Response Characteristics of Spring-Mass System under Impact of Momentum Ball
-
摘要: 冲量是爆炸空气冲击波的重要威力参数，基于动量块的测试方法是获取冲量的途径之一。通过开展弹簧-质量块系统在动量球撞击下的响应特性研究，尝试将动量球的动量转换为弹簧的定量压缩位移。研究过程中，选定一种弹簧-质量块组合，通过开展聚甲醛、聚四氟乙烯、铝、钢4种不同动量球撞击试验，获得了弹簧-质量块压缩响应特性和动量转化效率。结果表明，在所试验的测试范围内，弹簧的最大压缩位移与动量球的加载速度线性相关，聚四氟乙烯动量球与弹簧-质量块系统耦合最稳定，适合作为冲击波冲量测试的转换载体。该系统可以为冲击波测量提供一种新方法。Abstract: Impulse is an important power parameter of explosive air shock wave, and the momentum-block test method is one of the ways to measure the impulse. This paper attempts to convert the momentum of the momentum-ball into the quantitative compression displacement of the spring by investigating the impact response characteristics of spring-mass system. Four different momentum-balls impact tests, such as polyformaldehyde, polytetrafluoron, aluminum and steel, were conducted to obtain the spring-mass compression response characteristics and momentum/energy conversion efficiency. The results show that the maximum compression displacement of the spring is linearly related to the loading velocity of the momentum-ball. The polyformaldehyde momentum-ball spring coupling system shows the most stable properties, which is suitable for the transfer carrier of shock wave impulse measurement. This work can provide a new method for shock wave measurement.
-
Key words:
- explosive shock wave /
- momentum block /
- spring-mass system /
- impact stiffness /
- flutter wave
-
图 2 Ptfe球碰撞弹簧-质量块系统全过程和数据处理的标记
Figure 2. Ptfe ball impact spring-mass block system marking the whole process and data processing
图 3 4种动量球撞击弹簧-质量块系统的位移-时间曲线
Figure 3. Displacement-time curves of momentum balls impacting spring-mass system
图 4 动量球碰撞速度与弹簧最大压缩位移的关系
Figure 4. Relationship between loading velocity of momentum balls and maximum compression displacement of the spring
图 5 不同加载速度下4种动量球的动量转化率
Figure 5. Momentum conversion rate of four kinds of momentum balls at different loading velocities
图 9 不同Ptfe球加载速度下质量块位移时程曲线
Figure 9. Displacement-time history diagram of mass block under different loading velocities of Ptfe ball
表 1 动量球参数
Table 1. Parameters of momentum ball
Material Shape Diameter/mm ρ/(g·cm−3) Mass/g Al Sphere 30.02 2.71 38.27 Pom Sphere 30.02 1.35 18.98 Steel Sphere 30.01 7.91 111.71 Ptfe Sphere 29.98 2.20 30.25 
下载: 导出CSV
表 2 弹簧参数
Table 2. Parameters of spring
Material Wire diameter/mm Diameter/mm Height/mm Turns Shear modulus/GPa Mass/g Spring steel 2.20 30 100 10 80 27.85
下载: 导出CSV
表 3 质量块参数
Table 3. Parameters of mass block
Material Shape Diameter/mm Height/mm Mass/g 45 steel Cylinder 30 10 50.50
下载: 导出CSV
表 4 不同工况下的实验结果
Table 4. Experimental results under different working conditions
Material Mass of ball/g Mass of block/g v/(m·s−1) v1/(m·s−1) v2/(m·s−1) x/mm Ptfe 30.25 50.50 3.77 0 2.07 14.30 Ptfe 30.25 50.50 4.36 0 2.13 15.40 Ptfe 30.25 50.50 4.82 0 2.61 16.40 Ptfe 30.25 50.50 5.91 0 2.98 19.60 Ptfe 30.25 50.50 6.64 0 3.33 20.30 Ptfe 30.25 50.50 7.32 0 4.31 24.60 Ptfe 30.28 50.50 10.77 0 6.21 35.45 Ptfe 30.28 50.50 11.92 0 6.61 39.37 Ptfe 30.28 50.50 13.43 0 7.42 44.20 Al 38.26 50.50 4.82 0.25 2.57 15.70 Al 38.26 50.50 7.25 1.47 3.92 22.73 Al 38.35 50.50 7.78 2.04 3.86 23.95 Al 38.35 50.50 8.81 2.72 3.70 28.60 Al 38.32 50.50 9.28 2.40 3.67 28.23 Al 38.32 50.50 9.70 2.62 4.59 29.95 Al 38.32 50.50 10.02 2.93 4.61 32.40 Al 38.32 50.50 11.37 3.35 5.24 34.68 Steel 111.71 50.50 2.67 0.78 3.66 19.80 Steel 111.71 50.50 2.93 0.91 3.88 21.10 Steel 111.71 50.50 3.86 1.26 3.85 25.27 Steel 111.71 50.50 4.86 2.06 6.25 33.30 Steel 111.71 50.50 6.70 2.87 6.55 41.10 Steel 111.71 50.50 7.13 2.74 6.31 44.00 Steel 111.71 50.50 8.42 3.81 9.40 55.30 Steel 111.71 50.50 9.66 4.07 11.10 64.40 Pom 19.07 50.50 4.11 −1.28 2.03 12.37 Pom 19.07 50.50 4.70 −1.74 2.39 13.80 Pom 19.07 50.50 8.36 −3.38 4.41 23.93 Pom 19.07 50.50 9.07 −3.97 4.82 24.20
下载: 导出CSV
表 5 4种动量球动量转化率对比
Table 5. Comparison of momentum conversion rate of four kinds of momentum balls
Material Momentum conversion range/% Average/% Stdev Steel 40.01−61.97 51.77 0.094 Al 26.72−70.24 34.35 0.057 Ptfe 81.56−98.30 90.05 0.057 Pom 97.88−99.51 98.80 0.008
下载: 导出CSV
表 6 4种不同材料动量球加载下弹簧的压缩率
Table 6. Compressibility of the spring under 4 momentum ball loads
Material Loading velocity/(m·s−1) Compression ratio/% Remark Steel 2−13 19−70 A few more than 60% Al 3−13 12−37 Ptfe 3−14 14−45 Pom 3−11 11−25
下载: 导出CSV
-
[1] 赵传荣, 孔德仁. 基于量纲分析的平面冲击波经验模型研究 [J]. 高压物理学报, 2016, 30(6): 526–530. doi: 10.11858/gywlxb.2016.06.014ZHAO C R, KONG D R. Empirical model of plane shock wave on the impact surface of target based on dimensional analysis [J]. Chinese Journal of High Pressure Physics, 2016, 30(6): 526–530. doi: 10.11858/gywlxb.2016.06.014 [2] 孟令存, 闫明, 杜志鹏, 等. 外界条件对中空结构物内爆冲击波的影响 [J]. 高压物理学报, 2020, 34(4): 79–88. doi: 10.11858/gywlxb.20190849MENG L C, YAN M, DU Z P, et al. Influence of external conditions on implosion shock wave of hollow structure [J]. Chinese Journal of High Pressure Physics, 2020, 34(4): 79–88. doi: 10.11858/gywlxb.20190849 [3] 郭炜, 俞统昌, 王建林. 空气冲击波压力的地面测量技术 [C]//第三届全国爆炸力学实验技术交流会. 合肥, 2004: 7.GUO W, YU T C, WANG J L. Surface measurement of air shock wave pressure [C]//The Third National Explosion Mechanics Experiment Technology Exchange Conference. Hefei, 2004: 7 [4] 翟永. 冲击波存储测试系统的同步技术研究 [D]. 太原: 中北大学, 2016: 18−19.ZHAI Y. Research on synchronization technology of stored testing system for shock wave [D]. Taiyuan: North University of China, 2016: 18−19. [5] 叶希洋, 苏健军, 姬建荣. 冲击波测试效应靶法综述 [J]. 兵器装备工程学报, 2019, 40(12): 55−61, 124.YE X Y, SU J J, JI J R. Review of effect target method for shock wave measurement [J]. Journal of Ordnance Equipment Engineering, 2019, 40(12): 55−61, 124. [6] CLOETE T J, NURICK G N, PALMER R N. The deformation and shear failure of peripherally clamped centrally supported blast loaded circular plates [J]. International Journal of Impact Engineering, 2005, 32(1): 92–117. doi: 10.1016/j.ijimpeng.2005.06.002 [7] 仲倩. 燃料空气炸药爆炸参数测量及毁伤效应评估 [D]. 南京: 南京理工大学, 2012: 15.ZHONG Q. Research on measurement of explosion parameters and evaluation of damage effect of fuel air explosive [D]. Nanjing: Nanjing University of Science and Technology, 2012: 15. [8] MANFRED H. Momentum method to measure the blast contour [C]//17th International Symposium on Ballistics. Midrand, South Africa, 1998: 23−27. [9] 李钰钢. 基于动量块的冲击波比冲量测试装置 [D]. 长沙: 国防科技大学, 2021: 50−57.LI Y G. Research on shock wave impulse measurement method based on momentum block [D]. Changsha: National University of Defense Technology, 2021: 50−57. [10] WITTRICK W H. On elastic wave propagation in helical springs [J]. International Journal of Mechanical Sciences, 1966, 8(1): 25–47. doi: 10.1016/0020-7403(66)90061-0 [11] PHILLIPS J W, COSTELLO G A. Large deflections of impacted helical springs [J]. The Journal of the Acoustical Society of America, 1972, 51(3B): 967–973. doi: 10.1121/1.1912946 [12] COSTELLO G A. Radial expansion of impacted helical springs [J]. Journal of Applied Mechanics, 1975, 42(4): 789–792. doi: 10.1115/1.3423707 [13] SINHA S K, COSTELLO G A. The numerical solution of the dynamic response of helical springs [J]. International Journal for Numerical Methods in Engineering, 1978, 12(6): 949–961. doi: 10.1002/nme.1620120607 [14] 赵宗昌, 何水清, 何大同, 等. 螺旋弹簧质量系统动态响应的特征线法[J]. 哈尔滨工程大学学报, 1989(1): 62−73.ZHAO Z C, HE S Q, HE D T, et al. The characteristics method of the dynamic response of the spring-mass systems[J]. Journal of Harbin Shipbuilding Engineering Institute, 1989(1): 62−73. [15] 薛瑞娟, 郭敬彬, 王君, 等. 环形弹簧静刚度与冲击性能有限元分析 [J]. 舰船科学技术, 2018, 40(10): 67–71. doi: 10.3404/j.issn.1672-7649.2018.10.013XUE R J, GUO J B, WANG J, et al. Finite element analysis of static stiffness and shock performance of ring spring [J]. Ship Science and Technology, 2018, 40(10): 67–71. doi: 10.3404/j.issn.1672-7649.2018.10.013 [16] 赵亚敏, 崔俊宁, 邹丽敏, 等. 约束膜式空气弹簧的刚度建模与分析 [J]. 振动与冲击, 2022, 41(1): 60−67, 115.ZHAO Y M, CUI J N, ZOU L M, et al. Stiffness modeling and analysis of constrained membrane air spring [J]. Journal of Vibration and Shock, 2022, 41(1): 60−67, 115. [17] 张英会, 刘辉航, 王德成. 弹簧手册 [M]. 北京: 机械工业出版社, 2017: 389.ZHANG Y H, LIU H H, WANG D C. Spring manual [M]. Beijing: China Machine Press, 2017: 389. [18] 盛宏玉. 结构动力学 [M]. 合肥: 合肥工业大学出版社, 2012: 17−19.SHENG H Y. Structural dynamics [M]. Hefei: Hefei University of Technology Press, 2012: 17−19. -
下载:
点击查看大图
计量
- 文章访问数: 274
- HTML全文浏览量: 110
- PDF下载量: 37
