Dr.-Ing. Wolfram Vogel, Dr.-Ing. Wolfgang Scheunemann
The wire rope celebrated its 175th birthday in 2009. Since its invention, it has been one of the essential design elements of our technological society. The invention of the steel wire rope by senior mining advisor Julius Albert marked the beginning of intensive analysis of the service life steel wire ropes running over sheaves, a branch of research which is cultivated in depth to this day in a variety of research institutes. The results of service life analyses (for example by Mül1952, Fey2000) have impacted on the dimensioning rules applied to rope traction in a variety of applications. Early examples include the DIN 15 020 standard, as well as more recently the EN 81-1, Annex N.
Findings derived from rope service life research and calls for adequate rope service life and reliable detection of the discard age of ropes form the basis for the rules applied when dimensioning wire ropes. Ropes, sheaves and drums for lifting appliances are designed on the basis of DIN 15 020, which was the first standard to take operational stability into account, as well as utilization frequency and intensity and the method of transport. One of the drawbacks of this standard is that it allows the determination of only a certain combination of rope diameter and sheave diameter. This restricts the scope of the designer. Fey2004 offered up suggestions for variable design taking into consideration conditions in the rope drive. EN 13 001-3.2 – which also contains a rope design method geared to the rope drive and operating reliability – is due to replacethe DIN 15 020 standard in the future, although this has so far failed to materialize due to justified objections.
In the field of passenger transport, the dimensioning rules for steel wire ropes used in traction sheave lifts, shaft conveyor systems and cable railways are known. In shaft conveyor systems and cable railways, the sheave to rope diameter ratios D/d have been practically defined. In cable railways this also applies to a large extent also to the rope safety factor Sf, which describes the ratio of admissible load to minimum rope breaking force/computational rope breaking force. In shaft conveyor systems, somewhat surprisingly the safety factor is reduced with increasing depth. There are economic reasons for this, whereby this “loss of safety” is compensated by additional measures performed during inspections. The Technical Rules for Lifts TRA, and also the earlier draft of EN 81-1:1994 called for a diameter ratio of D/d ≥ 40 and Sf ≥ 12 against the minimum rope breaking force/practically the equivalent Sf ≥ 14 against the computational rope breaking force. Limits were laid down for maximum compressive forces. The drawback was that a combination (D/d; Sf) was defined without taking into account the bending sequence in the rope area most exposed to tensile, flexural and compressive forces. This gave rise to a risk of permitting rope drives with small rope service lives in which the discard age could not be reliably recognized between two inspection intervals. In the valid draft of EN 81-1:1998, Annex N presents a dimensioning rule in which an equivalent number of bends is determined for the bending sequence of the most exposed rope section, the sheave diameter and groove geometries, resulting in the calculation of a safety factor. The calculation is based on a number of trips until the discard age (N = 200,000 trips/year for 3 years), so allowing the discard age to be recognized between two inspection intervals in more highly frequented lift installations. This method draws on the findings described by Fey2000 and was described in detail for the fi rst time in Schi2002.
Extended requirements for traction sheave lifts
The definitions laid out in EN 81-1, Annex N result in a rope drive whose service life is limited and in many cases, for instance in the mid and high-rise sector, is considered low. It should be borne in mind here that the intention of this computation method is predominantly to satisfy safety objectives.
However, the world of lifts and elevators is highly diversified. In complete contrast to the highly frequented installations discussed above, in the field of residential lifts or when dealing with installations known to be little frequented, the definition provided by EN 81-1, Annex N is saidto be too “lavish”. When dealing with this type of lift, the obvious solution is to design the rope drive in such a way that the D/d ratio and safety factors are reduced in order to save traction-related costs and also permit optimization of the installation space. However, as might be expected, smaller D/d ratios and rope safety factors result in a reduced rope service life.
DRAKO 250T d ≤ 8 mm and D/d < 40
For the DRAKO steel wire rope type 250T d = 6 mm, d = 6,5 mm and d = 8 mm, the number of trips to discard is calculated for practically any optional sheave-torope diameter ratios, safety factors independently of the EN 81-1 calculation and differently shaped sheave grooves. This applies here for a case in which the rope section exposed to the highest levels of stress runs over the traction sheave andtwo deflecting pulleys. Both identical diameters in the traction and deflecting pulleys DTraction sheave = DDeflecting pulley and different diameters DTraction sheave ≠ DDeflecting pulley are analysed.
For the traction sheaves, V-grooves from γ = 35° to γ = 60° and U-grooves with undercut angles φ = 75° to φ = 105° are used. Reduction factors in accordance with EN 81-1, Annex N are applied. Unlisted reduction factors are determined by extrapolation.
EN 81-1 is based on a minimum number of trips to discard age, which in some casescannot be achieved with the above sheave-to-rope diameter ratios. The aim is now to demonstrate the number of trips which may be expected until discard age with the small D/d ratios for different rope safety factors Sf, differently shaped grooves and different sheave combinations.
As the parameters we are dealing with here are unconventional in the elevator construction sector, calculation errs on the side of safety, for instance by taking into consideration increases in rope force due to uneven rope tension, friction, acceleration and so on. Higher fatigue bending performance in DRAKO ropes compared to the total population according to Feyrer are taken “cautiously” into consideration.
Fatigue bending tests with Drako 250T d ≤ 8 mm
Extensive fatigue bending tests have been executed in the past on the DRAKO 250T d ≤ 8 mm. Inspection of the ropes during testing always permitted the discard age to be determined in plenty of time prior to rope breakage. The determined mean number of bends to discard in DRAKO ropes is substantially higher for small safety factors than the values shown in Fey2000. With rising rope safety factors, this benefit is increased.
Increase of rope tensile forces
The anticipated static rope tensile forces were increased on a fl at-rate basis for the calculations in order to take account of effects arising from acceleration, guidance, distribution of force etc.
Deviation
Calculation of the mean and statistically restricted number of alternating bends to discard in accordance with Fey2000 is based on fatigue bending tests using a large number of ropes of the same design from different manufacturers and product batches. The standard deviation is specified here at approximately lgs = 0.3. The number of alternating bends to discard determined during fatigue bending tests with the rope DRAKO 250T d ≤ 8 mm taken from different product batches show a smaller scatter of less than one third of the above mentioned standard deviation.
Damage accumulation hypothesis
In the case under analysis, for instance, the rope section exposed to the highest level of stress passes over two deflecting pulleys and the traction sheave. The number of trips up to discard age is
Type testing certificate G515
Steel wire rope DRAKO 250T is intended for lifts both inside and outside the requirements set out in EN 81-1. The safety factor Sf and/or the traction sheave to deflecting pulley diameter ratio D/d may deviate from the requirements of EN 81-1. If the safety factor Sf falls within the requirements of EN 81-1, Annex N, the lift in question is in compliance with the standard. No additional measures are needed for operation. If the safety factor Sf lies outside the requirements of EN 81-1, Annex N, the lift in question is one with a “reduced number of trips”. Additional measures are required for operation, such as a reliable trip counter.
Where the rope section exposed to the highest level of stress travels over the traction sheave and two deflecting pulleys (with the bending length determined on the safe side corresponding to two distances between storeys), the anticipated number of trips can be estimated for different diameter ratios D/d and safety factors Sf in accordance with available graphs, whereby “single variety D/d” and different D/d ratios for the traction and deflecting pulley were taken into consideration. Intermediate values can be interpolated using a provided method. Finally, the range of validity of the type testing certificate G515 is summarized in Table 1.
Summary
To date, the availability of cost-optimized drive systems to serve the field of low and medium-frequented traction lifts has been unsatisfactory. Reducing the costs of the traction system always entails reducing the sheave-to-rope diameter ratio D/d. The requirements outlined by EN 81- 1 restrict the degree to which this ratio can be reduced. Type testing certificate G515 introduced by Pfeifer DRAKO on 21/08/2009 formulates additional measures which can be taken, so opening up scope for almost any optional sheaves, diameter ratios D/d ≥ 25 and rope safety factors to be used in deviation from the computation method set out in EN 81-1, Annex N, while still ensuring compliance with safety requirements.
Bibliography
Fey2000 Feyrer, K.: Drahtseile. Bemessung, Betrieb, Sicherheit (Wire ropes. Tension, Endurance, Reliability). SpringerVerlag 2000
Fey2004 Feyrer, K.: Berechnung der Seillebensdauer in Seiltrieben (Calculation of rope service life in rope drives ). Konstruktion (2004) 6, p. 78–81
Mül1952 Müller, H.: Versuche an Drahtseilen und ihre Ergebnisse für den Betrieb (Tests on wire ropes and their results for operation ). Fördern und Heben 2 (1952) 9, p. 229–234
Schi2000 Schiffner, G.: Anhang N: Ermittlung des Sicherheitsfaktors von Tragseilen. (Annex N: Determining the safety factor of suspension ropes) Heilbronn Lift Conference Publication 2000
DIN 15 020 Lifting Appliances; Principles Relating to Rope Drives; Calculation and Construction. 1974-02
DIN CEN/TS 13 001-3.2 Cranes – General design – Part 3.2: – Limit states and proof of competence of wire ropes in reeving systems. Preliminary Standard, 2009-05
EN 81-1 Safety rules for the construction and installation of lifts. Teil 1: Electric lifts, German draft 1998