Rope/sheave contact wear: a fine tuning – First part
Rope/sheave contact wear: a fine tuning
Steel wire ropes and traction/deflection sheaves are generally considered a “commodity”. This is in a way correct, considering that steel ropes have been produced for over 175 years, but from another point of view there are several aspects that need to be carefully considered. In the beginning of the lift industry, great care was devoted to the checking of specific pressure between ropes and sheaves , and also to the linearity of the reeving arrangement.
Not only was this, but also the number of start per hour and rope speed were taken into consideration to assess the maximum value of the specific pressure. It seems that in the recent years such requirement has been withdrawn as it is perceived as “old fashioned”, and the new harmonized standard removed completely any explicit reference to the Specific Pressure calculation.
With the result that today very hard working condition are in service for both ropes and sheaves and consequently shorter life time have to be expected from them.
The aim of this paper is simply to analyze the working condition between ropes and sheaves and pointing out the importance of some issues like specific pressure, deflection angles, sheaves rotated by 90°, etc.
1 – Introduction
Defining the reasons behind the rope/sheave contact wear is not a simple issue: a lot of parameters interact with each other and further to this their mutual relationship are not always clearly understood.
Despite that some simplification could be addressed just to identify the mean causes of “fast” wear when this happens in service after a short period of time. On a traction lift the car movement is achieved by the combination of a finely tuned system; the rope/sheave.
These two elements are transmitting with each other movement with surface contact that in turn creates friction. The surface interaction that develops wear is the main point that will be analyzed hereafter.
Depending on the condition of this contact a lot of consequences are generated into the daily working activity of the traction lift.
Due to the fact that no technical rules are available to address surface wear, and that little extensive research has been performed related to this topic, the following information reported are mainly based on experience gained on the application field. The numerical values reported in this paper are intended only as a rough reference and are purely indicative. All the examples are based on ropes and sheaves manufactured to current standards that technology allows.
2 – Assessment of the main causes affecting Rope/Sheave wear
There are a lot of elements contributing to each other affecting the performance of the rope/sheave wear in service. In the following an attempt is mode to identify the main elements involved in this relationship to understand the different influences that they could develop and in which way they could influence each other.
Before starting the analysis of main elements, it is important to subdivide them into groups, just to have a rough identification.
Causes affecting the surface wear can be classified into the three main groups of elements:
3. load spectrum.
Table 1 – Classification of main causes of surface wear
The above table makes no presumption to be exhaustive. It only deals with the main elements affecting the performance in service of the contact Rope/Sheave.
The way in which the several parameters affect each other is not a simple issue to be assessed, and to try and illustrate this in the table have been drawn three coloured arrows to represent the transversal relationship between the elements:
– Red arrow → raw material relationship
– Black arrow → fine tuning relationship
– Blue arrow → design relationship.
Several other relations could have been identified, but for simple and clear understanding only the above mentioned have been drawn on the table.
This simple classification of the main elements will help in the following description to understand the phenomena that will be discussed, keeping clearly in mind that the wear appearance of the sheaves could have different forms: surface wear or negative imprinting or even a combination of the two.
Such imprints shapes are the result of a combination of several causes that have to be present at the same time to create the above mentioned phenomena.
One of the causes mentioned in Table 1 is not enough to create surface wear, but a combination of few of them could easily lead to the expected wear very quickly. This will be clarified in the following paragraphs.
3 – DEFINITION OF THE CONTACT: STATIC POINT OF VIEW
3.1 Number of strands
Before discussing the details of the various elements that are affecting the wear of both rope and sheaves, we must understand how this contact varies in the groove depending on the number of strands in the rope and this can range from 6 strands up to 9 strands. The most commonly used ropes are the fibre cored with 6 or 8 strands, but a lot more constructions are available in the market: full steel core, mixed core (fibre and metallic), natural fibre core and man-made fibre core (synthetic cores). The most simple indication on the number of points of contact is to look at the cross section of the rope and to examine how
many strands are in contact with the shape of the groove (see the upper part of the Figure 1); but this is not the only element to be considered.
Of greater importance is to examine the longitudinal contact between ropes and sheave (see the bottom part of Figure 1), because a rope with a higher number of outer strands, produces in turn a higher number of points of contact.
In practical terms this means that in a stated condition, if a rope with a higher number of strands is selected, the surface of contact is increased and also the actual local pressure contact is reduced [8,12].
Figure 1 – Increased number of points of contact with the sheave having rope with more outer strands.
3.2 Elementary wires contact
Figure 2 – Basic element of surface contact between a sheave and a rope of 6 strands ordinary lay
When two steel surfaces come into contact, especially when they have different shapes and thus the surface contact will be on discrete points, the first elements that will drive their relationship will be the reciprocal hardness  in conjunction with the contact pressure: from a static point of view when the two surfaces contact each other with great pressure, the hardest one tends to generate elastic-plastic deformation of the softest one.
In the particular case of contact between rope and sheave, it must be understood that the harder surface is the wire and to this must also be added that the contact surface is limited to a discrete “collection” of parallel wires, as represented in the Figure 2.
What is displayed above, for representative purpose, is the area of contact that will be developed between one rope strand and the groove surface of the sheave. What is evident is the surface of single wires composing the strands, and which part of them will be in contact with the surface of the sheave. From that schematic view it is easy to understand that the contact surface is represented by parallel lines in which the wires are touching the groove. The highest will be the number of the rope strands (as discussed before), and the wider will be the surface contact, with obvious benefit to the contact pressure.
3.3 Relationship between rope and sheave hardness
The rope surface hardness is strictly related to the actual tensile of the wires, the higher this is the better the class of ropes and the higher the surface hardness will be. The relationship between rope tensile and surface hardness is represented in the following graph (Figure 3). As an example, in the graph it shows with a dotted line the situation for a rope with a nominal tensile of 1,570 N/ mm2 (or 160 kg/mm2). It can be easily seen that the surface hardness of wires is very close to 450 HB.
It must be understood that the nominal tensile is an average value and that depending on the origin of the wires could develop hardness a little bit higher, so the actual hardness could reach value around 460/470 HB.
To provide some guideline in identifying the required hardness of the sheaves, and due to the fact that no technical rules or extensive research has been performed, the only applicable rule is practical experience.
From some field surveys it has been found that a good balance between rope and sheave hardness is identified when the sheave hardness is roughly the half of the actual wire hardness. Coming back to the previous example, for a rope of tensile 1,570 N/mm2 (or 160kg/mm2) and an actual hardness of 460 HB, the required surface hardness of the sheave is considered around 230 HB.
Figure 3 – Relationship between wire tensile and wire hardness [8, 12].
With these parameters and a fine tuning of the other elements of the project of the complete lift, service life of both has proved to produce a good performance. The surface hardness in itself would not solve the problem of rapid wear or negative imprints, but also other elements concerning the complete lift design have to be taken into consideration.
Despite this the surface hardness plays an important role in the relationship. In case of any doubt it is always advisable to ask the opinion of an expert.
4 – Definition of the contact: Dynamic point of view
After the description of the static contact between rope and sheave we must understand the dynamic behaviour of this system: the rope is not “glued” to the surface of the groove, and during the lift trips some reciprocal movement is generated for several reasons that are analyzed in the following section.
4.1 How the T1/T2 ratio develops
As a fact that must be pointed out that the axial rope stress changes in the act of wrapping around a traction sheave: this is mainly due to the different load applied on the car side (T1) and counterweight side (T2) of the traction sheave.
Figure 4 – Typical simple reeving arrangement 1:1 and 2:1, with detail of traction sheave with T1 and T2.
The variation of axial stress is distributed by friction between rope and groove along the arc of contact. Further to this must be considered that the axial rope stress in the car side could also vary depending on how many passengers are into the car, or empty or also depending on the position of the car in the shaft (also the weight of the suspended ropes could play an important role) [2,6,15].
Considering the above description it is easy to understand that the ratio T1/T2 is a parameter that can vary significantly depending on the operational condition of the lift. The simplest arrangement for a traction lift is represented in the following picture: traction machine at the top; on one side the car and in the other side the counterweight. The rope reeving could be direct 1:1 or indirect 2:1, in both cases different tensions will be developed on the two sides of the traction sheave (Figure 4).
A generally accepted rule is that the system is balanced at 50%, this means that the counterweight balance the weight of the car and fixtures plus half of the rated load. In practical terms if the car and accessory weight is 500 kg and the rated load is 400 kg, the counterweight mass will be 500+(400/2)= 700kg. This situation will generate two different tensions on the sides of the traction sheave, named T1 and T2.
Such differences in load guarantee not only the friction conditions, but also an energy saving in the size of the electric motor, which is directly related to the difference between T1-T2.
4.2 The elastic elongation
One of the most annoying situations linked with the maintenance of traction and suspension ropes, is related to the permanent stretch that is expected in the first period of use after installation.
This stretch is a constructional phenomenon displayed by all kind of ropes, but depending on the application other solutions can be considered to limit this phenomenon: ropes with full steel core or mixed core (steel and natural fibre) could limit the elongation in service and lead also to other benefits like a more comfortable and smooth ride for passengers [8,12]. Related to the elongation, and thus with the relative movement and contact pressure between the rope and the sheave, there is also another important point: the wear and abrasion of the traction groove .
In a traction lift all the possible calculations are made to assure that in every condition the adherence between the rope and the sheave is guaranteed. But in any case clarification of the differences between slip and relative movement for elastic elongation of ropes are necessary.
The first one happens when the friction between rope and sheave is insufficient. The second one happens when the rope passes from a certain degree of stress to another one  (for example, passing from the car side to the counterweight side of the traction sheave: a different stress into the rope is imposed).
To better understand the movement caused by elastic behaviour of the rope, consider a simple lift (reeving 1:1) with the car stopped at the landing floor, the system is in an equilibrium state as represented in the left side of the Figure 5, even if there are different stresses imposed on the two sides of the rope no relative movement is displayed at that time.
Now imagine that the car is filled with the maximum number of passengers allowed: it is easy to understand that into the car side of the rope a significant load rate change will be imposed (see the right side of the Figure 5).
Figure 5 – Elastic elongation phenomena.
To evaluate the magnitude of the movement a mark has to be drawn on the rope and on the sheave at the points where they start to touch each other: in the unloaded condition the sign 1a and 1b represent the condition in the counterweight side, and the marks 2a and 2b represent the condition on the car side.
When the car is loaded with the full payload, and elastic extension will take place on the car side of the rope, the marks 2a and 2b are moved away by a certain amount. Such deviation is a clear indication of the elasticity of the rope and consequently a reciprocal movement has happened between the rope and the traction sheave.
Such movement has to be considered in a positive way, because it makes the groove surface smooth, and the risk for negative imprints is greatly reduced . The amount of elongation displayed in the image has been exaggerated for clarity.
One of the most important concepts that must be clarified is that the modulus of elasticity for a rope is not a constant value: it depends on the rope construction and could vary depending on the loading rate of the rope, and it could also happen that during the life time of the rope other variations could happen [8,12]. The steel wire rope is not a round steel rod for which the elasticity modulus is constant though the cross section.
The rope is composed of several hundred wires wound together to form a strand and each strand is helically wound around a core to form the rope. Considering such complicated geometry it’s easily understood that the modulus of elasticity of such complicated and heterogeneous body is not so simple to be stated. Only empirical tests can allow for the identifying of rough figures. To have the correct figures to evaluate the elongation for each construction the advice of the manufacturer of the rope must be sought.
4.2.1 How determine the elastic elongation of a rope
Figure 6 – Diagram load/extension for 6 and 8 strands ropes fibre cored d. 13 mm.
Is mentioned above, the only way to obtain a reliable figure regarding the elongation characteristics is to perform empirical tests on the rope. Here as an example in the following picture (Figure 6) and is a graph of a practical test performed in Drako facilities on its own production ropes.
The lines do not start from the value zero because before they were obtained, there has been performed several pre-stressing operations to ensure that the rope displayed will achieve its permanent elongation (also called constructional elongation).
Every rope fitted after the manufacturing process once put. in service, in the first weeks of work will display permanent elongation related to the internal assessment of wires and strands.
After this short explanation, it is easily understood that the lines drawn on the previous graph are mainly depicting the “elastic” performance of the ropes subjected to the axial stresses. The inclination of the lines is a clear indication of the elasticity modulus, and is quite simple to observe that such inclination is continuously varying depending on the level of stress imposed to the rope.
There are no fixed values for the modulus of elasticity of a rope, but it can only be estimated after practical tests carried out on the rope after a pre-stressing procedure to eliminate the constructional elongation. Such “elastic” curves are quite interesting in being able to understand the amount of elastic elongation that the rope will perform in service and are a powerful tool especially for a designer dealing with high rise and high speed lifts.
In conclusion, at the varying rate T1/T2, there is also a varying elastic behaviour that will be displayed in service as explained above.
4.3 Fleet angle (or deviation angle)
Another cause of the mutual sliding movement between sheaves and ropes, irrespective whether it is a traction sheave or a deflection sheave, is the fleet angle (as shown with the letter α in the Figure 7). The higher the value of the angle α then the quicker will be the phenomena of mutual damage: the groove sheave will be wearing on one side and the rope will start to be distorted. Further to this unpleasant vibration on the rope body could be generated and self imposed, simply because the strands are rubbing against the groove flange and every time that another strand touches the groove a new transversal vibration is transmitted to the rope. Particular care must be devoted to this aspect in both the design stage and modernization of an old lift: generally the alignments between rope and sheaves are mainly performed by “eye” and this is not a reliable tool.
The fleet angle (or deflection angle) can be estimated by geometrical parameter as the value of the dimensions “x” and “H” of the previous sketch (Figure 7).
Figure 7 – Definition of the “deviation angle”.
Figure 8 – Groove sheave wear mainly on one side, and the resulting distortion of the rope.
As already mentioned in this paper, the rope has a complicated construction made up of hundreds wires wound around strands that themselves are wound around the rope.
This means that there are constructional limits that can not to be overcome, and one of the parameters that highly affect the distortion of such geometry is the Deflection Angle. When a rope approaches a groove sheave in one side of the flange, a lot of torsion is put into the rope up to a limit  over which the strands start to distort and the core protrusion is the result.
At this point the rope needs to be replaced very urgently (see Figure 8).
A practical method to understand the value of the deflection angle is to check the value of the geometrical parameter “x” and “H” as stated in the Figure 7, and with such values entering into the graph drawn into the Figure 9: this picture represents a graphical aid to better understand if the working conditions are acceptable for the rope or not. If the data collected in the field application show you working into the red area of the graph, the physical limits of the arrangement are overwhelmed and damage will occur.
Figure 9 – Deflection Angle graph
Again it must be clarified that such limits are mainly based on practical experience and are not mentioned in any legislation or technical rule. The only rule that states something in this area and that could
be accepted as a recognised standard is the ISO 4309 dealing with steel wire ropes for cranes .
4.3.1 Sheaves turned by 90°
There is a particular situation in which a variable deflection angle could be generated, depending on the position of moving sheaves into the shaft.
As an example see Figure 10 which represents the deflection sheave on the top of the counterweight in the most critical position: the reeving arrangement 2:1 is considered with machine on the top of the shaft. When the car approaches the bottom landing, the counterweight is in the highest position.
In this particular configuration the deflection sheave on top of the counterweight is in its closest position to the traction sheave. If not well evaluated at the design stage, this condition could lead to several problems mainly related to lateral wear of the sheaves, noise in the shaft during the approaching to the bottom landing of the car, torque induced into the rope, etc.
Figure 10 – Sheaves turned by 90° in the most critical configuration
Figure 11 – General indication for Sheaves Turned 90°
No technical rule is available to advise the designer on the right geometrical parameter to realize such sheave turning of 90°, but based on field experience and on several reeving arrangements studied during the research for this paper, some indication can be gained from the examining the following Figure 11.
When a turning of 90° of the fall of ropes has to be performed, the first suggestion that should be assessed is to be sure that the rims of the two sheaves are centred on the vertical line. Referring to the symbols reported on Figure 11: the centre grove (No.3) of the top sheave (A), have to be placed exactly into the vertical line of the centre grove (No.3’) of the bottom sheave (B).
Having paid attention to this empirical rule, it can be assumed that the system is symmetrical and that the worst condition will happen to the rope on the extremity of the arrangement (named 5-5’ in the Figure 11). Taking into consideration the reeving arrangement 2:1 as reported in Figure 10, the analysis of the Fleet angle could be limited to the extremity rope. Such checking is not very simple, but with the basically trigonometric knowledge and referring to the symbols reported in Figure 11 viewed in elevation, a rough assessment for the deflection angle α referred to the sheave A can be identified.
If this checking gives the result of an angle α < 1° for traction sheave, or α < 1,5°-2° for deflection sheave, it could be stated that the appearance of sheave or rope wear in service is unlikely to occur for a considerable period, if at all. The smaller the vertical distance H between the two sheaves, the higher will be the deflection angle generated on the external ropes.
From such a schematic view it is easier to understand the variations in length that ropes are being subjected to by this fleet angle or such “turning” of the sheaves: rope in position 3 is practically vertical and represents the shortest length, but the rope in position 5 will need a longer length because it is inclined by an angle α. Such different lengths will have an influence also on the different stresses imposed into the ropes: the more fleet angle or incline on the rope, the higher will be the axial stress on it. From this point of view an inharmonious distribution of stresses will take place between the set of ropes.
This is a dynamical situation and the more the sheaves A and B are close and the higher will be this disharmony.
4.4 Groove tolerances and their effect on the rope motion
At the design stage of the lift, considerations are carried out to identify the correct pitch diameter of the traction sheave. Based on this parameter the rated speed of the car is also deduced. During the service life, for whichever reason, unequal wear of the groove could take place, and this will lead to increased phenomena of slipping of the ropes, this in consequence will increase the wear of all the grooves. Checks have to be performed from time to time to assess the condition of wear of the groove set, and if unequal wear is found, consideration has to be given on what is the maximum limit for this wear.
As a practical rule a straight edge could be placed on top of the ropes and the difference in height between the several ropes can be measured.
If such difference, called Y (as in Figure 12), is higher than 1.5 mm than action has to be taken to restore a more harmonious condition for both sheave groove and ropes .
Such unequal wear could occur for several reasons that have been partially covered in the previous paragraphs. What is important to point out is that, when a re-grooving of the sheave is carried out, attention must be paid to have a strict tolerance between the set of grooves.
Figure 12 – Groove tolerance.
Further to this the advice of the sheave manufacturer must be sought to understand what is the maximum depth of steel surface that could be removed without losing the surface hardness (in case of heat-treated sheaves, the re-grooving operation is generally not possible).
Figure 13 – Wrong shape of the grove, compared to the nominal diameter of the rope.
End of Part 1
Practical experience has shown that modern traction sheaves do not allow for re-grooving and that those sheaves that have had the process carried out only last 12 to 18 months before they have to be replaced completely Particular care must be paid to the shape of the groove, so it is important to use the correct tool for the re-grooving, in order to avoid incorrect shapes that could lead to premature failure of the ropes after short period of time.
Ever what process is used new ropes must be fitted if the traction sheave is replaced or recut so that they can work as a compatible system.
Worn ropes fitted to new grooves will cause premature sheave wear especially if reduction in diameter of the old ropes was the reason for changing the sheave in the first place.
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