为探明变双曲圆弧齿线(Variable hyperbolic circular-arc-tooth-trace,VH-CATT)圆柱齿轮接触疲劳裂纹的扩展机制,指导齿轮的设计优化,降低裂纹扩展速度,基于齿轮曲率特性,建立了 VH-CATT圆柱齿轮接触椭圆数值计算模型,通过有限元法和数值计算法,分析了齿面椭圆接触轨迹,确定了齿轮易萌生裂纹的危险位置.针对裂纹运用扩展有限元(Extended fmite element method,XFEM)的分析方法,研究了 VH-CATT圆柱齿轮接触疲劳裂纹的扩展规律.通过建立VH-CATT圆柱齿轮应力强度因子分析模型,分析了模数、齿线半径及裂纹预置角对Ⅰ型应力强度因子的影响规律.结果表明,长裂纹扩展阶段,齿轮模数越大,裂纹在齿宽和齿芯方向的应力强度因子越大;齿线半径较大时,能够有效减小长裂纹扩展阶段裂纹前缘的应力强度因子;裂纹预置角较大时,朝齿宽及齿芯方向的应力强度因子也随之变大.
Contact Fatigue Crack Propagation Characteristics of Cylindrical Gear with Variable Hyperbolic Circular-arc-tooth-trace
In order to explore the propagation mechanism of contact fatigue crack of the Cylindrical Gear with Variable Hyperbolic Circular-arc-tooth-trace gear(VH-CATT),guide the design optimization of gear and reduce the crack propagation speed,a numerical calculation model of contact ellipse of VH-CATT cylindrical gear is established based on the curvature characteristics of gear.The contact trajectory of tooth surface ellipse is analyzed by finite element method and numerical calculation method,and the dangerous position of gear crack is determined.The extended finite element method(XFEM)is used to analyze the propagation law of contact fatigue cracks in VH-CATT cylindrical gears.By establishing the stress intensity factor analysis model of VH-CATT cylindrical gear,the influence of modulus,tooth line radius and crack preset angle on mode I stress intensity factor is analyzed.The results show that in the stage of long crack propagation,the larger the gear modulus,the larger the stress intensity factor of the crack in the direction of tooth width and tooth core.The stress intensity factor of the crack front in the long crack propagation stage can be effectively reduced when the radius of the tooth line is large.When the crack preset angle is large,the stress intensity factor in the direction of tooth width and tooth core also increases.
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