基于游丝刚度量化的擒纵调速机构动力学分析
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摘要
擒纵调速机构是机械手表机心中最重要的组成部分,运动状态十分复杂,但钟表业界对其研究较少。鉴于此,建立了擒纵调速机构的动力学有限元模型,并基于该机构中关键弹性元件游丝的实际微观晶粒结构,对其弹性性能进行了量化计算。该模型预测了擒纵调速机构的零部件在工作过程中的应力状态,与ROLLAND模拟结果保持一致;同时,还预测了摆轮摆幅对瞬时日差的影响并与试验数据进行了对比,在一定程度上具有良好的精度,模拟结果符合埃利定理。该模型为进一步优化国产机械机心结构提供了有效的数据支持。
The escapement mechanism is the most important element of a mechanical watch movement with a complicated motion,though little is known about it. A dynamics Finite Element model of escapement mechanism is established,and based on the real micrograin structure of the key elastic element in the mechanism, the elastic properties of the hairspring are quantitatively calculated. The model is able to predicts the stress state of the parts of escapement speed regulating mechanism during the working process, which is consistent with ROLLAND simulation results. At the same time, the influence of the pendulum oscillation amplitude on the instantaneous daily rate is predicted and compared with the experimental data, it has good precision to some extent, the simulation results are in line with Airy Theorem. This model could be used to provide useful support in order to optimize the structure of the domestic mechanical watch movement in the future.
The escapement mechanism is the most important element of a mechanical watch movement with a complicated motion,though little is known about it. A dynamics Finite Element model of escapement mechanism is established,and based on the real micrograin structure of the key elastic element in the mechanism, the elastic properties of the hairspring are quantitatively calculated. The model is able to predicts the stress state of the parts of escapement speed regulating mechanism during the working process, which is consistent with ROLLAND simulation results. At the same time, the influence of the pendulum oscillation amplitude on the instantaneous daily rate is predicted and compared with the experimental data, it has good precision to some extent, the simulation results are in line with Airy Theorem. This model could be used to provide useful support in order to optimize the structure of the domestic mechanical watch movement in the future.
引文
[1]王泽生.钟表营销与维修技术[M].北京:中国轻工业出版社,2016:181-198.
[2] ROUP A V,BERNSTEIN D S. On the dynamics of the escapementmechanism of a mechanical clock[C]//Proceeding of the 38th IEEEConference on Decision&Control,December 7-10,1999,Phoe-nix,AZ,USA. New York:IEEE,1999:2599-2604.
[3] FU Y. A study on the dynamics of periodical impact mechanism withan application in mechanical watch escapement[D]. Hong Kong:The Chinese University of Hong Kong,2008:1-142.
[4]茅健,傅裕.机械手表擒纵机构动力学分析与仿真[J].机械科学与技术,2011,30(9):1561-1564,1568.
[5]陈世佳,陈麟,龚翔.机械手表机心擒纵调速机构动力学仿真分析[J].机械传动,2018,42(7):142-146.
[6] HUNT K H,CROSSLEY F R E. Coefficient of restitution interpret-ed as damping in vibroimpac[tJ]. ASME Journal of applied mechan-ics,1975,42(2):440-445.
[7] ROLLAND J,BERRE H W,SAULOT A,et al. Instrumentation ofa contact with the finite element method and experimental coupling:the case of the swiss lever escapement mechanism[J]. Tribology In-ternational,2017,111:176-183.
[8] GIALLONARDO J D,ERB U,AUST K T,et al. The influence ofgrain size and texture on the Young’s modulus of nanocrystallinenickel and nickel-iron alloys[J]. Philosophical Magazine,2011,91(36):4594-4605.
[9]王勖成.有限单元法[M].北京:清华大学出版社,2003:468-522.
[10] TROMAS C,STINVILLE J C,TEMPLIER C,et al. Hardness andelastic modulus gradients in plasma-nitrided 316L polycrystallinestainless steel investigated by nanoindentation tomography[J]. ActaMaterialia,2012,60(5):1965-1973.
[11] FIZANNE-MICHEL C,CORNEN M,CASTANY P,et al. Determi-nation of hardness and elastic modulus inverse pole figures of a poly-crystalline commercially pure titanium by coupling nanoindentationand EBSD techniques[J]. Materials Science&Engineering A,2014,613(8):159-162.
[12] CAZZANI A,ROVATI M. Extrema of Young’s modulus for cubicand transversely isotropic solids[J]. International Journal of Solidsand Structures,2003,40(7):1713-1744.
[13]毛卫民,杨平,陈冷.材料织构分析原理与检测技术[M].北京:冶金工业出版社,2008:1-8.
[14] TURLEY J,SINES G. The anisotropy of Young’s modulus,shearmodulus and Poisson’s ratio in cubic materials[J]. Journal of Phys-ics D:Applied Physics,1971,4(2):264-271.
[15]天津大学精仪系编.机械计时仪器[M].天津:天津科学技术出版社,1980:10-110.
[16]全国钟表标准化中心.机械手表:QB/T 1249-2013[S].北京:中国轻工业出版社,2013:1-15.
[2] ROUP A V,BERNSTEIN D S. On the dynamics of the escapementmechanism of a mechanical clock[C]//Proceeding of the 38th IEEEConference on Decision&Control,December 7-10,1999,Phoe-nix,AZ,USA. New York:IEEE,1999:2599-2604.
[3] FU Y. A study on the dynamics of periodical impact mechanism withan application in mechanical watch escapement[D]. Hong Kong:The Chinese University of Hong Kong,2008:1-142.
[4]茅健,傅裕.机械手表擒纵机构动力学分析与仿真[J].机械科学与技术,2011,30(9):1561-1564,1568.
[5]陈世佳,陈麟,龚翔.机械手表机心擒纵调速机构动力学仿真分析[J].机械传动,2018,42(7):142-146.
[6] HUNT K H,CROSSLEY F R E. Coefficient of restitution interpret-ed as damping in vibroimpac[tJ]. ASME Journal of applied mechan-ics,1975,42(2):440-445.
[7] ROLLAND J,BERRE H W,SAULOT A,et al. Instrumentation ofa contact with the finite element method and experimental coupling:the case of the swiss lever escapement mechanism[J]. Tribology In-ternational,2017,111:176-183.
[8] GIALLONARDO J D,ERB U,AUST K T,et al. The influence ofgrain size and texture on the Young’s modulus of nanocrystallinenickel and nickel-iron alloys[J]. Philosophical Magazine,2011,91(36):4594-4605.
[9]王勖成.有限单元法[M].北京:清华大学出版社,2003:468-522.
[10] TROMAS C,STINVILLE J C,TEMPLIER C,et al. Hardness andelastic modulus gradients in plasma-nitrided 316L polycrystallinestainless steel investigated by nanoindentation tomography[J]. ActaMaterialia,2012,60(5):1965-1973.
[11] FIZANNE-MICHEL C,CORNEN M,CASTANY P,et al. Determi-nation of hardness and elastic modulus inverse pole figures of a poly-crystalline commercially pure titanium by coupling nanoindentationand EBSD techniques[J]. Materials Science&Engineering A,2014,613(8):159-162.
[12] CAZZANI A,ROVATI M. Extrema of Young’s modulus for cubicand transversely isotropic solids[J]. International Journal of Solidsand Structures,2003,40(7):1713-1744.
[13]毛卫民,杨平,陈冷.材料织构分析原理与检测技术[M].北京:冶金工业出版社,2008:1-8.
[14] TURLEY J,SINES G. The anisotropy of Young’s modulus,shearmodulus and Poisson’s ratio in cubic materials[J]. Journal of Phys-ics D:Applied Physics,1971,4(2):264-271.
[15]天津大学精仪系编.机械计时仪器[M].天津:天津科学技术出版社,1980:10-110.
[16]全国钟表标准化中心.机械手表:QB/T 1249-2013[S].北京:中国轻工业出版社,2013:1-15.
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