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gvy

timing belt tension , the frequency method

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Hi,

I know that the frequency method for measuring timing belt tension only applies to the rounded tooth belt of the later cars. I think it is to be measured at 30° before TDC and the result should be between 110 Hz and 120 Hz.

I know for sure that this way of measuring ( with current smartphone apps for measuring frequency) is way more easy and accurate, IF only we knew the target frequency on our trapezodial belt.Z

So I tried to do some calculation on it.

Please check and comment:

Frequency is function of Tension , weight , lenght.

The formula of the basic frequency is :

image.png.4838ad0a7f320c28e4dabb0561eddac2.png

n = 1 ( we are looking for the basic harmonic)

f = frequency we are looking for.

L = length of the belt between aux wheel and inletcam wheel : I measured 0,23m (23cm)

T = required tension of the belt : 90lbs, this is 400N (Newton)

µ = mass/m of the belt : I have measured two belts: the lotus A907E0191Z and the Gates powergrip 5146. Both are 1.28m long but different in weight : the lotus belt weights 0.12266kg/m, the gates belt weights 0.09453kg/m.

 

With these figures: The formula gives me the following frequencies to receive a tension of 90lbs (400N)

Lotus belt  : f=124 Hz

Gates belt : f=141 Hz

My question : Am I right to state that the required tension is 90lbs (400N) ?

Remark : You can see that the used belt (its weight) is important. For example , the gates belt (SJ-sportscars alternative) is a thinner lighter belt then the original lotusbelt . I do not have a round toothed belt of the later esprits to weight and compare. If someone has this belt on his workbench, please measure its weight for me on a digital kitchen scale or letter scale and report.

Second question : Could someone do me a favour and measure the frequency on his belt and report here. Please do mention the type of belt used and if possible the burroughs or krikit measurement. This way lots of us could benefit and learn how to tension using the frequency method safely. i dont have a krikit or burroughs, so I can't test it myself. I always tensioned using frequency

 

Geert

 

 

Edited by gvy

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Think you are wrong with your calcs - Its 100-110Hz at 30 degree BTDC 

A user on here (Ralph, I recall) worked out the formula previously (maybe it was 114?).   I have a trapezoid belt and have only used the frequency method for many years on a car that is still used fairly hard and regularly.   Although we know the earlier belt is lighter than the later belt and the frequency should therefore be higher, I still set around 108-110 as it feels about right  (bearing in mind that the official figures have a very generous tolerance of over 10% - so if  114Hz is ballpark top tension, then 10% tolerance of that would be around 103Hz. 

NB - I have never seen any conclusive evidence that the frequency method cannot be used for earlier cars, only that it should be used for later cars...   

 

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Steve,

About the round tooted belt you are right. It is between 100Hz and 110Hz at 30° BTDC

But please do explain where I have it wrong with the calculation in case of the trapezodial belts ?

The formula itself is physics, so that is correct

the variables:

µ : I have measured length and weight of the two types belts today and did it  pretty accurate so µ will be ok. Would love to measure the weight of a round toothed belt, to compare, since the weight of the used belt makes a great deal in the calculation.

T : required tension : I have mailed with Tim Engel. He suggested I should use 95lbs (422Newton) instead of 90lbs (400N) as the target belt tension.

L : exact length between aux wheel and inletcam wheel : I measured 0,23m (23cm). This is a bit difficult to measure exact, because of the teeth on the belt and camwheels. This is infact the free resonating part of the belt. Look at it as a guitar string.

 

you mention:

NB - I have never seen any conclusive evidence that the frequency method cannot be used for earlier cars, only that it should be used for later cars...   

Of course the frequency method can be used on earlier cars. But as the formula explains, the targeted frequency for a certain tension is very dependant on the weight of the used belt. So you can not simply state that what is the frequency reading for one belt will be fine for another type of belt. Look at the difference I calculated for the two types of belt I have in my workshop.

for industrial maintenance, gates has a sonic tension meter. On this device you have to input mass and with of the belt and the span. It is obvoius that different beltmass ( kg/m) requires different frequencyreadings

 

Now I have used the frequency method also for years , and as you , I have set my belts to around 114Hz. Always been fine.

But recently , with the change of my belt I noticed a slight vibration when revving to around 2500Hz, so I really wanted to do the maths this time, not just presuming it is the same for all belts.

Spoiler

 

 

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Hi Geert, I've no idea if your calcs are right or wrong, I was commenting on your incorrect statement that a round profile belt Hz should be between 110-120.   If you search for Ralph's posts, he published his formula, which you can compare against.  I also seem to recall that Ralph had a professional connection with automotive belt design - or something along those lines 

However, I would have thought 124/141 Hz will be way too tight, I certainly get no resonance or whining at 108Hz  (typical indicators of too slack or too tight).

Two other observations - I have had personal experience of 'non standard' belts resonating.   I also think its important that the tensioner springs are in good order, otherwise you can take all the 'slack' out of them before reaching the required tension.    

 

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Steve,

I rebuilt the automatic tensioner with a new bearing. I didnt use new springs. I will order and install them as you suggest.

About your first observation : The non standard' gates belt that SJ-sportscars sells as an alternative is indeed a lot lighter then the original lotus belt. That may explain, why it resonates when tensioning it to approx. 110Hz. This is what I could conclude when doing the math.

I do use the lighter gatesbelt and it is set at 114Hz. This may be fine for the original lotus belt , but to low for this gates belt. ( especially with the combination of the older springs)

It would be good if Ralph could comment on his calculation. I like to discuss his method and come to a conclusion.

Edited by gvy

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User was Ralphw, you could search his posts.   I couldn't find the original thread, but I found this, which I believe I quoted from Ralph's  original:

From the above lifted from the Stevens Technical Room (Thanks Georgio) some simple mental arithmatic suggests that the tension for the Trap belt is 114.55Hz

eg 4*142*L(trap)�*F(Trap)� = 4*154*L(HTD)�*F(HTD)�

L is the same for both belts and F(HTD) is 110Hz

Therefore

154*110*110/142= F(Trap)�

√13122.535= F(Trap) = 114.55Hz

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Thanks Steve,

This is helpfull. After some research and looking in to the old topics, I came to the conclusion that Ralphw used the same formula as I did, so why the difference...

He says : T=4ml²f²  this is exactly the same as f= 1/2l x sqrt(T/m) wich I used. (of course it is , its physics:P)

Next I have seen in these topics that two different people (scales) provided the weight (mass) of two different timing belts.

   One said that the HTD belt ( rounded thoot belt) weights 154gr

   Another said that the lotus square toot belt A907E0191Z weights 142gr (strangly I have weighted this belt to be 157gr???? . I try it on another scale later, my scale can be wrong....or his)

So:

Assuming tension needs to be the same for the later cars HTD belt as for the trapezodial belt then:

4m(trap)l²f²(trap) = 4m(htd)l²f²(htd)

      we know that f(htd) should be 110Hz:

f(trap)=110 x sqrt(154gr/142gr) = 114.55Hz

So Ralph did come to this conclusion assuming that the weights given by two different people ( two different scales) on these two belts are right. It might be , but it is a bit dangerous.

Now lets go on:

If I assume the 114.55Hz is right for the original square tooth belt A907E0191Z and I use the same principal to calculate the frequency for the lighter square tooth gates powergrip 5146 ( SJ sporscars alternative)

but I use the weight measurements of both belts on the same scale , my scale (so even if it is not exact the ratio is exact because measured on the same scale)

I get

f(gates)=114.55Hz x sqrt(157gr/121gr)=130.48Hz

My point is:

1. To get an exact comparison, we need to have the weight of the belts measured on 1 scale. So I need a round toothed HTD belt to weigh.

2. The gates powergrip 5146 (sj-sportscars alternative) is way lighter then the original lotus A907E0191Z, so it should be tuned higher (and yes I am using Ralphs method) to have the right tension. And I have two of them here weighing exactly the same 121gr

 

The most interesting thing to conclude: It is really important to know which belt you install if you use the frequency method.

Geert

 

 

Edited by gvy

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To add to my  topic :

I have seen that also people with the later round toothed belt (Stevens esprits) have a choice to 3 types of belts :

-The OEM lotus belt

-The SJ-sportscars alternative ( I guess gates?)

-The gates racing blue belt.

Al three will have different mass and the 100-110Hz will only apply to the OEM lotus belt. I really need an exact weight of this OEM lotus belt.

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OK - I've found 3 belts, an original, a Gates (not 100% sure of P/N as can only see '5 42 7DS' marked)  also a Quinton Hazell QTB122.   Interestingly the printed 'instructions', block and colour of dye on the Gates & QH are identical, so I assume the QH is also made by Gates, as is the original Lotus.

I agree with you findings Geert, the Gates branded belt weighs 127grammes and in addition to being 1.5mm narrower, its also slightly lighter construction (i.e. both narrower & thinner).    However, the QH belt weighs pretty much the same as the original at 147grammes and is also 26.5mm wide (as original).   So the QH belt is the same as the original Lotus?   Not sure, as memory recalls this was the belt that always resonated, so I swapped it out 

What does it all mean?   Dont know, but I'll keep fitting the original belt tensioned to circa 108Htz, as it works for me      

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Thanks Steve,

Barry, I don't have a gates racing blue belt so I can't put it on a scale  I read that it has a heavier construction, so I assume it will weight more than the original. In that case , to receive an equal tension, the frequency reading must be lower then 100-110Hz. I can only do the math if I have the exact weight of an original lotus round toothed belt (The one that lotus prescribed the spec of 100Hz-110Hz) and I have the weight of the belt that will be used. ( in your case the gates blue racing belt)

Today I could weigh the two types of trapezodial belts I have on a calibrated scale . I got the exact same measurements as @ home, so I am confident my digital kitchen scale is exact.

the lotus A907E0191Z : 157gr

the Gates powergrip 5146 : 121gr ( I have 2 of them weighting exact the same 121gr)

 

For the record : people that lost me : The calculation to retrieve the frequency setting for a certain belt is :

f(belt)=110Hz x sqrt (mass (htd)/mass(belt)) 

  f(belt) = frequency to tension your specific belt 

  mass(belt) = weight of your specific belt (gr)

  110Hz = frequency that lotus stipulated for their original round thooted belt ( infact they say 100hz-110Hz @30°BTDC)

  mass(htd) = weight of this original lotus round thooted belt (gr) If only I knew that mass????or have someone to weight one.

Edited by gvy

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Thanks,

I hope this post will be usefull for other people struggling with Krikit or other gauges and use a simple smartphone with an app to regulary check their cambelt tension. They just need to know which belt they have installed.

Edited by gvy

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I use the OEM! Gates 'Carbon Drive' app (think its actually for push bike belts)  however, its sensitive and gives a clear reading in Htz.   My difference in spring lengths was more dramatic than yours, but overall effect similar   

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I get the same results with the different apps, but the gates "carbon drive app" is by far the most user friendly with the clearest reading. Thanks Steve.

This app is made by gates for measuring belt tensions

 

 

 

 

 

Edited by gvy

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Good work Geert! Interesting to see the difference the new springs make is almost exactly the difference you calculated for the different weight of the belts. Could be coincidence, but does explain why your belt seemed slack before.

Now go and enjoy the car. ;)

Filip


I have made many mistakes in my life. Buying a multiple Lotus is not one of them.

 

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