures the fracture propagation and contact behavior of rock mass,surface flow,as well as the bidirectional water–rock interaction during the water inrush of Qiyueshan tunnel with multiple caves.A larger cave radius and smaller minimum distance between the cave and tunnel increase the deformation and damage index of the surrounding rock.When the cave radius and cave area ratio increase,the failure pattern shifts from overall to local failure.These findings potentially have broad applications in various surface and subsurface scenarios involving water–rock interactions.

Propagation of plane waves at the imperfect boundary of elastic and electro-microstretch generalized thermoelastic solids

The problem of reflection and transmission of plane waves incident on the contact surface of an elastic solid and an electro-microstretch generalized thermoelastic solid is discussed. It is found that there exist five reflected waves, i.e., longitudinal displacement （LD） wave, thermal （T） wave, longitudinal microstretch （LM） wave and two coupled transverse displacement and microrotational （CD（I） and CD（II）） waves in the electro-microstretch generalized thermoelastic solid, and two transmitted waves, i.e., longitudinal （P） and transverse （SV） waves in the elastic solid. The amplitude ratios of different reflected and transmitted waves are obtained for an imperfect boundary and deduced for normal force stiffness, transverse force stiffness, and perfect bonding. The variations of amplitude ratios with incidence angles have been depicted graphically for the LD wave and the CD（I） wave. It is noticed that the amplitude ratios of reflected and transmitted waves are affected by the stiffness, electric field, stretch, and thermal properties of the media. Some particular interest cases have been deduced from the present investigations.

Numerical investigation on the caving mechanism with different standard deviations of top coal block size in LTCC

The size distribution of the broken top coal blocks is an important factor,affecting the recovery ratio and the efficiency of drawing top coal in longwall top coal caving(LTCC)mining panel.The standard deviation of top coal block size(dt)is one of the main parameters to reflect the size distribution of top coal.To find the effect of dt on the caving mechanism,this study simulates experiments with 9 different dt by using discrete element software PFC.The dt is divided into two stages:uniform distribution stage(UDS)whose dt is less than 0.1(Schemes 1–5),and nonuniform distribution stage(NDS)whose dt is more than 0.1(Schemes 6–9).This research mainly investigates the variation of recovery ratio,drawing body shape,boundary of top coal,and contact force between particles in the two stages,respectively.The results showed that with the increasing dt,the recovery ratio of the panel increases first and then decreases in UDS.It is the largest in Scheme 3,which mainly increases the drawing volume at the side of starting drawing end.However,the recovery ratio decreases first and then increases quickly in NDS,and it is the largest in Scheme 9,where the drawing volume at the side of finishing drawing end are relatively higher.In UDS,the major size of top coal is basically medium,while in NDS,the size varies from medium to small,and then to large,with a distinct difference in shape and volume of the drawing body.When the major size of top coal is medium and small,the cross-section width of the initial boundary of top coal at each height is relatively small.Conversely,when the top coal size is large,the initial boundary of top coal has a larger opening range,the rotating angle of lower boundary is relatively small in the normal drawing stage,which is conducive to the development of drawing body and reduces the residual top coal,and the maximum particle velocity and the particles movement angle are both larger.This study lays a foundation for the prediction of recovery ratio,and suggests that the uniform top coal is more manageable and has a larger recovery ratio.

Key technology for construction of connection between steel pylonand concrete pile cap of middle pylon of Taizhou Bridge

Taizhou Bridge is a suspension bridge with three pylons and two 1 080 m main spans. The middle pylon is a steel frame with longitudinal herringbone shape and lateral gate shape. The connection between steel pylon and concrete pile cap is a key part to transfer the huge inner force from the pylon to the foundation. Its construction quality is a critical factor to the overall structural loading of the whole bridge ; therefore the contact ratio between the bearing steel plate of pylon and concrete pile cap is required to be over 75 %. The inclined joint surface in two directions, longitudinally at 39/1 920 and laterally at 1/4, posted a challenge to the construction work. A procedure test was carried out to find an optimal construction method by comparison, and finally the post-injection method was selected as it can meet the requirement of concrete strength and contact ratio at the connection. The successful application of the post-injection method in Taizhou Bridge can nrovide an examnle and reference for similar nroiects in the future.

Geometric design and simulation of tooth profile using elliptical segments as its line of action

A mathematical model of gear tooth profiles using the ellipse curve, whose curvature is convenient to control by changing the mathematical parameters as its line of action, was built based on the meshing theory. The equation of undercutting condition was derived from the model. A special epicycloidal tooth profile was also presented. An example gear drive with variation of the ellipse parameters was taken to illustrate the proposed method. The contact ratio of the gear drive designed by the proposed method was analyzed. A comparison of the property of the gear drive designed with the involute gear drive was also carried out. The results confirm that the proposed gear drive has higher contact ratio in comparison with the involute gear drive.

考虑磨损的大重合度直齿圆柱齿轮动力学分析

以大重合度直齿圆柱齿轮为研究对象。基于Archard磨损模型,计算了齿轮的齿面磨损量;基于能量法,求取了考虑齿面磨损的齿轮对总啮合刚度,给出了对应的分段函数表示形式,并结合齿轮单自由度动力学模型,研究了齿面磨损对齿轮动力学的影响。研究表明,轻载状态下大重合度直齿圆柱齿轮动力学特性受齿面磨损的影响较大,随着磨损量的增加,齿轮系统在拟周期运动与混沌运动之间有着复杂的变化过程;重载状态下,其动力学特性受磨损影响极小,齿轮系统长时间保持周期性运动。

砂-粉混合料颗粒接触状态的临界条件确定

砂-粉混合料被广泛应用于高速铁路路基、人工筑岛及海底沉管隧道垫层等重大工程,如何科学地表征砂-粉混合料复杂的颗粒接触状态及连续演变的力学行为特征,并深入揭示其对混合料静/动力学特性的影响已是一项紧迫的基础性科学研究任务。本文基于代表性砂-粉混合料的基本物理性能指标及力学特性指标试验数据,验证Rahman等提出的区分“细粒填充砂粒”和“砂粒悬浮细粒”的阈值细粒含量FCth半经验公式预测能力。基于理想二元介质材料的理论最小孔隙比计算方法,提出确定中间性态土颗粒接触状态临界条件参量FC_(in-min)和FC_(in-max)的方法,分析各参数对FC_(in-min)和FC_(in-max)的影响规律,建立基于基本物理性能指标的FC_(in-min)和FC_(in-max)预测方法,最终提出全FC范围(FC=0~100%)的砂-粉混合料各颗粒接触状态临界条件参量的有效评价方法。

高接触比螺旋锥齿面修形方法及动态特性研究

为抑制高接触比螺旋锥齿轮传动的振动,提出一种新的高阶齿面修形方法。根据高接触比螺旋锥齿轮的啮合特点,提出一种新的修形曲线,采用辅助齿面修形方法生成高阶修形螺旋锥齿轮。在考虑齿变形的情况下,计算了高阶修正弧齿锥齿轮传动的载荷传递误差和啮合冲击,在此基础上建立了降低高接触比螺旋锥齿轮传动的载荷传递误差和啮合冲击的优化模型。仿真结果表明:与二阶修形弧齿锥齿轮相比,高阶齿面修形方法不仅可以有效降低高接触比螺旋锥齿的载荷传递误差、啮合冲击和动态负载系数,而且可以提高其在全速范围内的动态性能。

高压作用下水泥基粉末材料的接触硬化研究综述

在高压作用下,一些具有无定型相的水泥基粉末材料会发生接触硬化现象,粉末颗粒在压力作用下发生缩聚运动,并在粉末颗粒间形成结构键,进而快速形成具有一定强度及耐水性的人造石材。本文综述了压力作用下水泥基粉末材料接触硬化的成键机理以及粉末水分含量、干燥条件、钙硅比、压制过程对其接触硬化性能影响的研究进展。相关研究结果表明,压力作用下粉末颗粒间会形成氢键、范德华力、固体桥键等结构键;粉末水分含量是影响接触硬化性能的重要因素,在压力作用下,水分可以改变粉末颗粒的表面性质并影响颗粒之间的结合,进而改变压制成品的力学性能;钙硅比对接触硬化性能的影响显著,不同粉末材料在压制时的最佳钙硅比亦是不同;摩擦力的存在降低了压制效率,造成压制成品密度、强度分布不均匀,润滑剂的加入可以有效降低摩擦力的影响;此外,降低压制模具高径比并使用双面压制可有效提升压制成品的质量。

基于离散元法的雨滴-沙粒碰撞数值模拟

为探明单个雨滴和土壤颗粒相互作用的力学机理,通过假定雨滴是柔软的固体材料,采用离散元法模拟计算了雨滴-沙粒碰撞过程中的沙粒动能份额随杨氏模量、泊松比及接触角的变化趋势。结果表明:模拟计算的沙粒动能份额为0.1%~10%,与实验观测结果基本一致;沙粒动能份额对杨氏模量和接触角变化较为敏感,而对泊松比不敏感。

基于加州承载比试验的隧道弃渣颗粒接触力场形状影响因素分析

对级配碎石而言,不同的颗粒表面性质会影响颗粒接触力场形状、大小及梯度,进而改变试样所受约束力。分析加州承载比(California bearing ratio,CBR)试验过程中试样侧板及底板的受力演变,探究试样颗粒细观参数对试样颗粒接触力场及试样约束力的影响。通过对比不同刚度比、摩擦系数与黏结强度(设定其比值为1下)对试样接触力场形状的影响。结果表明:以刚度比值6为界,随法向刚度的增大,颗粒接触力场长细比先增加后减小;随摩擦系数或黏结强度增大,接触力场长细比相应减小。考虑颗粒相对运动中黏结强度比中法向及切向参数作用不同,以黏结强度比4为界,随法向黏结强度增大,其接触力场长细比先增加后减小;随切向黏结强度增大,所得接触力场长细比变化趋势则为先减小后增加。研究成果可为研究隧道弃渣制成的级配碎石颗粒细观参数与其接触力场形状间关联性提供一定参考。

大重合度直齿轮动载特性分析

针对大重合度直齿轮啮合齿数与普通直齿轮间的差异性变化,以一对大重合度直齿轮和普通直齿轮为研究对象,通过有限元法求解齿轮时变啮合刚度,建立大重合度直齿轮啮合耦合型动力学模型,利用Newmark-β时域积分求解齿轮系统动态响应,对其进行时频域分析并与普通直齿轮进行对比,获得了大重合度直齿轮在不同转速、误差影响下的动载系数变化规律。结果表明,大重合度直齿轮啮合刚度与普通齿轮有较大差异,其动态响应结果波动幅值较普通直齿轮有明显降低,提升了系统稳定性;大重合度直齿轮动载系数与普通直齿轮相比有明显下降,并且随着转速的升高和误差的增大出现不同程度的增加,其中在共振转速区域范围内增幅明显。

外加电压对明胶膜液荷电与润湿性能的影响及其预测模型

目的 探究不同荷质比明胶溶液的润湿性能,并建立预测模型。方法 以明胶可食涂膜为研究对象,利用感应荷电施加外源静电场以改善膜液润湿性能,探究电场电压对明胶液滴荷质比与表面张力,以及液滴在疏水表面接触角的影响,并通过机器学习建立荷质比与表面张力/接触角之间预测模型。结果 随着电压升高,明胶液滴荷质比不断增大,且仅以司盘20为表面活性剂(tw0组)时液滴具有最高的荷质比(-50 nC/g)。在0~7 kV内,明胶液滴的表面张力随电压升高从35.99~40.65 mN/m降至31.38~35.65 mN/m,其中tw0组表面张力下降最为明显。明胶液滴在石蜡表面的接触角也随电压升高而减小,在表面活性剂吐温20与司盘20质量比为1∶1时具有最小值,即电压7 kV时接触角为64.99°。深度神经网络预测模型决定系数接近于1,均方误差小于0.08,平均绝对误差小于0.15,具有最好的预测效果。结论 静电喷涂能够有效改善膜液在食品表面的润湿性能,利用深度神经网络能够建立膜液液滴荷质比与表面张力/接触角的良好预测模型。