Calculation of the anticipated service life of steel ropes in elevators has recently become a frequently imposed requirement – a request which would frequently seem to call for the powers of a crystal ball. The result of any service life calculation depends on a wide range of factors, which are described and appraised in the following essay. This article seeks to refute the impression that service life is something that cannot be influenced. It provides system users with a number of pointers which permit a positive impact to be exerted on rope service life. The players involved here are elevator operators, elevator producers and rope manufacturers, whose combined work exerts a determining and sustainable effect on the service life of ropes, Fig. 1.

It should be noted at the outset that use of the term service life implies that a definitive time period has been calculated. In fact the calculations which follow always refer to elevator trips and still have to be transposed to a utilization periodtaking into consideration the utilizationfrequency of the elevator.
The individual spheres of influence are indicated in Fig. 2. This graph also indicates which players exert an influence at which time / which phase is affected.
It is clear that the elevator operator exerts only a limited influence on rope service life. Maintenance of the installation is the only area in which the operator appreciably impacts on service life. Maintenance in this context encompasses rope maintenance and monitoring of rope tension during operation. These points are specifically weighted in the following.
Rope design and rope diameter
The single most important aspect through which the rope manufacturer exerts an influence on rope service life is, alongside the actual manufacturing process itself, through the design, i.e. the structure of the rope. The following description of the calculation process includes a presentation and evaluation of the influencing factors determined here. The determining factors for which the rope manufacturer is responsible also include the wire material used and the components lubricant and fibre material.
The rope diameter is generally determined by the elevator designer. It is only where close discussion takes place with the rope manufacturer during the elevator configuration phase that the rope manufacturer can exert any influence on this parameter. In close correlation with the selected sheave diameter, this represents a focal aspect for the anticipated rope life.
The variables which determine service life are defined at the latest when the rope course, the necessary drive capability and the resulting groove diameter have been determined by the elevator builder. Elevator producers are increasingly confronted by the conflict between the need to make cost savings on the one hand and to find a technically acceptable solution on the other. This challenge encompasses factors such as determining the necessary number of ropes, the consequent withstandable pressure of ropes on the sheave and the required power transmission. It is evident that higher tensile stress – where all other parameters remain constant – will lead to a reduction of rope service life.
As the service life of ropes can be influenced by factors during installation, other important points of relevance for rope service life should be taken into consideration at this point. Running over sharp edges or soiling by dust or dirt from the building site will bring about a sustained reduction in the service life of ropes. Consequently, efforts should be made to ensure the straightest possible rope course without diagonal pull. These are factors over which the rope manufacturer has no influence.
During the operating phase of the elevator, the maintenance contractor should pay attention to the rope system by taking steps to ensure even tensile stress and an adequate supply of rope lubricant. Analyses performed by the Institute of Mechanical Handling and Logistics at the University of Stuttgart have shown a marked reduction in resistance to flexural fatigue when ropes are tested without lubrication. The study concluded a reduction of the bending resistance to just 20 % of the level expected in a lubricated rope. Another aspect exerting a significant influence on rope service life is regular monitoring and adjustment of rope tension. Table 1 indicates that levelling out of the rope tension can achieve an extension of rope life. The potential here is considerable.

If it is possible to reduce the force differential between the individual suspension ropes of an elevator installation to 10 % then – with all other application conditions remaining equal – a service life increase of almost 40% can be achieved. Modern systems of measurement for rope force measurement and adjustment can significantly simplify the work involved here, [Henn09].
2. Calculation of the service life of running ropes according to Feyrer
The formula below has appeared in a number of publications (such as [Feyr2000]) and in the form shown below was devised by Prof. Feyrer.
whereby
b0 – b5: Calculation factors, so-called Feyrer factors
D: Diameter of the pulley / traction sheave
d: Rope diameter
R0: Strength category of the rope
l: Bending length
S: Rope tension
The service life formula was devised on the basis of an extremely high number of continuous flexure tests using the test set-up illustrated in Fig. 3 [Feyr2000].
Calculation of the bending resistance for an elevator rope takes place using a multiple- stage process. Firstly the forces are determined on the basis of the elevator data. Calculation of the final rope tension forces is performed on the assumption that the dynamic forces of relevance for service life will be determined by means of correction factors (fs1 – fs4). For this, assumptions are made in respect of the car guidance, the rope efficiency, the number of parallel ropes and the acceleration forces in order to arrive at the operating speed.
For calculation, the bending lengths are superposed by the relevant load changes in rope operation, and the resulting specific service life determined for each rope section. To simplify the process for a specific elevator, it is possible to assume a bending length of l = 6 m, which corresponds to approximately the distance between two storeys and represents the rope zone subject to the highest degree of stress.
The bending resistance obtained from the above formula is corrected in the nextstep by the factors fN1 – fN4. These factors take into account rope construction, rope lubrication and parameters from the installation, diagonal pull and the shape of the profile used in the traction sheave to achieve traction.
Using this methodology, the relevant bending resistance can be calculated for each element of the rope drive. A distinction must be made here according to whether testing takes place up until rope failure or retirement point. For practical application in elevators, the retirement point should be taken as a basis for calculation.
It is also important to note that the calculation only needs to be performed for the most heavily damaged section of the rope. All individual bending resistance values are now available as an intermediate result. Using the so-called Palmgren Miner rule, the individual incidences of damage can be cumulated over the number of trip cycles
Depending on application in residential, office or hospital installations, further correction of the number of trip cycles can be performed on the basis of the divergent number of internal trips taken within the building.
3. Sample calculations
To illustrate the calculating method used, a service life calculation has been performed in the following for the elevator illustrated in Fig. 4, based on the assumption of freely selected elevator parameters.
Calculation was performed at Pfeifer DRAKO using a program developed specifically to work with this methodology. Fig. 5 shows a printout.
With the aid of this program, it is relatively simple to carry out comparisons for different rope configurations and load situations.
Fig. 6 illustrates the development of rope life as a result of varying for instance the rope diameter while retaining constant elevator components.

It is clearly evident that with the same sheave diameter the service life of the ropes diminishes as the rope diameter reduces. The tendency currently in evidence towards miniaturization in the elevator construction industry may be assumed on the basis of this graph to be detrimental to rope service life. Provided this process is carried out against the backdrop of a pending decision, it is still possible to take steps to avoid surprisingly short rope service life. It is vital for the question of the required or expected number of trips to be raised as early as the planning phase. For a lift that is only rarely used, it is easily possible to reduce installation costs by compromising on rope service life. In contrast, however, the service life of ropes used in high-performance elevators can be increased at minimal expense. The program presented here provides a tool for calculation of the service life of ropes in elevators which provides a meaningful basis for a decision and which permits different elevator configurations to be compared.
4. Outlook
Two underlying tendencies are evident in the elevator industry. On the one hand, elevators are being installed and also retrofitted in an increasing number of buildings in order to enhance their residential value. On the other hand, a new elevator requirement profile has come about for particularly high buildings in respect of factors such as rope length and travel comfort, and consequently also for the ropes themselves.
As a rope manufacturer, Pfeifer DRAKO has risen to these challenges and developed new rope types to address the relevant application requirements. In some cases, certificates have to be supplemented by a service life calculation in order to ensure that the rope set offered for the simple elevators described above is safe. On the other hand, ever increasing travel heights are calling for further development advances in rope technology. To this end, we offer joint development between the elevator and the rope manufacturer. It is only by joining the two sets of development capacity that custom-tailored solutions can be developed. The rope cross-sections in Fig. 7 illustrate possible methods of not only enhancing bending resistance but also impacting positively on deflection behaviour.

Compacting strands for elevator ropes is conceivable with a view to extending service life and also reducing the diameter of ropes. Plastic cores improve the support action of the strands. These developments were presented to the trade public at the interlift 09.
Bibliography:
[Feyr2000]: Feyrer, Klaus: Drahtseile: Bemessung, Betrieb, Sicherheit (Wire ropes: Dimensioning, operation, safety) Springer Verlag 2000
[Henn09] Company Publication Henning GmbH WeightWatcher mobil MSM12
[Sche09] Scheunemann, Wolfgang: Berechnung der Seillebensdauer in Aufzügen (Calculation of rope service life in elevators)
Lecture delivered at the 7th Schwelmer Lift Symposium