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The Meccano driving band problem

(Author: Paulo Kroeff de Souza)

The first problem with Meccano driving bands is the name. The origin is probably in rubber bands used to wrap money or other paper stacks. If you use one of those between two pulleys it becomes a “driving band”. In usual engineering we call “belts” those things that connect pulleys. So, being Meccano “engineering in miniature”, I think “belt” suits better than “driving band”, being also a simpler and shorter denomination.

In general there are the flat belts, capable of transmitting big horsepower, the V-belts, like those used in cars and some appliances, and there are small rubber belts of square or round sections used in electro-electronic hardware. The Meccano belt problem fits in this latter class.

The angle of the groove of usual pulleys for V-belt use is 40º or less. Smaller groove angles require less tension in the belt to assure adherence to the pulley. The adherence takes place in the lateral face of the groove and the belt shall never touch the groove bottom. The stretching force produces forces on the belt that pull it down the groove, The forces developed against the lateral faces sum up to about 3 times the force pulling the belt down a 40º groove. And these forces are bigger for smaller groove angles. To calculate those forces is quite an involving process but that force multiplication makes a V-belt capable of transmitting several horsepower with a few tens of kilograms stretching force. Square and round section belts, though generally smaller, work in a similar way.

The standard Meccano belts (part numbers 186_) are of a square section of 1/16” side for the “light” ones, according to data in the Meccanospares site (see reference 1) and 3/32” for the “heavy” ones according to the Meccano engineering drawings found in Tim Edwards site (see reference 2). I found some reproduction “heavy” belts 1/8” squared or even bigger.

Since the nominal Meccano pulley groove angle is 64º the gain of force to produce adherence of the belt to the pulley groove is smaller than in usual V-belts. And, unlike the case of usual V-belts, which section accurately matches the groove, the latter does not match the 90º angle of the square belt section. The Meccano grooves also differ from V-belt pulleys’ in that they do not have a flat bottom and so, even small section belts will adequately touch only the sides, which is good! Otherwise, the Meccano pulleys groove angle is like that because pulleys are used also for other purposes as we know. Additionally, the bigger angle implies less adherence and this protects the rather frail belts that will, generally, slip before breaking.

So, a square section belt riding a Meccano pulley groove will produce adherence in the outer part of the belt section touching the groove and that area grows with stretching force since the belt section deformation grows (see figure above).

If a circular section belt is used the area of contact will be somewhat further below the center of the belt section as can be seen in the figure. However, the resulting adherence will not be significantly different since it is basically determined by the groove angle. Besides, round section belts are currently used in many low power applications in appliances and electronic devices, sizes and powers involved being similar to the Meccano cases.

Therefore, the choice between square and round sections is basically a matter of convenience or availability with the exception of the collector’s “application” who, by definition, will not put the belts to work...

Looking back at the standard Meccano belts (square section) a problem immediately appears: the original belt lengths available are too much apart. Light types are 2.5”, 6” and 10”, whereas heavy types are 10”, 15” and 20”. This means, for example, that if you need an exactly 10” long belt you have to use a 6” belt because the 10” belt would give you no adherence to the pulleys without stretching. Stretching a 6” belt to 10” implies a deformation of 67%! A “heavy” 10” belt applied to obtain a 15” length is another critical example where the deformation is at 50%. These enormous deformations produce excessive loads in the axles, and in the holes where those turn, and reduce the lifetime of the belt. Besides, a blockage in the driven pulley will probably brake the belt. Using a 2.5” belt for, say, a 5.5” long application will probably brake the belt at installation since the deformation exceeds 100%.

Real life experience corroborates that: I remember that the belts included with my set 10 where all broken very soon. In the reproduction market, the heavy non-standard Meccano 7.5”, 12.5” and 17.5” sizes were introduced, attenuating this situation. Yet, from 7.5” to 10” there is still a 33% strain. And this implies using non-standard Meccano parts anyway…

The other aspect of the problem is cost. Many belts in the Meccano market cost more than £1 and the bigger ones may exceed £4. This is quite expensive for a part that should rather be considered expendable.

On the other hand, using parts in a way that they will be short lived somehow contradicts the Meccano philosophy. Meccano is about reuse and durability... And I consider this anti-waste philosophy one of the best things taught by the Meccano hobby (or toy).

Long time ago, when I worked in aircraft maintenance engineering, I had a happy experience. I was looking for replacement belts for the small French Meccano set 5 I had bought for my daughters. The idea was to use O-rings as belts. O-rings are rubber rings with a circular cross section used for sealing purposes in fluid handling devices such as hydraulic actuators or fuel pumps. And there were all those hundreds of O-rings of various sizes junked by the ‘fuel and oil’ and the ‘hydraulics’ shops of the airline. In aviation, for safety reasons the reinstallation of rubber seals is forbidden even if the part concerned appears to be in perfect condition. So, among the O-rings in rubbish bins, there were plenty that could be used as Meccano model belts. So much better that they were made of very high quality rubber quite immune to contact with oil. And so I got, at no significant cost, a handful of those junk parts. This happened in the late ‘70s and the ones that were not lost since then are today, after 40 years, still soft and in perfectly usable condition for Meccano belting!

With that experience in mind I set to study O-rings again aiming at their general use as Meccano belts. I downloaded and examined the “Parker O-Ring Handbook” published by Parker Hannifin Corp. in 2007 (reference 3) that contains precious and very complete information on O-rings. In pages 3-24 and 3-25 there are comments on the use of O-rings as belts. Parker has even developed the rubber compound, E0751-65, for belt use and lists three other compounds they tested and recommend for the specific use as belts. Examining table 3-23 of this document, the conclusion is that the best compound for the Meccano applications would be the polyurethane compound P0462-70. Then, in pages 5-20 and 5-21 they show calculation procedures for the correct design of belt drives. There, they recommend the use of 8% to 12% stretching with a maximum of 15% for O-ring belts. The other interesting recommendation is to operate the belts with the tension resulting from stretching between 0.6N/mm2 and 1.0N/mm2. Finally, from pages 9-2 on, information on O-ring sizes is depicted.

Looking at data from other manufacturers, such as EPM Inc. from Stockbridge, Georgia, US, and also local Brazilian suppliers I found that, though O-ring part numbers are different for each manufacturer, most of them use a standardized set of “inch” sizes and identify them by a standardized dash number of the O-ring part number. Also, in handbooks and in day to day practice, they translate the measurements in millimetres... In the standard size series there are groups of O-rings that have circular sections with diameters of 1.78mm, 2.62mm and 3.53mm that may be of interest. The 1.78mm section has an area of 2.49mm2 which is very close to the 2.52mm2 area of the Meccano light belts that are 1/16” square. The 2.62mm section has an area of 5.39mm2 which is quite close to the 5.67mm2 area of the Meccano heavy belts 3/32” square.

Based on the above information it is possible to determine a series of O-ring sizes capable of covering all belt lengths that may be needed in Meccano. However, using a maximum of 15% stretch, would require an excessive number of types, therefore leading to a rather high cost for the stock. So I decided to work with 5% to 25% stretching. 5% would probably give enough grip for most applications and 25% probably would not apply excessive forces on axles and bearing holes. The 25% stretch is excessive compared to the Parker Hannifin recommendation and therefore may lead to reduced O-ring life but, anyway, it is much less of an abuse than the stretching implied in most Meccano belts sizes.

This led to 10 sizes from 2.5” to 11” lengths for light belts among the standard O-rig sizes of 1.78mm diameter section. In the table below L stands for length and Nom. Diam. is the O-ring inside diameter, when relaxed, which is its main characteristic measure appearing in manufacturer lists. L @ 1.05 and L @ 1.25 are the minimum and maximum belt lengths possible at 5% and 25% stretching respectively. In the last column the corresponding standard dash number of the O-ring is listed.

As will be shown, the lower cost of the O-rings when compared to the Meccano belts will more than compensate for the bigger number of part types.

L nom. in L nom. mm Nom. Diam. mm

L @ 1.05 mm

L @ 1.25 mm Std. dash nº
2.5 64 20.35 67.1 79.9 -019
2.9 74 23.52 77.6 92.4 -021
3.5 89 28.30 93.4 111.1 -024
4.0 104 33.05 109.0 129.8 -027
4.7 119 37.82 124.8 148.5 -029
5.5 139 44.17 145.7 173.5 -031
6.7 169 53.70 177.1 210.9 -034
7.8 199 63.22 208.5 248.3 -037
9.4 238 75.90 250.4 298.1 -041
11.0 278 88.62 292.3 348.0 -043

For the heavy belts I also arrived at a 10 sizes series of 2.62mm O-rings. As in the case of Meccano belts I provided an overlap between the two series. The heavy series goes up to 30” whereas the original Meccano square section belt series stops at 20”. For maximum economy the last three sizes of each series may be omitted and still all Meccano lengths will be covered with 14 sizes.

L nom. in L nom. mm Nom. Diam. mm L @ 1.05 mm L @ 1.2 mm Std. dash nº
7.6 194 61.6 203.2 241.9 -143
9.0 228 72.7 239.8 285.5 -150
10.1 258 82.2 271.2 322.9 -152
11.7 298 94.9 313.1 372.8 -154
14.1 358 114.0 375.9 447.6 -157
16.5 418 133.0 438.8 522.4 -160
19.6 498 158.4 522.6 622.1 -164
22.7 577 183.8 606.4 721.9 -168
26.7 677 215.6 711.1 846.5 -173
30.6 777 247.3 815.8 971.2 -178

For the sake of completeness I added another five sizes of the next O-ring section which is 3.53mm, the area being 9.79mm2 which could be called “very heavy belts”. To have longer belts this is necessary since the biggest standard 2.62mm O-ring is the -178. I chose 5 sizes going to about 40”, which is consistent with a belt “going around” a 49-hole girder, the longest Meccano part... Again there is an overlap of 3 sizes between these and the 2.62mm sizes.

L nom. in

L nom. mm

Nom Diam mm

L @ 1.05 mm

L @ 1.25 mm

Std dash nº

22.7 577 183.7 606.1  721.5 -263
26.7 677 215.5 710.8  846.2 -268
31.4 797 253.6 836.5  995.8 -274
36.1 916 291.7 962.2  1145.5 -277
40.8 1036 329.8 1087.9  1295.1 -279

With these tables I went to a good O-ring retailer, Vedasul (vedasul.com.br), which sells parts from a Brazilian manufacturer, to discuss the rubber compound.

The price of an O-ring is affected by 3 main factors: size (obviously), type demand (the bigger the demand of a type, the lower the price) and the compound. We can only control cost by properly choosing the latter.

The ideal compound for the Meccano application would be polyurethane. However, polyurethane is not in the Brazilian version of the Parker Handbook and with the Brazilian chosen supplier this compound is under special order, which means either high cost or altogether impossible in small quantities. (May be in some more industrialised country this situation is different…) This is a pity because since a polyurethane such as the Parker P0462-70 supports an elongation of more than 500%. The 25% I used in the design of the series would be of little significance in terms of durability, recalling that durability is inversely related to stretching. The series could otherwise be redesigned with less types and the stretching be limited only by the forces on axles and bearings.

Viton is another compound of choice, with excellent properties but it is also very expensive.

So I decided to try Nitrile Butadiene Rubber or NBR, also known as Buna-N. This compound is not listed as preferred for belts but, being the most common of all O-ring compounds, its price is very low and the standard sizes are readily available. The good coincidence is that this compound is highly immune to petroleum oil, an essential requirement for Meccano use. The parts are so inexpensive that the salesman gave me one -152 and one -236 rings to play with.

For a cost comparison, let us take the types in the first table, which functionally correspond to the Meccano light belts, however using far more ‘healthy’ stretching. Let us consider 3 each of the 2.5”, 2.9” and 3.5” lengths and 2 each of the remaining 7 lengths. The 23 so selected O-ring belts would replace the standard set of 7 light belts (3 pieces 2.5” long, 2 each of 6” and 2 each of 10” length) found in a Meccano outfit 10. It cost me a total of £3.50 for this set of belts considering the approximate exchange rate during Jan 2018. This is a little over 50% of the cost of the 7 standard light belts as sold in most of the Meccano new reproduction parts market. It is, nevertheless, not impossible to find this set of 7 belts at prices even a bit lower than the set of 23 O-rings described above. However, the difficulty to operate in intermediate lengths with the three standard types plus the difference in the number of belts available (23 vs. 7) between the compared options leaves no room for reasonable doubt…

As for the heavy parts, a set 10 has two each of the 10”, 15” and 20” lengths. So let us consider the cost of 2 each of the O-rings from 10.1” to 22.7” lengths in the second table (total of 16 belts) as a replacement option. This will give you 12 belts costing approximately £6.22. The 6 belts of the three standard Meccano sizes would, probably, cost around 3 times more in the Meccano new reproduction parts market!

These two comparisons show that though implying more than twice the number of belts and using far better stretching parameters, O-rings provide you a possibly better service at a fraction of the cost of the regular repro market square section belts. No miracle: the NBR O-rings are massively produced therefore keeping costs very low.

If, for the collector, the O-rings mean nothing, for the modeller, considering the functionality and cost, they may be a vastly superior choice. In my case I bought a set of Meccano standard repro “driving bands” just to make my set 10 complete. After all we Meccano people have a collection corner in our hearts. I did not buy originals as I did with some replacement tyres because old rubber, chiefly in small sections, is usually fragile.

Needless to say I took a massive order of 6 each of the 14 smaller types and 4 each of the 11 bigger types of the tables above, therefore empowering my set 10 with 100 belts and the old French set 5 with 28 belts, all for less than £75. The average belt cost was still less than 60p even if O-rings in the third table are far more expensive due to size and smaller scale production. The bigger ones, 40.8” long, cost around £3 each, probably less than a 20” long Meccano repro belt.

As far as performance is concerned I made some tests using a modified version of my Meccano tensile stress tester. This tester is a machine that applies a force, measured by a dynamometer, to a specimen under test and the length of the object can be measured. In this case, I used a Salter 0-5kgf dynamometer. To test a belt, its stretching between a fixed and a movable pulley, caused by a known force, is measured. Measuring the outside diameter of the belt over a pulley it is possible to estimate the position of the median line of the belt and therefore its length over the pulleys. The distance between the centres of the pulleys is equal to the length of the straight portions of the belt. Adding these quantities, the total length of the stretched belt can be calculated and dividing it by the nominal (≈relaxed) belt length the stretching percentage may be obtained.

 

Since during the stretching process the volume of the material tends to stay constant the cross section area of the stretched part can be estimated as the nominal area divided by the ratio of stretched to nominal (≈relaxed) length of the belt. The measured force actuates over the area of both straight belt lengths, so, dividing the force measured by twice the estimated resisting rubber section of the belt, the stress is:

stress(N/mm2)=force(N)÷2(nominal lenght÷total lenght)nominal area(mm2)

This exercise is not a high accuracy operation even if the dynamometer used is a 0.5% of full scale accurate instrument. Therefore, I will not carry an error analysis of these measurements and so consider the results as estimates, good to a few percent units.

Tests were conducted for one -041 and one -150 Buna N “O” Rings and for one 186b and one 186c reproduction Meccano type belts. An additional problem with the repro belts is that they are somewhat different from the original Meccano belts. The 186b lights I got are 1.7mm squared or 2.89mm2 in section area as compared with the Meccano lights at 2.52mm2, whereas the 186c heavies are 7.56 mm2 in section area, far thicker than the 5.67mm2 Meccano originals. Additionally, the heavies I bought are made of a quite rigid rubber as will be clear from the measured values. A harder rubber has the advantage of transmitting more torque for the same stretching but will apply a bigger load to the axle bearings.

 

The results were much more uniform for the Buna N “O” rings than for the repro belts. This suggests that the quality control of the characteristics of the “O” ring rubber compounds is much tighter than that of the repro belts. No surprise since “O” rings have to comply with industrial equipment specifications…

From the results graphs it can readily be seen that, for the “O” rings, the stress versus stretch curves are almost identical implying uniformity of the elasticity of the rubber compound. Of course the force values for them are quite consistently proportional to the area of the cross section of the parts. For the repros, the 186b is of a softer rubber than that of the 186c. Also, the 186b is almost twice as soft as the “O” rings whereas the 186c is somewhat stiffer.

It may be interesting to point out that the Parker Hannifin recommended stress range (see above) from 0.6N/mm2 and 1.0N/mm2 really occurs for 10% to 16% stretching of the “O” rings.

In the high stretch part of the 186b curve, the resulting high and growing stress points to the risk for the integrity of the part. Not only the force grows nearer to what appears to be the failure limit of the material (shown by the inflection of the curve) but also the resisting section is considerably reduced. This excessive stretching is very probably the explanation for the short life I observed in my old original Meccano belts. It obviously emphasizes the advantage of having more intermediate belt sizes which imply less stretching abuse.

Back to the “O” ring results, since the stress graphs for the two parts is almost identical these data can be treated and used for the design of belt transmissions. The -041 ring stress is 2.14N/mm2 at 35% stretch, whereas the -150 ring stress is 2.01N/mm2 at 33%. Now I will approximate the curves by straight lines passing through the origin and the measured points, which is quite reasonable. This leads to a slope of 0.0611N/%mm2 for the -041 ring and a slope of 0.0609N/%mm2 is the result for the -150 ring. Then I can write a unified approximate expression for the relation between stress and stretching for any of these Buna N “O” rings:

 stress(N/mm2)=0.061×stretching(%)

I can use this expression for the estimation of the force on the bearings applied by any of my “O” ring belts by multiplying the stress by twice the nominal area of the cross section of my belts (2X2.49mm2, 2X5.39mm2 or 2X9.79mm2 for the light, heavy and very heavy belts respectively). Of course, the use of the nominal areas leads to the forces being slightly overestimated, which is unimportant as I am interested in rough estimates.

Example: Suppose a 19b and a 23a pulleys placed 8 holes apart and connected by a -178 belt (306mm). I measure the stretched length wrapping a piece of string of the same approximate thickness of the belt and I find 325mm. The stretching is 325/306≈1.0621 or 6.21%. The stress will be 0.061X6.21≈0.38N/mm2 and the force on the axles will be 0.38X2X5.39≈4.1N

References:

1-Meccanospares site: https://www.meccanospares.com/

2-Meccano Tech Drawings.pdf in Tim Edwards site: https://www.meccanoindex.co.uk/Drawings/Meccano_Tech_Drawings.pdf


3-PARKER HANNIFIN CORP., ORD 5400 Parker O-Ring Handbook, Cleveland, Ohio, 2007.
 

 

Paul D      (at 6:43am, Sun 4th Oct, 20)

This is wonderful! Reading online though, the graph labels are illegible.


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