Journal of Textile Research ›› 2020, Vol. 41 ›› Issue (12): 144-150.doi: 10.13475/j.fzxb.20200401207

• Machinery & Accessories • Previous Articles     Next Articles

Natural frequency characterization based on Euler-Bernoulli beam theory on knitting seamless underwear

DAI Ning, PENG Laihu(), HU Xudong, CUI Ying, ZHONG Yaosen, WANG Yuefeng   

  1. Key Laboratory of Modern Textile Machinery & Technology of Zhejiang Province, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China
  • Received:2020-04-04 Revised:2020-07-29 Online:2020-12-15 Published:2020-12-23
  • Contact: PENG Laihu E-mail:laihup@zstu.edu.cn

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Abstract:

Aiming at the lack of theoretical models of natural frequencies of knitting needles in knitting seamless underwear and the difficulties in capturing needle vibration characteristics during knitting, Euler-Bernoulli beam theory was used to solve the vibration equation of knitting needles in the tangential direction of the cylinder to obtain the mode curve and natural frequency the knitting needle. ANSYS simulation was used to perform the model analysis on 6 needle exit positions on the second clear cam. The theoretical and numerical results are consistent and the relative error in calculating needle natural frequency is below 2.3%. The DIMAX series high-speed camera from German PCO company was used to obtain the lateral vibration curve of the knitting needles when they were forced to move along the triangular arc surface. The experimental results show that the natural frequency characteristics of the knitting needles can be accurately analyzed using the Euler-Bernoulli beam theory. The method of capturing the lateral vibration of the knitting needles involved in the experiment is of reference significance for the experimental research on the vibration characteristics of the knitting needles in circular weft knitting machines.

Key words: knitting needle, knitting process, natural frequency, vibration mode curve, Euler-Bernoulli beam theory, ANSYS simulation

CLC Number: 

  • TS103.7

Fig.1

Plane sketch of seamless underwear machine cylinder"

Fig.2

Constraint of needle in cylinder (a) and its cantilever (b) model"

Tab.1

Theoretical value of first order natural frequency of 6 needle positions"

出针长度/mm 27 28 29 30 31 32
第1阶频率/Hz 508 472 440 411 385 361

Fig.3

First third-order mode curves of needle"

Fig.4

Diagram of knitting needle simulation constraint. (a) Constraint from needle groove inner wall left side; (b) Constraint from needle groove inner wall right side; (c) Spring coil constraint; (d) Constraint from needle groove inner wall back side"

Fig.5

Diagram of knitting needle simulation mode result. (a) First-order mode; (b) Second-order mode; (c) Third-order mode"

Tab.2

Comparison of calculation results between simulation and numerical analysis"

组别
编号		 伸出长
度/mm		 数值分析
频率/Hz		 仿真计算
频率/Hz		 偏差/
Hz		 相对偏
差/%
1 27 508.1 517.4 9.3 1.8
2 28 472.5 480.6 8.1 1.7
3 29 440.5 450.9 10.4 2.3
4 30 411.6 421.1 9.5 2.3
5 31 385.5 392.2 6.7 1.7
6 32 361.7 367.0 5.3 1.4

Fig.6

Test platform for knitting needle vibration characteristics. (a) Knitting needle marking diagram; (b) Test platform physical map"

Fig.7

Shooting screen of high-speed camera. (a) Movement track of knitting needle; (b) Free attenuation oscillation process of knitting needle"

Fig.8

Vibration characteristics of knitting needles at high and low positions. (a) Time domain plot at high position; (b) Frequency domain plot at high position; (c) Frequency domain plot at low position"

Fig.9

Vibration characteristics of knitting needles moving along cam track surface. (a) Displacement curve; (b) Vibration time domain curve; (c) Vibration frequency domain curve"

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