Issue 6/2004
11/02/04
On the use of small-diameter steel wire ropes as suspension means
Dr.-Ing. Wolfram Vogel (Institute of Mechanical Handling and Logistics at Stuttgart University)
The traction elevator occupies a rather unique position at the juncture between many disciplines: mechanical engineering, electrical engineering, computer science, civil engineering, architecture and facility management technologies. The requirements set forth in terms of technical equipment and safety as well as in cost management during both the construction and operation phases are many and varied. And in the center of this catalogue of related disciplines and (in some cases competing) requirements, the suspension means are a central mechanical element in traction elevators.
Category: Issue 6/2004
Posted by: Editor
Steel wire ropes are normally used in traction lifts. Cost pressures in the building and operation of traction lifts, reducing space requirements with a view toward lifts without a separate machine room and the desire for unique selling propositions on the market have given rise to alternatives in suspension means such as aramid fiber rope, flat belts with steel cord reinforcement, etc. Drive sheave diameter can be reduced significantly with the application of such innovations. With the potential elimination of the limitations on the smallest permissible diameter for steel wire ropes, otherwise set at d = 8 mm in the technical regulations, using smaller diameter ropes while maintaining the same ratio of rope to sheave diameters (D/d) will make it possible to achieve smaller sheave diameters, as well. In addition, there is a desire not to increase the number of ropes – and thus the load-bearing metallic cross-section – in spite of the smaller rope diameter. Ropes at diameters of 6 mm and exhibiting higher wire strength levels have already been tested in conjunction with the traction drive and have been awarded an EC design certificate; such ropes can now be found in service.
Testing for wire ropes covers the requirements relevant to safety – in regard to adequate service life, reliable recognition of readiness for replacement, i.e. detecting the point at which the rope has to be changed out, and this in good time, before a hazardous status occurs, and sufficient but at the same time also limited traction capacity. Any alternate suspension means will also have to satisfy these requirements.
The service life and retirement point for steel wire rope will be dependent on a number of parameters associated with the rope and the elevator. The ratio of the sheave and deflection pulleys diameters to the rope diameter, the rope’s tensile strength and the shapes of the grooves on the sheave and deflection pulleys along with the rope diameter itself will all influence the rope’s service life and the point at which it will have to be replaced. The following discussion will examine the service life of steel wire ropes running over sheaves along with, and in particular, the influences specific to elevators on rope service lives and the methods used to calculate the service life for running ropes. We will examine all this against the background of international standardization in elevator engineering. The influence of rope diameter on the pressure exerted by the rope on the groove and thus on traction capacity will be touched upon.
The life of a running elevator rope
The car and counterweight, both guided by rails, are joined one with another by means of ropes and are connected to the drive sheave by way of friction. The differential force resulting from the weights of the car and the counterweight will have to be transferred to the rope by the drive by way of the friction at the drive sheave grooves. The ropes are subjected alternately to flexure and tension, but also to pressure, as they pass over the drive sheave and deflection pulleys. A rope’s running across a drive sheave with a vee groove and a deflection pulley with a semi-circular groove induces alternating stresses in the rope; those stresses tend to force the rope to assume an oval cross-section.
The service life, when running over sheaves, is dependent upon rope parameters such as
- Rope design,
- Rope diameter d,
- Rope core,
- Nominal wire strength R0,
- Lubrication, etc.
but also upon other system parameters such as
- Rope tension S,
- Ratio D/d of sheave diameter to rope nominal diameter,
- Bending length l,
- Deflection angle,
- Groove profile (semi-circular groove, shaped groove),
- Skewing angle,
- Groove material,
- Type of bending,
- Multilayer winding,
- Combination of tensile and bending loading, etc.
The “multilayer winding” parameter has been included on the basis of the tradition of the IFT research efforts in regard to cranes but is not in fact relevant for elevator engineering.
The rope’s running, i.e. the bending of the rope, is made easy only because the wires in the rope can slip one against the other. It is due these relative movements, however, that various manifestations of wear appear at the wires. Figure 1 shows typical traces of wear at the contact points between wires and between the rope and the groove. This wear at the wires has made it impossible to date to calculate rope service life, even where exact information is available about all wire tension values.
Only by way of continuous flexure testing was it possible to establish the safety-relevant magnitudes of service life and retirement point, i.e. the number of alternate flexures (N) for steel wire ropes through to failure of the rope or until the time (NA) when the rope will have to be changed out, well in advance of rope failure.
Continuous flexural testing
Continuous flexural testing machines such as the one shown in Figure 2 are used for endurance testing. The rope is passed in the machine around the test sheave (below) and the rope drive sheave (above). In response to the oscillating motion of the rope drive sheave the rope moves up and down over the test sheave; the rope assumes the “straight” and “flexed” states alternately and is subjected to flexural loading. During endurance testing the test sheave is placed under load with a lever and fixed masses so that the tensile forces within the rope are kept constant.
The flexing frequency during endurance testing is set so that the ropes being tested will not be heated to above 50 °C. At the IFT laboratory these continuous flexure tests are normally conducted at room temperature, in a dry atmosphere. The test sheaves feature semi-circular grooves at a radius of r = 0.53 times nominal rope diameter (d) and a groove opening angle of 60°; testing is continued until the rope or at least one strand fails. The effect of conditions deviating from the above will be discussed later. Continuous flexural testing is normally suspended as per the R10 series in order to inspect the rope status at regular inter vals. At these recurring inspections the number of wire breaks in certain reference lengths are determined, the diameter is measured, changes in the rope are recorded and all this is used to establish the retirement age and criteria for replacement.
Rope diameter in the service life equation for steel wire ropes, after Feyrer
The service life of steel wire ropes, that is the number of alternate bends under the defined conditions found in flexural endurance testing, can be calculated for wire stress levels less than the so-called Donandt force, i.e. before the 0.2 offset limit of the wire is exceeded,
using Freyer’s equation for rope service life [3].
Taken into account in Feyrer’s equation, in addition to the influencing factors of rope tensile force S, nominal wire strength R0 and bending length l are above all the rope tensile force S, the ratio of diameters D/d and the rope diameter d. The rope diameter, to which the present article pays particular attention, is contained in a single quotient and in mixed quotients in conjunction with the sheave diameter D and bending length l.
There’s no way around statistics
Regression coefficients b0 to b5 are placed in front in the various elements in the service life equations. The regression coefficients have been calculated for the frequently used and standardized rope designs, doing so on the basis of numerous flexural endurance tests using ropes of identical design, drawn from differing lots and made by differing manufacturers. This calculation of the number of bends to break N and the number of bends to retirement NA is effected through multiple linear regression. Figure 3 shows by way of example the number of flexes to break N, plotted against the rope tensile force, related to the diameter for a standard rope with good flexural characteristics, in a double-log depiction. The straight-line regression curves, i.e. in this case the mean values for the numbers of bends within the useful rope tensile force range and smaller than the Donandt force, are also plotted here.
The individual results are scattered around the calculated mean values. Due to the scattering of the test results the statistically limited numbers of bends, N10 and NA10, were determined. They correspond to safety levels of 95 % or a maximum of 10 % of the ropes exhibiting breaks or being ready for replacement. The corresponding constants b0 to b5 are summarized in [3]. The service lives for fiber ropes running over sheaves are very similar to steel wire ropes [5, 9, 10, 11, 12].
It was only possible to make assumptions for belts using steel or fiber reinforcing cord for use in elevator engineering; ultim ately we are dealing here, too, with ropes exhibiting small diameters. The IFT does not yet know of any testing to evaluate the number of bends to failure or retirement, carried out either in the laboratory or in the field.
Influence of rope and sheave diameter on rope service life
The service life formula for steel wire rope will have to be explained by way of examples so as to make clear the influence exerted by several parameters on rope service life, these being rope diameter, sheave diameter and rope tensile force.
We see in Figure 3 that as the ratio of diameters D/d rises, the number of bends to failure rises sharply as a result of declining flexural stresses. For an 8 x 19 Filler rope with fiber core with a nominal diameter of 12 mm the number of bends to failure, at rope safety factor of ν = 12, rises by a factor of 8 when the diameter ratio is raised from D/d = 25 to D/d = 40.
The influence of rope diameter on the service life – at smaller rope diameters the service life increases, all other factors being equal – is, as set forth by Feyrer [3].
Equation (2) shows that the rope service life will be extended by 25 % if the diameter of the rope is halved. The influence of rope diameter on rope service life is hardly negligible when compared with the D/d ratio but is indeed less significant.
Retirement – Timely replacement
The number of bends to break is determined on the basis of retirement criteria such as rope deformations, major rope damage, strand failure, wire failure, rope diameter, rope lay length, corrosion, wear. In exceptional cases the time in service will also be used. With the exception of major rope damage, the other criteria will advance over time and indicate the retirement point by their appearance, in part across reference lengths. The wire breaks are far and away the most important replacement criterion. For elevators, the number of breaks to retirement are applied as per DIN 15020 [2] and drive groups 2 m to 5 m.
Laboratory and practice – A mismatched pair?
Calculation methods and flexural endurance testing are both models which are intended to replicate reality as closely and precisely as possible. Calculation methods used in safety-relevant sectors, such as the suspension means used in traction lifts, will have to be measured against this expectation.
The calculation of service life for ropes running over sheaves (Equation (1)), using constants typical for ropes, applies only to test conditions found in the laboratory. In real-world elevator operations, the conditions will normally deviate from the test conditions. In preparation for forecasting service life for an elevator which is being planned or has been built, the influences of the system’s parameters on the rope service life will have to be known; they will have to be taken account of by employing adjusted correction factors when calculating the number of trips.
Regarding the topic of correction factors, two research projects at the Institute of Mechanical Handling and Logistics, Stuttgart University, should be mentioned; they are devoted particularly to the derivation of correction factors for elevator conditions, such as skewing and a combination of grooved profiles.
In a research project which was approved and launched in November 2003 (sponsored by the Industry Association for Escalators and Lifts, a unit of the VDMA in the Working Group of Industrial Research Associations [AiF]) aimed at a systematic and in-depth examination of the influence of the groove shape on rope service life, the intention was to use continuous flexure testing for the first time while taking slip and groove geometries and combinations into account, under conditions very closely approximating those found in elevators today. The objective is – working on the basis of reproducible continuous bending trials in a situation close to the conditions found in practice – to derive correction factors for the particular groove shape, this in comparison with the “corresponding semi-circular groove.”
The influence of angular strain on rope service life and the retirement point is currently being studied in detail at the IFT in a project sponsored by the German Research Society (DFG). In this research project systematic flexural endurance trials are being conducted using rope designs typical for elevators in which the angle of incidence or skew and the feed direction, the groove opening angle, the rope tensile force and the ratio of diameters are all varied within broad limits. The service life will decline at varying rates as the skewing angle rises, the exact variation depending on the rope design. The results of the investigation, to be included in a dissertation [7] soon to be submitted, would indicate that the correction factors previously used for skewing will have to be reworked.
Calculation of rope service life as per EN 81-1, Annex N
The method used to calculate the service life for wire ropes, described in detail in [3], is based on the statistical evaluations of continuous flexural testing carried out in the main at the IFT, along with the consideration of bending loads resulting from the travel sequence and particular rope drive data which influence the service life.
The sequence of steps used in service life calculation (Figure 4) is subdivided into the analysis of the rope drive and the calculation of the number of bending cycles throughout the service life. In the analysis of the rope system the most severely loaded section of rope is determined; this is the segment subjected to the largest number of bending cycles and changes in tensile forces. The bending sequence for the most severely loaded rope section is divided into the socalled “bending load elements” (simple bending, reverse bending, combined tensile and bending loads, etc.). The number of bends is established for the bending load elements using the rope tension forces, which will have to be determined as precisely as possible. Using the cumulative damage hypothesis as per Palmgren-Minder, the individual numbers of bends are then compiled and the number of bending cycles over the rope service life is determined.
In EN 81-1, Annex N [1], the requirements in regard to the combination of the safety factor and the ratio of sheave-to-rope diameter are formulated so that – taking into account the number of pulleys, their arrangement and the various diameter ratios within the rope configuration – a minimum service life of 3 years at n = 100,000 return trips will be ensured; Schiffner [4].
The most severely loaded rope segment is identified within the roping configuration, this being the section which experiences the most loading due to bending reversals. The most heavily stressed rope section will run over the drive sheave and a certain number of deflection pulleys. The elements used in the calculation in EN 81-1, Annex N [1], are depicted in Figure 5.
The influence of the drive sheave and the individual deflection pulleys on rope service life will be expressed as an equivalent number of pulleys with semi-circular grooves and with a diameter for the drive sheave. The equivalent number of pulleys for the drive sheave is determined by the type of groove (vee groove, undercut groove) and the geometric parameters for the groove. The correction factors from [3] are converted here, without limitation, to achieve the equivalent number of pulleys Nequiv(t). When determining the equivalent number of pulleys it is necessary to take into account the diameter and the type of bending (simple bends Nps, reverse bends Npr). As regards reverse bending, which is assigned a factor of 4 in recognition of the greater damage potential, the limitation to stationary pulleys with a spacing of less than 200 times rope diameter has been made. Differing diameters at the drive sheave and the deflection pulleys are taken account of by factor Kp. The safety factor Sf can be calculated using the equivalent number of pulleys Nequiv, the drive sheave diameter Dt and the rope diameter dr.The foundations here are the coefficients ai from [3] for the statistically limited number of bends to retirement for a rope with 6 parallel-lay strands, 19 wires per strand and fiber core.
The fairly complex equation is also depicted graphically in EN 81-1, Annex N. See in this regard Figure 6, which shows the minimum safety factor Sf plotted against the sheave-to-rope diameter ratio Dt/dr for selected equivalent numbers of pulleys Nequiv. The values have been plotted for the safety factor Sf = 12 and diameter ratio of Dt/dr = 40.
Rope pressure
Fundamental demands are set forth in EN 81-1 [1] in regard to traction capacity. Adequate traction has to be assured during normal operations, when loading the car and at emergency stops. The suspension means will, however, have to slip if the car should become blocked in the hoistway or if the counterweight should seat on its buffers. EN 81-1 also provides the basis for calculating traction capacity.
While in TRA 003 and in an earlier version of EN 81-1 requirements were set forth in regard to the pressure of the rope in the drive sheave groove, these requirements are lacking in the internationally valid EN 81-1 now in force.
The surface of the rope is exhibits a certain structure and thus the exposed tops of the wires are in contact with the grooves in the drive sheaves and the deflecting pulleys. When observing the pressure phenomena in traction drives in elevators the actual structure of the rope is not used to evaluate the pressure arising between the rope and the groove. Rather, in the case of semi-circular grooves, the rope is always seen as a smooth-surfaced cylinder in the mating groove.
In the vee groove the rope will be in contact with the flanks of the groove only along a single curved line. Defined as a comparison value for pressure is
Here d is the rope diameter and q’ is the pressure, referenced to length, for a portion of the flank of the groove. The pressure, referenced to length, is
Here q is the pressure force, referenced to length, exerted by the rope in the direction of the shaft of the sheave. This pressure (referenced to length) exerted by the rope in the direction of the shaft of the sheave is
where T is the rope tensile force, D is the sheave diameter and z is the number of ropes.
Thus specific pressure in the vee groove is
Rope tensile force T is equal to the weight of the car, the counterweight and any compensating ropes, to include the traveling cable.
Assumed in the case of the undercut groove when deriving the specific pressure at [13] and [14] is progress of pressure across the groove, perpendicular to the rope, following a cosine curve, i.e.
as shown in Figure 7. Maximum pressure perpendicular to the groove occurs in the groove at the transition from the undercut section to the groove, at φ1. Using the contact angle of the rope in the groove φ2 and by integrating the pressure across the groove, one finds the pressure, referenced to length, to be
The pressure in the undercut groove – here once again designated as k – is
The pressure in the semi-circular (not undercut) groove, with a groove opening angle of δ, is
The traction trials using vee grooves, carried out by Molkow at the IFT [6], have demonstrated that the pressure also influences traction. Traction declines as pressure rises.
This, in turn, clearly shows that when dealing with suspension means in elevators a change in one of the “suspension means parameters” will prompt a series of further, interdependent questions.
Summary
Laboratory trails and practical experience belong together in successful product development and optimization. In the theoretical, laboratory calculation of the service life for ropes used as elevator suspension means this becomes clear, as demonstrated by the application of the calculation techniques in daily practice. Amazing in spite of the demonstrated correlation between the calculation and reality, is that individual parameters – and particularly those such as the rope diameter and sheave diameter – can have a strong and ongoing influence on service life. Even small reductions in the sheave-to-rope diameter ratio will induce a serious reduction of rope service life, and these can either no be compensated at all, or only to an incomplete extent (depending on the cost situation), through other measures such as the rope design. One may never forget the other safety-relevant requirements for traction elevators in any discussion of service life: “recognition of retirement age” and “traction capacity.” The Lifts Directive, the formulation of fundamental safety objectives and the elimination of rigid regulations with a narrowly national focus will pave the way for innovative products and systems in elevator engineering. Satisfying all the safety requirements in coordination with the industrial partners participating in the project, the testing institutes and the notified bodies will result in elevators which are safe and reliable and which are accepted on local and international markets.
Bibliography
[1] DIN EN 81-1, Edition: 2000-05. Safety rules for the construction and installation of lifts – Part 1: Electrically powered passenger and goods lifts.
[2] DIN 15?020, Edition: 1974-02. Part 1: Hebezeuge; Grundsätze für Seiltriebe, Berechnung und Ausführung Part 2: Hebezeuge; Grundsätze für Seiltriebe, Überwachung im Gebrauch.
[3] Feyrer, K. Drahtseile: Bemessung, Betrieb, Sicherheit. 2nd edition. Springer Verlag 2000.
[4] Schiffner, G. „Zur Ermittlung des Sicherheitsfaktors von Tragseilen.” Speech at the Heilbronn Lift Conference, 1999.
[5] Wehking, K. H. “Endurance of high-strength-fibre ropes running over pulleys.” OIPEEC Round Table Reading, 1998.
[6] Molkow, M. Die Treibfähigkeit von gehärteten Treibscheiben mit Keilrillen. Dissertation, Stuttgart University, 1982.
[7] Schönherr, S. „Reduzierung der Lebensdauer von Drahtseilen durch Schrägzug bei Seilscheiben.” Speech, 1st Stuttgart Rope Conference, Institute of Mechanical Handling and Logistics, Stuttgart University, 2001 (in 2004 in a dissertation to be submitted at Stuttgart University).
[8] Feyrer, K., Hemminger, R.: “New rope bending-fatigue-machines constucted in the traditional way.” OIPEEC Bulletin, No. 45, Torino, 1983, pp. 59–66.
[9] Feyrer, K., W. Vogel. „Hochfestes Faserseil beim Lauf über Seilrollen.” Draht, Vol. 42 (1991) No. 11, pp. 814–818. English: “High strength polyethylene fibre ropes running over sheaves.” WIRE, Vol. 42 (1992), No. 5, pp. 455–458.
[10] Vogel, W. „Dauerbiegeversuche an gedrehten und geflochtenen Faserseilen aus hochfesten Polyethylenfasern.” Technische Textilien, Vol. 41 (1998), No. 3, pp. 126–128. English: “Bending tests with high-strength PE fiber ropes.” Technical Textiles, Vol. 41 (1998), No. 5, E 39–E 40.
[11] Vogel, W. „Einfluss der Schlaglänge auf die Lebens dauer laufender hochfester Faserseile.” EUROSEIL, Vol. 121 (2002), No. 3, pp. 57/58.
[12] Vogel, W. „Atlasseile beim Lauf über Scheiben.” EUROSEIL, Vol. 121 (2002), No. 4, pp. 64/65.
[13] Hymans, F., Hellborn, A. V. Der neuzeitliche Aufzug mit Treibscheibenantrieb. Berlin, Springer Publishers, 1927.
[14] Donandt, H.: Über die Berechnung von Treibscheiben im Aufzugbau. Dissertation, Karlsruhe University of Applied Sciences, 1927.
[15] Scheffler, M., Feyrer, K., Mathias, K. Fördermaschi nen – Hebezeuge, Aufzüge, Flurförderzeuge. Braunschweig/Wiesbaden, Vieweg Publishers, 1998
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