外文翻译--对矿井提升机钢丝绳的内部阻尼特性进行非平面横向震动分析

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1、对矿井提升机钢丝绳的内部阻尼特性进行非平面横向震动分析概要本文介绍的工作是为了增加现在矿井提升机钢丝绳的疲劳知识，特别是进行周期性非平面横向震动的钢丝绳线间的国际电线/钢绞线在摩擦时从中损失的内部能量。这种摩擦能量损失现在是限制有益的工作生活中使用悬挂钢丝绳的主要因素之一。实验采用的方法指出了钢丝绳的两种机械特性,主要是由于钢丝绳结构的类型，它们独立了振幅和频率。兴趣是集中在曲率的变化率这一主要参数，它影响了内部的阻尼机理。经验结果显示,振幅和模态数在内部的量化损失中起重要的作用,还透露出，由于上升振动疲劳指数潜在的较高水平，一个关键的曲率半径在伤害下存在。介绍在现代南非黄金深矿井中，伤害的问

2、题由于振动疲劳仍在继续，它限制了缠绕速度，缠绕深度和有效载荷。直到钢丝绳的横向振动产生内在的内能损失这一原理得到充分理解,这样的伤害将继续显著地影响着南非采矿工作的运行成本和效率。在这一地区阻碍工程上的突破性进展的两个主要原因是内部阻尼机制的复杂性和按时间边界情况的钢丝绳动态响应的非线性。到目前为止,这个问题仅仅的一个数学解决方案显得很棘手，而且必须要越来越认真考虑实验结果。因此,这里描述的调查的主要目标是由实验的方法(由实验室模拟)确定矿井提升机钢丝绳在进行大幅度非平面横向震动产生的内部损失，这个振幅是在它的基本的和更高的谐振频率附近的光谱中。调查的范围被限制在矿井的几何尺寸中，在南非的深矿

3、采矿工作中这些几何尺寸很可能在实践中遇到,即单绳和布莱尔多绳缠绕系统。钢丝绳绳从提升滚筒延伸到首轮的这一段长度,通常被称为悬链线,在实践中遭受到最剧烈的横向振动,因此这一部分成为这次钢丝绳调查的模范。所使用的符号定义在文章最后。历史记录在19世纪50年代初于传导着结构型钢丝绳内部阻尼特性的基本方面和分析方面的基础还有这两个方面对横向震动影响的基础。使用的钢丝绳是一个由6根螺旋线围绕一根单芯线绞成一股而成型的7-电线样品(0,4 kg.m-I)。所有的组成电线是镀锌线或类似化学成分的电线，公称直径大约9.5毫米,总长度2000毫米,捻据1270毫米。于的调查集中在标本滞回阻尼特性的测定，这些标本

4、在不受力状态下进行平面振动。尽管采用的技术规范和试验法明显地远离了现代矿井提升钢丝绳的几何条件和动态条件,如下从早期的调查研究得到的观察值具有重大的作用,并描述在绞线进行自由平面振动时内部阻尼的基本性质。（1） 金属丝材料的刚性内摩擦很小。（2） 实际上,可以假设只有干摩擦（内摩擦)存在。（3） 与内部干摩擦有关的衰减能量(每个周期的能量耗散）是一个振幅线性函数。（4） 一个临界的振幅似乎存在,它的上面具体的阻尼特性曲线开始极快地上升。过去的三十年中,看来小独立研究更深层次地运用了于的首创理论并试图扩大矿井提升钢丝绳的阻尼特性的现有知识。然而，许多调查已经处理了大量拉缆的静态和动态响应。Dav

5、enporf 给出了一张这个领域发展趋势的明细表。在这张表中他指出于的结论清楚地确立了等效粘滞阻尼大约是临界阻尼的20%到70%。虽然对于简单几何形状的干性钢丝绳这一理论可能是正确的,但当它应用到大量拉缆和矿井提升钢丝绳中就出现了问题，因为这些钢丝绳的结构复杂地多：同轴左旋和右旋螺旋线包含内芯线，它会在塑形区变形（聚丙烯、剑麻和大麻等含有沥青基的润滑油)。利用粘滞阻尼机制与速率之比的绞缆的简化模型明显在文献中更加受欢迎主要因为它相对上解除了构想和解答。然而,当分析说明了沿着钢丝绳长度方向的张力梯度，除了内部结构阻尼与振幅和频率之比,一个非线性响应以拖延和跳跃现象的形式显现出来。这些现象主要描述

6、了介质的响应，这一介质产生了改变共震频率的强制震动。Vanderveldr还引用于的文章,并补充说考虑横向阻尼行为的简单的模型不可以被假定。此外,他认为至少两种常见的结构和粘性类型的阻尼必须包含在任何试图预测在绞缆中传播的横向波衰减分析中。Vanderveldr通过假设一个粘滞阻尼的频变系数来克服这一数学难题。通过这种方式,并提供激励周期,其他类型的内部的阻尼机理现在被假设包含在阻尼系数中。他的理论和实验结果显示地特别一致,该处相关的是被看作补充于的实验结果如下。（a） 对于一个金属芯,内部阻尼被拉伸载荷所影响。(径向力和链间力随着轴向拉力的增高而增强以至于干摩擦阻尼也表现出了增长)。（b）

7、对于非金属芯,阻尼能力随着轴向载荷减少而增加。里值得提到的是,虽然于对振幅阻尼的依赖性进行了评论,Davenporf和Vanderveldr都没有明确地认为曲率参数和曲率变化率参数会影响能量耗散这一效应。Kolsky给出了这个参数的数学形式:考虑到一水平畸变(大部分)波以x轴方向传播而y轴方向几乎不移动,控制运动方程可以表现为 一般的解决方案 b和C都是频变,m是质量密度，u是剪切模量，是剪切粘度。注意力集中在末项方程(1),可以清楚地把曲率变化率与剪切粘性联系起来。初步讨论在图1中，一段钢丝绳的封皮以基本形式进行自由非平面震动，它展现了四分之以参数的一个完整的循环。跨度的长度是2.L，中跨幅

8、度是S。在一阶条件中,根据任意时刻震动的钢丝绳描绘出数学曲线可以近似为一个抛物线，这个抛物线的轴垂直于连接边界支撑结构的弦。正如迪安所指出的,当弦是水平的而且下降距离与跨距之比小于0.02，该曲线的数学近似值采用了小的误差。当弦不是水平的时候，对称性会丧失,而且钢丝绳在平衡位置会坚持被切去顶端的悬链线数学微量。然而,对于相对较小的下降距离与跨距之比，浅抛物线弧的近似值是足够地精确和而且在分析中不采用很大的误差。抛物线和悬链线的近似法经常出现在文献中,尤其对有倾斜跨度的巨大拉索的动态分析。边界条件当钢丝绳直径相对于跨度足够大,而且钢丝绳振动的曲率半径很小,弯曲应力的局部斜度将建立在钢丝绳中。根据

9、边界条件的类型,弯曲应力的两种渐变是可能的。(i)恒定的渐变和(ii)随不同振动模式而变化的时间相关的渐变。在接下来的分析中,这两种类型的渐变都会被考虑而且是连接震动钢丝绳和支撑物的球铰式安排的结果，被仅有控制边界强加的回转约束条件的类型影响着渐变。图1-钢丝绳封皮进行以基本形式进行自由非平面横向震动在这个例子中滚珠球窝接点以一种方式被约束住，这种方式允许钢丝绳绕它的几何中心旋转而且在跨距附近循环（图2）。因此,这边采用的边界条件允许球形接头以3个自由度在套借口内自由旋转。这就等于绕跨距旋转的钢丝绳刚性长度由支撑结构规定。图二显示了这一钢丝绳的一个平面截面的圆轨道发生在平面y-z的中跨；这边的

10、跨度采取了正常的页面。字母A假定代表钢丝绳的横断面,这儿值得注意的是,字母A绕跨度旋转而且被看作绕相对于固定在支架上的惯性参考的几何中心。发生在字母A顶尖的弯曲应力的倾斜度也是同样显示在图二上而且被公认为是永远恒定不变的t。在图2中指标(c -)和(T +)分别代表相对压缩和拉伸的状态，这些状态发生在持续循环截面的表面上。从基本的横梁理论来看这儿的弯曲应力是拉伸应力,因为振动时顶尖继续留在圆截面的最外面的纤维上。约束的性质也可以避免中性轴(NA)相对于固定指标A移动。在这个例子中，弯曲应力的定值归因于旋转钢丝绳的离心效应连同弯曲效应。 图2-法生在钢丝绳不动点的弯曲应力,旋转运动时变弯曲应力在

11、这个例子中的边界条件与上面的那些相似，除了绕横坐标的旋转被限制了。因此,如图3所示,字母A的引用目前已成为不可以旋转的。这个事实通过超过一个完整周期不改变字母A的垂直方向来被证实。此外,当字母A顶点在跨距周围完成一个旋转周期时，它的引用经历了一次弯曲应力的循环。这里值得注意的是的在被看作相对于纤维旋转的地方中性轴时间方向包含了钢丝绳。在图3中，发生在A的顶尖的弯曲应力的变化在超过两个循环周期内以最快的速度被标绘。再次,张应力恒定的成分归因于当钢丝绳气球到动态的稳定的结构时离心效应随着弧长的增长而上升。 图3-发生在钢丝绳不动点的弯曲应力,旋转运动实验器具在这次调查中使用矿井钢丝绳的规格是43.

12、5毫米(公称通径)与 6 x 32(14/12/6 tri)F和线性质量密度800 kg m-I的结构。图4中,显示一段钢丝绳从不同高度的支撑结构上悬吊下来。边界条件在支撑结构绕钢丝绳的中心纵轴纯转动时限制钢丝绳的运动。最大的止推轴承就是用于这种用途的。通过一个放置在下端的液压千斤顶和固定在电源和上面支撑结构末端的轴承箱体上的锁紧装置得到一个先已决定的张力和钢丝绳几何。由悬索规定的垂直面里的水平转换约束了千斤顶的移动和较低的支持结构。上面的止推轴承被装上铰链,以适应任何预期的斜坡,而且一旦上面的轴承的斜坡加以调整以适应钢丝绳的倾斜，轴承箱体就被锁定在固定位置上。通过这种方式,两个推力轴承受通过

13、他们的轴向中心的纯轴向推力(张力)支配。悬索兴奋地旋转下端,通过一台电动机，齿轮减速器,一系列的链传动装置,以及一个雷诺联轴器。雷诺联轴器位于钢丝绳的轴伸端和驱动装置之间,而且有利于隔离激励产生的钢丝绳的动态响应。这是令人满意的因为以反射的纵向和横向波的形式的机械成果能够（给足够的积累时间)调制激励频率和激励振幅,特别是在共振条件附近。电机的速度由一个3.7千瓦的三相变频传动装置控制,而且由一个光电的转数器检测。张力的水平分量由一个内联的液压传感器测量，它坐落在较低的推力轴承后面而且与钢丝绳一起旋转。给雷诺联轴器应用的扭矩由一个流动场测功机的功当量决定。发动机、变速箱、和链传动装置被封装在在一

14、个单一机组内,这一机组被安装在耳轴上并且在扭转力矩的下面,这个机组可以绕耳轴轴承旋转而且通过移动的大量东西达到平衡。因此,平衡的大量东西的相对运动充当了应用扭矩的一种指示。为了去除本生钟摆式摆动的主要的测力计底座,一个安装在底座的伸出臂被浸在车用机油中，浸没的部分存在的一个平浆被放置在正常的震动方向。图4-测试装置布局的等距略图 结论在这次调查中实证研究方法的使用引起了为量化复杂的阻尼机制而产生的高度全面、有效的技术，这个阻尼机制发生在所有的谐波模式中进行横向非平面振动的矿井吊装钢丝绳上。到目前为止按照作者的经验,没有以（无旋的-旋转的)机械等价为基础的理论或实验证据已经出现在文献上。因为方法

15、的基本原理在于对寻找内部的摩擦特性的实际钢丝绳的测试,这边所描述的任何有适合实验尺寸的钢丝绳可以受动态测试。两种弯曲型阻尼特性由一种实验法鉴定。阻尼被口述出来这一精确形式主要以方便计算。但是,它与在模拟系统中遇到的阻尼相一致,而且定性地符合剪切粘度阻尼这种类型,或者与曲率变化率成正比的这种类型。在这种情况下缺乏大量具体的阻尼的确切性质的信息,被鉴定的阻尼特性的类型是合乎情理的:他们有把复杂简单化这个优点,并且确保获得内部能量损失的量化地正确的评价。应该强调,下面的结论是基于动力学响应的测试，这个动力学响应是固定建筑的一个单一矿井提升钢丝绳上的。结果,把下面的观察结果应用于其它具有不同的几何结构

16、的矿山提升钢丝绳中可能会有一些困难。然而,尽管这些潜在的不同,有些定性趋势可以概括和总结如下。（1） 一个矿井提升钢丝绳的内能损失可以定性和定量地被描述，通过两个实验确定参数:阻尼性能系数C1和曲率特性C2。一种发展的数学关系使它变成可能,这个数学关系被给予了这两个系数和钢丝绳的动态环境(振幅、跨度和频率),来评估内部能量损失的总数。（2） 一个关键的曲率半径存在内能损失随着增加的振幅与跨距的比率成直线上升的上方区域。实验也有证据显示在这一线性地区的内能损失随着振动模态数的平方增加。（3） 对于曲率半径小于临界值的情况,内能损失以指数形式上升,而且不试图调查在那个区域发生的内能损失。（4） 对

17、于典型的矿井装置,更高的非平面横向振动模式在与不良后果相关的振动疲劳造成的损失上有重大影响。这个观察是基于这儿获得的现有金矿的动态条件的实验结果的应用。Internal damping characteristics of a mine hoist cable undergoing non-planar transverse vibration by A.A. MANKOWSKI*SYNOPSISThe work described in this paper is an attempt to increase present-day knowledge of fatigue in mine

18、hoisting cables, particularly the internal energy loss arising from interwire/strand friction in a cable undergoing periodic non-planar transverse vibration. Such frictional energy loss is known to be one of the major influences limiting the useful working life of hoisting cables in use today, and i

19、s responsible for the large capital outlay required to maintain the high safety factors prescribed by the mining industry.The experimental method employed identifies two mechanical characteristics of cables that are independent of amplitude and frequency, and are primarily attributed to the type of

20、cable construction. Interest is focused onthe time rate of change of curvature as the major parameter influencing the internal damping mechanism. Empirical results confirm that amplitude and mode number play an important role in quantifying the internal losses, and also reveal that a critical radius

21、 of curvature exists below which damage due to vibration fatigue rises exponentially to potentially high levels.INTRODUCTION The problem of damage due to vibration fatigue continues to impose limits on winding velocities, depths of wind, and payloads in modern, deep South African gold mines. Until t

22、he mechanism of internal energy loss inherent in the transverse vibration of cables is thoroughly understood, such damage will continue to have a marked effect on the running costs and efficiency of SouthAfrican mining operations. Two major reasons impeding engineering breakthroughs in this area are

23、 the complex nature of the internal damping mechanism and the nonlinearity of the dynamic response of the cable to time-dependent boundary conditions. To date, a purely mathematical solution to the problem appears intractable, and it has become necessary to give increasingly more serious considerati

24、on to experimental results. Accordingly, the primary objective of the investigation described here was to determine experimentally (by laboratory simulation) the internal losses of a mine hoisting cable undergoing non-planar transverse vibration of large amplitude in the spectral neighbourhood of it

25、s fundamental and higher harmonic frequencies. The scope of the investigation was limited to the mine geometries most likely to be encountered in practice in deep South African mining operations, namely the single-drum and the Blair multi-drum winding systems. The length of cable extending from the

26、winding drum to the headsheave, commonly referred to as the catenary, suffers the most violent transverse vibration in practice, and hence served as the section of cable to be modelled in this investigation. The symbols used are defined at the end of the paper.HISTORICAL NOTE The groundwork on the f

27、undamental and analytical aspects of the internal damping characteristics of structural cable and their influence on transverse vibration was conducted in the early 1950s by Yul. The cable used was a 7-wire specimen (0,4 kg. m-I) formed by 6 helical wires stranded round a single-core wire. All the c

28、onstituent wires were zinc-coated and of similar chemical composition, the nominal diameter being approximately 9,5 mm, the overall length 2000 mm, and the lay length 127,0 mm. Yus investigation concentrated on the determination of hysteretic damping characteristics of a family of these specimens un

29、dergoing planar vibration in a state of zero tension. Although the specifications and experimental method employed were distinctly far removed from the geometry and dynamic conditions of present-day mine hoisting cable, the following observations from that early investigation are relevant and descri

30、be the basic nature of the internal damping of stranded cable undergoing free planar vibration.(1) The solid internal friction of the wire material is small.(2) For practical purposes, it can be assumed that only dry friction exists (interstrand friction).(3) The damping capacity (dissipation of ene

31、rgy per cycle) associated with internal dry friction is a linear function of amplitude.(4) A critical amplitude seems to exist, above which the curve of specific damping capacity begins to rise hyperbolically. In the past three decades, it appears that little independent research has carried Yus pio

32、neering efforts further in an attempt to expand present knowledge on the damping characteristics of mine hoisting cable. A number ofinvestigations, however, have dealt with the static and dynamic response of massive guy cables. A detailed account of developments in this field is given by Davenporf,

33、in which he points out that Yus conclusions clearly establish an equivalent viscous damping to be of the order of 2 to 7 per cent of critical damping. While this may be true for dry cables of simple geometry, its application to massive guy cables and mine hoisting cables is questionable on the groun

34、ds that these cables are much more complex in their construction: concentric left- and right-handed helices containing inner cores that deformin the plastic regions (polypropylene, sisal, and hemp impregnated with bitumen-based lubrication). Simplified models of stranded cables employing viscous dam

35、ping mechanism proportional to velocity are decidedly more popular in the literature mainly because of the relative ease of formulation and solution. However, when the analyses account for tension gradients along the length of a cable in addition to internal structural damping proportional to amplit

36、ude and frequency, a nonlinear response manifests itself in the form of drag-out an jump phenomena3. These phenomena primarily describe the response of the medium to forced vibration of varying frequency passing through resonant conditions. Vanderveldr also cites the work ofYu1, and adds that no sim

37、ple model taking into account the transverse damping behaviour can be assumed. Furthermore, he contends that at least both the usual structural and viscous types of damping must be included in any analysis attempting to predict the attenuation of transverse waves that are propagated in a stranded ca

38、ble. Vanderveldr surmounted this mathematical difficulty by assuming a frequency-dependent coefficient of viscous damping. In this way, and providing the excitation is periodic, any other type of internal damping mechanism present is assumed to be contained in the damping coefficient. Histheoretical

39、 and experimental results show particularly good agreement and, where relevant, are seen to complement Yus experimental results as follows.(a) For a metallic core, the internal damping is affected by the tensile load. (Radial forces and inter-strand stress increase with increasing axial tension so t

40、hat dry-friction damping also shows an increase.)(b) For non-metallic cores, the damping capacity increases as the axial loads decrease. It is worth while mentioning here that, although YUl commented on the dependence of damping on amplitude, neither Davenporf nor Vanderveldr explicitly considered t

41、he effect of curvature and its time rate of change as a parameter influencing the dissipation of energy. The mathematical form of this parameter is given by Kolsky: considering a plane distortional (bulk) wave that is propagated in the positive x direction with its particle motion in the y direction

42、, the governing equation of motion can be shown to bewith general solutionwhere band C are both frequency-dependent, m is the mass density, u the shear modulus, and a the shear viscosity. Attention is drawn to the last term of Equation (1), which clearly associates the time rate of change of curvatu

43、re with the shear viscosity.PRELIMINARY DISCUSSION In Fig. 1 the envelope of a length of cable undergoing free non-planar transverse vibration in the fundamental mode is shown over one complete cycle in increments of one-quarter periods. The length of the span is 2. Landthe amplitude at mid-span is

44、S. To within first-order terms, the mathematical curve traced out by the cable during vibration at anyone instant can be approximated by a parabolic arc having its axis perpendicular to the chord joining the supports at the boundaries. This mathematical approximation of the curve, as pointed out by

45、Dean6, introduces errors that are small when the chord is horizontal and the sag-to-span ratio is less than 0,02. When the chord is not horizontal, symmetry is lost, and the cable will hang in the mathematical trace of a truncated catenary in its equilibrium position. However, for relatively small s

46、ag-to-span ratios, the approximation to a shallow parabolic arc is sufficiently accurate and does not introduce significant errors in the analysis. Parabolic-for- catenary approximations are frequent in the literature, particularly for the dynamic analysis of massive guy cables having inclined spans

47、.Boundary Conditions When the diameter of the cable is large enough compared with the span, and the radius of curvature of the vibrating cable is sufficiently small, a local gradient in flexure stress will be set up in the cable. Depending on the type of boundary conditions, two gradients in flexure

48、 stress are possible: (i) a constant gradient and (ii) a time-dependent gradient varying with the mode of vibration.In the following analysis, both types of gradients are considered and are the result of ball-and-socket arrangements connecting the vibrating cables to the support, the types of rotati

49、onal constraints imposed at the boundaries being the sole controlling influence on the gradients. Fig. 1-Envelope of cable undergoing free non-planar transverse vibration in the fundamental mode Constant Gradient in Flexure StressIn this example the ball-and-socket joints are constrained in a manner

50、 that allows the cable to rotate about its geometric centre and revolve round the span (Fig. 2). Thus, the boundary conditions employed here allow the ball joints 3 degrees of rotational freedom within the sockets. This is tantamount to a rigid length of cable whirling round the span defined by the

51、supports. Fig. 2shows the circular orbit of a plane section of this cable occurring at mid-span in the y-z plane; the span here is taken normal to the page. The letter A is assumed fixed to the transverse section of cable, where, it is noted, the letter A revolves about the span and is seen to rotat

52、e about its geometric centre relative to an inertial reference fixed to the supports. The gradient in flexure stress occurring at the apex of the letter A is also shown in Fig. 2 and is seen to be constant for all time t. The indicators (c - ) and (T + ) in Fig. 2 represent the relative compressive

53、and tensile states respectively occurring on the surface of the sections indicated as it continues its cycle. From basic beam theory the flexure stress here is tensile owing to the fact that the apex remains at the outermost fibres of the circular section during vibration. The nature of the constrai

54、nts also prevents the neutral axis (NA) from moving relative to the fixed indicator A. The constant value of the flexure stress in this example is attributed to centrifugal effects of the whirling cable combined with the bending effects. Time-dependent Flexure Stress The boundary conditions in this

55、example are similar to those above with the exception that rotation about the X axis is constrained. As a consequence, the reference letter A, as shown in Fig. 3, now becomes irrotational. This fact is borne out by the unchanging vertical orientation of the letter A over one complete cycle. Furtherm

56、ore, the reference of the apex of letter A experiencesa flexure-stress cycle as it completes one revolution round the span. Noteworthy here is the time-dependent orientation of the neutral axis where it is seen to rotate relative to the fibres comprising the cable. The variation in flexure stress oc

57、curring at the apex of A is plotted against time over a period of two cycles in Fig. 3. Again, the constant component of tensile stress is attributed to the centrifugal effects arising from the increase in arc length as the cable balloons to a dynamically stable configuration. Fig. 3-Flexure stress

58、occurring at a fixed point on the cable,irrotational motionEXPERIMENTAL APPARATUS The specifications of the mine cable used in this investigation were 43,5 mm (nominal diameter) with construction 6 x 32(14/12/6 tri)F and linear mass density 8,00 kg m-I. In Fig. 4, a length of cable is shown suspende

59、d from supports of unequal height. The boundary conditions restricted the motion of the cable at the supports to pure rotation about the central longitudinal axis of the cable. Full thrust bearings were used for this purpose. A predetermined tension and cable geometry were obtained by a hydraulic ja

60、ck positioned at the lower end and locking devices fixed to the bearing casings at the lower and upper support ends. The movement of the jack and lower support were constrained to horizontal translation in the vertical plane defined by the suspended cable. The upper thrust bearing was hinged to acco

61、mmodate any desired slope and, once the inclination of the upper bearinghad been adjusted to match the slope of the cable, the bearing casing was locked into position. In this way, both thrust bearings were subject to purely axial thrust (tension) through their axial centres. The suspended cable was

62、 excited by rotating the lower end by an electric motor, gear-reduction transmission, a series of chain drives, and a Reynold coupling. The Reynold coupling was situated between the driven end of the cable and the driving unit, and had the advantage of isolating the dynamic response of the cable fro

63、m the excitation. This is desirable since mechanical feedback in the form of reflected longitudinal and transverse waves could (given sufficient build-up time) modulate the frequency and amplitude of the excitation, especially in the neighbourhood of resonant conditions. The speed of the electric mo

64、tor was controlled by a 3,7 kW three-phase variable-frequency driving unit, and monitored by an electro-optical revolution counter. The horizontal component of tension was measured by an inline hydraulic transducer, which was situated behind the lower thrust bearing and rotated with the cable. The a

65、pplied torque to the Reynold coupling was determined by a mechanical equivalent of a floating field dynamometer. The motor, transmission, and chain drives were housed in a single unit, which was mounted on trunnions and, under torque reaction, this unit could rotate about the trunnion bearings and be counterbalanced by movable masses. Thus, the relative movement of