ELEVATOR WORLD India • 2nd Quarter 2009 •84

Engineering

Traction in Elevatorsby Snehal Toralkar

Snehal Toralkar is a

design consultant with TAK

Consulting Pvt. Ltd. She

has four years of experi-

ence in elevator design.

Toralkar started her career

with Schindler India as a

design engineer, where she

was involved in launching

the S3300/5300 products. She is a Mechanical

Engineering graduate.

“Seven people had escaped withminor injuries on a Sunday eveningwhen the elevator carrying themcame down crashing from the thirdfloor.” There was no doubt that theelevator was overloaded, and thiswas established as the obvious causeof the incident. Yet a deeper investi-gation appeared to reveal that theoverloading was just a trigger, withthe root cause of loss of tractionprobably being an angle of contactless than 120° (Figure 1) on accountof a design flaw that overlooked thiskey aspect of traction elevators. Adiscussion with the lift supplier re-vealed that it had established thelayout based on thumb rules ratherthan any detailed calculation. Thisappears to be a trend with manysuppliers.

The situation is further complicatedas the Indian standards appear to besilent on this crucial aspect, givingno direction to designers. In compar-ison, EN 81 mentions all the minutedesign details required for traction,yet does not prescribe a minimumangle. ASME A17.1 mentions thatsufficient traction shall be providedbetween the rope and groove tosafely stop and hold the car withrated load in the down direction.

In most mechanical systems, con-siderable emphasis is placed on reduc-ing friction between parts; the reverseis the case in elevators. A lot moreimportance is given to utilizing frictionfor traction-driven machines. In lay-man’s terms, traction is the grippingforce along the surface. In technicalterms, traction is the frictional force.

Starting with the elevator basics,the elevator system first consists ofthe car, which carries the passengersto the destination floor. The counter-weight is placed either at the side orrear with respect to the car positionin the hoistway shaft. This balance isprovided to conserve energy. Thesecomponents are held by steel ropeslooped around the sheave. The sheaveis a pulley with grooves around itscircumference. The sheave is drivenby the motor. The sheave grips thehoist ropes so that when it rotates,the ropes move, too. This gripping isdue to traction.Traction Calculation

Consider a rope passing over adriving sheave (Figure 2). Let T1 bethe tension in the car side, and T2 in

Figure 1: This article explores the fundamentalsof traction. Figure 2: Traction calculation

Continued

ELEVATOR WORLD India • 2nd Quarter 2009 •86

Engineering Continued

the counterweight side. The requiredtraction for any elevator system isexpressed as T1/T2. T1 is the addi-tion of all weights (i.e., 125% of ratedload, car weight, ropes and traveling-cable weight), whereas T2 is thecounterweight.

The maximum available tractionthat can be developed is a functionof the actual coefficient of frictionbetween the rope and groove, theshape of groove and angle of contact.

Maximum available traction = e fΘ

where e = the base of natural logarithmf = coefficient of friction

Θ = angle of contactHence the condition so that the eleva-tor does not lose traction is given by:

T1/T2 X C < e fΘ

where C is constant, consideringacceleration and deceleration, and isgiven by:

C = (gn + a)/(gn - a), where gn =acceleration due to gravity and a =rated speed of the elevator.

Obviously, from the above expres-sions, we can conclude that the max-imum traction can be achieved whenthe value of fΘ is increased.Factors Affecting TractionAngle of Wrap

“Angle of wrap” or “angle of con-tact” is the angle that the rope makeswith the circumference of the sheave.The maximum angle for single-wraptraction (SWT) that can be achievedis 180º (Figure 3). However, the prob-lem occurs when there is a diverterpulley. In this case, the angle decreases,

but with suitable arrangements likeadjusting the height and length be-tween the sheave centers, maximumangle can be achieved.

The other option by which to achievethe maximum angle is double-wraptraction (DWT) (Figure 4). In DWT,traction is considerably increased, asin this case, angle becomes (S1 + S2).But this system has some disadvan-tages. The design of the machine iscomplicated. The height is greater,and the width of the sheave rim islarger, as the number of grooves isdoubled. The rope bends number isgreater, resulting in additional ropewear. This also results in an overallcost increase of the equipment.Sheave Diameter

The ratio of rope diameter tosheave diameter also plays an im-portant role in traction. Per Indianstandards, sheave diameter shouldbe equal to 40 times the rope diame-ter. The larger the sheave diameter,the more the contact area betweenthe rope and sheave is achieved. Thesheave diameter should also be largeenough to account for the bendingstresses exerted by the ropes. How-

Figure 3: SWT (angle of contact: 180°) Figure 4: Double-wrap traction

ever, cost is also to be consideredwhile setting the final diameter. Itwill also result in a larger machineassembly, which will create problemsduring installation. Type of Groove

The other important factor thataffects traction is the shape of thegroove. Commonly used grooveshapes are U-groove, U-groove withundercut and V-groove.U-Groove

The U-groove is the sheave ofchoice for optimum life (Figure 5). Itslarge size, in combination with itssupportive grooves, minimizes abra-sion and fatigue. Note the largegroove area with which the ropecomes in contact. The groove cra-dles the rope, resulting in low groovepressures, allowing the wires andstrands to move about freely whilethe rope is operating. Unfortunately,however, the U-grooved sheave pro-vides the least amount of traction. U-Groove with Undercut

When compared to the U-groove,the surface area of the rope makingcontact with the undercut U-groovedecreases. Note the undercut where

Continued

ELEVATOR WORLD India • 2nd Quarter 2009 •88

Engineering Continued

the rope no longer makes contact withthe groove (Figure 6). Thus, groove-bearing pressure is increased uponwhich the higher available traction isbased. The available traction can beincreased by increasing the angle ofundercut in the sheave groove. How-ever, it has limitations, since thelarger the undercut, the less supportit receives from the groove andtherefore the less load we can put onthe ropes without causing rapidsheave wear and rapid rope failure.The undercut angle is therefore keptbetween 90º and 106º.V-Groove

The V-groove is the most widelyused type of groove (Figure 7). Theseprovide the greatest amount of bear-ing pressures, hence maximum trac-tion. The angle of the groove is keptbetween 32º and 40º. Traction in-creases with decreasing angle of thegroove, but it also leads to shorterrope life.Conclusion

While the magnitude of the groovepressure distributions associated witheach groove varies, it is to be notedthat in no case does the “actual”rope-to-groove coefficient of frictionchange. However, the “apparent” coefficient is a direct function of the

Figure 6: The U-groove with undercut has itsundercut at the bottom.

Figure 5: This illustrates the support given to therope by the groove.

Figure 7: V-grooves provide maximum traction.

groove pressures and actual coeffi-cient of friction, and it does changeas the groove shape changes. For thelatter case, elastomer-lined drive-sheave grooves are used. These havea higher coefficient of friction andafford a very efficient method ofincreasing available traction. It is alsoto be noted that specific pressure ofthe ropes does not exceed the pres-sure value with the car loaded withits rated load:Specific pressure of ropes

P ≤ 12.5 + 4 vc____________1 + vc

Finally, summing up the proof con-cludes the following:1) Available traction can be increased

by increasing the arc of contactthat the rope subtends with thesheave.

2) Available traction can be increasedby changing the shape of thegroove.

3) Available traction can be increasedby increasing the actual coefficientof friction of the material.Note that all the above parame-

ters are dependent on one another.Compromising on any of the abovefactors should not change the finaltraction value. With this background,elevator system designers need to bevery careful in estimating tractionand establishing their designs.References[1] Elevator Mechanical Design (Third Edition)

by Lubomir Janovsky[2] Elevator World Educational Package and Ref-

erence Library Volume 3[3] Bethlehem Elevator Rope Technical Bulletin

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