the tube being straightened, and affects the product quality.    
Therefore, it is an urgent problem that needs to be solved
currently to establish a calculation system for straightening
force which is accurate and in conformity with real
production. From an overview both at home and abroad, in
1978, MASIJILIEXUN[1]
 of former Soviet Union proposed
the straightening theory for tube material and round
material in “tube straightening machine”, and first
published the method for determining the basic calculating
parameters comprising force and energy parameters and the
design method of all forms of roller shape of straightening
machines. In 1981, GAILAIKE[2]
 of former Soviet Union
proposed a simple computing method for torque in oblique
roller straightening machine. In 1987, CUI[3]
 first
domestically mentioned calculation system for
straightening force in “Straightening theory and parameter
calculation”. In 1995, LI, et al[4]
, has the same basic idea
with Ref. [3], and it increased the flattening force by 32%,
and added temperature influence coefficient and offset load
compaction coefficient. In 2005, CUI
[5]
 has improved the calculation system for straightening force in Ref. [3] to
increase the flattening force by 144% in “straightening
theory and straightening machine” .
In this research, a new calculating system for the
straightening force is established based on the analysis of
roller-shaped curve, flattening straightening force and bend
straightening force with the application of materials
mechanics and curved beam theory.   
2  Traditional Straightening Force Calculation System
 The calculation system for straightening force in the
six-rollers straightening machine was first domestically
mentioned in Ref. [3], which was based on the idea that the
flattening calculation formula can be deduced from the
stress of the beam described in materials mechanics and the
elastic strain energy of the ring. The basic idea is expressed
as follows: taking a tube ring from the compaction domain
(Fig. 1, Fig. 2), and then separating one-fourth from the
obtained tube ring. Suppose the radius of tube is  R, the
flattening force is F'2, the shearing force  q applied on the
cross-section of the ring is uniformly distributed, and
whose magnitude is  Where b  is the contact length of the tube and the pressed
roller 2′ (mm); R is the external radius of tube (mm);  M is
the plastic bending ratio,M =1.2–1.3 for the straightening
tubes;  Lc  is the length of the contact area(mm),
c cos , Lb α = α is the inclination angle between the central
line of the tube to be straightened and the axis of the
straightening roller;
s
σ is the yield limit of the tube (MPa);
p is the roller distance between rollers;  Mt is the elastic
limit bending moment for the tube (N•mm), and
 
When the traditional straightening force calculating
system was initially established, the shape for the
straightening rollers was designed as hyperbola; therefore,
the contact length between the tube and the straightening
roller is small, which is only 0.1–0.2 times of the length of
the roller. Therefore, when the pressing force applied to the
tube by the upper and lower roller was analyzed, it was
usually considered as centralized force. The new system for
calculating the straightening force is bases on envelope
method of the roller shape that was designed under the
condition that the tube and the roller body are in ideally full
contact, so that the contact length between the tube and the 矫直力的计算体系创新英文文献和翻译(2):http://www.751com.cn/fanyi/lunwen_6191.html