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外文資料翻譯
MODELING AND OPTIMIZATION FOR A 20-H COLD ROLLING MILL
QUALITY and its reproducibility are dominant criteria for cold rolled products.In particular,high strip surface quality can be achieved with special mill arrangements such as the 20-h mill.This type of mill uses small work rolls in contact with the strip,that are kept in place with a variety of intermediate and backup rolls.The use of different actuators which,in part,only act indirectly to affect the roll bite geometry,makes the presetting of the mill with regard to strip thickness and flatness a complex task.
This article describes a model the objective of which is optimizing the entire rolling process in a 20-h mill.Results obtained from several on-line applications are discussed.
A closed sendzimirmill arrangement,shown in Fig.1,illustrates the main actuators that affect roll bite geometry with regard to strip thickness and glatness.Side eccentrics located at the backup rolls are used to adjust the overall position of the corresponding roll axis over a wide range which,indirectly,adjusts the roll gap geometry with regard to the millpassline and strip thickness.Side eccentrics may be mechanically or electrically coupled.Crown eccentrics are available at several locations over the barrel length.Those,typically on upper backup rolls,are capable of providing special roll gap contours.They match the gap to the profile of the strip entering the mill.Crown eccentrics are the major actuators for achieving strip flatness.Shiftable,first intermediate rolls are also shape actuators;they mainly serve for modifications in the strip edge area using a tapered roll profile.
Measurement of mill geometry is available only indirectly through the rotation of the side and crown eccentrics and through the position of the first intermediate rolls.
Consideration of mill spring and elastic deformation effects in the stack leads to the roll gap geometry.Accounting for mill spring and elastic deformation requires knowledge of the roll separating force which,in a closed 20-h mill,is measured indirectly through the adjustment pressure needed for the main side eccentrics.Apart from hysteresis effects,the effects of the variable geometry make this indirect measurement critical.
Besides roll gap geometry,the task of presetting the mill also includes the design of pass schedules tailored to meet requirements of a product and the current mill condition.While optimal utilization of the mill is a major objective,the pass schedule must achieve the required produce quality.Generation of pass schedules to cover the statistical average and storing them in databases related to steel grade,surface and coil geometry is state of the art technology,In particular,mill parameters such as roll geometry or the thermal condition of the work rolls require dynamic correction of the pass schedules to obtain a reproducible final product.The same applies to variations in the material characteristics of the coils rolled.
Because of the complexity of 20-hmills,achieving reproducibility of the final product quality and the optimum use of available mill resources to increase productivity represents an extremely difficult task.This task can be accomplished with a comprehensive model approach that takes all relevant mill and process parameters into account.
To optimize the porcess,various mathematical models are needed to describe the elastic stand behavior and the elastic/plastic characteristics of the material to the rolled because neither direct geometrical information nor accurate roll force measurements exist.
1.Force,torque and power
The roll force,roll torque and drive power necessary to form the material are some of the most important items of process information.While power requirements affect the design of a pass schedule for optimal use of the available mill resources,roll force is mandatory for presetting the geometrical actuators.Both force and torque,on the other hand,need to be known for mill presetting so that mechanical or practical limits are not exceeded.
The approach selected to describe the effects in the roll gap with regard to power,torque and force,is based on a strip fiber model using the basic theory developed by Karmanand Siebel.The roll gap model provides both vertical and tangential stress components acting on the work roll.The roll separating force results from the integration of the vertical pressure components.Torque and drive power are derived from the tangential stress.
The roll gap model simultaneously provides accurate information about the vertical and tangential stress components acting on the roll and,thus,the drive power and roll force.
The ability to evaluate the rolling process,based on accurate calculation of the roll separating force and main drive power,enhances,in particular,the material yield stress evaluation.This is beneficial since the roll force measurement is affected,to a large extent,by measurement hysteresis present in a closed 20-h mill.
2.Material yield stress adaption
Material yield stress adaption is required in any case where there is the need to roll a wide range of steel grades.Also,the demand for self-learning model algorithms forces the use of adaptive methods with regard to the yield stress.
The yield stress of the material is initially evaluated in off-line tests using torsion bar samples.While off-line tests provide good initial information,each process and product has its own personality.This may result from the annealing practices or variations in the chemical composition of the steel grades.
The yield stress adaption is broken down into a short-term adaption to rapidly adjust the yield stress curve,and a long-term adaption,where complex relationships between strain,strain rate and temperature are evaluated and represented. Statistical yield stress information is available by grade and also on an individual coil basis if needed,which improves quality assurance.
3.Friction representation
Besides obtaining a representation of the material yield stress,it isalso mandatory to describe the friction in the roll gap.In a variety of applications,the friction coefficient is adjusted so that during long-term analysis the most appropriate friction coefficient;ie,,the coefficient that provides the best match between calculation and measurement,is applied.
Another approach is to carry out rolling tests and analyze the results.While rolling tests affect production, the analysis method is time-consuming and may often have the disadvantage that not all relevant factors affecting friction are adequately considered.The approach selected in the current study is based on an artificial neural network.
The entry layer of the neural network receives all relevant information as it has been gathered and may affect friction.This information is processed through the multilayer perceptron feed forward network in an off-line investigation using the back propagation method for training that,finally,leads to the friction coefficient.With a representative work,even physical relationships between the friction coefficient and process information can be evaluated.
The results derived from the neural network have been used as the basis for an analytical model,which was implemented on-line.
The accuracy of the representation has been evaluated in several on-line rolling tests in industrial facilities.Since mill speed is one of the main variables affecting friction,one pass was made during the commissioning phase of the model with different mill speeds.Both the measured and calculated roll force were recorded.
Apart from the friction coefficient,both the temperature of the strip approaching the roll bite and the strain varied in the test.
3.Elastic mill stand behavior
In addition to roll force,power and torque,the elastic behavior of the mill stand must also be described to allow propagation from the measured eccentric adjustments to the roll bite contour,which is the target for further optimization steps.
One requirement in the elastic mill stand model was its ability to cover a variety of different mill configurations,roll profiles and roll materials.These variables were also specified with respect to each individual roll in the stack to cover situations where unusual roll combinations are selected and to allow the model to be used during design phases.
To provide maximum flexibility,the description of the elastic mill stand behavior is based on a numerical solution approach for the roll stack.The different effects,such as flattening between the rolls,flattening between the strip and the work rolls,and deflection of the several rolls,are derived from multiple iterations.
The elastic mill stand model for the 20-h cold rolling mill can,generally,be divided into two parts.The initial phase involves a rapid determination of the load share in the second phase.The initial load share derived is then taken,in the second phase,as basis for the iterative determination of the interaction between load distribution,flattening and deflection.
The deflection of each roll is derived from the load distribution determined in each iteration step.The geometrical differences between neighboring rolls are interpreted as flattening of the rolls for which a certain load distribution must be present.This leads to a new load along the contact area of the various rolls.This new load distribution leads,again,to a new deflection.
The total effect of elastic deformation between the rolls produces a new load at the saddle segments of the backup rolls.Thus,the mill spring appears to be different,and a new iteration needs to be performed.The iteration is carried out until a solution has been reached,where the entire load,the deflection and flattening match.
3.Summary
The accuracy of force measurement in a closed sendzimir mill is inadequate for high-precision process control.To solve this problem,special model for determination of roll force and roll torque has been developed.The tangential and vertical stress components acting on the work rolls are described to permit the calculation for yield stress adaptions based on the power consumption of the main drive.
A model has been developed that describes the elastic mill stand behavior and considers the interaction of roll deflection with load distribution and roll flattening.The model represents a multiple iterative solution approach.
20-h冷軋機(jī)的模型化和優(yōu)化
質(zhì)量和其再現(xiàn)性是冷軋產(chǎn)品的主要標(biāo)準(zhǔn)。尤其像20-h軋機(jī)，通過(guò)特殊的軋機(jī)布置，可以達(dá)到高標(biāo)準(zhǔn)的鋼板表面質(zhì)量。這種類(lèi)型的軋機(jī)利用小工作輥來(lái)軋制鋼板，而小工作輥又是通過(guò)多個(gè)中間輥和后備輥來(lái)保持其位置。各種調(diào)節(jié)器的使用實(shí)際上僅僅間接影響輥?zhàn)拥膸缀我耄鵀榱诉_(dá)到鋼板的厚度和平直度要求預(yù)先對(duì)軋機(jī)進(jìn)行調(diào)整卻是一項(xiàng)復(fù)雜的工作。
本文描述了在20-h軋機(jī)中優(yōu)化整個(gè)軋制過(guò)程的模型，討論了一些在聯(lián)機(jī)應(yīng)用中可能獲得的結(jié)果。
一臺(tái)封閉式的森吉米爾軋機(jī)舉例說(shuō)明了在鋼板厚度和平直度方面對(duì)軋輥幾何咬入產(chǎn)生影響的主調(diào)節(jié)器是如何布置的。位于后備輥旁的偏心邊是用來(lái)在一個(gè)較大的范圍內(nèi)調(diào)整其相應(yīng)的輥軸的位置，并且還可以間接調(diào)整能夠影響軋制線和鋼板厚度的軋輥開(kāi)度。偏心邊可以是機(jī)械連接或是電器連接的。偏心頂可以在一些位置上調(diào)整輥身長(zhǎng)度。那些一般位于后備輥上的偏心頂還能夠調(diào)整特殊的軋輥開(kāi)度輪廓。他們與被軋制鋼板的側(cè)面間隙相匹配。偏心頂是實(shí)現(xiàn)板帶平直度的主要調(diào)節(jié)器。第一中間輥也是形狀調(diào)節(jié)器；他們主要是利用細(xì)小的輥側(cè)對(duì)鋼板邊緣部分進(jìn)行修正。
軋機(jī)幾何形狀的測(cè)量可以通過(guò)旋轉(zhuǎn)邊和偏心頂，以及第一中間輥的位置來(lái)間接獲得。
軋機(jī)的彈塑性變形會(huì)影響軋輥的間隙。解釋軋機(jī)的彈塑性變形需要軋輥間分開(kāi)的力，在封閉的20-h軋機(jī)中，這些力可以通過(guò)調(diào)整作用在主偏心邊上壓力來(lái)間接測(cè)量獲得。除了滯后的影響外，各種各樣的幾何影響是間接測(cè)量的關(guān)鍵。
除了軋輥開(kāi)度外，軋機(jī)預(yù)設(shè)置的任務(wù)還包括為了滿足產(chǎn)品和當(dāng)前軋機(jī)條件要求需要的軋制表的設(shè)計(jì)。軋機(jī)應(yīng)用的主要目標(biāo)就是利用軋制表制造出所需要的產(chǎn)品。有關(guān)軋制表的最新生產(chǎn)技術(shù)是統(tǒng)計(jì)軋制過(guò)程中一些數(shù)值的平均值并將這些數(shù)值存儲(chǔ)在數(shù)據(jù)庫(kù)中，數(shù)據(jù)庫(kù)中包含鋼的等級(jí)，表面質(zhì)量，鋼卷數(shù)量等等。此外，軋機(jī)參數(shù)還包括諸如軋輥幾何參數(shù)或者在最終產(chǎn)品中獲得的隨時(shí)間變化的工作輥溫度變化情況。軋制表同樣還可以應(yīng)用在卷曲軋制的材料中。
由于20-h軋機(jī)的復(fù)雜性，要實(shí)現(xiàn)最終產(chǎn)品的質(zhì)量再現(xiàn)性和最大化的利用軋機(jī)資源來(lái)增加產(chǎn)量成了一項(xiàng)極端困難的任務(wù)。這個(gè)任務(wù)可以利用一個(gè)接近于軋機(jī)和生產(chǎn)過(guò)程參數(shù)的模型來(lái)綜合研究分析。
為了對(duì)過(guò)程進(jìn)行優(yōu)化，同時(shí)又因?yàn)樵谲堉七^(guò)程中沒(méi)有可以直接測(cè)量軋制力的方法， 所以可以利用各種各樣的數(shù)學(xué)模型來(lái)研究材料在軋制時(shí)產(chǎn)生的彈性變形和其彈塑性變形的特點(diǎn)。
1.軋制強(qiáng)度，扭轉(zhuǎn)力矩和動(dòng)力矩
軋制強(qiáng)度，扭轉(zhuǎn)力矩和驅(qū)動(dòng)力矩是材料在軋制過(guò)程中最重要的參數(shù)。當(dāng)設(shè)計(jì)一份需要最佳化利用可使用的軋機(jī)資源的軋制表時(shí)，對(duì)于強(qiáng)度的要求是調(diào)節(jié)器預(yù)先強(qiáng)迫施加軋制強(qiáng)度。換一方面講，在軋機(jī)預(yù)置時(shí)施加軋制強(qiáng)度和扭轉(zhuǎn)力矩，在實(shí)際軋制時(shí)就不會(huì)因?yàn)閺?qiáng)度過(guò)大或力矩過(guò)大而形成失效。
在卡爾曼和西貝爾所創(chuàng)造的一種鋼板纖維模型理論中描述了與軋輥開(kāi)度之間的動(dòng)力矩，扭轉(zhuǎn)力矩和軋制強(qiáng)度所接近的結(jié)果。軋輥開(kāi)度模型展示了作用于工作輥間的垂直應(yīng)力和切線應(yīng)力，切軋制力與垂直應(yīng)力是分開(kāi)研究的，而扭轉(zhuǎn)力矩和驅(qū)動(dòng)力矩則是由切線應(yīng)力產(chǎn)生。
軋輥開(kāi)度模型同時(shí)相對(duì)準(zhǔn)確地提供了作用于工作輥垂直應(yīng)力，切線應(yīng)力以及驅(qū)動(dòng)力矩和軋制強(qiáng)度信息。
對(duì)于軋制過(guò)程能力的評(píng)價(jià)，尤其是提高金屬材料壓力的評(píng)價(jià)，主要是基于對(duì)軋制力和驅(qū)動(dòng)力矩的準(zhǔn)確計(jì)算。在封閉的20-h軋機(jī)中，軋制強(qiáng)度的測(cè)量在很大程度上受到要延遲作用的影響，但這并沒(méi)有多大壞處。
2.材料屈服強(qiáng)度自適應(yīng)
材料的屈服強(qiáng)度自適應(yīng)在各種等級(jí)的鋼材軋制時(shí)都需要用到。同時(shí)，關(guān)于屈服強(qiáng)度的自學(xué)習(xí)模型要求使用自適應(yīng)方法來(lái)計(jì)算。
材料屈服強(qiáng)度初期是在脫機(jī)測(cè)試中利用扭轉(zhuǎn)杠桿抽樣的方法來(lái)測(cè)量，如果想要脫機(jī)測(cè)試?yán)锏玫胶玫臏y(cè)試結(jié)果，那么每個(gè)步驟和每個(gè)產(chǎn)品都要分別進(jìn)行測(cè)試，不同等級(jí)的鋼的化學(xué)成分不同，退火時(shí)產(chǎn)生不同的變形體，所以測(cè)試的結(jié)果也不同。
屈服強(qiáng)度在短期自適應(yīng)中下降，在長(zhǎng)期自適應(yīng)中被快速調(diào)整上升，這期間的主要代表因素有變形，變形率和溫度。屈服強(qiáng)度數(shù)值的統(tǒng)計(jì)是基于鋼材的等級(jí)，并且如果有需要提高或保證質(zhì)量的需要，可以從一個(gè)單獨(dú)的帶卷中測(cè)試得到。
3.摩擦表示
軋輥開(kāi)度間除了要表示材料的屈服強(qiáng)度外，還要將摩擦的情況表示出來(lái)。在各種應(yīng)用里，為了在長(zhǎng)期的分析計(jì)算中得到最優(yōu)化的摩擦系數(shù)，摩擦系數(shù)需要經(jīng)常修正；可以說(shuō)，為了計(jì)算和測(cè)量的準(zhǔn)確性，總要利用到摩擦系數(shù)。
還有一個(gè)比較接近的方法就是進(jìn)行軋制測(cè)試并且分析其結(jié)果。當(dāng)軋制測(cè)試關(guān)系最終生產(chǎn)時(shí)，分析結(jié)果的方法經(jīng)常消耗大量時(shí)間并且會(huì)由于各種影響到摩擦的因素沒(méi)有被充分考慮而對(duì)最后的結(jié)果產(chǎn)生不利的影響。目前關(guān)于摩擦的研究都是在一個(gè)人工中樞網(wǎng)絡(luò)進(jìn)行的。
當(dāng)周?chē)男畔⒈皇占饋?lái)并且可能因摩擦?xí)r，這個(gè)中樞網(wǎng)絡(luò)的進(jìn)入層會(huì)收到所有有關(guān)的信息。獲得有關(guān)摩擦的信息的方法是在脫機(jī)測(cè)試中使用聯(lián)合視感控制器來(lái)處理前方網(wǎng)絡(luò)的情況，然后利用后臺(tái)傳送的方法將摩擦系數(shù)的信息分析計(jì)算出來(lái)。有了這個(gè)分析工作，摩擦系數(shù)體現(xiàn)出來(lái)的物理關(guān)系和過(guò)程信息都可能表示出來(lái)。
中樞網(wǎng)絡(luò)計(jì)算得出結(jié)果可以作為用來(lái)聯(lián)機(jī)計(jì)算分析模型的基礎(chǔ)。
在工業(yè)設(shè)備中有些聯(lián)機(jī)測(cè)試的表示方法的準(zhǔn)確性已經(jīng)被認(rèn)同。軋機(jī)的軋制速度是摩擦系數(shù)的主要影響因數(shù)，軋制期間不同的速度會(huì)產(chǎn)生不同的摩擦系數(shù)，同時(shí)測(cè)量和計(jì)算的軋制強(qiáng)度也被紀(jì)錄下來(lái)。
除了摩擦系數(shù)，鋼板被軋輥咬入時(shí)的溫度和變形也在測(cè)試范圍內(nèi)。
4.機(jī)座彈性變形
除了軋制強(qiáng)度，力矩和扭轉(zhuǎn)力矩外，為了進(jìn)一步的優(yōu)化工作，在軋輥咬入角的偏心調(diào)整測(cè)量中，需要將軋機(jī)機(jī)座的彈性變形表示出來(lái)。
在機(jī)座彈性變形模型中需要的前提條件是各種軋機(jī)的配置情況，鋼卷的輪廓和鋼卷材料。在設(shè)計(jì)階段，每個(gè)單獨(dú)的軋輥與指定的軋輥之間結(jié)合的情況中產(chǎn)生的各種變量也被明確說(shuō)明。
為了提供最大的撓度，對(duì)機(jī)座彈性變形的表示是基于鋼卷的數(shù)字解決方案。多重的反復(fù)性工作造成了不同的結(jié)果，例如不同軋輥間的矯直，鋼板和工作輥之間的矯直，和一些軋輥的偏轉(zhuǎn)等。
20-h冷軋機(jī)的機(jī)座彈性變形模型一般分為兩部分。第一階段包括了對(duì)第二階段所承受負(fù)荷的快速分析，然后這個(gè)快速分析的結(jié)果在第二階段被用來(lái)作為負(fù)荷的分配，矯正，偏轉(zhuǎn)間相互作用的基礎(chǔ)。
每個(gè)軋輥的偏轉(zhuǎn)量都取決于這兩個(gè)階段中確定的負(fù)荷分配量，相鄰的軋輥間存在的差異是因?yàn)橐玫揭欢ǖ呢?fù)荷分配量而必須對(duì)軋輥進(jìn)行矯直造成的，這就導(dǎo)致在不同的軋輥間產(chǎn)生了一個(gè)新的負(fù)荷，而這個(gè)新的負(fù)荷被再次分配，又引起了一個(gè)新的偏轉(zhuǎn)。
軋輥間的彈性變形所引起的所有效果是在后備輥的托架部分產(chǎn)生一個(gè)新的負(fù)荷，要是軋機(jī)的彈性變形看起來(lái)不對(duì)，就需要重新計(jì)算負(fù)荷，直到計(jì)算出來(lái)的一個(gè)負(fù)荷可以使其分配，偏轉(zhuǎn)，矯正相互平衡。
5.總結(jié)
一臺(tái)封閉式的森吉米爾軋機(jī)的強(qiáng)度測(cè)試的準(zhǔn)確性對(duì)于一個(gè)高精度的控制過(guò)程是不夠的，為了解決這個(gè)問(wèn)題，開(kāi)發(fā)了測(cè)定軋制強(qiáng)度和軋制扭轉(zhuǎn)力矩的特殊模型。為了要計(jì)算作用于主驅(qū)動(dòng)輥上的主應(yīng)力，它可以被分成作用在工作輥上的切線應(yīng)力和垂直應(yīng)力兩部分。
本文還例舉了一個(gè)模型，它簡(jiǎn)單地描述了軋機(jī)機(jī)座的彈性變形以及負(fù)荷的分配與軋輥間的偏轉(zhuǎn)和矯正的關(guān)系。這個(gè)模型代表了一種多重的可疊加的比較接近的解決方法。
畢 業(yè) 設(shè) 計(jì)（論文）
題目：立式軋機(jī)的軋輥機(jī)構(gòu)設(shè)計(jì)
姓 名:
系 部: 機(jī)電工程系
專 業(yè): 機(jī)電一體化技術(shù)
指導(dǎo)教師:
洛陽(yáng)理工學(xué)院畢業(yè)設(shè)計(jì)（論文）
立式軋機(jī)的軋輥機(jī)構(gòu)設(shè)計(jì)
摘 要
軋鋼生產(chǎn)是鋼鐵工業(yè)生產(chǎn)的最終環(huán)節(jié)，鋼鐵軋制在國(guó)家工業(yè)體系中占有舉足輕重的基礎(chǔ)地位。軋機(jī)是指完成金屬軋制生產(chǎn)全過(guò)程的裝備，包括有主要設(shè)備﹑輔助設(shè)備﹑起重運(yùn)輸設(shè)備和附屬設(shè)備等。但一般所說(shuō)的軋機(jī)往往僅指主要設(shè)備。
本設(shè)計(jì)的主要內(nèi)容就是在對(duì)立式軋機(jī)功能結(jié)構(gòu)進(jìn)行全面分析的基礎(chǔ)上，利用大學(xué)所學(xué)的相關(guān)知識(shí)對(duì)立式軋機(jī)的軋輥結(jié)構(gòu)及其調(diào)整機(jī)構(gòu)進(jìn)行設(shè)計(jì)，并結(jié)合立軋機(jī)工作過(guò)程中的受力情況對(duì)主要零部件的承載能力和強(qiáng)度進(jìn)行了校核。
通過(guò)立式軋機(jī)的設(shè)計(jì)，不僅鍛煉了自己綜合運(yùn)用各種知識(shí)解決問(wèn)題的能力，還深化了對(duì)大學(xué)所學(xué)各種知識(shí)的理解，提高了獨(dú)立從事工程設(shè)計(jì)工作的能力。
關(guān)鍵詞：立式軋機(jī)，軋輥機(jī)構(gòu)，機(jī)構(gòu)設(shè)計(jì)
The Designing of The Vertical Rolling Mill
ABSTRACT
The production of the steel is the final part of the steel industry, Steel rolling plays a decisive foundation on the national industrial system.Rolling mill is the equipment that finish the process of the metal rolling mill production. Including the main equipment, auxiliary equipment, lifting transportation equipment and ancillary equipment etc. But the rolling mill is only the major equipment in general.
The main content of this design is on the function structure of the vertical rolling mill based on the analysis of comprehensive utilization of the university knowledge of vertical mill roll adjusting device structure and design, And combining with the working process of the rolling force that is made of main components of the bearing capacity and strength
It is not only exercise their comprehensive use of various knowledge, but also the ability to solve the problem of university that deeps the understanding of all kinds of knowledge through the vertical mill design and improves the independent working ability in engineering design.
KEY WORDS: Vertical rolling mill，The structure of the vertical roll ,The designing of the machanism .
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目 錄
前 言 1
第1章 軋鋼機(jī)械的概述 3
1.1軋鋼生產(chǎn) 3
1.2軋鋼機(jī)械 3
1.3軋機(jī)的用途及其發(fā)展 4
1.4立輥軋機(jī)的國(guó)內(nèi)外發(fā)展現(xiàn)狀 4
第2章 立式軋機(jī)的軋輥結(jié)構(gòu)設(shè)計(jì) 7
2.1 間隙調(diào)節(jié)方案的確定 7
2.2 軸承的選擇 9
2.2.1 軸承的介紹 9
2.2.2 軋機(jī)中軸承的選用 9
2.3 軸承座的分析 10
2.4 軋輥材料的確定 11
2.5 軋輥的直徑和長(zhǎng)度的確定 11
2.6 軸承端蓋的結(jié)構(gòu) 12
第3章 立式軋機(jī)部件的校核 14
3.1 軸承的失效形式 14
3.2 滾動(dòng)軸承的計(jì)算準(zhǔn)則 14
3.3 滾動(dòng)軸承的校核 14
3.4 軋輥的強(qiáng)度校核 17
結(jié)論 20
謝辭 21
參考文獻(xiàn) 22
外文資料翻譯 23