Geometry Design and Tooth Contact Analysis of Crossed Beveloid Gears for Marine Transmissions

Beveloid gears,also known as conical gears,gain more and more importance in industry practice due to their abilities for power transmission between parallel,intersected and crossed axis.However,this type of gearing with crossed axes has no common plane of action which results in a point contact and low tooth durability.Therefore,a geometry design approach assuming line contact is developed to analyze the tooth engagement process of crossed beveloid gears with small shaft angle for marine transmission applications.The loaded gear tooth contact behavior is simulated by applying a quasi-static analysis to study the effects of gearing parameters on mesh characteristics.Using the proposed method,a series of sensitivity analyses to examine the effects of critical gearing parameters such as shaft angle,cone angle,helix angle and profile-shift coefficient on the theoretical gear mesh is performed.The parametric analysis of pitch cone design shows that the dominant design parameters represented by the angle between the first principle directions（FPD） and normal angular factor are more sensitive to the shaft and cone angles than they are to the helix angle.The theoretical contact path is highly sensitive to the profile-shift coefficient,which is determined from the theoretical tooth contact analysis.The FPD angle is found to change the distribution of contact pattern,contact pressure and root stress as well as the translational transmission error and the variation of the mesh stiffness significantly.The contact pattern is clearly different between the drive and coast sides due to different designed FPD angles.Finally,a practical experimental setup for marine transmission is performed and tooth bearing test is conducted to demonstrate the proposed design procedure.The experimental result compared well with the simulation.Results of this study yield a better understanding of the geometry design and loaded gear mesh characteristics for crossed beveloid gears used in marine transmission.

Mathematic model and tooth contact analysis of a new spiral non-circular bevel gear

A novel spiral non-circular bevel gear that could be applied to variable-speed driving in intersecting axes was proposed by combining the design principles of non-circular bevel gears and the manufacturing principles of face-milling spiral bevel gears.Unlike straight non-circular bevel gears,spiral non-circular bevel gears have numerous advantages,such as a high contact ratio,high intensity,good dynamic performance,and an adjustable contact region.In addition,while manufacturing straight non-circular bevel gears is difficult,spiral non-circular bevel gears can be efficiently and precisely fabricated with a 6-axis bevel gear cutting machine.First,the generating principles of spiral non-circular bevel gears were introduced.Next,a mathematical model,including a generating tooth profile,tooth spiral,pressure angle,and generated tooth profile for this gear type was established.Then the precision of the model was verified by a tooth contact analysis using FEA,and the contact patterns and stress distributions of the spiral non-circular bevel gears were investigated.

TOOTH CONTACT ANALYSIS OF CONICAL INVOLUTE GEARS

The mathematical model of conical involute gears is developed based on the theory of gearing and the generating mechanism. Tooth contact analysis （TCA） is performed to examine the meshing and bearing contact of the conical involute gear pairs with intersected and crossed axes. In addition, the principal directions and curvatures of the gear surfaces are investigated and the contact ellipses of the mating tooth surfaces are also studied. Finally, the numerical illustrative examples are provided to demonstrate the computational results, test gears are made for tooth-bearing tests, and the conclusion is verified that the theory has the applicability.

Complex geometric modeling and tooth contact analysis of a helical face gear pair with arc-tooth

A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate system of an APC face gear pair is established based on meshing theory.Combining the coordinate transformation matrix and the tooth profile of the cutter,the equations of the curve envelope of the APC face gear pair are obtained.Then the surface equations are solved to extract the point clouds data by programming in MATLAB,which contains the work surface and the fillet surface of the APC face gear pair.And the complex geometric model of the APC face gear pair is built by fitting its point clouds.At last,through the analysis of the tooth surface contact,the sensitivity of the APC face gear to the different types of mounting errors is obtained.The results show that the APC face gear pair is the most sensitive to mounting errors in the tooth thickness direction,and it should be strictly controlled in the actual application.

Dynamics of a Dual Power-split Transmission Based on Loaded Tooth Contact Analysis

In order to implement the dynamic characteristic of a dual power-split transmission, a dynamic me- chanics model is built. Firstly, according to the method of theoretical analysis of the tooth contact analysis （TCA） and loaded tooth contact analysis （LTCA）, the actual meshing process of each gear pairs is simulated, and the time-varying mesh stiffness excitations are obtained, which can improve the numerical precision. Second- ly, by using the lumped mass method, the bending-torsional coupling three dimensional dynamic model of the dual power-split transmission is established, and the identical dimensionless equations are deduced by elimina- ting the effect of rigid displacement and the method of dimensional normalization. Finally, by the method of the fourth order Runge-Kutta algorithm with variable step lengths, the responses of this system in a frequency domain and time domain are obtained, and the dynamic load change characteristics of each gear pairs are analyzed. The results show that the establishment, solution and analysis of the system dynamics model could provide a basis for the dynamic design, and have an important significance for the dynamic efficiency analysis and dynamic perform- ance optimization design of the dual power-split transmission.

Mesh excitations of spur gear considering strong correlation among tooth contact parameters,contact force,and tooth profile deviations

Gear mesh excitations are widely concerned in the dynamic studies of the gear transmission system.Meanwhile,intentional and unintentional tooth profile deviations often occur in gears.At present,the established calculation models of gear mesh excitations consider tooth profile deviations as displacement excitation.However,gear mesh excitations calculated by such models have reduced stability compared with the actual situation.Therefore,in this study,an improved analytical model of gear mesh excitations with tooth profile deviations is established.This established model considers tooth profile deviations,extended tooth contact,and the structure coupling effect of the gear body simultaneously.More importantly,the model considers the strong correlation among tooth contact parameters,contact force,and tooth profile deviations to better reflect the actual gear mesh.A calculation flowchart with a simple calculation method of contact forces is also proposed to calculate the gear mesh excitations.Finally,the effects of tooth profile deviations on gear mesh excitations are studied.The results show that the effects of tooth profile deviations on tooth contact position,the direction of contact force,and equivalent basic circle radii should be considered in the calculation of gear mesh excitations because of smaller system transmission errors,larger double-teeth meshing area,and slighter extended tooth contact.Tooth profile deviations also cause jumps in tooth contact position and time-varying mesh stiffness.Thus,our findings show that the proposed model can be used to calculate the gear mesh excitations more accurately when the tooth profile deviates greatly.

Generation Principle of Helix Tooth Profile in Hypocycloid Pinw heel Transmission and Its Contact Characteristics

The transmission characteristics of gear drive can be improved with the use of novel tooth profiles.A theoretical study on tooth profile of the hypocycloid pinwheel transmission and contact analysis of gear pair based on finite element method(FEM) are carried out,respectively.The line contact between mated tooth surfaces becomes point contact according to a plus movement.Through loaded tooth contact analysis(LTCA),the contact stress and load distributions for the proposed hypocycloid pinwheel transmission and the traditional one are discussed.The analysis results show that the developed tooth surfaces have anticipatory point contact characteristics under loads and contact fatigue dangerous area locates around the ultimate contact position.

Influence of Setting Error of Tool on Tooth Profile and Contact Point of Face Gear Drive

In order to analyze the influence of setting error of tool on both tooth profile and contact characteristic of orthogonal face gear drive,the coordinate systems with and without setting error are established.Moreover,the equations of tooth profile and contact points of face gear drive are derived by envelope principle.According to the equations,the change of tooth profile and the contact points position on face gear are analyzed.The tooth surface and contact points are obtained by numerical simulation.Results show that the tooth profile and contact characteristic of face gear drive are not sensitive to the setting error of tool.

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.

Design of Pinion Machine Tool-settings for Spiral Bevel Gears by Controlling Contact Path and Transmission Errors

This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion ma- chine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.

内凹刀盘加工的直齿锥齿轮齿面接触分析

为了在国产数控弧齿锥齿轮机床上采用内凹刀盘加工直齿锥齿轮,对使用内凹刀盘加工直齿锥齿轮的原理和齿面接触分析(Tooth Contact Analysis,TCA)方法进行了研究。基于内凹刀盘的加工原理和结构特点,建立了内凹刀盘加工的直齿锥齿轮的齿面数学模型,给出了相应的齿面接触分析方法;编写齿面接触分析程序,计算得到了齿轮副的接触斑点和传动误差曲线;通过实际的切齿加工和接触斑点检验,验证了齿面数学模型以及TCA方法的正确性。研究为锥齿轮加工参数及刀具参数的确定与啮合质量控制提供了理论依据。

安装误差对双圆弧齿轮啮合特性影响分析

为深入研究安装误差对双圆弧齿轮副啮合特性的影响,基于有限元法建立齿轮加载分析模型,研究啮合过程中单齿凸、凹齿廓的接触性能,对比分析安装误差对接触性能以及传动误差的影响规律。结果表明:啮合周期内,双圆弧齿轮的凹齿廓先接触且承担较大的法向接触力,但凸齿廓的啮入端接触应力最大,凸、凹齿面接触压力差与转矩成正比;安装误差对齿面接触性能影响较大,其中中心距误差容易引起齿轮分阶处应力集中,轴线平面的安装误差会引起齿面接触偏载,且对安装误差影响最大。

直纹面面齿轮共轭小齿轮的滚齿加工研究

针对直纹面面齿轮与圆柱齿轮不满足共轭关系而限制其在小传动比应用场合的情况,提出与直纹面面齿轮共轭的小齿轮及其滚齿加工方法。首先建立了直纹面面齿轮及其共轭小齿轮的齿面方程,获得共轭小齿轮相比圆柱齿轮的齿面偏差形貌;随后推导了阿基米德齿轮滚刀的齿面方程,并根据滚齿加工运动坐标系和啮合原理建立了圆柱齿轮的数学模型;在滚齿加工圆柱齿轮的运动基础上,通过增加滚刀的径向移动和工件的附加转动使滚刀切削刃逼近共轭齿面,附加运动由泰勒多项式表示,通过建立敏感矩阵方程并采用奇异值分解法迭代求解方程获得附加数控运动多项式系数,最后获得数控加工齿面;为评价直纹面面齿轮副的传动性能,进行了齿面承载接触分析,并与传统面齿轮-圆柱齿轮副进行了对比。研究结果表明:相同参数下,直纹面面齿轮副与传统面齿轮副的承载性能基本相同,完全能够代替传统面齿轮副传动;数值算例和仿真加工对该方法的验证表明,其数值算例误差不超过1μm,仿真结果误差不超过6μm,证明了该方法的可行性和准确性。

非圆齿扇齿条副齿面接触应力分析及仿真

针对汽车转向器摇臂轴非圆齿扇的工作齿面易发生磨损、点蚀甚至断裂等现象,围绕非圆齿扇齿条副的齿面接触应力理论建模与有限元仿真分析开展研究,提出一种非圆齿扇齿条副接触应力理论计算模型,研究齿扇齿宽B、齿条压力角α和齿扇锥角φ等几何参数对齿面接触应力的影响规律;将非圆齿扇齿条副三维参数化建模与齿面动态啮合有限元仿真分析集成,提出一种非圆齿扇齿条副接触应力参数化、全流程仿真分析计算方法。预期为汽车转向器非圆齿扇齿条副的设计分析提供理论和方法指导。

双重螺旋法准双曲面齿轮啮合性能研究

针对采用双重螺旋法(全工序法)加工的准双曲面齿轮副,运用数值分析的方法研究了安装误差、螺旋运动系数与啮合性能之间的作用规律。利用矢量法建立切齿加工数学模型,求得齿面方程并建立齿轮副装配数学模型,利用齿面接触分析(TCA)研究含多种安装误差的齿面接触特征;建立齿面失配数学模型,分析螺旋运动系数对齿面接触特征、几何形貌的影响规律,揭示双重螺旋法对轮齿工作面、非工作面不同的修形原理;结合刀具与齿坯之间的相对位置关系,阐述了展成线的求解过程,研究了螺旋运动系数对展成线位置的影响规律。对准双曲面齿轮副(7×43)进行磨齿和滚检实验,与数值分析结果进行对比验证了分析模型的正确性。

基于几何接触算法的摆线针轮传动误差分析

在摆线针轮传动的轮齿接触分析(ToothContactAnalysis,TCA)模型中,通常将误差值设为一个定值,易造成计算结果不合理,且计算过程中常出现计算不收敛等问题。对此,建立了包含修形、加工误差等多因素综合作用下的摆线针轮传动误差分析模型;在对啮合点矢量方程分析后,提出了一种解决数值不收敛等问题的方法,即在求得的摆线轮和针齿上纵横坐标相等的点中,找到法向量相等的啮合点。对回转体误差形式分析后,提出了一种解决计算结果不合理的方法,即令摆线轮周节误差、摆线轮齿廓径向跳动误差和针齿中心圆半径误差在公差带内呈周期性变化。以RV-80E减速器为试验对象,对比试验结果,验证了理论模型的正确性;研究各误差对传动误差的影响,开展了各误差灵敏度分析。结果表明,针齿半径误差和针齿与针齿壳间隙综合作用下的法向间隙是影响传动误差的主要因素。

弧齿锥齿轮TCA接触印痕与传动误差协同求解方法研究

弧齿锥齿轮齿面接触分析(Tooth contact analysis,TCA)可以精确计算得到反映传动性能的重要评价指标接触印痕以及传递误差。然而由于存在强烈的非线性和数值耦合关系,导致求解精度差、效率低和稳定性差。因此,提出了一种同时考虑接触印痕与传动误差的TCA协同求解新方法。首先基于啮合原理进行齿面参数化表达,同时在三维坐标空间中利用旋转矩阵模拟齿轮副的啮合运动进行接触轨迹和传递误差求解;再根据数值齿面的曲率特征,进行接触印痕精确解析求解。算例结果验证了本文所提方法的可行性。

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。

齿槽表面多级微织构构筑及其润湿机理

目的使外科手术器械表面具有超疏水功能,有效防止感染,解决医疗器械的清洁问题,降低设备维护成本。方法通过电火花线切割(WEDM)复合纳秒激光烧蚀在3Cr13不锈钢表面制备了亚毫米/微米多级复合织构表面,随后在表面上制备了1H,1H,2H,2H-全氟癸基三乙氧基硅烷溶液(PFDS)自组装超疏水涂层。利用台式扫描电镜和激光共聚焦显微镜观察复合织构表面形貌特征,使用接触角测量仪对水滴与复合织构表面的接触状态进行观察,并测量水滴的接触角与滚动角。利用表界面张力仪对多级织构表面黏附力进行表征。结果微米沟槽在亚毫米齿槽斜面上均布且不同高度的沟槽形状一致,方向与齿槽平行。水滴与齿槽阵列表面为Wenzel模型接触,水滴与多级结构表面为Cassie-Baxter模型接触。齿槽阵列试样最大黏附力为164.1μN,最小黏附力为123.5μN,多级织构试样的黏附力分别为77.2、47、24.1μN。结论微米沟槽的存在改变了水滴接触状态,在亚毫米尺度上水滴与表面的接触状态由Wenzel状态转为Cassie-Baxter状态,有效改善了水滴的接触性能与滚动性能。多级织构试样齿槽顶角的减小,有效减小了固液接触面积,水滴接触角最大为163.2°。

Pinion Tooth Surface Generation Strategy of Spiral Bevel Gears

Aviation spiral bevel gears are often generated by spiral generated modified（SGM） roll method.In this style,pinion tooth surface modified generation strategy has an important influence on the meshing and contact performances.For the optimal contact pattern and transmission error function,local synthesis is applied to obtain the machine-tool settings of pinion.For digitized machine,four tooth surface generation styles of pinion are proposed.For every style,tooth contact analysis（TCA） is applied to obtain contact pattern and transmission error function.For the difference between TCA transmission error function and design objective curve,the degree of symmetry and agreement are defined and the corresponding sub-objective functions are established.Linear weighted combination method is applied to get an equivalent objective function to evaluate the shape of transmission error function.The computer programs for the process above are developed to analyze the meshing performances of the four pinion tooth surface generation styles for a pair of aviation spiral bevel gears with 38/43 teeth numbers.The four analytical results are compared with each other and show that the incomplete modified roll is optimal for this gear pair.This study is an expansion to generation strategy of spiral bevel gears,and offers new alternatives to computer numerical control（CNC） manufacture of spiral bevel gears.