VIII 
轧制过程模拟经验公式模拟 





编号 
项目名称 
项目介绍 
客户 
63 
摩根轧制力计算程序检查以找出弱点 
Requested by Morgan [摩根]’s top management to examine [检查] the force [轧制力]
prediction [轧制力预报] procedure [预报方式]. Attention was also focused to examine [检查]
the algorithm [算法] and Material [材料] data [数据] used for Morgan [摩根]’s roll [轧辊]
pass [道次] program [孔型设计程序] CAPE. It was found that the procedure [程续] used at
the time was only valid for the strain [应变] rate [应变速度] below 100/s, while the
actual rolling [轧制] process [轧制过程] had a strain [应变] rate [应变速度] up to 3000/s. 
Morgan 
64 
摩根实验室轧机五年轧制试验的数据分析 
[数据] was collected in a fiveyear lab mill [试验轧机] test [试验], during
which about 1000 sample [试样] were rolled [轧后]. For each rolled [轧后] piece, over
70 Parameter [参数], including free radius, cross section [断面] area, forward slip
[前滑], etc. were measured [测量] or calculated. It was one of the primary data [数据]
sources to develop rolling [轧制] process [轧制过程] model [模型]. However, due to
certain weaknesses in the experiment design and limited [有限的] understanding of
rolling [轧制] process [轧制过程], the prior engineers who designed the tests [试验] had
difficulty deriving Mean [平均]ful model [模型] from such largescale rolling [轧制]
tests [试验]. In the new work the missing parts were added from other data [数据]
sources (e.g., those from 15year rolling [轧制] tests [试验] from the institute in
Germany, in a fourstand [四机架] highspeed [高速] continuous mill [连续轧机]), to make
the data [数据] fully useful. 
Morgan 
65 
宽展模型开发，尤其针对高速轧制 
The existing Shinokura formula [公式] used in Morgan [摩根]’s computer aided
design was expanded to add more influence factor [影响系数]. Various spread [宽展]
prediction [预报] procedure [预报方式], such as Hensel, Wusatowski, etc. were studied
and verified [验证]/modified [修改] based on the large amount of experiment data
[数据]. spread [宽展] procedure [程续] were later also verified [验证] by the field data
[现场数据] collected from the NoTwist Mill [无扭轧机] (e.g. ASW mill), etc. 
Morgan 
66 
兼适用于低速和高速轧机的准确的流变应力模型开发 
Traditional flow stress [流变应力] model [模型] were verified [验证] and improved
with the flow stress [流变应力] data [数据] I collected worldwide, and with mill
results and especially field data [现场数据]. To fit high speed [速度] mill,
traditional model [模型] (valid up to the strain [应变] rate [应变速度] 100/s) were
extended to including the temperature [温度]/strain [应变] rate [应变速度] interactive
[相互关联] factor to allow it to be valid up to the strain [应变] rate [应变速度] 500/s
and can be roughly used for the highspeed [高速] rolling [轧制] up to the strain
[应变] rate [应变速度] 3000/s (100m/s). This is the nearest approach to the highest
rolling [轧制]. Neither formula [公式] is available nor the flow stress [流变应力]
measurable in the range of 3000/s with constant strain [应变] rate [应变速度] values.
flow stress [流变应力] model [模型] for major Grade [钢种] groups and key Grade [钢种]
were determined based on the new formula [公式]. 
Morgan 
67 
为圆椭圆和椭圆圆道次开发的经验宽展估算模型 
This was the direct modeling [模拟] of the spread [宽展] based on Morgan [摩根]’s
lab mill [试验轧机] data [数据]. model [模型] can be used for the first assessment [预估]
of the roll [轧辊] pass [道次] because it does not need so much geometry [几何形状]
calculation [几何形状计算] as Shinokura formula [公式] does. Some colleagues did roll
[轧辊] pass [道次] design [孔型设计] with ΔB = k ΔH to estimate width spread [宽展] from a
height reduction [压下率], with k ~ 0.33 for OVRD [椭圆圆] and k ~ 0.6 for RDOV
[圆椭圆]. Therefore, I developed [开发] a simple formula [公式] to determine value of
the k by considering several key parameters [主要参数]. 
Morgan 
68 
钢轧钢厂轧制力模型开发，与平均流变应力，接触面积和形状因子的研究 
Roll 轧辊] separating force
[轧制力] during rolling [轧制] actually depends on three primary factors [因素]: the
Mean [平均] flow stress [流变应力], the projective contact area [接触面积] [投射接触面积] and
the shape [形状] factor [形状系数Q]. Mean [平均] flow stress [流变应力] depends on Material
[材料] only (including deformation [变形] history), and the shape [形状] factor
[形状系数Q] is affected by the strain [应变] state [应变状态] and stress state [应力状态] in
the deformation [变形] zone [变形区]. Accurate prediction [预报] of the rolling [轧制]
force [轧制力] requires that all those three factors [因素] be accurately modeled
[建模], which was one of my primary areas of the rolling [轧制] process [轧制过程]
modeling [轧制过程模拟]. I also studied various force [轧制力] prediction [轧制力预报]
procedure [预报方式] for flat rolling [平棍轧制] [平辊轧制], which lead to only different
shape [形状] factor [形状系数Q] Formulas [公式]. 
Morgan 
69 
接触面积的预测模型开发以求准确预测轧制力，特别是对型钢轧制 
The shapes [形状] of the contact area [接触面积] for various rolling [轧制] process
[轧制过程] [轧制过程] are complicated and are different in various pass [道次] sequence
[道次系列]. Mathematical 项目介绍 of the actual shape [形状] and the projective
contact area [接触面积] [投射接触面积] is critical [严峻] for accurate force [轧制力]
prediction [轧制力预报]. contact area [接触面积] model [模型] for various pass [道次]
sequence [道次系列], such as RDOV [圆椭圆], OVRD [椭圆圆], SQOV [方椭圆], OVSQ [椭圆方],
etc., were developed [开发] with the formulation [公式表述] of the actual shapes [形状]. 
Morgan 
70 
形状因子预测模型开发以求精确预测轧制力 
Actual modeling [模拟] for the shape [形状] factor [形状系数Q] needs to consider
friction [摩擦] condition [摩擦状况] and groove [孔型] geometry [孔型几何尺寸]. My modeling
[模拟] for the shape [形状] factor [形状系数Q] started from an universal formula [公式]
that covers all the pass [道次] sequence [道次系列], created by some German colleagues
based on the tens years of measurement [测量] and modeling [模拟]. With rich
experience results [试验结果] and mill field data [现场数据] at hand, I did verification
[验证], modification [修改] and simplification, so I established accurate model [模型]
for RDOV [圆椭圆], OVRD [椭圆圆], RDRD (For Morgan [摩根] Sizing Mills [定径机]), SQOV
[方椭圆], OVSQ [椭圆方], etc. The model [模型] fit both the low speed [速度] rolling
[轧制] and high speed [速度] rolling [轧制]. 

71 
为低速和高速轧制的圆椭圆和椭圆圆道次进行的前滑模型开发 
Neutral angle [中性角] model [模型] for RDOV [圆椭圆] and OVRD [椭圆圆] were
established based on the lab mill [试验轧机] data [数据] and followed by necessary
modification [修改]. On the basis, the forward slip [前滑] were calculated with
Wusatowski procedure [程续]. predicted [预报的] result fits excellently with the
field measurement [现场测试] from ASW NTM, etc. 
Morgan 
72 
轧钢厂摩擦模型的开发以改进摩根的设计过程 
The model [模型] considers factors [因素] such as type of groove [孔型],
temperature [温度], speed [速度], steel grade [钢种], etc. As effects of temperature
[温度] and steel grade [钢种], the metallurgical [金属学] constituent [金属学构成] of the
scale and its property [性能] were also studied. 
Morgan 
73 
精确的温度预报模型和热传递系数模型的开发 
The model [模型] is based on the energy balance [能量平衡] between the stock [轧件]
and rolls [辊]. Heat transfer coefficient [热传递系数] were based on the past
measurement [测量] in various researches. Thermal properties [热性能参数] were all in
temperature [温度] dependence [随温度变化的]. 
Morgan 
74 
ASW 无扭轧机数据处理和模型验证 
Processed [处理过的] ASW
data [数据] pass [道次] by pass [逐道次的]; used the model [模型] I had developed [开发] to
repredict [再预报] the measured [测量] data [数据] and so, to verify [验证] and improve
the developed [开发] models [开发的模型]. 
Morgan 
75 
对钢铁的热轧过程微观结构模型开发以预测再结晶，晶粒尺寸等 
The model [模型] was developed [开发] by combining the major model [模型] (both
Formulas [公式] and data [数据]) published worldwide. Quite a portion of my $10,000
research funds was spent for acquiring publication [发行物]. The model [模型]
consists of the submodel [子模型] to determine: (1) strain [应变] or time, for start
and 50% completion of the dynamic [动态] and static [静态] recrystallizations
[静态再结晶]; each of those may consist of two or more ways of prediction [预报]; (2)
volume fraction [体积分数] of, and grain size [晶粒尺寸] after, the dynamic [动态]al and
static [静态] recrystallizations [静态再结晶]; and (3) grain growth [晶粒长大], equivalent
[当量] grain size [晶粒尺寸] at the start and end of a pass [道次], and the equivalent
[当量] interpass [道次间隙] time [道次间隙时间] under temperature [温度] modification [修改].
Over 10 Formulas [公式] and overt 30 coefficient [系数] were used to describe the
model [模型] of a steel grade [钢种]. Microstructural model [微观组织模型] for over 10
steel grade [钢种] were collected. model [模型] were examine [检查]d with data [数据]
collected from publication [发行物]. 
Morgan 
76 
张力对宽展, 前滑和轧制力修正模型 的开发 
Tension [张力] correction
[张力修正] to spread [宽展] and forward slip [前滑] is critical [严峻] for roll [轧辊] pass
[道次] study of existing NoTwist Mill [无扭轧机] (NTM) because all stands are tied
(driven [驱动] by a single motor [马达]) and it is very hard to avoid tension [张力].
Without this correction, any field data [现场数据] from the NTM would not lead to
any Mean [平均]ful model [模型]. In the Development [开发], German results were
accepted but Japanese formula [公式] (definition of tension [张力定义] and tension
[张力] correction [张力修正] Formulas [公式]) were used. However, Japanese results,
which were based on products of larger size, didn’t fit the NTM data [数据] and
thus were filtered [过滤] out. 
Morgan 
77 
关于机架间张力确定的开发 
The Development [开发] involved the definition of tension [张力定义]. Many German
results on tension [张力] effects [张力效果] were based on the definition of tension
[张力定义] as the relative difference of the speed [速度]. The actual tension [张力],
calculated from the specially modified [修改] flow stress [流变应力] model [模型] was
used (even the best flow stress [流变应力] formula [公式] available still doesn’t work
for a small strain [应变] below 0.05). 
Morgan 
78 
轧件轧后与辊非接触区轮廓形状的模型开发 
The free contour [与辊非接触区轮廓] was modeled [建模] based on the measurement [测量] in
Morgan [摩根]’s lab mill [试验轧机] data [数据]. This model [模型] was used for accurate
calculation [精确计算] of the rolled [轧后] crosssection [横断面] area [横断面积]. 
Morgan 
79 
流变应力模拟程序以基于流变应力基础数据库产生流变应力模型 
The program accesses database [数据库] to read in the flow stress [流变应力] in
various strain [应变], strain [应变] rate [应变速度] and temperature [温度], and
calculates flow stress [流变应力] coefficient [流变应力系数] for temperature [温度], strain
[应变] and strain [应变] rate [应变速度]. The calculation was based on various criteria
[准则]. See www.metalpass [金通].com/bli/L2Net/FSmodel [模型].htm. The program
determines factors [因素] m1 to m5 and A1 to A3, and Kf0, through both linear [线性]
and nonlinear [非线性] regression [回归]. It also allow user to select special needs
for modeling [模拟], such as minmidmax, best peak strain [应力最大值应变], best
Rsquare [R平方准则], etc. 
Metal Pass 
80 
从工作告，出版物等对轧钢厂实验结果广泛的数据收集，数据结果存储于数据库中 
Mill test [试验] results on rolling [轧制] and controlled [控制] cooling [控制冷却],
collected in past years as published or unpublished [没发表的] reports, published
papers, books, Ph.D. dissertations, etc., were processed [处理过的] and stored in
the relational database [数据库]. Great portions of the data [数据] were roll [轧辊]
pass [道次] related measurement [测量], force [轧制力] measurement [测量], controlled
[控制] cooling [控制冷却] data [数据], rolled [轧后] product properties [轧后产品性能] and a
portion of the microstructure [微观组织] data [数据]. Further data [数据] would be added
into the database [数据库]. 
Metal Pass 
81 
约2000个钢种的流变应力数据的收集 
Flow stress [流变应力] data [数据]
and model [模型] were collected from various available sources. Currently about
2000 model [模型] are available on the web. Other data [数据], another 2000 sets,
et., would soon be processed [处理过的] and uploaded [上载]. 
Metal Pass 
82 
坐标测量工具以读取曲线（如流变应力曲线）数据 
This application was initial [初始]ly developed [开发] to measure [测量] flow
stress [流变应力] from flow stress [流变应力] curves [曲线]. The scanned [扫描的] picture
with the curves [曲线] is to be measured [测量] for coordinate [坐标]. Mouse clicking
is made against the points on the existing curve [曲线] to draw another curve
[曲线], in order to make sure the clicking is not off the line. For every click,
the coordinate [坐标] is recorded. The coordinate [坐标] is immediate calculated
into the physical value based on an initial [初始] setup against the coordinate
[坐标] system [坐标系] in the picture. The value from every click is displayed on the
form for doublechecking. When the Submit button is clicked, the data [数据] is
sent to the database [数据库]. 
Metal Pass 
83 
对金属性能的数据清单汇编（约3000个） 
Compiled data [数据] list for the metal properties [金属性能]. Particular focus was
on high temperature [温度] properties [高温性能] while room temperature [温度]
properties [室温性能] were also collected. 
Metal Pass 
84 
轧制，控制水冷和控制空冷的热传递系数模型开发 
For interface between rolls [辊] and hot metals during rolling [轧制], for steel
cooling [冷却] in the air in the function of the travel speed [速度] and environment
temperature [环境温度], and for the controlled [控制] water cooling [控制水冷] depending
on water flow [水流] volume [体积水流量], water pressure [水压], water temperature [水温]
and turbulence [搅动], etc. For example, for the water box cooling [冷却] alone,
several hundred pages of the fieldtest [试验] reports were used. High quality
model [模型] were derived from the rich mill data [数据]. 
Metal Pass 
85 
不同类型的轧制过程中各种钢种的宽展模型开发 
Some stainless steel may have twice as high as spread [宽展] as the plain
carbon [普碳] steel [碳钢] [普碳钢], while other stainless steels may have low spread
[宽展]. Different metals have different spread [宽展] tendency. 
Metal Pass 
86 
不同类型的轧制过程中各种钢种的前滑模型开发 
This part of the model [模型] focused on the steel grade [钢种] influence on the
forward slip [前滑]. It was the further Development [开发] based on the unpublished
[没发表的] writing of Dr. A. Hensel. data [数据] for over 30 steel grade [钢种] were
developed [开发]. Not to be published but is available in the further mill project
[轧钢厂项目]. 
Metal Pass 
87 
摩擦模型的进一步开发 创建一个适合所有轧钢过程的摩擦模型 
Different Material [材料] have different friction [摩擦] values; for the same
pair of the Material [材料], friction [摩擦] depends on surface condition
(roughness, amount and type of the lubricant [润滑剂], etc.), groove [孔型] type,
speed [速度], and temperature [温度]. temperature [温度] has different effects to
friction [摩擦] in different temperature [温度] range. Formulas [公式] were collected
and further developed [开发] with available new data [数据]. 
Metal Pass 
88 
出版一本关于计算机模拟在钢热轧过程应用的专著（德国1996） 
Compared Experimental and Theoretical Investigations [理论研究] of Forming
Technical Parameter [参数] in shape [形状] Rolling [型钢轧制] [型钢轧制] with Example of the
Hot rolling [轧制] of angle steel [角钢]. TU Bergakademie Freiberg, Freiberg,
Germany, 1996 (in German). ISBN 3860120298. 

89 
写了一本书  钢铁厂：过程建模与计算机应用 
Broad topics, with fundamentals [基础], technoLog [日志]ies and industrial
project examples. The book is not yet intended for publishing. Contents may be
available for clients or work colleagues. See www.metalpass [金通].com/bli/home/book2.htm
(under updating). 
Metal Pass 
90 
轧钢厂资源的收集和处理 
Collected rolling [轧制] Mill [轧钢厂] modeling [模拟] resources for over 20,000
pages; processed [处理过的] over 10,000 pages of the resources 
Metal Pass 