# A Study on Kinematic Analysis of Crank-Type Flying Shear Mechanism for Production-Oriented Design and Motion Control

- 71 Downloads

## Abstract

Flying crank shears are used for the cross-cutting of moving metal in rolling mills and downstream processing lines. Based on many factors including the product quality and knife wear, these machines are considered an excellent choice for cutting flat material of thickness exceeding 3 mm. During the cutting process using these shears, the knife velocity must match that of the material during the cut, making the knife trajectory complex, involving simultaneous translation and rotation. In this study, the model of a crank-type flying shear is developed following the kinematic analysis of its mechanism from the basic principles of multibody dynamics. This model is then used in the numerical simulation of a flying crank shear in cold shearing line, thereby validating for a given production speed, the machine dimensions, the motion control philosophy and prediction of the cut surface quality.

## Keywords

Crank–rocker-type four-bar chain Point-to-point motion control Trapezoidal velocity profile Flatness and squareness error of cut## List of symbols

- \( a_{\text{cl}} \)
Angular acceleration during cutting phase

- \( B \)
Length of knife holder link

- \( {\text{Bu}} \)
Flatness error of cut profile

- \( l_{\text{c}} \)
Length of cut per piece, m

- \( n_{\text{c}} \)
No. of cuts per minute

*t*Time reckoned from the start of cycle, \( t \in [0 \;t_{\text{c}} ] \), s

- \( t_{\text{cl}} \)
Time taken in linear cutting phase

- \( t_{\text{st}} \)
Time taken from end of cutting phase to end of cycle

- \( t_{\delta } \)
Dwell time between cuts

- \( T, \;T_{ \hbox{max} } \)
Strip thickness and maximum allowed strip thickness

- \( t_{\text{c}} \)
Cycle time for a single cut

- \( V_{\text{l}} \)
Line speed, m/min

- \( V_{C} (t) \)
Tangential velocity of the knife cutting point (

*C*)- \( V_{\text{CC}} (t) \)
Component of \( V_{C} \) in the direction of cut (knife penetration)

- \( V_{\text{CM}} (t) \)
Component of \( V_{C} \) in the direction of strip travel

- \( x_{1} (t),\;y_{1} (t) \)
Knife holder instant center coordinates (

*Z*)- \( x_{2} (t),\;y_{2} (t) \)
Coordinates of the pin joint of knife holder and rocker arm (

*R*)- \( x_{3} (t),\;y_{3} (t) \)
Coordinates of the pin joint of knife holder and crank (

*Q*)- \( x_{4} (t),\;y_{4} (t) \)
Knife cutting point coordinates (

*C*)- \( \alpha (t) \)
Crank angular displacement

- \( \alpha_{l1} ,\;\alpha_{l2} \)
Crank angular displacement with linear time–velocity relationship, before and after the end of cut

- \( \alpha_{\text{c}} ,\;\alpha_{\text{cm}} \)
Crank angular displacement during cut for thicknesses \( T \) and \( T_{\hbox{max} } \)

- \( \beta (t) \)
Rocker arm angular displacement

- \( \delta \)
Angle between knife holder link and cutting face

- \( \sigma (t) \)
Angle between the knife cutting face and positive

*X*-axis- \( \theta (t) \)
Angle between \( V_{\text{C}} \) and the positive

*X*-axis*ω*(*t*)Crank angular velocity

- \( \omega_{1} (t) \)
Rocker arm angular velocity

- \( \omega_{2} (t) \)
Knife holder angular velocity about the instant center

- \( \omega_{\text{cs}} ,\;\omega_{\text{cf}} \)
Crank angular velocity at the start and finish of actual cut

- \( \omega_{{{\text{cl}}1}} , \;\omega_{{{\text{cl}}2}} \)
Crank angular velocities at the beginning and end of cutting phase

## References

- 1.H. Malinowski, Finishing lines for hot Strip and plate, SMS Schloemann-Siemag Aktiengesellschaft (1985)Google Scholar
- 2.A.I. Tselikov, V.V. Smirnov,
*Rolling Mills, Chap III*(Pergamon Press, Oxford, 1965)Google Scholar - 3.P. Polukhin, N. Fedosov, A. Korolyov, Y. Matveyev,
*Rolling Mill Practice*(Peace, Moscow, 1964), pp. 314–316Google Scholar - 4.C. Tao, H. Yaping, Z. Jingpeng, Solid modeling and optimization design of crank rocking flying shear. Appl. Mech. Mater.
**608**, 7–13 (2014)Google Scholar - 5.Y.M. Ding, in
*Design and Study on Crank Flying Shear*, https://www.globethesis.com/?t=2181330422471075. Accessed 10 Oct 2018 - 6.
*Kinematics and Blade Clearance Analysis of Crank Rocker Flying Shear*. Chen Jie. www.cnki.com.cn/Article_en/CJFDTOTAL-ZXJX201301012.htm. Accessed 10 Oct 2018 - 7.H. Baruh,
*Analytical Dynamics*(McGraw-Hill, New York, 1999), pp. 200–202Google Scholar - 8.N. Repanich,
*Introduction to Motor Sizing*, pp. 1–3. www.mechatronicscenter.com. Accessed 10 Oct 2018