提出一种风电变桨轴承齿轮修形的精确建模方法,用以确定风电变桨轴承齿轮的修形量。根据齿廓方程建立离散齿廓点,使用B样条拟合得到精确齿廓线建立齿轮模型,划分网格并使用栅格法加密齿轮接触区;根据渐开线法线性质几何推导出加密区域节点的偏移方向,通过修形曲线函数计算出节点偏移量,沿偏移方向按照偏移量偏移节点,得到修形后风电变桨轴承齿轮模型;建立多个不同修形量风电变桨轴承齿轮模型,分别装配到风电变桨轴系中进行齿面接触计算,对比计算结果确定最佳修形量。最大修形量为40 um时齿面接触应力最小,与两种经典修鼓量公式计算结果基本相同,证明模型的可靠性。根据该文的建模方法,能快速有效地确定风电变桨轴承齿轮修形量。
Abstract
In this paper, an accurate modeling method for pitch bearing gear modification is proposed to determine the modification amount of pitch bearing gear. Discrete tooth profile points are established according to the tooth profile equation, accurate tooth profile lines are obtained by B-spline fitting, and the gear model is established. The grid is divided and the grid method is used to densify the contact area of the gear. Based on the properties of normals of involute, the offset direction of nodes in the encrypted area is derived geometrically. The offset amount of nodes is calculated through the modification curve function, and the nodes are offset along the offset direction to obtain the modified pitch bearing gear model. Establish multiple models of pitch bearing gears with different modification amounts, assemble them into the pitch shaft system for tooth contact calculation, and compare the calculation results to determine the optimal modification amount. When the maximum modification amount is 40 μm, the tooth contact stress is the smallest, which is basically the same as the calculation results of two classic drum modification formulas, proving the reliability of the model. According to the modeling method in the article, the modification amount of pitch bearing gears can be quickly and effectively determined.
关键词
有限元分析 /
栅格法 /
齿轮修形 /
齿面接触分析 /
变桨轴承齿轮
Key words
finite element analysis /
grid method /
gear modifications /
gear contact analysis /
pitch gearing gear
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] İMREK H, DÜZCÜKOĞLU H. Relation between wear and tooth width modification in spur gears[J]. Wear, 2007, 262(3/4): 390-394.
[2] 赵西伟, 张煜, 吴国新, 等. 风力发电机高速齿轮磨损故障趋势预测方法研究[J]. 太阳能学报, 2023, 44(7): 463-468.
ZHAO X W, ZHANG Y, WU G X, et al.Research on wear failure trend prediction method of high-speed gear for wind generators[J]. Acta energiae solaris sinica, 2023, 44(7): 463-468.
[3] 曹然, 夏建芳. 鼓形修形和偏载对直齿轮强度的影响研究[J]. 机电工程, 2018, 35(11): 1172-1177.
CAO R, XIA J F.Influence of drum-shaeped modification and deflected load on strength of spur gears[J]. Journal of mechanical & electrical engineering, 2018, 35(11): 1172-1177.
[4] 刘惠达, 郑鹏. 盾构机主轴承内啮合齿轮修形优化设计[J]. 重型机械, 2023(2): 109-115.
LIU H D, ZHENG P.Optimization design on profile modification of main bearing internal gear for shield machine[J]. Heavy machinery, 2023(2): 109-115.
[5] 宋乐民. 齿形与齿轮强度[M]. 北京: 国防工业出版社, 1987.
SONG L M.Tooth shape and gear strength[M]. Beijing: National Defence Industry Press, 1987.
[6] 相涯. 渐开线圆柱齿轮齿向鼓形修形方法研究[J]. 机械传动, 2018, 42(6): 49-52, 107.
XIANG Y.Research of axial crowning modification of involute cylindrical gear[J]. Journal of mechanical transmission, 2018, 42(6): 49-52, 107.
[7] LI X Y, WANG N N, LYU Y G.Tooth profile modification and simulation analysis of involute spur gear[J]. International journal of simulation modelling, 2016, 15(4): 649-662.
[8] 杨硕文, 唐进元. 一种新的直齿轮复合修形设计方法[J]. 中南大学学报(自然科学版), 2019, 50(5): 1082-1088.
YANG S W,TANG J Y.A new design method for compound modification of spur gear[J]. Journal of Central South University(science and technology), 2019, 50(5): 1082-1088.
[9] LI X Y, WANG N N, ZHONG P S, et al. Profile modification method for involute spur cylindrical gear pairs and matched dedicated parameterized CAD system: CN111488659[P].2017[2023-10-17].
[10] HU X X, SONG B B, DAI X X, et al.Research of gear contact based on Hertz contact theory[J]. Journal of Zhejiang University of Technology, 2016, 44(1): 19-22.
[11] ZHANG H M, ZHAO G Q, MA X W.Adaptive generation of hexahedral element mesh using an improved grid-based method[J]. Computer-aided design, 2007, 39(10): 914-928.
[12] SU Y, LEE K H, SENTHIL KUMAR A.Automatic hexahedral mesh generation for multi-domain composite models using a hybrid projective grid-based method[J]. Computer-aided design, 2004, 36(3): 203-215.
[13] BLACKER T.Automated conformal hexahedral meshing constraints, challenges and opportunities[J]. Engineering with computers, 2001, 17(3): 201-210.
[14] SCHNEIDERS R.A grid-based algorithm for the generation of hexahedral element meshes[J]. Engineering with computers, 1996, 12(3): 168-177.
[15] 董惠敏, 安海鹏, 张楚. 基于栅格法的人字齿有限元接触精确建模方法[J]. 华中科技大学学报(自然科学版), 2022, 50(3): 87-93.
DONG H M, AN H P, ZHANG C.Accurate finite element contact modeling method of herringbone gear based on grid-based method[J]. Journal of Huazhong University of Science and Technology (natural science edition), 2022, 50(3): 87-93.
[16] 曾攀. 有限元分析及应用[M]. 北京: 清华大学出版社, 2004.
ZHENG P.Finite Element Analysis and Application[M]. Beijing: Tsinghua University Press, 2004.
[17] 黄丽丽. 有限元三维六面体网格自动生成与再生成算法研究及其应用[D]. 济南: 山东大学, 2010.
HUANG L L.Research on the algorithm for 3D hexahedral mesh automatic generation and regeneration and its applications[D]. Jinan: Shandong University, 2010.
[18] 黄丽丽, 赵国群. 基于栅格法的三维六面体网格质量优化[J]. 中国机械工程, 2009, 20(21): 2603-2608.
HUANG L L, ZHAO G Q.Optimization of grid-based three-dimensional hexahedral meshes[J]. China mechanical engineering, 2009, 20(21): 2603-2608.
[19] 王鹏, 包道日娜, 吴胜胜, 等. 基于静力学分析的新型变桨风力机关键齿轮参数优化[J]. 太阳能学报, 2023, 44(7): 456-462.
WANG P, BAO D, WU S S, et al.Optimization of key gear parameters of new variable pitch wind turbine based on static analysis[J]. Acta energiae solaris sinica, 2023, 44(7): 456-462.
[20] XIN J W, WANG S Z.Research on the gear's modification and its processing[J]. Machinery, 2009, 36(5):19-21.
[21] CHEN S Y, TANG J Y, LUO C W. Effects of the gear tooth modification on the nonlinear dynamics of gear transmission system[J]. Advanced materials research, 2010, 97/98/99/100/101: 2764-2769.
[22] LI R L, MU S, WANG C X, et al.Simulation Analysis of the GearModification of Wind Power Gearbox based on Romax[J]. Journal of mechanical transmission, 2015,39(4):106-109.
[23] HAN J, ZHU Y G, XIA L, et al.A novel gear flank modification methodology on internal gearing power honing gear machine[J]. Mechanism and machine theory, 2018, 121: 669-682.
基金
辽宁省科学技术计划项目(2022JH2/101300209); 辽宁省揭榜挂帅项目(2021JH1/10400099)