二辊矫直机理论

Theory of Straightening on Two Roll Bar Straighteners
关于二辊棒材矫直机的矫直理论
Bars are straightened on a two roll straightening machine by bending the bar beyond its yield point and at the same time rotating it. The bending is carried out across the horns of the concave roll.
在二辊矫直机上棒材得到矫直，是靠将棒材超过其屈服强度下进行弯曲，并同时将其旋转。

在棒材通过凹辊的两个喇叭口处时，对其进行弯曲。

Consider the simplified case of ‘point’ support and application of loads.
按简化的“点”支承和施加载荷考虑。

W = Straightening Load 矫直力
L = Bending Centres 弯曲中心距
≈ Profile Length 辊身曲线长度
From bending theory 按弯曲理论 M = s I y
Where 式中:-
M = Bending Moment 弯矩
= W .x L
2 2
= W.L / 4
I = 2nd Moment of area of bar being straightened 被矫直棒材面积的第二个弯矩
= p.D 4 / 64 where 其中 D = bar diameter.棒材直径
s = Stress induced in section of bar material being considered. 所计算的棒材断面上承受的应力 y = Distance from neutral axis to point of bar being considered. 所计算的棒材上一点到中心轴线的距离
施加在棒材上的弯矩
Stress distribution through bar, s max ≤ bar material yield strength
通过棒材的应力分布，s max ≤ 棒材屈服强度
In order to straighten the bar, sufficient bending moment must be applied to yield the bar some way below the surface. The depth of material subject to yielding must be sufficient for the outer straightened portion of the bar to overcome the unstraightened inner portion. In practice it is found that if the calculated stress induced at the surface of the bar is 1.3 times the material yield strength s y then the required straightening effect is achieved.
为了矫直棒材，必须施加足够的弯矩，以使棒材表面以下在某种程度上得到屈服变形。

棒材外层被矫直部分达到材料屈服的深度必须足以用于抑制芯部未矫直的部分，事实发现，如果施加在棒材表面的计算应力为其材料屈服强度s y 的1.3倍，才能达到所需的矫直效果。

The maximum stress is induced in the outer fibres of the bar. 施加棒材外表的最大应力，即： i.e. y = D/2
Shaded area has been subject stress reversals greater material yield. Un-shaded remains un-straightened. 棒材 中心线
棒材 中心线
Therefore 所以： W x L x 64
= s y x 1.3
4 p x D 4
D/2
W = s y x 1.3 x 4 x p x D 4 x 2
L x 64 x D
=
s y x D 3
1.96 x L
The straightening load produces a deflection in the bar being straightened, the deflection can be calculated as follows
矫直载荷使棒材在矫直时产生挠度，挠度可计算如下:-
d = W x L 3 48 x E x I
=
s y x D 3 x L 3 x 64
1.96 x L x 48 x E x p x D 4
=
s y x L 2
4.62 x E x D
From the above it can be seen that the deflection required to induce sufficient stress to straighten the bar is proportional to the yield strength of the bar material and inversely proportional to the diameter of the bar.
从上面计算可看出，对被矫直的棒材所承受使其变形的足够应力与棒材材料屈服强度成正比，而与棒材直径成反比。

The deflection required to straighten a bar is obtained by the bottom (convex) work roll bending the bar over the horns of the top (concave) work roll. The angle that the top work roll is set at determines the maximum amount of deflection that can be applied.
被矫直棒材所需的变形靠下工作辊(凸形)与上辊(凹形)形成的弯曲获得，上辊设定的角度决定其能施加变形的最大值。

Effect of Top Work Roll Angle on Deflection Applied to Bar 上辊角度对棒材变形的影响
Effective shape of Top Work Roll
on Centre Line of Bar at Various Roll Angles. 在不同辊子角度时，沿棒材中心线，上辊的有效形状
The above shows that as the top roll angle is increased, the deflection that can be applied
to the bar over the horns is reduced.
上图所示当上辊角度增加，沿喇叭形施加在棒材上变形减小。

Effect of Bottom Work Roll Angle 下工作辊角度的影响
The effective shape of the bottom work roll is also affected by the angle at which it is set. 下辊的有效形状也被其设定角度所影响。

Effective shape of Bottom Work Roll
on Centre Line of Bar at Various Roll Angles. 在不同辊子角度时，沿棒材中心线，下辊的有效形状
实际辊子曲线 (辊子角度为0º)
辊子角度为10º 辊子角度为20º
实际辊子曲线
(辊子角度为0º)
辊子角度为10º
辊子角度 为20º
Top Roll Angle and Vertical Adjustment Setting上辊角度及垂直调整设定
The deflection required to straighten a bar is achieved by a combination of the setting of the top roll angle and the height of the top roll, which regulates the gap between rolls.
矫直棒材所需的变形通过上辊角度和上辊高度(调整两辊之间的辊缝)设定的组合而实现。

The setting of the top roll angle determines the potential maximum amount of deflection that can be applied to a bar, but the amount of deflection that is actually applied can vary from zero up to this maximum by different vertical adjustment of the top roll.
上辊角度的设定决定了潜在的可施加给棒材的最大变形，但实际施加的变形可通过调整上辊的垂直位置，从零到最大，
The two diagrams below show two different combinations of setting that achieve the same magnitude of deflection to the bar. In both cases the diameter of the bar is relatively large compared to the capacity of the machine, although a similar situation would apply to smaller bar diameters.
下面的两个图显示了实现同样棒材挠度所做的两种不同设定的组合。

在两种情况下，棒材直径相对矫直机能力都显得比较大，尽管类似情景对小棒材同样适用。

In Figure 1 the top roll angle is small and the vertical adjustment such that the roll gap is considerably larger than the bar diameter. The deflection may be sufficient to straighten the bar, but this is not a good setting. The small length of contact between the bar and top roll, (localised at the roll horns) results in high contact stress and wear to the rolls and potential scroll marking of the product.
图1中上辊角度小，而垂直辊缝的比棒材直径大得多，对矫直棒材，挠度可能够，但这不是好的设定，棒材与上辊之间的接触长度小(集中在辊子两个喇叭口处)，导致高的接触应力和对辊子的高磨损，以及潜在的对产品的螺旋压痕。

Figure 1.图1.
Figure 2 shows a better combination of angle and vertical adjustment. The top roll angle is smaller and the gap reduced to be just larger than the bar diameter. The contact length on the top roll is longer, reducing the contact pressure and danger of scroll marking the product.
图2所示为角度及垂直调整比较好的组合，上辊角度较小，辊缝减小到刚好比棒材直径大一点，上辊的接触长度较长，较小了接触压强，和对产品产生的螺旋压痕的危险。

Figure 2图2
Bottom Roll Angle Setting下辊角度设定
The setting of the bottom work roll angle is less critical in achieving good straightness, in fact it would be possible to achieve acceptable results for most bars with the roll angle fixed near to 20º. However for optimum surface condition of the straightened bars the angle of the bottom roll should be reduced to follow the path of the bar. This means for bars requiring less deflection the bottom roll angle should be smaller.
对达到好的直线度来说，下工作辊的设定不是那么关键，事实上，将辊子角度固定在接近20º，可能对绝大多数棒材都能达到可以接受的结果。

然而，被矫直棒材的表面状况，下辊角度应随着棒材通过路径而减小，这意味着棒材需要挠度越小，辊子角度越小。

Care should be taken to avoid too small a bottom roll angle for any particular top roll angle, in which case a pinch condition can occur near the top roll horns. This gives little straightening effect, produces badly marked bars and can result in spalling damage to the work rolls.
对任何一种上辊角度，都应当特别注意避免太小的下辊角度，因为那种情况容易在上辊喇叭口处可能发生卡钢。

这会对矫直有一点影响，但在棒材上留下压痕，导致工作辊破裂。

Guide Bar Setting导板设定
For correct straightness it is important that the guide
bars are set equally about the machine centre line
and are adjusted correctly as wear occurs.
为了得到好的直线度，导板对矫直机中心线等距离设
定和磨损后正确地调整非常重要。

The following diagram shows how opposite ends of
the guide bars are loaded, the guide bars wear most
where the contact load is highest. As wear occurs
the guide bar should be adjusted in towards the bar,
this will ensure the bar continues to take the correct
path through the centre line of the machine.
下面图示显示导板两端的荷载情况，导板在载荷最大
处磨损最大，磨损发生后，应当将导板向棒材方向调
整，这将确保棒材连续按正确的路径通过矫直机中心
线。

If the guide bar wear is not compensated the bar will
start to take an angled path through the machine,
reducing the potential amount of deflection available
into the top work roll and resulting in poor
straightness.
如果导板磨损不能得到补偿，
棒材将开始按照一个有角度的
路径通过矫直机，这就使棒材
在减少了可用的潜在挠度量情
况下进入上辊，并且导致较差
的直线度。