附录1机械英语文章翻译

附录1机械英语文章翻译 附录1 英文原文 Internal damping characteristics of a mine hoist cable undergoing non-planar transverse vibration by A.A. MANKOWSKI SYNOPSIS The work described in this paper is an attempt to increase present-day knowledge of fatigue in mine 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 is 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 cable construction. Interest is focused on the 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 of curvature exists below which damage due to vibration fatigue rises exponentially to potentially high levels. SAMEVATTING Die werk beskryf in hierdie referaat is 'n paging om die teenswoordige kennis van vermoeidheid in mynboukabels, en veral die inwendige energieverlies as gevolg van tussendraad/stringwrywing in 'n kabel wat aan periodieke nieplanere dwarsvibrasie onderhewig is, uit te brei. Dit is bekend dat sodanige wrywingsenergieverlies een van die belangrikste faktore is wat die nuttige werklewe van hyskabels wat tans gebruik word, beperk, en verantwoordelik is vir die groot kapitaaluitleg wat nodig is om die hoe veiligheidsfaktore wat deur die mynboubedryf voorgeskryf word, te handhaaf. Die eksperimentele mode wat toegepas is, identifiseer twee meganiese eienskappe van kabels wat onafhanklik van amplitude en frekwensie is en in die eerste plek aan die tipe kabelkonstruksie toegeskryf word. Die belangstelling is toegespits op die tempo van krommingsverandering as die belangrikste parameter wat die inwendige dempmeganisme be'invloed. Empiriese resultate bevestig dat amplitude en modusgetal 'n belangrike rol in die kwantifisering van die inwendige verliese speel en toon ook dat daar 'n kritieke krommingstraal bestaan waaronder skade as gevolg van vibrasievermoeidheid eksponensieel tot potensieel hoe vlakke styg. 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 the 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 South African mining operations. Two major reasons impeding engineering breakthroughs in this area are 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 consideration 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 its 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 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 fundamental 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 constituent 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. Yu's investigation concentrated on the determination of hysteretic damping characteristics of a family of these specimens undergoing 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 in vestigation are relevant and describe 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 energy 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 Yu's pioneering efforts further in an attempt to expand present knowledge on the damping characteristics of mine hoisting cable. A number of investigations, 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, in which he points out that Yu's 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 grounds that these cables are much more complex in their construction: concentric left-and right-handed helices containing inner cores that deform in the plastic regions (polypropylene, sisal, and hemp impregnated with bitumen-based lubrication). Simplified models of stranded cables employing a viscous damping 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 amplitude and frequency, a nonlinear response manifests itself in the form of drag-out and 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 simple 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 cable. 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. His theoretical and experimental results show particularly good agreement and, where relevant, are seen to complement Yu's experimental results as follows. 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 that dry-friction damping also shows an increase.) 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 the 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, the governing equation of motion can be shown to be (1) with generalsolution (2) where 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 curvature with the shear viscosity. 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. Land the amplitude at mid-span is S. o 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 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 sag-to-span ratios, the approximation to a shallow parabolic arc is sufficiently accurate and does not introduce significant errors in the analysis. Parabolicfor-catenary approximations are frequent in the literature, particularly for the dynamic analysis of massive guy cables having inclined spans. 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 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 rotational constraints imposed at the boundaries being the sole controlling influence on the gradients. Constant Gradient in Flexure Stress In this example the ball-and-socket joints are constrained in a manner 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 supports. Fig. 2 shows 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 rotate 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 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 constraints 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 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. Furthermore, the reference of the apex of letter A experiences a 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 Fig. 2-Flexure stress occurring at a fixed point on the cable, rotational motion to the fibres comprising the cable. The variation in flexure stress occurring 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. Internal Energy Loss versus Boundary Conditions In the former case of a vibrating cable having a fixed . Fig. 3-Flexure stress occurring at a fixed point on the cable, irrotational motion stress gradient, it becomes clear that no internal losses occur because there is no relative movement between adjacent layers or strands, nor is there any physical distortion of individual wires themselves. In the absence of aerodynamic damping, and of interstrand friction and frictional losses in the ball-and-socket joints, the cable in this instance (once set in motion) would continue to vibrate indefinitely. The latter case, however, has much more practical appeal in that the study of irrotational motion is more prevalent in systems of vibrating cables and similar structures governed by the hyperbolic wave equation. Under these boundary conditions, it can be appreciated that all the fibres of the cable in the span area are cyclically sliding over or against adjacent fibres. The radial and normal components of flexural (bending) stress are clearly time-dependent and a function of the cable's orientation in space. Likewise, the shear-flow, and longitudinal and transverse shearing-stress components, are also dependent on the orientation. Moreover, as both of these complementary stresses are dependent on the radius of curvature, R, defined by the relation the sag-to-span ratio or dynamically equivalent amplitude-to-span ratio and the frequency of vibration play an important role in governing the rate of internal energy loss. The end physical result of the energy loss described above can generally be classified as transverse cable fatigue. Fatigue in this instance is manifest by worn individual wires accompanied by a general loss in their tensile strength as well as ductility. In the more severe cases of sustained violent vibration fatigue, individual broken wires are common-place. Modern in situ non-destructive testing techniques and periodic inspections, however, are quick to identify such damaged cables and alert the mining engineers of impending cable failure. EXPERIMENTAL 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 suspended from supports of unequal height. The boun dary conditions restricted the motion of the cable at the upports 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 jack 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 accommodate any desired slope and, once the inclination of the upper bearing had 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 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 from 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 motor 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 in-line hydraulic transducer, which was situated behind the lower thrust bearing and rotated with the cable. The applied 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 the balancing masses served as an indication of the applied torque. To rid the central dynamometer carriage of its natural pendulum-type vibration, an extension arm fixed to the carriage was immersed in motor oil, the immersed section (8) are multiplied by a factor of 2. This is clarified in Fig. lO(a), where the dynamic and physical properties of the laboratory model are embedded in a simulated vibrating system experiencing twice the internal power loss. Of particular note in the simulated model is the distance between the support points shown here as 2. L. Similarly, Fig. lO(b) shows the equivalence between the laboratory model and a simulated model vibrating in the second mode. The distance between the supports in the simulated model shown here is 4. L, and the internal power loss is 4 times that of the laboratory model. Lastly, reference to Fig. 10(c) shows the equivalence between the laboratory model and a simulated model vibrating in the third mode. The loss and the span distance of the simulated model are shown to be 6 times those of the laboratory model. Obviously, the term sag-to-span ratio as used conventionally in the literature poses some degree of difficulty Application to Kloof Gold Mine The present investigation is part of an ongoing research project initiated in the early 1970s at the Chamber of Mines Research Laboratories, Johannesburg. The majority of research publications3,7-9 resulting from these continuing efforts used on-site data collected from Kloof Gold Mine as source material. As the present author is familiar with the geometry, frequencies, and amplitudes of transverse vibration occurring at that Mine, it is thought a worth while exercise to close this paper with an analysis of the internal power losses in a single cable of the Blair double-drum winding system installed in the No. 1 Shaft at that Mine. A resonant condition occurring during normal operations is chosen for discussion, i. e. when the natural transverse frequency of the cable (catenary) extending from the drum to the headsheave is an integral multiple of the Lebus liner cross-over frequency at the winding drum. For purposes of discussion, worst-case amplitudes are used. Data Applying to No. 1 Shaft The following data apply to No. 1 Shaft. The physical properties of the cable employed at Kloof are cable construction 6 x 30(12/12/6 tri)F and linear mass density 8,49 kg' m -1. The geometry and density of that cable are not too dissimilar to the properties of the cable used in the investigation described in this paper. For this reason only, the cable characteristics Cl and Cz are assumed to take on the values 42,75 J and 0,34 m-I respectively. The use of Equation (9) and the mode parameters given above as inputs results in the following power losses: A t first glance, these values appear insignificant and to some engineers perhaps not even worthy of consideration. This is certainly true when they are compared with the 6300 kW d.c. motor assemblies that drive the winding drums. However, taking into account that damage due to cable fatigue is an irreversible phenomenon lasting over an average of 75000 trips per cable, serious consideration must be directed to the relative orders of magnitude between the losses in modal power and the cumulative effect they may have in limiting the working life of the cable. CONCLUSION The use of an empirical approach in this investigation gave rise to a highly comprehensive and efficient technique for quantifying the complex damping mechanism occurring in mine hoisting cables undergoing non-planar transverse vibration in all the harmonic modes. In the author's experience to date, neither theoretical nor experimental evidence based on the (irrotational-rotational) mechanical equivalence has been encountered in the literature. Because the basis of the method lies in the testing of the actual cable whose internal frictional characteristics are sought, any cable having suitable laboratory dimensions can be subjected to the dynamic test described here. Two flexural-type damping characteristics were identified by an experimental method. The precise form that the damping took was dictated mainly by convenience in computation. It is, however, consistent with the damping encountered in analogous systems, and conforms qualitively to a type of shear-viscosity damping, or one that is proportional to the time rate of change of curvature. In the absence of a large body of concrete information on the exact nature of damping in this situation, the type of damping characteristics identified are justified: they have the virtue by being simple and ensure that a quantitatively correct assessment of the internal power loss is achieved. It should be emphasized that the following conclusions are based on the testing of the dynamic response of a single mine hoisting cable of fixed construction. As a result, there may be some difficulties in the application of the following observations to other mine hoisting cables having different geometric construction. However, in spite of these potential differences, certain qualitative trends can be generalized and summarized as follows. (1) The internal power loss of a mine hoisting cable can be characterized qualitatively and quantitatively by two experimentally determined parameters: a damping capacity coefficient, Cl, and a curvature characteristic, Cr A mathematical relationship was developed that makes it possible, given these two coefficients and the dynamic environment of the cable (amplitude, span, and frequency), to assess the amount of internal power loss. (2) A critical radius of curvature exists above which the internal power loss increases linearly with increasing amplitude-to-span ratio. Experimental evidence also shows the losses in this linear region to increase as the square of the mode number of vibration. (3) For radii of curvature below the critical value, the internal losses rise exponentially, and no attempt was made to investigate the losses occurring in that region. (4) For typical mine installations, the higher modes of non-planar transverse vibration have a significant influence on the undesirable effects associated with damage from vibration fatigue. This observation is based on the application of the empirical results obtained here to the dynamic conditions of an existing gold mine. PROPOSAL FOR FUTURE RESEARCH A variety of critical questions surfaced during the investigation, the most relevant being those relating to the unknown behaviour of cables differently constructed from the single cable used in the analysis. Further research could well take into consideration the factors that may influence the damping capacity and curvature characteristics of the various types of mine hoisting cables in use today. Briefly, the following factors thought to be of prime importance in this regard are the effects of (1) lay length, (2) number of constituent wires composing the strands, (3) the various types of strand construction: round, triangular, non-spin, and locked coil, (4) the physical properties of the core material, and (5) bitumastic-based cable lubricants. An appraisal of the five points above leads to the tantalizing question: Does a functional relationship exist between the damping characteristics (Cl and Cz as defined in this paper) and the well-documented expected fatigue-life cycles of the various types of mine hoist cables in use today? The author.believes a relationship does exist, and a well-coordinated investigation into this area should have exciting practical and financial implications for the mining industry. The experimental technique and testing apparatus developed in the Mechanical Engineering Laboratories at the University of Durban-Westville have proved to be accurate and reliable, and with the necessary modifications can provide information on the internal damping. 附录2 中文翻译 煤矿提升机钢丝绳曲面横向振动的内部阻尼特征 by A.A. MANKOWSKI 概论 本文所描述的是有关煤矿提升钢丝绳疲劳的当代知识,特别是来自在钢丝绳周期曲面横向振动中钢丝芯/钢丝束摩擦内部能量损失。在当今使用的提升机钢丝绳中这样的摩擦产生的能量损失限制了钢丝绳的有效工作，这也是在挖掘工业中为了维持安全系数产生的高额的大型资本输出的原因。实验 分析 定性数据统计分析pdf销售业绩分析模板建筑结构震害分析销售进度分析表京东商城竞争战略分析 方法确定了两种不依赖频率和振幅的钢丝绳力学特性,主要是钢丝绳结构的不同类型。作为影响内部阻尼机制的主要参量，弯曲改变的时间率极为重要。实验结果证实那振幅和模态在定量内部损失中扮演着重要角色，同时揭示了当振动疲劳以指数增长上升到一定水平时一种临界曲率半径的存在。 引言 由于振动疲劳产生的破坏问题仍然给现代化的大型的南非金矿的弯曲速度，气流深度，设备带来限制。直到在钢丝绳固有的横向振动中内在能量损失彻底的损耗，不然这样的损耗将会继续显著影响着南非采矿作业的运行成本和效益。 这方面的两个阻碍技术突破的主要原因是内部阻尼机制的复杂性和钢丝绳的非线性动态响应的时间依赖性。直到今天，一种完全的数字式的解决问题的方法还是很难对付的，这将增大对实验结果的认真考虑。因此，这里调查分析的主要目的通过实验模拟(试验仿真)煤矿提升机钢丝绳曲面横向振动的内部阻尼特征。调查的主要范围仅限于矿山工程最有可能在实践中遇到的南非的采矿作业的煤矿几何结构，即单绳和多绳缠绕系统。钢丝绳从卷筒到天轮延伸的长度，通常称为悬连线在实践中遭遇最为猛烈的横向振动，因此在本次的调查蓝本中作为钢丝绳调查的一部分。文中使用的符号定义在文章的末尾。 历史因素 关于钢丝绳的结构及其对其由横向振动产生的内部阻尼特性的背景和基础起源于20世纪50年代初。该钢丝绳用的是一七线标本(0.4kg/mm)的6芯线组成。所有成分是锌涂层和类似的化学成分，名义直径约9,5毫米，总长度2000毫米，而提升长度127.0毫米。在零拉力的状态下，调查集中在紧张状态的零平面振动迟滞阻尼特性。虽然计划书和试验方法采用了明显远离几何和当今矿井提升钢丝绳动态环境，接下来的描述是相关的提升机钢丝绳阻内部自由平面阻尼的基本性质。导线内部固体材料的摩擦很小;从实际情况出发，我们可以假设只有干摩擦存在(链间摩擦)。阻尼容量(每个周期耗能)与内部干摩擦是一个线性相关的函数;关键幅度似乎存在，上述这些具体的阻尼能力曲线开始大幅度上升。 在过去30年来，似乎很少有开拓性努力，更进一步的关于矿井提升钢丝绳的阻尼特性的独立研究。然而，众多的调查处理了大量的提升机钢丝绳静态和动态响应。Davenporf在这个领域的发展情况作了详细的介绍。其中他指出，Yu的结论指出建立一个等效2阶粘性阻尼是占百分之七临界阻尼。虽然这可能是简单的几何关系，其应用大规模钢丝绳和矿井提升钢丝绳是有问题的，理由是这些钢丝绳在他们的使用领域要复杂得多:同心左，右手螺旋含内内核，塑性变形的区域(聚丙烯，剑麻，并与沥青基润滑浸渍大麻)。 粘性阻尼机制发展速度与阻尼钢丝绳发展成正比，它的简化模型更为流行，这是由于它相对而言解决问题更简答。然而，当分析了除了内部振幅和频率特性以外的钢丝绳静张力梯度变化。振幅和频率的非线性反应 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 现为拖动与震动现象。这些现象表现了不同频率的谐振条件下合格的振动响应。Vanderveldr还列举了YU的工作，并补充说，鉴于横向阻尼的复杂模型也可以假设。此外，他还争辩说，至少有两个通用的粘性阻尼结构及类型必须在钢丝绳传播横波衰减分析包括在进行力学分析。Vanderveldr克服基于频率依赖性粘性阻尼系数的这一假设的数学难题。通过这种方式，并提供周期性的震动，任何存在的其他类型内部阻尼机制都被定阻尼系数控制。他的理论和实验结果表明，与Yu的工作特别的一致和相关，被视为Yu的实验补充，结果如下: 对于一个金属芯，内部阻尼受拉伸载荷的影响。(干摩擦阻尼应力随着径向力和内芯钢丝束的增加而增加)。对于非金属芯，干摩擦阻尼应力随着径向力减少而容量增大。 值得一提的是，而在这里，尽管Yu根据对振幅阻尼的评论，明确考虑曲率效应及其影响作为一个耗能参数变化。，给出了科尔斯基参数的数学形式:考虑平面畸变波是在X正向在y方向的轴向运动，运动控制方程可以证明是: (1) 解方程得: (2) 其中:常量C是双频率，m是质量密度，u是剪切模量。请注意的是方程(1)的最后端，其中明确提出了剪切粘度的曲率变化率。 在图1中,钢丝绳长度阻尼系统在横向平面显示了一个完整的周期增量，跨度为2。 用数学曲线来描绘钢丝绳在任何瞬间振动，可以用一个垂直于轴线的抛物线的边界弧近似模拟。这种近似的数学曲线，正如Dean介绍的是，水平和垂直跨比为0.02以下错误率很低。当弦不水平，对称性丢失，钢丝绳将挂在一个平衡位置截断其接触网数学跟踪。然而，相对较小的凹跨度的比例，近似抛物线弧，足够准确和不会引入在分析中的重大错误。当边界条件为钢丝绳的直径比有足够大的跨度，钢丝绳的振动的曲率半径为足够小，弯曲应力梯度地方将被设置在钢丝绳上了。根据边界条件的不同类型，两种弯曲应力梯度是可能存在的。(i)恒定梯度及(ii)时间依赖型梯度与不同的振动模式有关。下面的分析中，这两种类型的梯度考虑是球和插座连接钢丝绳振动的安排结果，在作为唯一的控制影响的梯度边界施加转动约束后产生的类型。 这个球关节的链接方式是，钢丝绳旋转几何中心，围绕跨越约束如图(2)。因此，这里的边界条件允许使用3自由度球关节的接头。 这等于一个刚性的钢丝绳支持旋转轮的定义的长度范围。图2显示了这一工作在yz平面进行中大跨度索面部分出现圆形轨道的现象;这里是采取跨度的正常页面。字母A处是假设固定在钢丝绳那里，人们注意到的横截面，字母A围绕有关跨度大约是看到它的几何围绕个相对固定在惯性参考中心旋转。弯曲应力梯度在A也是如图信发生。 图2这些指标 (c -) 和(T + )代表着相对压缩和拉伸分别就有关条文的表面，因为它发生表示其周期。从基本的弯梁理论来讲，这里强调的是由于拉伸顶点，在最外面的圆截面纤维仍然在振动。该性质的限制，还可以防止移动相对固定的指标，(NA)的中性轴答。作者在这个例子中弯曲应力值不变，是因为弯曲的影响与钢丝绳相结合的旋转离心力的影响。依赖的弯曲应力在这个例子中边界条件，类似的是，对X轴旋转约束的例外以上。因此，参考字母A，如图所示。 3，现已成为无旋。这一事实证明了一个不变的超过三分之一由垂直方向的文字完整周期。此外，顶点的信参考A遇到弯曲应力循环，因为它完成一个革命一轮跨度。这里值得一提的是在那里被认为是相对中性轴转动时变方向。 图3曲线中表示无旋运动应力发生的静点。 该图表明得很清楚:应力梯度内部没有损失的原因是相邻层之间没有相对运动的股，也没有任何钢丝自身扭曲。在气动阻尼的情况下，与链间的摩擦和球及插座接头，钢丝绳的摩擦损失在这种情况下(曾设置过)将继续无限期地震动。但是，在这有很多的无旋运动的研究钢丝绳的振动和波动方程的双曲管相似的结构系统普遍较实际更加有吸引力。在这些边界条件，可以得知，所有的跨区域的钢丝绳的周期性下滑超过或对邻近纤维。弯曲的径向和正常组件(弯曲)胁迫明显的时间依赖性和对钢丝绳的定位功能的空间。同样，剪切流动，纵向和横向剪应力分量，也就方向而定。此外，由于这两个相辅相成的，强调是对曲率R的定义的关系。凹陷到跨比或动态幅度相当于对跨比和振动频率发挥理事的内部能量损失率具有重要作用。 最终以上大致可以划分为横向钢丝绳疲劳所描述的能量损失的物理结果。在这种 情况下疲劳是由在他们共同拉伸强度下一般损失以及韧性中个别钢丝体现。在持续的暴力振动下，疲劳较为严重，个别断丝是可能的。现代采矿工程师使用原位非破坏性检测技术，定期检查，能很快查明这些损坏的钢丝绳和提醒即将损坏的钢丝绳。 实验装置 在本次实验中所用的矿用钢丝绳的规格为43.5毫米(标称直径)、规格6 × 32(14/12/6三)F、线性质量密度为8.00公斤/毫升。 在图4中，一定长度的钢丝绳是从不等的高度支撑。边界条件的限制在支撑钢丝绳实验中，推力轴承是全部用于中央纵轴线旋转。 一个预定的张紧力和有限几何，可以得到了在上的较低端的位置，用一个液压千斤顶固定下轴承外壳的支撑锁装置的。该插孔运动受到限制。推力轴承上是铰链，以适应任何所需的斜坡，一旦上层轴承倾向进行了调整，轴承外壳被锁定到某个位置，以配合钢丝绳的斜坡。这样，推力轴承受到通过其轴向中心的纯轴向推力(张力)。悬挂钢丝绳通过一个电动马达的低端转动，齿轮传动，一系列的链条驱动器，以及雷诺的耦合减少。这是位于雷诺耦合之间的钢丝绳驱动的结束和传动装置，并有隔离从激发钢丝绳的动态响应的优势。这是可取的，因为在机械反馈的形式反映了纵向和横向波可以(有足够的时间)调节，特别是在附近的共振条件的频率和振幅的激励。 该电机速度由3,7千瓦的三相变频传动装置控制，进行了由一个光电革命计数器。张紧的水平分量是衡量一个在线液压传感器，这是位于下降的背后推力轴承与钢丝绳旋转。电机传动，链传动，这是安装在耳轴和下扭矩的反应，这个单位可旋转耳轴轴承和有关运动被抵消。因此，作为应用服务的平衡力矩指相对运动。为了摆脱中央测功机运载的自然自然摆型振动，延长臂固定在沉浸机油的长度中。图1(a)，那里的实验室模型的动态和物理性能均在模拟振动系统嵌入式经历两次内部的功率损耗。在模拟模型特别值得注意的是支撑间的距离如2点所示。图1(b)表明实验室之间的模型和模拟模型的第二模式振动等价。之间的支持，这里给出的模拟模型距离是4 L，其内部功率损失的4倍，该实验室模型。最后参考图1(c)显示了实验室之间的模型和模拟模型在第三种模式振动等价。该损失和模拟模型显示距离跨度为6倍的实验室模型。 显然，传统文献中使用的长期下垂的跨比带来了一些难度。 Kloof金矿的应用实例 该调查是正在进行的研究项目的一部分，在20世纪70年代初开始在矿业研究实验室，约翰内斯堡会议厅。该出版物3 ,7 - 9刊用于从Kloof金矿作为源材料收集现场数据，努力造成这些研究多数。由于笔者熟悉该煤矿的几何特征，频率和横向振动振幅特征，因此认为这是一个值得的工作，本文随着一根钢丝绳在1号矿井的井筒安装系统的双鼓缠绕内部的功率损耗分析结束而结束。在常用情况下，共振条件是选择性讨论的 举例说明，当钢丝绳(接触网)从绳股扩大到天轮，横向频率是对Lebus的整数倍于卷筒交叉频率。为了便于讨论，最坏的情况使用振幅讨论。该数据适用于轴1以下第1号井。 Kloof使用的钢丝绳线的物理性质，是结构6 × 30(12/12/6 三)F和线性质量密度为8,49公斤/米。在本文所述的调查所使用的钢丝绳的性能的几何形状和密度的钢丝绳是不是太相似的。对于这个原因，钢丝绳Cl 和Cz假定为42,75 J和0,34毫升。 该方程的使用和模式如上面给出的参数，投入的结果如以下功率损耗: 初看，这些值看似微不足道，一些工程师甚至不会去考虑。但与6300 kW直流电机绕组这是很正确的。不过，考虑到由于钢丝绳疲劳损伤现象是不可逆转的，超过了75000人/次，平均每钢丝绳持久，必须认真考虑中模态之间的受力和累积损失效应，他们可能限制钢丝绳的工作寿命。 结论 本次调查采用实证的方法，引入了具有很强的综合性和高效率的技术量化的复杂矿井提升非平面横向振动钢丝绳发生所有谐波模式阻尼机制。笔者的经验来看，无论理论还是实验证据都以(无旋，旋转)机械等价为基础，这在文献中已经遇到。在该方法的基础上，实际的钢丝绳，其内部的摩擦特性测试要求是，任何具有合适的实验室钢丝绳尺寸可以受到这里描述的动态测试-----双弯曲型阻尼特性进行鉴定的实验方法。它是，但是，随着阻尼一致的过程中遇到的类似系统，并符合质量剪切到粘度阻尼，或一个是成比例的曲率变化率的类型。在一个关于在这种情况下阻尼确切性质具体的大量信息的情况下，所确定的阻尼特性类型是合理的:他们以简单明了，确保内部功率损失定量正确评估所取得的成果。 应该强调的是，以下结论是对单一固定施工矿井提升钢丝绳动态响应测试方法。因此，在应用到其他一些不同的几何构造矿井提升钢丝绳有些困难。然而，这些潜在的分歧具有一些定性的特征，可以概括和 总结 初级经济法重点总结下载党员个人总结TXt高中句型全总结.doc高中句型全总结.doc理论力学知识点总结pdf 如下。 (1)矿井提升钢丝绳内部功率损耗的特点可以用两个实验定性和定量的确定参数:1阻尼性能系数Cl和曲率特征Cr，随着数学发展，使之成为可能，这两点系数和钢丝绳(振幅，跨度动态环境，频率)，以评估内部功率损失数额。 (2)曲率半径存在的一个关键是上述内部功率损失随着幅度对跨比呈线性关系增加。实验证据也显示了这个线性区域的损失为振动模数增加的平方。 (3)临界值以下为曲率半径，内部损失成倍增加，并试图探讨在该地区发生的损失。 (4)对于典型的矿山设备，非平面横向振动模式有较高的振动与疲劳损伤相关的不良影响显着影响。这一观察是对实证结果的应用取得以这里现有金矿为动力条件。 研究前景 调查的过程中，出现了各种关键的问题，最相关的是在构造分析中使用的单个钢丝绳的那些与未知的行为不同的钢丝。进一步的研究很可能考虑的因素，可能影响阻尼性能和使用的矿井提升各类钢丝绳曲率特征。简言之，在这方面的影响下列因素是认为头等重要的: (1)拉伸长度，(2)组成的成份股的数目，(3)钢丝绳结构类型:圆形，三角形，非扭转，并锁定线圈，(4)核心材料的物理性能， (5)钢丝绳润滑剂。以上总结的五点评价了关键问题:在今天使用的矿井提升机钢丝绳在阻尼特性(如本文定义CL和CZ)和预期疲劳寿命周期之间是否存在一个函数关系,作者相信这种关系确实存在，并对这一领域具有一定影响，并应用于实际采矿业。 在德班韦斯特维尔大学开发的实验技术和测试仪器在机械工程实验室已被证明是准确和可靠，并提供内部阻资料必要信息。 徐州工程学院毕业设计(论文) I 徐州工程学院毕业设计(论文) 2 徐州工程学院毕业设计(论文)