The idea, in general, is clear. The required tension is known, the resonant frequency depends on it. But how exactly does it depend, by what formula can it be calculated? This is the author of Instructables, nicknamed Cactus workshop.
The formula itself is given below. At first, everything is incomprehensible in it. Well, you can guess that f - is the frequency, and the rest?
But then the master tells what each variable means. f is really the frequency [Hz], T is the tension [N], L is the free length [m], μ is the linear density [kg / m]. This value requires an additional explanation. Usually, density is measured as the ratio of mass to volume in units of kg / m3. But for objects whose cross-section is known, it is more convenient to measure the density as the ratio of mass to length in units of kg / m - this is the linear density. If we take the value of all variables in SI units, the result will also be in units of this system.
To calculate the linear density of the band saw, the master weighs it - it turns out 0.022 kg, but it is not necessary to change the length, it is indicated by the manufacturer - 1.425 m. The master measures the free length of the saw with a tape measure between the wheel centers of the band saw - it turns out to be 0.396 m.
The master believes that the optimal pressure for the band saw used by him is 100,000,000 Pa. The cross-section of the saw without taking into account the teeth is 0.00465x0.0003 m. Multiplying all three values, the master receives 139.5 N, rounds to 140.
The following shows how the master measures the cross section and mass of the saw:
The master substitutes all the obtained values in the formula:
It turns out 120 Hz, the master sets the tension of the saw with the band-saw engine off (the mushroom must be locked in the pressed position), while periodically pulling the saw with a guitar pick (not with your finger, as in the next photo, but with a pick as in KDPV!) And measuring the resonant frequency of the smartphone on which the guitar tuner application is running. A hardware guitar tuner is also suitable.
The master recommends not to forget that in addition to the main frequency, the band saw, like a guitar string, emits oscillations at harmonics.Both hardware and software guitar tuners are designed to measure the fundamental frequency, but it happens that they are wrong. The measurement must be carried out several times, bringing the pick in different ways, and select the smallest of the displayed values. Otherwise, there is a risk of pulling the saw twice, and this is a serious danger even when the engine is stopped.