Standards for v-belt profiles

Basically, there are these groups of v-belt and other belt profiles in use in Europe today:

  • conventional or classic v-belts (German “klassische Keilriemen”): standardized in DIN 2215 / ISO 4184; using one-letter profile names in different sizes (Z, A, B, C, D, E), in many cases the profile is also named by its width in millimeters (10, 13, 17, 22, 32, 40).
  • narrow-profile v-belts (German “Schmalkeilriemen”): standardized in DIN 7753 Part 1 / ISO 4184; using SP profile names in different sizes (SPZ, SPA, SPB, SPC). Probably, “SP” stands for German “Schmalprofil” (“narrow profile”).
  • high-performance narrow-profile v-belts, open shoulder, toothed (German: “Hochleistungs-Schmalkeilriemen – flankenoffen, formgezahnt”): standardized in Europe in DIN 7753 Part 1; using XP… profile names in different sizes (XPZ, XPA, XPB, XPC).
  • wide-profile v-belts (German “Breitkeilriemen”, “Variatorriemen”): standardized in DIN 7719 / ISO 1604.
  • flat belts (German “Flachriemen”): used in different applications such as tangential belts, folding and conveyor belts and machine belts [source]. There seems to be no widely accepted standardization in this area, they are named by the measures of their rectangular cross-section.
  • round belts (German “Rundriemen): mostly used for conveying and driving tasks in mechanical engineering.
  • ribbed v-belts (German “Rippenriemen”, “Mehrrippenriemen”): in cross-section similar to flat belts, just that the bottom looks like multiple little v-belts running in parallel. Used for example in several modern vehicles.

For a short description of the different types, see HUG-Technik on Keilriemen [German]; for a more detailed introduction, read tedata.com on v-belts. For an overview about DIN and ISO standards relevant for v-belts and similar devices, see HUG-Technik on important standards for belts [German]. See also the English Wikipedia on mechanical belts and the German Wikipedia on v-belts; though both of them lack extensive information on belt specs yet.

The DIN and ISO standards cited above are used in Europe; in the US, the standard RMA/MPTA (and in the UK, BS 3790) specifies minimally different but overall compatible profiles with other profile names. [source]

Standards for v-belt length

Length conversion table. A very important tool to work with belt specs is a v-belt conversion table. That’s because the type of length for nominal length (the length to give when specifying a belt) is different for the different types of belts (for example, it is “inner length Li” for classic v-belts – also the only error in the v-belt  conversion table linked above).

Li, Lw, La. For every v-belt, one can give three lengths: inner length Li, effective length Lw and outer length La. These abbreviations are derived from German words “Innenlänge”, “Wirklänge” and “Außenlänge” respectively and might only be in use in Germany. Inner and outer length are the inner resp. outer circumference measure of the v-belt, without any linear tension on the belt and in circular shape. Effective length is a fictive median length of a v-belt that is the circumference at a certain depth of the belt profile. Namely, at a depth that has the “effective width” (German “Richtbreite”), for which see the corresponding column in the v-belt conversion table. Lw is used as the nominal length of belts with profiles SP*, XP* and X*. Synonymous to Lw, some manufacturers use Ld or Lp. [source]

Belt number. For classical v-belts, there is another identification system in addition to the “20 x 3500 Li” type: the belt number (German “Riemen-Nr.”). It consists of the normal profile size designation letter and a number that normally corresponds to the inner length in inches (rounded, where necessary); for example, “Z 22” or “D 150”. [source] A list of these numbers can be found on this v-belt index.

Measuring v-belt profiles

Real-life examples of measurements – all values below are measured with light touch of the caliper:

  • height of v-belts
    • nominal 10 mm; measured 9.3 – 9.7 mm (in convex curves, 9.8 mm)
  • width of v-belts
    • nominal 12.5 mm; measured 12.3 – 12.4 mm

Measuring v-belt lengths

Measuring v-belt length Lw. It is usually proposed to measure a v-belt by cutting it and nailing it flat to a board [source]. However, this is not what you want if you need to determine the size of a new v-belt that has lost its labelling. So here is a different procedure that I developed and tested successfully:

  1. Mark a line on your flat, hard floor by taping 2 measuring sticks to it, and also tape an end stop marker like a flat wood piece to the start of the first stick.
  2. Add a small cable tie around the v-belt to be measured and use that for marking the start and aligning it to the start marker you taped to the ground.
  3. Roll your v-belt on the ground along the measuring sticks until you went one full circle.
  4. Take the measure and interpret it as effective length Lw of the v-belt (which it is, approximately).

You could do two or three measurements and take the average, but this seems not necessary as this kind of measuring, properly executed, has repeatable results that are up to 1 mm exact. In contrast, measuring with a flexible measuring tape while holding the v-belt in your hands is not recommended, because the results are less exact (my experience: repeated measurement of a single belt resulted in 3505 mm Lw and 3520 mm Lw, while the result with the roll-on-floor technique was 3522 mm Lw). When measuring while holding the belt in your hand you have to take special care not to bend it during measuring, as bending will increase the measurement more towards La; for the above example, measuring with light bending increased the measurement to 3533 mm Lw while it should have been 3522 mm Lw).

It is said that the measure taken by this procedure is the “median length” of the v-belt [source], though “median” here it is probably not meant in the mathematical sense of “length at a profile height where half of the profile area is above and half is below that height”. In practice, these measurements are said to be a good enough approximation of the effective length Lw. While it is a good enough approximate, my tests suggest that the length measured this way also depends on the properties of the belt build-up, so is not always the average, median or whatever length that could be generically specified. The measurement is for “something between inner and outer length”; exactly which mostly depends on how the belt is built, namely, how far to the outside the pull-resistant strings are located. Because, these seem to work like a hinge when bending or unbending the belt, affecting the depth of the area on each side that gets either compressed (so, shortened) or pulled on (so, lengthened). These fibres are normally located right below the upper edge of the belt, so the measure is normally more towards the outer length than the Lw measure is.

Measuring v-belt length La. It is said that one can do that by placing the belt in circular shape on a flat surface and placing a flexible measuring tape around it [source]. However in practice, this is hard to do as you need some tension on the tape to not measure too much. It works well when the velt is still mounted, though.

Determining Lw without a belt. In case you have a device needing a belt but don’t know which one, place a rope around the belt path that has approx. the thickness of the pulley profile grooves. Mark the length of rope you need, take it out again and measure that length when laying it straight on flat ground. This is a  good approximate for the effective length Lw of a fitting belt. (As an alternative, there is a formula to calculate this from La or Li, and online calculators for that.)

Various experiences with measuring v-belts

  • At times, some v-belts seem to use the wrong signing schema. One belt had the classic profile, so the signing of “20 x 3550” was to be interpreted as Li = 3550 mm. However, all measurements turned out with Lw = 3522 mm, so an even larger measure of 3550 mm can only be La, not Li. The formula produces a result coherent with this: La = Lw + 31 mm = 3522 mm + 31 mm = 3553 mm. Another, quite old belt from Continental was SPA profile so should be labelled with Lw, yet the label said “12,5 x 1200 La“.
  • Amount of difference between measured flat length and Lw. In one case, a classic 20 x 2000 mm Li belt was measured with 2060 mm flat length. Lw according to the formula is Lw = Li + 48 mm = 2048 mm Lw. The difference of 12 mm is quite small and probably comes from the fact that the pull-resistant fibres are not exactly located at the diameter corresponding to Lw; see above.
  • Different formulas for converting to / from Lw. Interestingly, there seems to be at times a slight divergence of what formula is to be used for converting from effective length Lw to Li and La. For example, this v-belt conversion table and basically all other such conversion tables on the web state for a 17 mm wide classical v-belt: Lw = Li + 40. However, one 17 mm classical v-belt belt was found with an inscription saying “PETER-BTR 17 x 1320 Li / 1363 Lw”, corresponding to Lw = Li + 43.

Storing v-belts correctly

It is said that v-belts are normally built by manufacturers to reach a lab runtime of 25 000 hours [source]. If this is reached in practice also depends on proper storage conditions.

If properly stored, v-belt properties do not change for several years. However, most rubber-based products will deteriorate if improperly stored or handled (like being exposed to oxygen, ozone, extreme temperatures, light, humidity or various solvent agents). [source]

Therefore, the storage location should be dry and dust-free and must not contain chemicals, oils or solvents at the same time. V-belts should be stored without any force on them (pressure or pulling force) to avoid any permanent shape changes and other damaged. This also means that they should only be stored in hanging condition if the hanger pin is at least ten times the height of the belt profile. Additional maintenance hints for rubber products are found in DIN 7716. [source]

I had a really, really strange dream yesterday in the morning, while I was half sleeping, half awake. There was a frame made, like painted from thick black lines, and in it there were simple color drawings of objects, two at a time. And these drawings were exchanged at a frequency of 6-8 times per second (which means wall clock time, as I could compare the dream frequency, or the subjective impression of that, with the real-world time while slowly awakening). At first (while mostly dreaming) I was able to recognize some of the objects being shown in that high speed, but later (when being more awake) not so any more. Too fast.

This made me get on an idea about the (yet largely unsolved) meaning and role of dreams: namely, to develop and to train the raw material and the speed for flow state thinking. Because dreams go much faster than the real world, and flow state imaginary thinking of “what probably happens next” is just like that, much faster than reality and than normal thinking.

You know “flow state” from these horrific little moments when you see something bad happening to you physically some 0.5 to 2 s before it happens indeed. These seconds feel like slow motion: you think so much in this time about what happens and what to do to avoid it that you later wonder how it all did fit into these fractions of a second. That’s because thinking is much faster in this state of mind – and because reality provides no training to react to such situations, maybe the fast pace of dreaming is this training for the dangerous situations in life, training our mental abilities to react fast enough to avoid the worst outcome.

All speculation of course, but perhaps somebody feels inspired to do some research 😉

So now that we’ve grown up, and started to work for money, we finally start to ask ourselves: Wherefore should we live then? We see most people choose to live for children, and some choose to live for themselves instead. The former have children and no money, the latter have money to spend and no children.

Now, these both ways to live life could not stop the deterioration of Western societies, which started in (say) the mid 1990’s and is in good full swing as of 2011. It’s not the technichal challenges of more scarce resources that we face, or the dangers of unregulated greed (in the financial markets and at home). The real, real problem is that in a land of Cockaigne like this, parents can never succeed to transfer their builder mindset (of postponed consumption, investment, hope, betterment) to their children and grandchildren. These will find out that near everything can be had without work, and will get too comfortable to even be interested, to desire to learn, and to be creative. It’s bad with the children and worse with the grandchildren. Call it decadence.

Now what? Let’s doubt that taking part in decadence is never a life lived for what’s adequate, whether you have children more decadent than you, or no children, being decadent yourself. Instead, there has to be a life to be lived against decadence. Successfully. What do we need for that?

The new, new frontier. The US could only start to become decadent where the frontier for settlement had passed, leaving civilization, but without vision and without tasks. Of course, people found something to improve and to do during some of the following generations, but finally even that faded. There was something like a last try to remedy this by calling the race for the moon the “new frontier”. Nice try, but itself influenced by decadence: Is space travelling really the first thing that comes to mind when you think of “task” and “vision”?

What we need is the new, new frontiere. And then the new, new, new one. And so on. We need eternal pioneering. Look around and see that the world is in nearly no place as it should be. Sahara is a desert, the Congo struck by malaria, all of Africa by Aids, and much of the world by wrong belief systems. Just for the start. And we Westerners dare to say we see no tasks at hand, when questioning ourselves how to recreate vision and zeal in our society, or when questioning ourselves what to do with the >20% jobless in southern Europe? And then people dare to get on the idea that adding another child or two or three to already 7 000 000 000 people on Earth is a proper reason to live for, even though its more-than-apparent that even more people will even intensify the problems and resource conflicts on this planet?

Let’s get practical: we know how to do military operations, with respect to human resources. People get “deployed” in groups of several hundreds to some battlefield overseas, for some 6-8 months maybe. Then they are exchanged by a new group, and themselves go back to their home country to refresh and prepare again for their next deployment in another 6-8 months. Let’s take this over to all kinds of development aid. Because this is attributing the right role to civilization and homes: a place of refreshment and preparation for your “mission”.

Specifically, I propose to create settlements of ca. 4000 people, who travel to overseas development assistance deployments in groups of 1000. As this is no military operation, this can and should include the whole families (children can get schooled underway). The people at home would work to support them, from logistics to medical care etc.. As in military deployments, there will have to be like 4-5 (minimum) immediate support people behind everybody on a mission, and even more so working for money for these missions. But in any case, everybody’s goal should be to go on deployment (and if only for 6 in 36 months), being the reward for year-long support work.

Some ideas for specific missions:

  • Re-afforest the whole of Sahara. Yea, we had that above. Just plant the trees, it’s good for the planet 🙂
  • Build some big islands, or enlarge others. Having more land in nice climate is always a good thing. Why, for heaven’s sake, would people want to live in Siberia while there’s an island waiting for them?
  • Eradicate AIDS.
  • Eradicate malaria.
  • Eradicate hemorrhagic fevers. And all those other infection sicknesses.
  • We want the rain forest back where it was!
  • We want whales back, and the Indian elephant in big numbers, and all these other lovely creatures. Isn’t it somewhat … heavily self-conceited, that we allow 7 billion humans on Earth and reduced many of the other  creatures to just some thousands per species?
  • Yea and finally, once we repaired and tidied up the Earth, there are other planets to travel to. Yet, first things first!

Remember what the Lord God said after the deluge: spread and multiply and fill the Earth. But Josephus says, the people wanted to stay together in one location, building Babylon and its towever as their central collection point. Yet God wanted them to go and colonize the Earth, he wanted them to pioneer – maybe because of the danger of rapid decadence, should they stay together in all their civilization? So he had to mix up their language …

Pioneering never ends. It must not end, as it’s a crucial ingredient for human mental health.

I made some interesting observations of analogies between faith and economy. Of which we can learn – this time, not for economy, but for faith.

The boom and bust cycle of economy is based on mass psychology. The boom happens when everybody (for whatever reason) hope that the economy will improve, and subsequently invest and consume, which in turn makes their hope be fulfilled as a self-fulfilling prophecy. On the other side, the bust happens because of pessimistic expectations of the future, for whatever reason, well-founded or unfounded.

The interesting thing is when and why the boom tips over to become the bust, and vice versa. In my opinion, the transition from boom to bust happens when any substantial group that takes part in the economy has “hoped too much”. Now when they finally notice that their expectations have been unrealistic (and they probably lost much money that they invested into companies and ideas now not rewarded by the economic situation), they lose all hope. This is unreasonable, but understandable, as human beings are in practice not really guided by reason and logic. What is further unreasonable is that their lost hope spread to the other members of the economy like an epidemia, and the now prevalent expectation that the economy will get worse will let just that happen.

Now, isn’t it just the same in faith? Christians definitely have reasons to hope. But they also can start hoping for things that God did never promise to us. Like that all the sick will be healed during this time on planet Earth. Now when people see good things happen in God’s kingdom, like being part of a great church or having a great time with God, or seeing prayers answered in a row: then people might, inspired by this, start hoping for even better things. That were not promised though. So they inevitably get disillusioned (and the longer they maintained their false hope before that, by all cunny means of self-delusion and psychology, the harder the disillusioning will be). And like in the economy, these people will lose all hope. They fall in a depression, in the worst case even in a Great Depression. This affects their relationship to God, but even worse, it affects their Christian brothers and sisters, which might now also lose hope. That would not matter much if it would be just disillusioning as well, but the problem is, people tend to lose also a part of their justified hope in God, and it might also affect people who did not harbor false hopes. As, they might become desparate about the bad conditions in the Church, where it is possible that people do harbor false hopes and go uncorrected for long times until finally falling into despair.

The good news is, the bust is not the end. In economy, people finally get to their senses and say: we need to move on with life. Let’s use our last pennies and buy some food. And as everybody moves out and again buys the essentials for life for their last pennies, the demand is back on the market, and the economy starts to improve. And then, when people realize this, they can regain some hope, and the boom is back. (Hopefully they don’t get too much of that hope, to avoid the next bust; but that hope has never come true yet … .)

Likewise in faith: when you’re depressed, on the ground, lost your hope on God, you will finally get to your senses and think: Wait, at least the basics are true: Jesus is my saviour, and that’s great. Then you might pray, experience some answered prayers again, again visit your church.

And there, you might even infect others with your new-gained young hope. And this – everybody regaining hope in God – is called: revival.

The old testament law said: Thou shalt love thy neighbor just as yourself. Which establishes a balance: do not harm your neighbor for your profit, but also, do not harm yourself, or allow yourself to be harmed, for the profit of an (obviously greedy) neighbor. This law promotes a 50/50 distribution of resources to your personal well-being and that of your neighbor(s).

This equal distribution means, you are allowed to prevent being harmed yourself. No need to suffer in order to provide a better life four your neighbor than you have. See also Paul, who says that donations should be given “according to the principle of nivellation”.

So God’s law does not call for the full-fledged give-based society, which would be something like, give all to others, and live from what they give you. But I assume that God likes that even better than the 50/50 distribution. The reason for not commanding this is probably that God knows it would not come to pass because of the corrupt human nature, and without happening on society scale this model is not maintainable. Even the 50/50 model does not come to pass in our society (as we experience every day), but having “wasted” 50% of all personal resources for the good of others still leaves you 50% to survive. You might also waste 60% and survive on 40%, but I think God chose the 50/50 rule for simplicity. The exact numbers do not matter.

So after all, I expect that we will have a full give-based society in heaven.

Now I think I found a revealing formulation for different approaches towards a happy life and happy world.

What the different approaches have in common is the persuasion that the right human mindset is the key ingredient for both a happy life and a happy world. The right mindset for this would be (roughly), more optimism, hope that transcends death, and interpretations that can attribute deeper meaning to daily activities and to extraordinary events like affliction and disease. Such a mindset makes people happy, and also enables them and motivates them to go and fix the world.

Now the difference between the approaches is how to shape the mind. Let’s enumerate a little:

  • Psychotherapy.
  • Social therapy.
  • Meditation techniques.
  • Religious beliefs.

All these above approach have in common that they seek to shape the mind “directly”, by exchanging mind content, which could be considered as “software”.  While we don’t know exactly which or which combination of these approaches is the most effective one, it seems clear that they all are too weak, as no approach was able to permanently and effectively change the mindset of any large group of people to anything “near perfect”. From time to time, there are great individuals with an absolutely astonishing character, but all approaches failed on society scale.

Now why is this? Here is my opinion. What seems to be stronger than all these approaches seems to be the power of the “mind-eroding” objective circumstances. Which includes many things from bad example, to bad societal values, to natural catastropies, crime, physical frailty and much more. Shielding people might be done to a degree while changing their mindset, but after they are released to fix the world, they are again prone to erosion, and erosion will win over time. And I think the key reason for this is because the mind is hard-wired to try to find a representation of reality and to adapt to it. With a logic like: I see that objective reality does not justify that hope, so having hope in spite of this would make happier for a time but badly hurt when being disappointed in the end, which means we should better avoid it.

If this is correct, reality itself is the most powerful programmer of the mind. But this also gives a glimpse of hope: If objective reality is good at the bottom, and if we can find out that and experience it long and powerfully enough, then this will shape our mind more than the bad aspects of reality around us.

If you know what I’m up to, you know what this argument will lead to. Namely: If we could only experience that God is there, loves us, wants to saves us and even proves that by doing miracles in this world – then this could change our minds permanently because it both justifies and inspires hope. I hope to find these experiences in expeditions of the coming years.

There’s a lot of bad jokes about blondes being stupid. And sometimes I wonder if there could be some substance to it. But in a more general sense: is there any reverse correlation between intelligence and outward attractiveness? Or more precisely, between intelligence and ones subjective impression about ones own outward attractiveness? (Also note that correlation means just, some statistically significant interdependence, while there can be lots of exceptions, like pretty and  intelligent folks.)

There are some reasons that stand aside to explain such a correlation, should it exist:

  • The non-attractive people are those who have other interests than being attractive. Yes, I do think that everybody is “potentially attractive”, just some people do not take the time to reveal it by developing and maintaining a personal style. That is totally ok, people have different interests after all. Those folks might instead deal with a topic in depth, and thus reveal their potential technological / emotional / social or whatever intelligence to a fuller extend. They might also deal with other stuff, like success in entrepeneurship, but we’re after a correlation with intelligence only here. Note that intelligence is commonly thought to depend both on genetic disposition and education, which means much can be done by education independently of ones genetic disposition.
  • Likewise, those interested in making themselves attractive by styling might find that they lack the time to really pursue interests in other topics  like science, technology, society, arts, medicine or whatever.
  • People who are naturally attractive because of their genes (meaning, also if they don’t care about styling) will often find that they do not need to be anything else except attractive. Especially women can get all the advantages in life by being attractive – ok and sociable, but they need not be intelligent and learned in math, science, technology, music, art or whatever demanding discipline there might be. So why should they bother mastering these difficult matters?
  • Likewise, the not naturally attractive people might feel that they need some other content in life to feel worthy and some content to get accepted and maybe praised by others. So they might develop interests in other special areas, like science and technology.

As always, these is experimental thinking. And where I did include observations, I do not endorse them as to be right, legitimate or morally good.