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    Abstract: Currently in China, the computing system of the straightening force of the six-rollers straightening machine generally follows
    the traditional computing system. The force status of the traditional computing system for the straightening force deviates far away from
    the actual force status of the roller system in the six-rollers straightening machine. In the traditional system, the computing model of the
    straightening force of the six-roller straightening machine was based on the roller shape of hyperbola, which led to the length of the
    contacting line between the tube and the straightening roller to be excessively short, i.e., only 0.1–0.2 of the length of the roller. Thus
    the constructed computing system has relatively large difference from the actual measured result. To solve the above problems,
    flattening straightening and bend straightening are analyzed on the basis of materials mechanics and bend beam theory, the roller shape
    using the envelope method of  А.И.Целиков is generated, and a new computing system for straightening force in six-rollers
    straightening machine is built. The roller  shape of the straightening roller, on which the new computing system for the straightening
    force is based, is designed according to  the envelope method under the condition of ideally full contacting between the tube and the
    roller body of the straightening roller, therefore the new computing model accords with the practical status of straightening force.
    According to the comparison of the new computing system with finite element method and the actual measured result of straightening
    force, it has been proved that the computation accuracy of the new computing system  for straightening force satisfies the practical
    requirements of engineering. New six-rollers straightening machines are designed and manufactured according to the new calculation
    system, and the new machines not only have higher precision and quality, but also have adopted the force sensor and computer and
    combined with the new computing system for straightening force to realize the fully automatic adjustment of the straightening machine.
    The new six rollers straightening machine have obtained notable economical and social benefits.8010
     Key words: straightening, roller shape curve, flattening, bend, finite element analysis
      1  Introduction
    Tube straightening machine is the finishing device for
    straightening steel tubes. When straightening, the
    straightening force has a great influence on the quality and
    precision of the straightening steel tubes. Since the quality
    of straightening device currently at home is quite different,
    some theoretical problems are obscure, and the traditional
    model for calculating straightening force is too
    conservative, it results in that products of high quality are
    not able to be manufactured, especially in that straightening
    waste products are often produced and thus normal
    production are directly affected for some old or small
    factories.
    In the old straightening machine, many roller-shaped
    curves are hyperbola, which is proved to be flawed in
    practice and theory. Hyperbola is applicable for small
    straightening range, but its contact line is very short and
    contact stress is high, therefore, when the inclination angle
    for the straightening roller is big, two short contact lines are                                                                   
    formed when the tube being straightened contacts with the
    straightening roller, which leaves two obvious impress on
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