Response Characteristics of Spring-Mass System under Impact of Momentum Ball
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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.
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Key words:
- explosive shock wave /
- momentum block /
- spring-mass system /
- impact stiffness /
- flutter wave
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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 
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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
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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
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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
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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
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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
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