Abstract
Problem Statement (Relevance): This paper deals with a problem of building a smooth curve connecting the beginning and the end of the gauge idle zone under pre-defined initial conditions. Theoretically, there can be an unlimited number of ways to connect the two points. Elementary functions, which have their inflection point in the idle zone, offer the easiest ways of building such a curve. The relevance of this paper includes improved kinematics of a machine-tool used for gauge treatment, which is subject to the greatest load when passing the inflection point. Objectives: The objectives of this work include a minimized derivative of the selected function in the inflection point and minimizing the greatest value of the function when it approaches the point where the working area starts. Methods Applied: This paper is based on mathematical methods, including the iteration method applied for calculating the parameters of the target curve. The paper is also based on the Lipсhitz theorem stating that this problem can only have one unique solution. Cosinusoid was chosen for the target curve. The second curve that connects the points concerned is a cubic parabola. The paper looks at the maximum velocity with which the function increases in the idle zone, which sees its greatest load when the cam moves in the LZ-250 machine, as well as at the peak points of both curves in the idle zone. Findings: Following the findings and the results of numerical experiments, the authors finally chose to use the cubic parabola, as it has a lower maximum value compared with the cosinusoid and a lower value of the derivative function in the inflection point. This appears to be the first research effort that was based on a concrete function and a minimized load present in the idle zone in a gauge treatment operation. The method of calculating the idle zone gauge by connecting the working area start and end points in the form of a parabola under relevant initial conditions, has found a successful application in the LZ-250 machine installed at Krasnoyarsk Metallurgical Works. Practical Relevance: The practical relevance of this paper includes an extended life of costly machinery, i.e. the LZ-250 machine in this case.
Keywords
Pipe, cold rolling of pipes, gauge idle zone, cosinusoid, parabola, calculation, LZ-250 machine.
1. Kurmachev Yu.F., Skomoroshchenko S.I., Shamraev V.N. Metodika proektirovaniya i izgotovleniya ruchia kalibrov stanov KhPT. Tekhnologicheskaya rekomendatsiya [The method of designing and manufacturing die grooves for cold pipe mills. Technical recommendations]. Moscow: VILS, 1985, 31 p. (In Russ.)
2. Petrakov Yu.V., Pasechnik V.A., Martynov N.A. Designing CNC machine tool paths for the cold pipe mill groove grinding operation. Vostochno-evropeyskiy zhurnal peredovykh tekhnologiy [Eastern European journal of advanced technology]. 2008, no. 36.
3. Volkov E.A. Chislennye metody [Numerical methods]. Moscow: Nauka, 1982, 254 p. (In Russ.)
4. D'yachenko V.F. Osnovnye ponyatiya vychislitelnoy matematiki [Basic concepts of numerical mathematics]. M.: Nauka, 1977, 126 p. (In Russ.)
5. Yuri F. Kurmachev, Ruslan E. Sokolov, Denis S. Voroshilov, Vadim M. Bespalov, Vladimir V. Moscvichev. The analytical dependence of the filling billets value to a given relative degree of deformation during cold rolling of tubes. Journal of Siberian Federal University. 2012 5(7), pp. 731–736.
6. Orlov G.A. Ways of optimising cold pipe mill tool calibration. Stal’ [Steel], no. 12, 2004, pp. 83–85. (In Russ.)
7. Teterin P.K. Teoriya periodicheskoy prokatki [The theory of cold pilger mill technology]. Moscow: Metallurgiya, 1978. (In Russ.)
8. Osada Ya.E. Osnovnye voprosy kholodnoy prokatki trub: Avtoref. dissertatsii kand. tekhn. nauk [The fundamental problems of cold pipe mill technology. Extended abstract of Ph.D. dissertation]. Dnepropetrovsk; Moscow: 1947. (In Russ.)
9. Tselikov A.I., Grishkov A.I. Teoriya prokatki [The theory of rolling]. Moscow: Metallurgiya, 1970. (In Russ.)
10. Gubkin S.I. Plasticheskaya deformatsiya metallov [Plastic deformation of metals]. Moscow: Metallurgizdat, 1961. (In Russ.)