多股螺旋弹簧绕制成形的若干关键问题研究
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摘要
多股螺旋弹簧(简称多股簧)通常是由2~7股0.5~3mm的碳素弹簧钢丝拧成钢索冷绕卷制而成,分为有中心股和无中心股两种结构形式,其中压缩弹簧的钢索的旋向与弹簧的旋向相反,拉伸弹簧的旋向与弹簧的旋向相同。和普通单股弹簧相比,多股螺旋弹簧具有刚度强度好、吸振减振效果好等独特性能,在汽车仪器仪表减振系统、武器发射系统以及航空发动机等多个领域中都具有重要的应用价值。
到目前为止,已有文献对多股螺旋弹簧的静态响应特性进行了相关研究,而多股螺旋弹簧的优越性能在于弹簧变形时股中钢丝之间和股间钢丝之间的接触摩擦所产生的阻尼效果,这在很大程度上取决于多股螺旋弹簧的成形质量,但还未有针对此方面的研究工作。本文旨在通过对多股螺旋弹簧成形方法的研究,深入多股螺旋弹簧的相关理论研究基础,重点在于多股螺旋弹簧卸载回弹的理论基础、绕制试验和数值模拟的研究,以此指导弹簧的工艺生产,提高弹簧产品的成品质量。
本文主要从以下五个方面对多股螺旋弹簧的成形方法进行了深入、细致的研究和探讨工作:
首先,多股螺旋弹簧的各股钢丝在空间结构上皆为二次螺旋形式,通过空间坐标变换的方法,针对压缩螺旋弹簧和拉伸螺旋弹簧两种类型的弹簧,建立了钢索中各股钢丝中心线和弹簧中各股钢丝中心线的空间曲线数学模型,给出了钢丝螺旋倍数的定义,并用两种方法进行推导,为多股螺旋弹簧的几何微分理论研究建立了数学基础。
其次,现有文献是将多股螺旋弹簧简化为多股普通圆柱螺旋弹簧的并联作用和叠加效果进行研究,而在多股螺旋弹簧在成形过程中,各股钢丝承受了二次弯曲和扭转的复合作用,普通圆柱螺旋弹簧的成形只承受一次弯曲和扭转的复合作用,因此,多股螺旋弹簧的现有简化分析方法不够精确。因此,本文在单股钢丝中心曲线数学模型的研究基础上,基于空间曲线的微分几何理论,建立了钢丝中心线的曲率、挠率等微分表达式,给出与普通圆柱螺旋弹簧的微分参数的分析比较结果。
第三,多股螺旋弹簧的动态性能是研究的热点。基于微分几何原理,推导出了多股螺旋弹簧单股钢丝的曲率和挠率的表达式,分析了压缩和拉伸两种类型的弹簧承受应力的情况。通过有限元仿真分析了多股压缩弹簧承受速度载荷时的簧圈变形情况,股间载荷的分布情况等。在此基础上,分析了单股弹簧和单股钢丝在承载时变形特性,为多股螺旋弹簧的特性分析提供研究基础。
第四,针对三股螺旋弹簧和内层三股外层九股的三种弹簧的绕制成形过程进行了大量的试验,实验过程主要考虑了钢丝加载张力、弹簧螺距、钢索螺距、加载速度和钢丝直径对卸载后弹簧回弹量的影响。对于回弹量的分析主要分为轴向和径向两个方面。
第五,针对螺旋弹簧的绕制试验,采用基于ABAQUS准静态分析模式对弹簧的绕制成形和卸载回弹进行模拟分析。通过钢丝截面和接触下钢丝表面的应力变化情况表面应力情况的仿真分析,研究了钢丝材料的弹塑性变化情况。通过有限元的数值模拟结果与螺旋弹簧的绕制试验结果进行对比表明了有限元方法的有效性。
Stranded wire helical springs (multi-strand spring for short) is a cylindrically helical spring rolled by cable wire, which usually consists of 2 to 7 carbon steel wires of 0.4 to 3 mm in radius. It has two kinds of structures in accordance with whether it has central wire or not. The helix of strand is opposite in direction to that of the coils of helical compressing spring, while trenching spring and the coil spring have the same helical direction. Compared with the conventional single spring, the multi-stranded coil spring has strong rigidity and good effect of absorbing vibration, and therefore it has significant applying perspective in vibration-absorbing systems of the automobile instrumentations, discharge systems of weapons, aero-engine and other fields.
So far, research findings on properties of multi-strand coil spring have been made in static stress strain. However, researches seldom cover the damping effect generated by frictions of strand and wire when the coil spring deforms, which is largely dependent on the number of shares in the formation of coil spring. With widely studies on formation methods and other relative research findings of multi-strand coil spring, the present thesis tentatively concentrates on theory of rebounce by unloaded multi-strand coil spring, helical experiment and numerical simulation, which is expected to guide the production of springs and improve the quality of the finished products.
The present thesis makes efforts to detailed studies on formation of multi-strand coil spring from the following aspects:
Firstly, steel wires of multi-strand coil spring are all in second helical form. Through transformation of space coordinates, mathematical model of curve has been established to explore the space of central line of steel wires in cable and in spring concerning compressing coil spring and trenching coil spring. It also defines multiples of steel wire helix, and applies two deductive methods to establish mathematical foundations for theoretical study of differential geometry of multi-strand coil spring.
Secondly, the existing theory often simplifies multi-stranded coil spring as the parallel and overlay effects of ordinary cylindrical coil spring. Actually, multi-strand coil spring takes a second helix in its formation, while the ordinary cylindrical coil spring only takes one helical rotation. Therefore, the exiting simplified study method is not sufficiently precise. Based on studies of mathematical model of curve for center line of single steel wire and differential geometry of space curve theory, the present thesis gives expressions of curvature and helical ratio of the central line of steel wire as well as differential parameters for comparison with ordinary cylindrical coil spring.
Thirdly, the dynamic performance of multi-strand coil spring is hot issue for study. Based on the principle of differential geometry, the present thesis deduces the expressions of curvature and helical ratio of multi-strand coil spring, and analyzes the stress strains to loads by compressing and trenching springs. It also analyzes deformation of multi-strand coil spring under speed load by finite element simulation method, and distribution of load on strands, etc. On this basis, deformation of loaded single-strand spring and steel wire is studied to provide research foundation for multi-strand coil spring.
Fourthly, a large number of experiments have been made on winding formation of three-strand coil spring and multi-strand coil spring with three-strand interior and nine-strand exterior. Experiments mainly take into consideration elements such as the tension of steel wire, rotation moment of spring and cable, loading speed and wire diameter which have influence on the springback after unloading the spring. The analysis of springback is after axial and radial direction.
Fifthly, the present thesis makes simulative analysis on winding formation and on springback after unloading of coil spring on basis of ABAQUS quasi-static pattern. It studies elastic-plasticity of steel wire through simulative analysis of performance of cross-section and surface loaded. It is proved to be effective by comparison of finite element numerical simulation with experiment result of coil spring winding experiment.
到目前为止,已有文献对多股螺旋弹簧的静态响应特性进行了相关研究,而多股螺旋弹簧的优越性能在于弹簧变形时股中钢丝之间和股间钢丝之间的接触摩擦所产生的阻尼效果,这在很大程度上取决于多股螺旋弹簧的成形质量,但还未有针对此方面的研究工作。本文旨在通过对多股螺旋弹簧成形方法的研究,深入多股螺旋弹簧的相关理论研究基础,重点在于多股螺旋弹簧卸载回弹的理论基础、绕制试验和数值模拟的研究,以此指导弹簧的工艺生产,提高弹簧产品的成品质量。
本文主要从以下五个方面对多股螺旋弹簧的成形方法进行了深入、细致的研究和探讨工作:
首先,多股螺旋弹簧的各股钢丝在空间结构上皆为二次螺旋形式,通过空间坐标变换的方法,针对压缩螺旋弹簧和拉伸螺旋弹簧两种类型的弹簧,建立了钢索中各股钢丝中心线和弹簧中各股钢丝中心线的空间曲线数学模型,给出了钢丝螺旋倍数的定义,并用两种方法进行推导,为多股螺旋弹簧的几何微分理论研究建立了数学基础。
其次,现有文献是将多股螺旋弹簧简化为多股普通圆柱螺旋弹簧的并联作用和叠加效果进行研究,而在多股螺旋弹簧在成形过程中,各股钢丝承受了二次弯曲和扭转的复合作用,普通圆柱螺旋弹簧的成形只承受一次弯曲和扭转的复合作用,因此,多股螺旋弹簧的现有简化分析方法不够精确。因此,本文在单股钢丝中心曲线数学模型的研究基础上,基于空间曲线的微分几何理论,建立了钢丝中心线的曲率、挠率等微分表达式,给出与普通圆柱螺旋弹簧的微分参数的分析比较结果。
第三,多股螺旋弹簧的动态性能是研究的热点。基于微分几何原理,推导出了多股螺旋弹簧单股钢丝的曲率和挠率的表达式,分析了压缩和拉伸两种类型的弹簧承受应力的情况。通过有限元仿真分析了多股压缩弹簧承受速度载荷时的簧圈变形情况,股间载荷的分布情况等。在此基础上,分析了单股弹簧和单股钢丝在承载时变形特性,为多股螺旋弹簧的特性分析提供研究基础。
第四,针对三股螺旋弹簧和内层三股外层九股的三种弹簧的绕制成形过程进行了大量的试验,实验过程主要考虑了钢丝加载张力、弹簧螺距、钢索螺距、加载速度和钢丝直径对卸载后弹簧回弹量的影响。对于回弹量的分析主要分为轴向和径向两个方面。
第五,针对螺旋弹簧的绕制试验,采用基于ABAQUS准静态分析模式对弹簧的绕制成形和卸载回弹进行模拟分析。通过钢丝截面和接触下钢丝表面的应力变化情况表面应力情况的仿真分析,研究了钢丝材料的弹塑性变化情况。通过有限元的数值模拟结果与螺旋弹簧的绕制试验结果进行对比表明了有限元方法的有效性。
Stranded wire helical springs (multi-strand spring for short) is a cylindrically helical spring rolled by cable wire, which usually consists of 2 to 7 carbon steel wires of 0.4 to 3 mm in radius. It has two kinds of structures in accordance with whether it has central wire or not. The helix of strand is opposite in direction to that of the coils of helical compressing spring, while trenching spring and the coil spring have the same helical direction. Compared with the conventional single spring, the multi-stranded coil spring has strong rigidity and good effect of absorbing vibration, and therefore it has significant applying perspective in vibration-absorbing systems of the automobile instrumentations, discharge systems of weapons, aero-engine and other fields.
So far, research findings on properties of multi-strand coil spring have been made in static stress strain. However, researches seldom cover the damping effect generated by frictions of strand and wire when the coil spring deforms, which is largely dependent on the number of shares in the formation of coil spring. With widely studies on formation methods and other relative research findings of multi-strand coil spring, the present thesis tentatively concentrates on theory of rebounce by unloaded multi-strand coil spring, helical experiment and numerical simulation, which is expected to guide the production of springs and improve the quality of the finished products.
The present thesis makes efforts to detailed studies on formation of multi-strand coil spring from the following aspects:
Firstly, steel wires of multi-strand coil spring are all in second helical form. Through transformation of space coordinates, mathematical model of curve has been established to explore the space of central line of steel wires in cable and in spring concerning compressing coil spring and trenching coil spring. It also defines multiples of steel wire helix, and applies two deductive methods to establish mathematical foundations for theoretical study of differential geometry of multi-strand coil spring.
Secondly, the existing theory often simplifies multi-stranded coil spring as the parallel and overlay effects of ordinary cylindrical coil spring. Actually, multi-strand coil spring takes a second helix in its formation, while the ordinary cylindrical coil spring only takes one helical rotation. Therefore, the exiting simplified study method is not sufficiently precise. Based on studies of mathematical model of curve for center line of single steel wire and differential geometry of space curve theory, the present thesis gives expressions of curvature and helical ratio of the central line of steel wire as well as differential parameters for comparison with ordinary cylindrical coil spring.
Thirdly, the dynamic performance of multi-strand coil spring is hot issue for study. Based on the principle of differential geometry, the present thesis deduces the expressions of curvature and helical ratio of multi-strand coil spring, and analyzes the stress strains to loads by compressing and trenching springs. It also analyzes deformation of multi-strand coil spring under speed load by finite element simulation method, and distribution of load on strands, etc. On this basis, deformation of loaded single-strand spring and steel wire is studied to provide research foundation for multi-strand coil spring.
Fourthly, a large number of experiments have been made on winding formation of three-strand coil spring and multi-strand coil spring with three-strand interior and nine-strand exterior. Experiments mainly take into consideration elements such as the tension of steel wire, rotation moment of spring and cable, loading speed and wire diameter which have influence on the springback after unloading the spring. The analysis of springback is after axial and radial direction.
Fifthly, the present thesis makes simulative analysis on winding formation and on springback after unloading of coil spring on basis of ABAQUS quasi-static pattern. It studies elastic-plasticity of steel wire through simulative analysis of performance of cross-section and surface loaded. It is proved to be effective by comparison of finite element numerical simulation with experiment result of coil spring winding experiment.
引文
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