DE217012C - - Google Patents

Description

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IMPERIAL

PATENT OFFICE.

PATENT LETTERING

- JVl 217012 - CLASS 42 /. GROUP

Dr. MAX REINGANUM in FREIBURG i. Br.

Spring balance. Patented in the German Empire on September 21, 1907.

In the case of screw trolleys and torsion spring trolleys, suitable use the effect of gravity on an inclined lever arm that changes its inclination cause astasis that has not yet been used to increase sensitivity Was applied by spring carriage. This creates a kind of combination of spring and Grayitationwage, which in the following under I ίο for the coil springs (or more generally for Elongation elasticity), described under II for torsion springs (or torsional elasticity) shall be. A few areas of application for these wagons are then discussed under III.

I. Theory of the new spiral spring balance.

i. There is a helical spring, the length of which in the unloaded state is zero, i. H.

which, as it is easily conceivable and easy to manufacture, pulls itself together completely unencumbered into one level. The mass of the spring and thus also the effect of gravity on it should be negligible. One end of this spring is attached to a fixed point (fixed bar, stand), the other end is connected to the free end of a lever arm that can be rotated about its other end in a vertical plane, as shown in FIG. The axis of rotation of the lever arm is initially exactly vertically below the fixed end of the helical spring, at a (vertical) distance L, where L also means the length of the rotatable lever arm (measured from the axis of rotation to the attachment point of the spring). The vertical distance L is indicated in the figure by the broken line. Let the lever arm be uniformly occupied by the mass M ₁ , α be the angle of the same with the vertical, X ₁ the associated spring length. The perpendicular from the pivot point A of the lever arm to the (imaginary)

The axis of the helical spring forms the angle -

with the lever arm, which angle recurs at B in the manner shown in FIG. The tensile force K of the spring is directly proportional to its length, so that

where k is the proportionality factor. Let K be measured in grams. X means the spring length in centimeters. It is asserted: If the lever arm L is in equilibrium for any angle α, it is in equilibrium for any angle α , ie it is in indifferent equilibrium for every direction. Proof: The torque of gravity is M ₁ · - · sin α; the ,

2 DO

The torque of the spring force is:

- L * k * X ₁ * cos -;
2

so is in equilibrium:

(2) - M ₁ -sin α = L k ■ X ₁ cos -

2 2

Now there is still (3)

α X ₁

sin - - =

2 2 'L.

this follows from the triangle that is formed from the perpendicular from the pivot point A to the spring axis, half the spring axis and the lever arm L. Inserting this into the previous * equation gives

- M ₁ sm α
2

Because now

2 L * · k ' sin- · cos

sm a

2 nm

cos

is, then α stands out, so that the equilibrium condition no longer contains the angle α. Which was to be proved. All that remains is:

or

(4)

M ₁

that is, it is only necessary to ensure that the mass of the unit length of the lever arm of any length or its line density is 2 h. k is easy to determine by hanging the spring vertically and determining its length for any weight. If (4) is observed, the system is then in equilibrium for every angle α.

Has z. B. when using the spring as an ordinary (Jollysche) spring balance the load ι g caused the length 10 cm, so is

. according to (1) k = -; so it must be the mass of

ι cm lever arm according to (4) be 0.2 g, or, if this is to be 20 cm long, it must weigh a total of 4 g.
. 2. The given system is not a balance insofar as it is in indifferent equilibrium in every position. No matter how small a burden, one z. B. would bring in a small (massless) weighing pan attached at B , would bring the lever arm to the complete lowering down.

However, by still sticking to the helical spring with the presupposed properties (masslessness, length unloaded: zero, force directly proportional to the length), one can get from the discussed system to a sensitive balance by fixing the fixed point of the Spring no longer attaches vertically above the axis of rotation of the lever arm. but shifts something to the side. For the following calculation, the distance between the fixed point of the spring and the axis of rotation A remains as before = L-, but the connecting line is rotated against the vertical by the angle d (Fig. 2). Let ε be the angle between the imaginary connecting line and the lever arm; the angle between the latter and the vertical is again α. The angle at B between the spring axis and the normal to the lever arm is for the same reasons,

as before, now -. .

In equilibrium is now:

- M ₁ sin α = L k λ-, cos - 2 ^xl 2

M ₁ . . ε

- - sin α = k A ₁ cos

2 2

Since now analog (3)

sm - =

2, L

so follows

X ₁ = 2 L * sin - j

sin α = 2 k · L · sin

■ cos -

= k · L · sin ε

sin ε, _T sin (α

₁ ^

sm α sin a

sin (α - 8) = sin α · cos d - · cos α · sin ι

2 k L sin &

M ₁ = 2 k · L · cos 1

tg α

Now the angle of inclination α no longer stands out from the equilibrium condition; the equilibrium is no longer indifferent, but rather stable, since an increase in M _{1 is} associated with an increase in the angle α.

For another mass of the lever arm, if the length of the lever arm remains the same:

", _T. 2ÄZsini5

M ₉ ■ - = 2 k L cos δ

day ₂

By writing a _x for α in the penultimate equation and subtracting it before the last one, it follows:

M ₂ - M ₁ = 2 UL sin b (- ^ -

. I tg-θχ tga ₂

Instead of increasing the mass of the lever arm from M ₁ to M ₂ , we can also use the moving end of the lever arm from the

Mass M _{1 is} the mass

attach in the weighing pan. If we call this load μ, then it is

M.,

- M ₁ = 2 µ

(6) μ =

= UL sin & {- -

\ tg «ι. day a ₂

The load μ is measured by the difference between the angles a _{x of} the unloaded and a _{2 of} the loaded scales.

As the sensitivity E of this balance, we can consider the path covered by the lever end B divided by the associated load. So

(7)

in>

L (a ₂

where α is measured in radians.

This expression becomes particularly simple if we have the sensitivity to small loads Find Δ JH. Then it follows from (6)

Δ μ = - kLsin & A

, μ

= - k 'L sin & Δ (ctg α)
k · L ' sin 6 · Δ α

(8th)

Αμ

_{E =} J-

sin ⁴ α
. α sin ² α

Αμ

k · sin

We assume as an example that the angle S should be 2 °. Let the mass of the lever arm be such that α = 45 °. Let k again be as in the earlier example of the indifferent

Systems -. Then E, i.e. the

ratio of the arc covered by the end of the lever arm to the load

10 · sin ² 45 °
sin 2 °

= -143.3.

³ ^ ie ι mg load causes the path 1.433 mm. If one were to use the same spring as an ordinary Jolly spring balance, the extension caused by 1 mg would be only 0.1 mm. A vertically hanging spring is 14 times less sensitive than our arrangement. By making δ smaller, the sensitivity can of course be increased as desired. It is variable with the angle of inclination α in the manner that can be easily seen from equation (8). The sensitivity is at its maximum for QO ^0.

3. We have seen how, by moving the fixed point of the spring, one can get out of the theoretical systems first considered a sensitive balance or, of course, others Can make measuring device.

You can also leave the fixed point exactly vertically above the axis of rotation and for this Choose springs for which the tensile force is not exactly proportional to the length, i.e. Feathers as practically the only one that comes into question. So we return to Fig. 1, only instead of (1) we write for the spring force:

■ 60 ■. K = It-X ₁ + CX ₁ ² ,

where c means a new constant, the size of which is a measure of the deviation from the strict proportionality between force and elongation. We therefore maintain that the length of the spring in the unloaded state is zero. We now write:

= UX ₁ U + ^ X ₁

and the equilibrium condition becomes: L
2

The same calculation as in the first part, by replacing X ₁ on the right in front of the bracket with its value according to (3), results in:

- M ₁ sin o. = L k X ₁ (1 + - = - X ₁ I cos

! \ R j 2

^ X ₁ L.

A certain length of the spring X ₁ corresponds to a certain mass M _{1 of} the lever arm and thus, according to (3), a certain angle a _v

If we give the lever arm the mass M ₂ with the same dimensions, the following applies:

Subtracting the previous equation gives:

M ₂ - M ₁ = 2cL (X ₂ -1 ₁ ).

Instead of giving the mass M ₂ to the lever arm, we can also attach the mass M ₂ - M ₁ in the middle of the lever arm M ₁ or the load at the end of the lever arm in the (massless) weighing pan, as before

- ^L == μ. Hence is by onset

into the last equation:

100 (9) μ = c L (X ₂ - X ₁ ).

The load μ is directly proportional to the spring extension X ₂ - X ₁ . As »sensitivity« we can now define the relationship between elongation and stress:

E =

X,

This "sensitivity" is the greater, the smaller the deviation of the proportionality of strength and elongation, d. H. the smaller c is. It is also inversely proportional the length of the lever arm.

A comparison with the sensitivity of the same vertically freely hanging spring (Jolly- ^1! 5 see spring balance) is of interest. The spring equation was:

K - AX ₁ + CX ₁ ² .

It follows from this:

ΔΧ

AK

k + 2 c λ

Let k be as in our earlier examples

- ■, c Let - _? -. With freely hanging spring ok. 3600 ^b

is the sensitivity for the

Δ I \.

Length zero 10, for length X ₁ = 20 cm 9.

In contrast, the sensitivity is in the above

described arrangement, if the length of the lever arm is chosen to be 20 cm as before, for every spring length

ι 3600

cL

= 180,

so 20 times larger than the hanging one

Feather.

Let us define the sensitivity covered by the end of the lever as earlier in equation (7) Distance (arc that can be read on a circular scale) divided by the associated load, i.e.

for this purpose we first insert the value 2 L · sin - in (9) for λ according to (3) and obtain

sm

- sin

β \ 2 2

For small loads Δ μ we write:

= 2 CL ² · Δ sm - = CL ² cos - 22

Δα.

The sensitivity, measured as in (7), will be:

L-Aa

C · COS

This sensitivity is therefore even greater and has its maximum as it approaches a = i8o °, i.e. for a vertically hanging lever arm.

We could now take into account that the spring itself is not massless, but exerts a pressure on the lever arm at point B by virtue of its weight. It is also the case that springs are usually used, the length of which in the unloaded state is not zero, but a certain finite size. These formulas should not be given here, as this does not change the principle and the feasibility of the balance.

II. Theory of the new torsion balance.

The new torsion balance is directly connected to the spiral spring balance described. Imagine the helical spring in Fig. 1, but a torsional force is applied in the axis of rotation A itself, which tries to turn the lever arm L counterclockwise. This can be carried out in the following way, coming to Fig. 3 (in contrast to Fig. 1 and 2 drawn in perspective): A horizontal, stretched wire is clamped with its ends in two fixed points so that the ends of the wire are not rotatable in the attachment. The lever arm L is soldered to this wire, approximately in its middle, at an angle γ to the vertical. Now the lever arm is turned through the vertical until its torque of gravity, which tries to turn it further by itself, comes into equilibrium with the torsional torque of the horizontal axis wire acting in the opposite direction. The angle of the lever arm with the vertical (constructed upwards) in the equilibrium position is a. For the torsional moment, which we call T , we want to introduce the assumption (which corresponds to reality within wide limits) that it is proportional to the twist angle of the wire, i.e. proportional to α -f- γ , where we use the angles im for the following calculation Measure radians. (γ is calculated as positive if, as in FIG. 3, it is on the other side of the vertical than α.) So it is

(10) T = k (α 4- y),

where k is the proportionality factor which depends on the length, thickness and material of the horizontal wire. Then is in equilibrium

LM

(11) k (α -f γ) = sin α.

²

L and M ₁ have the earlier meanings. With the form of equation (11), we cannot achieve that with suitably chosen k, L and M ₁ the equilibrium becomes indifferent, that is, becomes independent of α, which we were able to achieve in the ideal case of the helical spring balance considered first. On the other hand, we can successfully demand that in the immediate vicinity of a certain angle a, say for the angle a -j- Δ a (where Δ "a is a very small quantity), except for the angle a, there is still equilibrium if the angle is unchanged M _1. So we demand that

Aa. +. Y)

^LM i ■,
sm (α

α).

Because now

sin (a + Δ α) = siri α · cos Δα-f cos α · sin Δ α and, since Δ a is small,

cos Δ α = ι, sin Δ a = Δ α

(v / if the angle, as assumed, is measured in radians), it follows from (12)

k (α + γ) + k - A α

LM ₁ :, LM ₁

= sm α H cos α · Δ α

2 2

and by subtracting (11) and after Division by Δ α

ίο (13)

LM ₁

= cos a,

from which, given the material and dimensions, the maximum (infinite) Sensitivity for small deflections, angles α to be observed are calculated.

Substituting (13) into (11) gives then furthermore the angle to the vertical at which the lever arm to this The purpose of soldering onto the untwisted wire is to:

(14)

γ = tg α ■

■ a.

For example, let α = 30 ° or in radians 0.5236. Then amounts to

7 -

30 ° - 0.5236 = 0.0538

in radians or 3.082 °. Instead of soldering at this angle, you can of course also attach the lever arm to the axle wire at any angle if one only ensures that the attachment points of the latter are rotated evenly can.

We also define E as sensitivity

35 x the quotient of the increase in the angle α to the increase Δ M ₁ Af of the weight of the lever arm _1, whereby we can think attached ₁ us the weight Δ M ₁ in the middle of the lever arm M unchanged.

^Δα

From (11) we get

M ₁ =

L · sin α

Δ M ₁

' Δα

E =

2k

Δα
ON ₁

[ι (α + ψ) ' cos α]

sin α sin ² α. J

L · sin α

2k I

^ΰ - + y \
te * }

The sensitivity then becomes infinite again for α '- \ - γ = tg α, as it must also be the case according to (14). '.

Now let's compare Z? with the sensitivity E 'of an ordinary (previous) torsion balance that has the same torsion wire. We receive such a B., if in Fig. 3 the lever arm L is only one half of a symmetrical two-armed straight balance beam, 'the second half of which extends to the other side of the pivot point. If we think of the lever arm L as being supplemented in this way, the center of gravity falls into the torsion wire; So there is no moment of gravity around the latter, which comes from the balance beam itself (not from the attached weight). The unloaded balance beam is therefore in equilibrium for every soldering angle α without further rotation taking place beforehand.

If the load is Δ M ₂ in the middle of L , then only a restoring torsional moment Δ T occurs, which is the same

AT = k- Δα.

The opposite acting moment of gravity is

sin (α + Δ α) · Δ M ₁

or, since Δ α is small,
L.

sin α · Δ M ₁ .

So it is:

k · Δ α = - sin α · Δ M ₁

Δα
⁼ ~ ΑΜ [ ⁼

L sin α
2k

We take the best case that the two-armed balance beam is horizontal, ie that sin α = ι, and then call the sensitivity E ". So:

sm α

E '

ι -

tga

According to this equation, the sensitivity is ours with the help of gravity astased balance larger than that of the usual torsion balance.

For example, for γ = 3.082 ° our balance was for α =. 30 ° infinitely sensitive. For α = 35 °, according to the last equation, the sensitivity (for small loads) is 11.29 times greater, at 40 ° it is 6.187 times greater than with the pure torsion balance.

III. Areas of application of the new
Spiral and torsion spring balances.

The main advantage of the arrangements described is that they are arbitrarily powerful Helical springs or torsion wires can be used and still have high sensitivity the spring balance is reached.

The applicability is very diverse, e.g .: sensitive scales for

Claims (2)

small 'loads (so-called microbalance), see Fig. 4, schematically showing an executed model. The sensitivity was up to 25 mm on the scale per milligram. Electrometers and galvanometers in very different Embodiments. So z. B. also as a hot wire galvanometer, by the current through the axis wire of the torsion instrument is guided and the torsional elasticity is achieved by heating changed or by guiding the same through the coil spring of the coil spring dare. The following applications of a mechanical nature also come into consideration: density determiners for liquids, by attaching a sinker to the lever arm. Furthermore, hair hygrometer by replacing the spiral spring by a clamped hair and balancing the weight of the lever arm according to the earlier Equations. Dynamic applications can also be considered. Namely, the device gives slow vibrations of strong springs or axle wires, something in the watch industry and is of importance for similar purposes. Also as a measuring device for vertical accelerations, such as those required for balloon flights are, can .the device apply. Pa τ ε ν τ - A ν s ρ R ü c η ε: ι. Spring carriage, characterized in that one with one end at one The other end has a coil spring attached to the tripod and subjected to tensile stress the free end of a lever arm serving to take up the load to be weighed is connected to a mass balanced in this way, that with a low load and inclination of the lever arm the spring is indeed is tensioned and its tensile force increases, but at the same time the lever arm is increased Moment of gravity receives and so the increase in the moment of the spring tension is almost due to the increase in the moment the gravity of the lever arm is balanced and therefore a small one, attached to the lever arm attached weight means a considerable stretch of the spring and therefore a considerable stretch of the lever arm evokes. 2. Spring trolley according to claim 1, characterized by the replacement of the helical spring by a torsional force acting in the axis of rotation of the lever arm, the mass and length of the lever arm so it is balanced that with a small load the restoring moment of the torsional force increases, but at the same time the increasing inclination of the lever arm acts in the sense of the load Moment of the heaviness of the lever arm increases so much that the increased pushing back Force of the torsion is almost balanced and therefore a very small, load suspended on the lever arm cause considerable rotation of the lever arm able. 1 sheet of drawings.