EP1516961B1 - Method for determining soil rigidity and soil compaction device - Google Patents

Description

Technical area

The invention relates to a method for determining a mass for the soil stiffness (degree of compaction) of a compacted or compacted soil area according to the preamble of patent claim 1, as well as a soil compacting device according to the preamble of patent claim 7.

State of the art

In the publication by R. Anderegg, "Vibratory rollers with controllable parameters and the FDVK", road and civil engineering, Giesel Verlag for publicity, Iserhagen, DE, No. 12. 1997, pp 11-17 was a nationwide dynamic compression control (FDVK ), which was used to monitor ongoing and a review of completed compaction work. Mainly bandage vibrations in the vertical direction were taken into account, whereby the bandage and the compacted or still to be compacted bottom area formed a vibration system. Since the bandage was not firmly connected to the ground, pressure could only be transmitted between the ground area and the bandage, but not tensile forces. The soil reaction force therefore only assumed positive values. The bandage was able to lift off the ground. The periodic loss of contact between the bandage and the ground resulted in non-linear effects, which led to harmonics. With a further increase in non-linearity, a subharmonic oscillation with half excitation frequency could occur. The compactor began to jump or stumble. If subharmonic vibrations occurred, it was suggested that they be avoided in order to reduce the imbalance, since the tumbling in particular led to fragmentation of the ground and damaged the building surface. A growing natural frequency of the system bandage / floor area serves as a measure of increasing compaction.

In the German Offenlegungsschrift DE-A 100 19 806 Attempts have also been made to prevent a "jumping" of a soil compaction device, since this can cause a loosening of the already compacted soil, as well as a rapid increase in machine wear occurs. For this purpose, vibrations were detected, which are harmonics of the exciting vibrations of a soil compaction element. It was assumed here that harmonics result from a reaction of an excessive impact energy on an already compacted soil.

In the DE-A 100 28 949 a system was presented which was suitable for determining a degree of compaction in both rolls and plate vibrators. A displacement sensor for measuring a vertical movement of the superstructure was arranged thereon. The signal measured with the sensor was in a first and a split second partial signal. The first sub-signal passed through a high-pass filter and the second sub-signal through a band-pass filter. The high pass filter was set to pass frequencies just below the excitation frequency, so at an excitation frequency of 60 Hz, 51 Hz could still happen. The bandpass filter was set so that frequencies could pass from 15% to 60% of the excitation frequency. The signals coming from the bandpass filter were divided by the signals coming from the high pass filter. The quotient continued to increase with the number of passages over a region to be compacted and should be a reliable indicator of soil stiffness.

• ➢ Auflastbetrieb: Die Vorrichtung bleibt in Bodenkontakt. Der Beschleunigungsaufnehmer misst nur die Umlauffrequenz der Unwucht (1 · f).
• ➢ Optimaler Betriebszustand: Die Bandage hebt periodisch vom Boden ab. Der Beschleunigungsaufnehmer misst Oberschwingungen (2 · f, 3 · f usw.) mit stark abnehmender maximaler Amplitude.
• ➢ Instabiler Zustand: Die ganze Bodenverdichtungsvorrichtung (Walze) fängt an zu springen. Es treten zu den Oberschwingungen Subharmonische (1/2 · f, 3/2 · f, 5/2 · f usw.) auf.

In the WO 98/17865 a soil compaction device with an accelerometer on a bandage is described. With the soil compaction device could according to embodiments in the WO 98/17865 the three following compression operations are set:

• ➢ Overload operation: The device remains in contact with the ground. The accelerometer measures only the rotational frequency of the imbalance (1 · f).
• ➢ Optimal operating condition: The bandage periodically lifts off the ground. The accelerometer measures harmonics (2 · f, 3 · f, etc.) with greatly decreasing maximum amplitude.
• ➢ Unstable condition: The whole soil compaction device (roller) starts to jump. Subharmonics (1/2 · f, 3/2 · f, 5/2 · f, etc.) occur for the harmonics.

A compression should always be optimal, d. H. fastest and with the least expenditure of energy feasible when resonance of the soil compaction system occurred. The soil compacting system was formed of the soil to be compacted and the compacting device acting on it.

In the US-A 4,546,425 it is explained how a soil to be compacted became harder and harder due to several crossings while the machine data remained constant and the compacting drum began to jump. To prevent this jumping, an adjustable eccentric was used.

In the US-A 5,695,298 were determined with a arranged on a bracket and a bandage accelerometer oscillations of this bandage. The measurement signal was applied to a first bandpass filter for the excitation frequency (or higher Frequencies) and given to a second bandpass filter for a half excitation frequency. With a division circuit, the output signal of the second bandpass (amplitude of the half excitation oscillation) was divided by the output signal of the first bandpass (amplitude of the excitation frequency). The quotient should not exceed a predetermined value, for example 5%, in order to be able to work stably while avoiding unstable states.

With only a slight excitation or a soft ground, the accelerometer measures a non-harmonic vibration. When the excitation was increased or a stiffer and more elastic ground was reached, a periodicity of the oscillation occurred at half the frequency. This condition was considered stable. If the stimulation was increased even more, or if the ground was even stiffer, jumping of the bandage occurred. The measured quotient was significantly higher than mentioned above.

In the US-A 5,727,900 a control device for a soil compaction device is described. In this case, the acceleration measured horizontally and vertically of the bandage, the position of the eccentric, the eccentricity of the eccentric and the rolling speed of the compacting device were measured. The soil compaction device described here worked analogously to US-A 5,695,298 with the same stability criterion that the appearance of a half excitation frequency with respect to the amplitude of the excitation frequency was limited to a maximum of 5%.

Presentation of the invention task

The object of the invention is to compress a soil area to a predetermined or to a maximum of a machine design according to achievable soil stiffness, to determine the degree of compaction achieved and to provide a soil compaction device with which this optimal soil compaction is to make.

solution

The object is achieved procedurally by the features of claim 1 and device moderately by the features of claim 7. In order to achieve optimum soil compaction, ie a soil compaction with a predetermined or maximum possible soil stiffness (degree of compaction) is a ground contact unit acting on the floor area of a soil compacting device moves over the latter. In this case acts on the ground contact unit a time periodically changing with at least one action frequency force. The vibrations of a vibration system, consisting of the soil compacting device with the ground contact unit and the respective ground area, are determined. The vibration form of the vibration of the vibration system is recorded, and the soil rigidity (degree of compaction) is then determined from the vibration mode, from the engine parameters of the soil compacting device and from the timing of the soil compaction force.

In contrast to the known soil compaction methods or the known soil compacting devices, no attempt is made here to eliminate subharmonic pertubation to the frequency of action. On the contrary, they are deliberately evaluated. In fact, according to the invention, it is based on the knowledge, as stated in the detailed description, that the frequencies of the subharmonics define an achieved degree of soil compaction. The lower the frequency of the deepest subharmonic, the greater the soil compaction level over which a ground contact unit of a soil compaction device is moved.

In a particular embodiment variant, not only the subharmonics are determined, but also their amplitudes, which are set in relation to the amplitude of the action frequency. Preferably, the maximum amplitude values will be used for this purpose. However, it is also possible to use amplitude values for a given phase position. As can be seen from a fig tree scenario described below, this consideration, in addition to the determination of the subharmonic results in a more accurate determination of the achieved or existing soil stiffness.

Now you can force the ground contact unit, which is in contact with the compacted or already compacted soil, with a single sinusoidal oscillation usually by a rotating eccentric or by two angularly mutually adjustable eccentric. However, it is also possible to use a plurality of eccentrics with different circulating frequencies. For each of these frequencies, a series of subharmonics results depending on the degree of soil compaction achieved. If several "fundamental frequencies" are used, a more detailed statement can be made about the achieved or measured soil compaction.

Preferably, however, one will choose the frequency of action on the ground contact unit adjustable. Namely, at an adjustable frequency, a resonance of the vibration system consisting of ground contact unit and the ground area to be compacted or compressed can be determined. Working in resonance results in compaction at reduced compaction performance. Since the vibration system is a damped system due to the compaction power to be provided, the degree of damping results in a phase angle between the maximum amplitude of the excitation (e.g., force due to the rotating imbalances) and the vibration of the system = vibration of the ground contact unit). In order to be able to determine this phase angle, a sensor will be mounted on the ground contact unit next to a sensor for the subharmonics, which measures the temporal deflection in the direction of soil compaction. The temporal deflection of the excitation (force application to the ground contact unit) can also be measured; However, it can easily be determined from the instantaneous position of the imbalance or imbalances. The temporal position of the maximum amplitudes (excitation oscillation to the vibration of the ground contact unit) will be determined with a comparator unit. The excitation is preferably adjusted such that the maximum amplitude of the excitation by 90 ° to 180 °, preferably by 95 ° to 130 ° ahead of the maximum amplitude of the ground contact unit.

Preferably, one will interpret the maximum amplitude of the exciting force adjustable. An adjustment of the exciting force may be avoided when using e.g. be achieved by two imbalances, which rotate at the same rotational speed and the angular distance is changeable. The imbalances can be moved in the same direction or in opposite directions.

The occurrence of subharmonics, if a soil compacting device having a ground contact unit is not designed accordingly, can lead to machine damage. It will therefore design damping elements between the respective ground contact unit and the remaining machine parts such that a transmission of the subharmonic is attenuated. One can, of course, interpret the entire soil compaction unit such that the low frequency subharmonics do no harm; their frequency is known according to the explanations in the detailed description. But you can also reduce the amplitude of the exciting force so far that the amplitudes of the subharmonic do no harm or are no longer available.

From the following detailed description and the totality of the claims, further advantageous embodiments and feature combinations of the invention result.

Brief description of the drawings

Fig. 1

eine schematische Darstellung zur Erklärung eines analytischen Modells eines schwingungsfähigen Systems mit einem beispielsweisen Walzenzug und einem zu verdichtenden bzw. verdichteten Bodenbereich,

Fig. 2

ein Beispiel einer Umsetzung eines dimensionslosen Modells in ein Simulink-Modell,

Fig. 3

einen Vergleich zwischen einer gemessenen (links) und einer berechneten (rechts) Bewegung einer springenden Bandage auf einem harten Bodenbereich, wobei auf der Abszisse die Zeit und in der Ordinate die jeweilige Auslenkung aufgetragen sind,

Fig. 4

ein vereinfachtes Modell einer schwingenden Bodenkontakteinheit auf einem zu verdichtenden bzw. verdichteten Bodenbereich,

Fig. 5

einen gemessenen (rechts) und einen berechneten (links) Phasenraum (Orbital) einer Bodenverdichtungseinheit (Bandage des Walzenzuges AC 110 Ammann), wobei die Abszisse die Auslenkung in x-Richtung und die Ordinate die Geschwindigkeit in X-Richtung zeigt (ein einzelner Kurvenzug schliesst sich immer nach der Zeit einer Grundschwingung = Anregungsfrequenz der Bandage),

Fig. 6

ein Bewegungsverhalten eines Walzenzuges bei gleichbleibenden Maschinenparametern über einem unterschiedlich harten Untergrund,

Fig. 7

ein Beispiel einer chaotischen Bewegung einer Grabenwalze auf hartem Untergrund (Bodenbereich), wobei die obere Abbildung eine Auslenkung des Oberwagens (gestrichelt) und eines Unterwagens (ausgezogen) der Grabenwalze über der Zeit darstellt, die mittleren beiden Abbildungen das zur Auslenkung gehörende Frequenzspektrum und die unteren drei Abbildungen links einen Phasenraum für den Oberwagen, die mittlere Abbildung die verwendete Grabenwalze und die rechte Abbildung einen Phasenraum für den Unterwagen zeigen,

Fig. 8

eine zu Figur 7 analoge Darstellung jedoch für eine Vibrationsplatte,

Fig. 9

eine Zusammenstellung dynamischer Verdichtungsgeräte im Verzweigungsdiagramm, wobei n = 1 eine Anregung mit einer Grundschwingung, n = 2 eine erste Subharmonische (f/2), n = 4 die nächste Subharmonische (f/4), n = 8 eine dritte Subharmonische /f/8) kennzeichnet,

Fig. 10

eine einfache Ausführung zur Abschätzung einer Bodenverdichtung, wie man sie vorzugsweise an einer Vibrationsplatte anordnen kann und

Fig. 11

eine Variante zu der in Figur 10 dargestellten Schaltung.

The drawings used to explain the embodiments show

Fig. 1

a schematic representation for explaining an analytical model of a vibratory system with an exemplary compactor and a compacted or compacted soil area,

Fig. 2

an example of a conversion of a dimensionless model into a Simulink model,

Fig. 3

a comparison between a measured (left) and a calculated (right) movement of a jumping bandage on a hard ground area, wherein the abscissa represents the time and the ordinate the respective deflection,

Fig. 4

a simplified model of a vibrating ground contact unit on a ground area to be compacted or compressed,

Fig. 5

a measured (right) and a calculated (left) phase space (orbital) of a soil compaction unit (bandage of the compactor AC 110 Ammann), where the abscissa shows the deflection in the x-direction and the ordinate the velocity in the x-direction (a single curve) always after the time of a fundamental oscillation = excitation frequency of the bandage),

Fig. 6

a movement behavior of a compactor with constant machine parameters over a different hard ground,

Fig. 7

an example of a chaotic movement of a trench roller on hard ground (ground area), wherein the upper figure represents a deflection of the upper carriage (dashed) and a lower carriage (pulled-out) of the trench roller over time, the middle two maps the frequency spectrum belonging to the deflection and the lower three figures on the left show a phase space for the superstructure, the middle figure the trench roller used and the right figure a phase space for the undercarriage,

Fig. 8

one too FIG. 7 however, analogous representation for a vibrating plate,

Fig. 9

a compilation of dynamic compaction devices in the branch diagram, where n = 1 an excitation with a fundamental, n = 2 a first subharmonic (f / 2), n = 4 the next subharmonic (f / 4), n = 8 a third subharmonic / f / 8),

Fig. 10

a simple embodiment for estimating a soil compaction, as they can be arranged preferably on a vibrating plate and

Fig. 11

a variant of the in FIG. 10 illustrated circuit.

Basically, the same parts and elements are provided with the same reference numerals in the figures.

Ways to carry out the invention

In an analytical description of dynamic soil compaction devices, consideration of a soil contact unit together with the compacted soil as a single system plays a central role. In FIG. 1 For this purpose, a compactor 1 with rear, rubber-tired wheels 3 and a front bandage 5 as a ground contact unit and a chassis 6 is shown. Based on this system, a one-sided bond between a bottom region 7 to be compacted (substructure) and the compactor 1 (compacting device) is the main reason for the occurrence of nonlinear effects. The one-sided binding is justified by the fact that between the compactor 1 and the bottom portion 7 compressive forces but no tensile forces can be transmitted. Accordingly, it is a force-driven nonlinearity; When the maximum ground force values are exceeded, the compaction apparatus 1 periodically loses contact with the ground area 7 (subsurface). Additional non-linear elements of the soil properties, such as shear strain-controlled stiffness changes, can be neglected in comparison. Also, the superlinear spring characteristic of (rubber) damping elements 8 between the chassis 6 and ground contact unit 5 (bandage), or a superstructure 9 and an undercarriage 11 of a trench roller 12 explained later is of minor importance and does not significantly affect the calculation results of an analytical description. The same applies to a vibration plate 14 with a superstructure 15 and a lower carriage 17th

further reference numerals FIG. 1

51

Floor Pen

52

bandages mass

53

Elastic suspension

54

vibration system

55

Floor damper

56

Model of the compactor

57

Model of the underground

58

Energy dissipated into the subsurface W

A compacting device generally, as well as the compactor 1 in FIG. 1 , a ground contact unit (bandage 5, undercarriage 11 or 17 ) with a vibrating part, for example with a rotating imbalance 13 with a mass m _d including an imbalance exciter. On this vibrating part 13 , a static Auflastgewicht of the chassis 6 is based with a mass m _f (static weight) via damping elements 8 (stiffness k _G , damping c _G ) from. The static weight m _f , together with the damping elements 8 , produces a point-point-excited vibration system which is tuned low (low natural frequency). The uppercarriage 9 or 15 or the chassis 6 acts in vibration mode with respect to the vibrations of the undercarriage 11 or 17 or the bandage 5 as a low-pass second order. Thus, the vibration energy transmitted into the chassis 6 or the superstructure 9 or 15 is minimized.

The compacted or compacted bottom of the bottom region 7 is a building material for which, depending on the properties investigated, different models exist. In the case of the above-mentioned system (ground contact unit - ground), simple spring-damper models (stiffness k _B , damping c _B ) are used. The spring properties take into account the contact zone between the soil compaction unit (bandage) and the elastic half-space (floor area). In the area of the excitation frequencies of compactors, which are above the lowest natural frequency of the system (ground contact unit - ground), the ground stiffness k _{B is} a static, frequency-independent variable. This property could be demonstrated in the present application in the field trial for homogeneous and layered soils.

If the machine and soil model are combined into an overall model, taking into account the one-sided binding, the following equation system (1) describes the associated motion differential equations for the degrees of freedom x _{d of} the drum 5 and x _{f of} the chassis 6 . $$\begin{array}{c}\begin{array}{cc}\hfill m_d{\ddot{x}}_d+F_B+c_G\left({\dot{x}}_d-{\dot{x}}_f\right)+k_G\left(x_d-x_f\right)& =m_u{r}_u{\mathrm{\Omega }}^2\cos \left(\mathrm{\Omega }\cdot t\right)+m_{d}G\hfill \\ \hfill m_f{\ddot{x}}_f+c_G\left({\dot{x}}_f-{\dot{x}}_d\right)+k_G\left(x_f-x_d\right)& =m_f\mathrm{G}\hfill \end{array}\end{array}$$

m_d : schwingende Masse [kg] z.B. Bandage 5 bzw. Unterwagen 11 bzw. 17
m_f : stat. Auflastgewicht [kg] z.B. Chassis 6 bzw. Oberwagen 9 bzw. 15
m_ur_u : stat. Moment Unwucht [kg m]
x_d : Bewegung schwingende Masse [mm]
x_f : Bewegung Auflastgewicht [mm]
Ω : Erregerkreisfrequenz [s^-1] Ω = 2π · f
f: Erregerfrequenz [Hz]
k_B : Steifigkeit der Unterlage/des Bodenbereichs [MN/m];
c_B : Dämpfung der Unterlage/des Bodenbereichs [MNs/m]
k_G : Steifigkeit der Dämpfungselemente [MN/m]
c_G : Dämpfung der Dämpfungselemente [MNs/m]Based on a one-sided, force-controlled binding results: $$\begin{array}{ll}{F}_B=c_B{\dot{x}}_d+k_{B}x& \hfill \mathrm{f}\ddot{\mathrm{u}}r{F}_B>0\\ F_B=0& \hfill \mathrm{otherwise}\end{array}$$

m _d : oscillating mass [kg] eg bandage 5 or undercarriage 11 or 17
m _f : stat. Load weight [kg] eg chassis 6 or superstructure 9 or 15
m _u r _u: stat. Moment unbalance [kg m]
x _d : motion oscillating mass [mm]
x _f : movement load weight [mm]
Ω: excitation circuit frequency [s ^-1 ] Ω = 2π · f
f : excitation frequency [Hz]
k _B : rigidity of the pad / ground area [MN / m];
c _B : cushioning of the underlay / ground area [MNs / m]
k _G : stiffness of the damping elements [MN / m]
c _G : damping of the damping elements [MNs / m]

A soil reaction force F _B between the bandage 5 and the compacted or compacted bottom region 7 controls the nonlinearity of the unilateral bond.

j = 1

lineare Schwingungsantwort, Auflastbetrieb

j = 1,2,3,...

periodisches Abheben (die Maschine verliert pro Erregungsperiode einmal den Kontakt zum Boden)

j = 1,1/2, 1/4, 1/8,....

und zugehörige Oberwellen: Springen, Taumeln, chaotischer Betriebszustand

The analytic solution of the differential equations (1) has the following general form: $$x_d={\displaystyle \underset{J}{\Sigma }}{A}_J\cos \left(j\cdot \mathrm{\Omega }\cdot t+{\phi }_J\right)$$

j = 1

linear vibration response, load operation

j = 1,2,3, ...

periodic take-off (the machine loses contact with the ground once per excitation period)

j = 1.1 / 2, 1/4, 1/8, ....

and associated harmonics: jumping, tumbling, chaotic operating condition

For trench rollers ( FIG. 7 ), Vibratory plates ( FIG. 8 ) and rammers are basically the same considerations, taking into account the respective excitation principle result in analogous equations.

A numerical simulation allows the calculation of the solutions of equations (1). In particular, for the detection of chaotic vibrations, the use of numerical solution algorithms is essential. With the aid of analytical calculation methods, such as the averaging method, very good approximate solutions and statements of a fundamental nature can be made for a bifurcation of the fundamental vibrations for linear and nonlinear oscillations. The averaging theory is described in Anderegg Roland (1998), "Nonlinear Vibrations in Dynamic Soil Compactors, Progress VDI, Series 4, VDI Verlag Dusseldorf." This allows a good overall view about the occurring solutions. In multi-branching systems, analytical methods are associated with a disproportionately high outlay.

Resonanzverhältnis: $\kappa =\frac{\mathrm{\Omega }}{{\omega }_0}$

mit Ω = 2π·f
d. h. K = f/f₀, wobei f die Anregungs- und f₀ die Resonanzfrequenz [Hz] ist.
ω₀ ist die Kreis-Resonanzfrequenz des Schwingungssystems "Maschine-Boden" [s^-1].
Ort: $\eta =\frac{x_d}{A_0};\varsigma =\frac{x_f}{A_0};\mathit{\eta ʺ}={\omega }_0^2\eta ;\mathit{\varsigma ʺ}={\omega }_0^2\varsigma ;$

Amplitude A₀ f ist frei wählbar
Materialkenngrössen: $\delta =\frac{c_B}{\sqrt{m_d{k}_B}}=2d_B;{\lambda }_c=\frac{c_G}{c_B};{\lambda }_k=\frac{k_G}{k_B};$

Massen und Kräfte: ${\lambda }_m=\frac{m_f}{m_d};A_{\mathit{th}}=\frac{m_u{r}_u}{m_d};\gamma =\frac{A_{\mathit{th}}}{A_0};f_B=\frac{F_B}{k_B\cdot A_0}=k_B{A}_0\left(\eta +\mathit{\delta \eta ʹ}\right);$

$\begin{array}{l}\mathrm{\eta ʺ}+f_B+{\lambda }_c\delta \left(\mathrm{\eta ʹ}-\mathrm{\varsigma ʹ}\right)+{\lambda }_k\left(\eta -\varsigma \right)={\mathit{\gamma \kappa }}^2\cos \left(\mathit{\kappa \tau }\right)+{\eta }_0\\ {\lambda }_m\mathit{\varsigma ʺ}+{\lambda }_c\delta \left(\mathrm{\varsigma ʹ}-\mathrm{\eta ʹ}\right)+{\lambda }_k\left(\eta -\varsigma \right)={\varsigma }_0\end{array}$

wobei gilt: $f_B=\begin{array}{cc}\delta \eta \prime +\eta & f_{B>0}\\ 0& \mathrm{sonst}\end{array}$

As a simulation tool the program package Mathlab / Simulink® is used. Its graphical user interface and the tools available are very suitable for dealing with the problem at hand. The equations (1) are first transformed into a dimensionless form in order to achieve the highest possible universality of the results.
Time: $\tau ={\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_{0}t;{\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_0=\sqrt{{}^{k_B}{/}_{m_d}}$

Resonance ratio: $\kappa =\frac{\mathrm{<figure-callout\; id="0"\; label="\Omega \; \omega "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\Omega \; </figure-callout>}}{{\omega }_{}}$

with Ω = 2π · f
ie K = f / f ₀ , where f is the excitation frequency and f _{0 is} the resonance frequency [Hz].
ω ₀ is the circular resonance frequency of the vibration system "machine-ground" [s ^-1 ].
Place: $\eta =\frac{{\mathrm{<figure-callout\; id="0"\; label="x\; d\; A"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">x\; </figure-callout>}}_d}{A_{}};\varsigma =\frac{{\mathrm{<figure-callout\; id="0"\; label="x\; f\; A"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">x\; </figure-callout>}}_f}{A_{}};\mathit{\eta "}={\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_0^2\eta ;\mathit{\varsigma "}={\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_0^2\varsigma ;$

Amplitude A ₀ f is freely selectable
Material characteristic values: $\delta =\frac{c_B}{\sqrt{m_d{k}_B}}=2d_B;{\lambda }_c=\frac{c_G}{c_B};{\lambda }_k=\frac{k_G}{k_B};$

Masses and forces: ${\lambda }_m=\frac{m_f}{m_d};A_{\mathit{th}}=\frac{m_u{r}_u}{m_d};\gamma =\frac{A_{\mathit{<figure-callout\; id="0"\; label="th\; A"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">th\; </figure-callout>}}}{A_{}};f_B=\frac{F_B}{k_B\cdot A_0}=k_B{A}_0\left(\eta +\mathit{\delta \eta \text{'}}\right);$

$\begin{array}{l}\mathrm{\eta "}+f_B+{\lambda }_c\delta \left(\mathrm{\eta \text{'}}-\mathrm{\varsigma \text{'}}\right)+{\lambda }_k\left(\eta -\varsigma \right)={\mathit{\gamma \kappa }}^2\cos \left(\mathit{\kappa \tau }\right)+{\mathrm{<figure-callout\; id="0"\; label="\eta "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\eta </figure-callout>}}_0\\ {\lambda }_m\mathit{\varsigma "}+{\lambda }_c\delta \left(\mathrm{\varsigma \text{'}}-\mathrm{\eta \text{'}}\right)+{\lambda }_k\left(\eta -\varsigma \right)={\mathrm{<figure-callout\; id="0"\; label="\varsigma "\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\varsigma </figure-callout>}}_0\end{array}$

where: $f_B=\begin{array}{cc}\delta \eta \text{'}+\eta & f_{B>0}\\ 0& \mathrm{otherwise}\end{array}$

The resulting equations (3) are modeled graphically with Simulink®, see FIG. 2 , The nonlinearity is simply considered a purely force-controlled function and modeled using the "switch" block from the Simulink library.

Fig. 2:

130:

superstructure

131:

Dead weight chassis

132:

Lambda damping chassis

133:

Acceleration chassis

134:

Acceleration bandage

135:

Speed chassis

136:

Speed signal chassis

137:

Way chassis

138:

Path signal chassis

139:

Phase curve chassis

140:

Lambda stiffness chassis

141:

0.025 <D <0.065

150:

Ground, decoupled

151:

Switch 1

152:

Way ground

153:

Stiffness / damping

160:

undercarriage

161:

External arousal

162:

Dead weight bandage

163:

Acceleration bandage

164:

Acceleration bandage

165:

Speed bandage

166:

Speed signal bandage

167:

Way bandage

168:

Path signal bandage

169:

zero

170:

Switch

171:

force

172:

rigidity

173:

damping

174:

Phase curve bandage

175:

Ground contact force

176:

working diagram

Parameter:

• A0 = 1 [mm]
• kb = 140 [MN / m]
• D-degree = 0.25
• AC 110, 28 Hz, 1.8 mm

The coordinate system of equations (1) and (3) includes a static depression due to the dead weight (static load weight m _f , swinging mass m _d ). In comparison with measurements resulting from the integration of acceleration signals, the static sinking has to be subtracted for comparison purposes in the simulation result. The initial conditions for the simulation are all set to "0". The results are given for the case of the steady state. As a solvent solver is chosen "ode 45" (Dormand-Price) with a variable integration step size (maximum step size 0.1 s) in the time range from 0 s to 270 s.

In FIG. 3 is a comparison between a simulated and a measured case of a "strong jumping" of a compactor 1, here a compactor from Ammann AC 110 with 11 t total weight, shown. A very good agreement between measured and calculated vibration behavior of a bandage 5 can be seen. In addition to an amplitude ratio of the fundamental (j = 1) to a subharmonic (j = 1/2), an identical phase angle can be seen during a measurement and during the calculation (same mode of oscillation). The measured data were recorded with an acceleration sensor mounted in the vertical direction on the non-rotating, oscillating part of the drum 5, the signal then amplified and analyzed using a program package, eg LabView / DIAdem®.

From this comparative example results that with the above-mentioned, comparatively simple model according to FIG. 2 or the equations (1) and (2) the operating behavior of a dynamic soil compaction device can be very aptly described even in the case of highly nonlinear effects, such as "jumping", and the calculation model thus takes into account all relevant parameters.

To determine the in FIG. 3 in the right figure, are represented in the in FIG. 2 As a parameter, an amplitude A ₀ of 1 mm and a ground stiffness k _B of 140 MN / m have been specified. If one measures the movement in a time range for the "jumping" of a compactor, an iterative calculation method can be used to determine the actual soil stiffness down to a tolerance. For this purpose, the machine parameters of the compacting device, the operating state and the time position of the imbalance or imbalances must be known.

The practically measured and numerically simulated operating state of jumping of the pulley AC 110 with respect to the chaos theory represents a nonlinear system after the occurrence of the first period doubling. The compactors are thus among the technical systems that are fundamentally capable of chaotic behavior. Their dynamics can thus be described using the methods of nonlinear and chaotic vibrational theory. This opens up a large field of different analysis methods, which can be applied in theory and practice of compaction technology.

Chaos theory has established various methods of observation of nonlinear oscillations, with the help of which the structure of deterministic, chaotic movement behavior is investigated and proven. It is on the publications of Moon, Francis C. (1992); "Chaotic and Fractal Dynamics, An Introduction to Applied Scientists and Engineers"; Mc Graw Hill as well Thompson, JMT; Stewart, HB, (2002) "Nonlinear Dynamics and Chaos, 2nd Edition, John Wiley & Sons, Ltd. stated s.

• Zeitreihen, d. h. Bewegungsverhalten in Funktion der Zeit;
• Spektralanalysen der Zeitreihe (Fast Fourier Transformation FFT), beispielsweise zur Erkennung subharmonischer Schwingungsanteile, chaotische Systeme besitzen kontinuierliche Spektren;
• Phasenraumanalysen, Betrachten der Weg-Geschwindigkeits-Entwicklung in Funktion des Parameters Zeit, x(t)-ẋ(t);
• Zeichnet man im Phasenraum nur jene Punkte auf, für welche t = nT (n = 0, 1, 2, 3,..) ist, erhält man die Poincaré-Abbildung; chaotische Systeme zeigen in diesen Abbildungen ihre fraktale Struktur besonders ausgeprägt;
• Berechnung des Ljapunov-Exponenten; für Werte des Exponenten grösser, bzw. gleich "0" verhält sich das System instabil. Im Bereich chaotischer Bewegungen und der jeweiligen Bifurkationspunkte tritt dieser Fall auf, es existieren mehrere Attraktoren gleichzeitig, man befindet sich im Grenzgebiet (Separatrix) zweier oder mehrerer Lösungs-Einzugsbereiche.

It is in particular the analysis of:

• Time series, ie movement behavior as a function of time;
• Time-series spectral analyzes (Fast Fourier Transformation FFT), for example for detecting subharmonic vibration components, chaotic systems have continuous spectra;
• Phase space analyzes, considering the path-velocity evolution as a function of the parameter time, x ( t ) - ẋ ( t );
• If one draws only those points in the phase space for which t = nT (n = 0, 1, 2, 3, ..), one obtains the Poincaré mapping; chaotic systems show their fractal structure particularly pronounced in these pictures;
• Calculation of the Ljapunov exponent; for values of the exponent greater than or equal to "0", the system behaves unstably. In the area of chaotic movements and the respective bifurcation points this case occurs, there are several attractors at the same time, one is in the border area (separatrix) of two or more solution catchment areas.

. In diesem Fall können die beiden Gleichungen in (1), bzw. (3) addiert werden und es ergibt sich eine Gleichung (4a) für einen Freiheitsgrad des schwingenden Elements x_d ≡ x . Das zugehörige analytische Modell findet sich in Figur 4 . $$F_B=-m_d\ddot{x}+m_u{r}_u{\mathrm{\Omega }}^2\cos \left(\mathrm{\Omega }\cdot t\right)+\left(m_f+m_d\right)\cdot g$$

To examine the chaotic machine behavior of soil compaction equipment, it is usually sufficient to examine the vibrating part. Especially with well-matched rubber damper elements in the elements (bandage, chassis, ...), the dynamic forces compared to the static forces negligible and it applies ${\ddot{x}}_j<<{\ddot{x}}_d$

, In this case, the two equations in (1) and (3) can be added together and an equation (4a) for a degree of freedom of the oscillating element x _d ≡ x results. The associated analytical model can be found in FIG. 4 , $$F_B=-m_d\ddot{x}+m_u{r}_u{\mathrm{\Omega }}^2\cos \left(\mathrm{\Omega }\cdot t\right)+\left(m_f+m_d\right)\cdot G$$

mit und $A_0=\frac{m_u{r}_u}{m_d}\mathrm{und}\begin{array}{cc}{F}_B=c_B{\dot{x}}_d+k_{B}x\hfill & \mathrm{f}\ddot{\mathrm{u}}r{F}_B>0\\ F_B=0\hfill & \mathrm{sonst}\end{array}$

als bodenkraftgesteuerte Nichtlinearität. F _B is the force acting on the floor area; please refer FIG. 2 , This ordinary differential equation of 2nd order is rewritten in the two following differential equations of 1st order: $$\begin{array}{l}{\dot{x}}_1=x_2\\ {\dot{x}}_2=-\frac{F_B}{m_d}+A_0{\mathrm{<figure-callout\; id="2"\; label="\Omega "\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">\Omega </figure-callout>}}^2\cos \left(\mathrm{\Omega }\cdot t\right)+\left(1+\frac{m_d}{m_f}\right)\cdot G\end{array}$$

with and $A_0=\frac{m_u{r}_u}{m_d}\mathrm{and}\begin{array}{cc}{F}_B=c_B{\dot{x}}_d+k_{B}x\hfill & \mathrm{f}\ddot{\mathrm{u}}r{F}_B>0\\ F_B=0\hfill & \mathrm{otherwise}\end{array}$

as a force-controlled nonlinearity.

The identity x ₂ ≡ ẋ holds.

From this a phase space representation with x ₁ ( t ) - x ₂ ( t ), or x ( t ) - ẋ ( t ) is derived.

The phase curves, also referred to as orbitals, are closed circles or ellipses in the case of linear, stationary and monofrequent oscillations. In non-linear oscillations, where additional harmonics occur (periodic lifting of the bandage from the ground), the harmonics can be recognized as modulated periodicities. Only at period doublings, ie subharmonic oscillations such as "jumping", does the original circle mutate into closed curves that have intersections in the phase space representation.

Related to the evaluation of FIG. 3 for the local compactor (Ammann AC 110) on a hard surface results in the FIG. 5 illustrated phase curve. The left display shows the measured and the left display the calculated values. Again the agreement of the simulation with the data measured in practice is shown.

As the number of subharmonics increases, more and more intersections occur, compare the phase curves in FIG. 7 for a trench roller and for a vibration plate in FIG. 8 ,

It has been shown that the occurrence of subharmonic vibrations in the form of branches or bifurcations is another central element of strongly nonlinear and chaotic vibrations. In contrast to harmonics, subharmonic vibrations represent a new, separately treated operating state of a nonlinear system; this operating state is very different from the original, linear problem. Harmonics are small in relation to the fundamental, ie the non-linear solution of the problem remains, mathematically speaking, in the environment of the solution of the linear system.

The associated amplitudes of the additional subharmonic vibration components, however, are of the same order of magnitude as the fundamental vibration. The FIG. 6 shows the measured, unmediated occurrence of jumping a roller (Ammann AC 110) during the transition of the machine from a very soft pad (tire) on an already compacted, hard sand-gravel mixture. With otherwise constant machine parameters, ground stiffness and damping are the variable system parameters. In FIG. 6 The measured vibration behavior is shown at the top, which reacts immediately to the system parameter change and begins to "jump" without additional energy supply, ie the first subharmonic with the frequency f / 2, or the periodicity 2T occurs immediately (time duration of the change: approx Revolutions of the unbalance at 36 [Hz] Vibration frequency => approx. 1/9 [s] Transition time, m _d = 4000 [kg]). Note that the bandage on the soft tire (area 201) (k _B = 30 MN / m) is in linear load operation, whereas on the hard pad (k _B = 140 MN / m) (area 203) it is immediately off-hook or jumping (bifurcation 202).

The performed FFT shows in FIG. 6 left, the linear, monofrequency vibration behavior on the tire, Pneu (soft bottom) 204; the subharmonic oscillation, which additionally occurs on a hard surface, has about twice the amplitude compared to the fundamental mode (right illustration in FIG. 6 If you measure with each unbalance rotation in an excellent position of the rotating eccentric the corresponding vibration amplitude, or the deformation value of the movement, this is always constant on the tire (harmonious), on the hard pad, however, the value alternates according to the additional subharmonic vibration component. Due to their periodicity, harmonics can not be detected in this type of signal acquisition. The measurement acquisition can in practice be triggered by the pulse of a Hall probe, which detects the zero crossing of the vibro wave. This can also generate Poincaré images. If the periodically recorded amplitude values are plotted as a function of the varied system parameter, in our case the ground stiffness k _B , then the bifurcation or so-called fig tree diagram is created (lower middle representation in FIG FIG. 6 In this diagram, on the one hand, the property of the amplitudes suddenly increasing with increasing stiffness in the area of the branching, the tangent to the corresponding curve (s) runs at the branching point vertical. Therefore, in practice, no additional energy supply for the jumping of the roller is required. The diagram further shows that when increasing Stiffness (compression) further branches follow, and in ever shorter intervals based on the continuously increasing stiffness k _B. The branches produce a cascade of new vibrational components with each half the frequency of the previous lowest frequency of the spectrum. Since the first branching off from the fundamental oscillation with the frequency f, or period T, splits off, the frequency cascade f, f / 2, f / 4, f / 8 etc. is generated. Analogously to the fundamental oscillation, the subharmonic harmonics also generate it creates a frequency continuum in the low-frequency range of the signal spectrum. This is also a specific property of the chaotic system, in this case the vibrating roller.

Note that the system of the compactor is in a deterministic rather than a stochastic chaotic state. Since the parameters that cause the chaotic state are not all measurable (not fully observable), the operating state of the subharmonic vibrations can not be predicted for practical compaction. The operating behavior in practice is also characterized by many imponderables, the machine can slip away due to the strong contact loss to the ground, the load of the machine by the low-frequency vibrations is very high. Ongoing further bifurcations of the machine behavior (unexpected) can occur, which immediately result in heavy additional loads. High stresses also occur between the bandage and the floor; This leads to the undesirable loosening of near-surface layers and causes grain breakup.

Thus, new devices that have an active control of the machine parameters in function of measured quantities (eg ACE: Ammann Compaction Expert) at the occurrence of the first subharmonic oscillation with the frequency f / 2 immediately reduces the imbalance and thus the energy supply. This measure reliably prevents the unwanted jumping or tumbling of the bandage. In addition, a force-controlled control of the amplitude and frequency of the compacting device guarantees control of the non-linearity and thus a reliable prevention of the jumping / tumbling, which is ultimately the result of non-linearity occurring.

Due to the fact that the subharmonic vibrations each represent a new state of motion of the machine, relative measurements, eg. B. for detecting the compaction state of the soil, for each newly occurring subharmonic oscillation on the reference inspection procedures, such as the pressure plate test (DIN 18 196) be calibrated. In the case of a "compactometer" in which the ratio of the first harmonic 2f to the fundamental vibration f is used for the compression control, the correlation basically changes with the occurrence of the jumping; only within the respective branching state of the movement exists a linear relationship of the measured value with the soil stiffness.

For the machines considered, the bifurcation occurs in the form of the period doubling scenario, the FIG. 7 or the FIG. 8 show this on the basis of the FFT spectrum for a trench roller or a vibrating plate.

Fig. 7

211

x _d undercarriage

212

x _f superstructure (exciter frequency f _E ≈ 30 Hz)

213

Damping insulation between upper and lower car

214

FFT x _f superstructure

215

FFT x _D undercarriage

Fig. 8

221

x _f undercarriage

222

_xd superstructure

223

FFT x _d superstructure

224

insulating effect

225

FFT x _f undercarriage

This scenario is basically valid for all technical and physical systems with one-sided binding. If a base stiffness k _B very, bez. "infinitely" high, one speaks of occurring impacts or bumps.

The phase space of the motions of the upper and lower carriage of the vibrating plate and the trench roller (x ' _d - x _d and x' _f - x _f ) show in comparison to the corresponding orbital of the compactor ( FIG. 5 ) significantly increase the complexity of the movements when the advanced period doubling scenario, or deterministic chaos, occurs.

With machine parameters kept constant, the cascading appearance of the bifurcations and harmonics with their associated period doublings can be used analogously to the large rollers as an indicator of increasing soil rigidity and compaction (relative compaction control).

While rollers, from compactor to hand-held trench roller, use the rolling motion of the bandages to move and there is no direct relationship between vibration and forward motion, the vibrating plate is always dependent on periodic lift off the ground for its travel, controlled by the inclination of its directivity , Therefore, the vibrations and the locomotion are directly coupled with each other, plates and rammers always have a non-linear oscillation behavior. As a result, the devices with increasing stiffness k _B fall faster into the range of the period doubling scenario, with chaotic operating states occurring more frequently in them than in rollers. In the FIG. 8 is a measured, chaotic frequency spectrum dargestelt; the lowest, pronounced vibration component with a frequency f _E / 8 occupies the third bifurcation of the system, the harmonics, especially at 3 ^x f _E / 8 (second harmonic of the Subharmonic f _E / 8; also the other subharmonics can form harmonics) are strongly pronounced.

Since plates and rammers are devices weighing between 50 and 500 kg, it can be casually said that the smaller the device, the greater the vibration challenge.

Decisive is the realization that all vibrating devices for mechanical soil compaction, from rammers to compactors, can be explained in their non-linear behavior with the help of chaos theory. All movement behavior forms can be unambiguously assigned to different bifurcation states during the period doubling scenario [from periodic withdrawal (no bifurcation) to fully developed chaotic behavior]. The chaos theory allows only the overall view of the movement behavior of the various device classes.

A note on the vibration isolation of the chassis, or superstructure: This machine assembly is tuned as a footpunk-excited subsystem deep. This vibration is very well isolated in the field of exciter frequency. As the number of bifurcations increases, the subharmonic vibration components increasingly reach the resonance frequency range of the superstructure / chassis, and the vibration components are thereby transmitted with an increasing number of bifurcations that have occurred. In practice, this can be recognized by the large movements of the corresponding machine parts. For this reason too, subharmonic vibrations are undesirable and should be avoided if possible.

Fig. 9

231

vibration plate

232

grave roller

233

drum compactor

234

amplitude

235

Degree of compaction% / stiffness k _B

The ground stiffness k _B achieved by a soil compaction device as determined by the soil compaction devices mentioned above can be dispensed with, as long as accurate (exact) ground stiffness values are desired and only an indication is given indicating whether soil rigidity increases or is already satisfactory on further traversal with the device Has achieved value, greatly simplified and thus inexpensive with the following in FIG. 10 shown measuring device 20 are made. Such a measuring device 20 for a Bodensteifigkeitsrichtwert will be installed mainly in the already inexpensive vibrating plates.

The vibrations of the undercarriage 17 are recorded with an acceleration sensor 21 , amplified by an amplifier 23 and integrated with an integrator 25 over a predetermined period of time. The integration is made from the acceleration value measured with the acceleration sensor 21 after two times Integration to get a way. Subsequently, the output signal of the integrator 25 is fed to a plurality of bandpass filters 27 . The bandpass filter is designed such that once the excitation frequency f, the first harmonic at twice the excitation frequency 2 · f, the first subharmonic with the half excitation frequency f / 2, the second subharmonic with a fourth excitation frequency f / 4 and the third subharmonic with a achtel excitation frequency f / 8 are transmitted to one output 29a to 29e . For example, the measuring device has four quotient formers 31a to 31d for monitoring the frequencies 2 * f, f, f / 2, f / 4 and f / 8 . The output 29b (output signal to f) is connected as a divisor to all quotient formers 31a to 31d . All outputs are each connected to a quotient generator 31a to 31d . The output 29a (output signal to 2 * f) is connected as a dividend to the quotient generator 31a whose output signal (quotient) is applied to its output 33a . The output 33a is routed via a normalization circuit 35 to two lights 37a in a display panel 39 .

The same procedure is followed by the outputs 29c (f / 2), 29d (f / 4) and 29e (f / 8) , which are fed as a dividend to the quotient formers 31b, 31c and 31d . An output 33b, 33c and 33d of the quotient generator 31b, 31c and 31d is guided via the normalization circuit 35 to two lights 37b, 37c and 37d in the display panel 39 , respectively. If only the lights 37a, the floor area in question is not yet sufficiently compacted. If the luminaires 37b are illuminated, an already better compaction is achieved, whereby the compaction becomes better and better up to the luminaires 37d . If, for example, the luminaires 37b do not light up even if they are repeatedly driven over with the vibrating plate, further compaction, be it due to the soil composition or the machine data of the vibrating plate used, is not possible. The same applies to the lights 37c and 37d .

Instead of the two lights, if only the appearance of the subharmonic should be displayed, only a single light should be used. However, not only the frequency behavior is determined with the measuring device 20 , but also the maximum oscillation amplitudes of the individual oscillations (influencing frequency f, harmonics n · f, subharmonic f / [2 -n]) are evaluated. In FIG. 6 In the middle lower representation ("fig tree scenario") the amplitudes A (f) and A (f / 2) of the action frequency f and the first subharmonic f / 2 are plotted for the occurrence of the first subharmonic f / 2 for a given state. The lower right image in the same FIG. 6 shows the two amplitude values. It can be seen here the maximum amplitude A (f) with the action frequency f is smaller than that A (f / 2) of the first subharmonic f / 2. The expected maximum amplitudes can be read analogously from the "fig tree scenario". On the abscissa of the "fig tree scenario", the soil stiffness k _B (degree of compaction) is plotted. Thus, if the lowest existing subharmonic as well as the maximum amplitudes of the oscillation frequencies are known, the soil stiffness k _B (degree of compaction) can be deduced. If an amplitude value predetermined by the normalization circuit 35 is reached, the respectively second luminaire of the luminaire arrangement illuminates. Of course, the luminous intensity can also be controlled as a function of the amplitude level.

Instead of the bandpass filter 27 , a unit which performs a fast Fourier transformation (FFT) may also be used.

Instead of a bandpass filter 27 , the respective oscillation amplitude can also be determined within time windows. In this case, starting from the lowest position of the eccentric and the known rotational speed, the amplitude values for the first harmonic and corresponding subharmonics will be recorded, if they are present.

In FIG. 11 is a variant of the in FIG. 10 shown circuit shown. In contrast to the circuit 20 in FIG. 10 In this circuit 40, an acceleration sensor 42 designed analogously to the acceleration sensor 21 is arranged on the uppercarriage 15 of a vibration plate 14 . By (not shown) damping elements between the upper and lower chassis is a vibration damping. The output signals of the acceleration sensor 42 for the first harmonic 2f and the first and second subharmonic f / 2 and f / 4 are now not integrated in contrast to the circuit 20 and processed as acceleration signals after amplification by the amplifier 23 in a bandpass filter 41st The signals are usually high enough. The signal of the third subharmonic f / 8 is now, since it is usually small, integrated with an integrator 43 and analogous to in FIG. 10 processed. It does not have to be integrated until the third subharmonic f / 8 . It is also possible to integrate the second subharmonic f / 4 or the fourth subharmonic f / 16 (x: factor, x ≈ 1-2).

The sensor for receiving the waveform of the vibration system is arranged according to the above description on the undercarriage 11 or 17 or on the chassis 6 ; he but can also be arranged on the superstructure 9 and 15 respectively. In the case of an arrangement on the uppercarriage 9 or 15, vibration influences due to the damping elements, as outlined above, must be taken into account.

The demonstration of the chaotic behavior of dynamically excited compaction devices places the vibration behavior patterns known from various investigations into a common context. The basis is the one-sided bond between soil (asphalt layer) and the oscillating part of the device. The increase in the vibration excitation and / or the increasing rigidity of the soil with increasing compression leads to the periodic lifting of the compactor from the ground. The resulting non-linearity increases with greater unbalance or increasing densification, which leads to the bifurcation of the movement behavior. The branching occurs suddenly and, depending on the type of machine, represents an undesirable or intended operating condition. Therefore, this is avoided in controlled rolls by reducing the vertical unbalance. In unregulated compaction equipment, the oscillating part enters the period doubling scenario, the movement behavior becomes chaotic. The non-linear vibrations of all compaction devices lead to deterministic chaos with increasing non-linearity over the period doubling scenario. The subharmonic vibrations are also transmitted to the superstructure or the chassis. The chaotic behavior of the bandage makes the steering of the machine impossible, Kornzertrümmerungen and loosening of the surface are other unwanted consequences. This operating state also stresses the machine very strongly and must therefore be prevented in practice.

Proof of chaotic performance shows the upper limits of the compaction performance of today's equipment. The maximum possible power to be entered into the ground is limited by the beginning period doubling scenario. If you want to build compactors with better performance, the energy must be introduced into the underground in an alternative way. The deterministic chaos is triggered by the force-driven non-linearity of the unilateral bond between the bandage / undercarriage and the ground. The optimum adjustment of amplitude and frequency as a function of the soil condition in the latest generation of self-regulating vibratory rollers and compactors is a very effective way to maximize the input of power into the soil.

The bandwidth of practically occurring vibration modes can be easily estimated with the chaos theory of the compactor and the individual Machine parts for the expected extreme loads are dimensioned. Many practical stress images can only be explained with the aid of subharmonic vibrations.

Classic and modern methods of comprehensive dynamic compaction control (FDVK) are based on chaos theory both in terms of their foundations and their practical applications (norms).

The findings from the application of the theory of deterministic chaos form an excellent basis for future compaction device development.

Claims (11)

1. Method for determining a measure of the soil rigidity (k_B) or level of compaction of an area of soil (7) that has been or is to be compacted, in which a soil contact unit (5; 11; 17) of a soil compaction device (1; 12; 14), which unit acts on the area of soil (7), is moved over the latter, a soil compaction force (F_B) changing periodically over time with at least one frequency of action (f) acting on the soil contact unit (5; 11; 17) and vibrations of a vibratory system which contains the soil compaction device (1; 12; 14), the soil contact unit (5; 11; 17) and the area of soil (7) being determined, a vibration mode of the vibration of the vibratory system (f, f/[2·n], A(f), A(f/[2·n])) being picked up and, from the vibration mode, from machine parameters of the soil compaction device and from a position in time of the one soil compaction force (F_B), the measure of the soil rigidity (k_B) or the level of compaction being determined, characterized in that a plurality of sub-harmonics (f/2, f/4, f/8 and so on) of the frequency of action (f) are determined from the vibration mode (f, f/[2·n], A(f), A(f/[2·n])) of the vibratory system and, from all the sub-harmonics (f/2, f/4, f/8 and so on) of the frequency of action (f), the one having the lowest frequency (f/[2·n]) is determined as a measure of the soil rigidity (k_B), a soil rigidity that is achieved being higher, the lower the frequency of the lowest sub-harmonic frequency (f/[2·n]).
2. Method according to Claim 1, characterized in that the periodically changing soil compaction force (F_B) is a pure "sinusoidal" vibration of a single frequency (f) or, preferably, a superimposition of a plurality of "sinusoidal" vibrations.
3. Method according to Claim 1 or 2, characterized in that the frequency of action (f) of the periodically changing soil compaction force (F_B) is set to a resonant frequency (f₀) of the vibratory system or is preferably set to a frequency which exceeds the resonant frequency (f₀) by a predefined frequency value that is determined only by adjustment stabilities.
4. Method according to one of Claims 1 to 3, characterized in that the respectively lowest sub-harmonic (f/[2·n]) during a movement of the soil contact unit (5; 11; 17) over a respective area of soil (7) is stored associated with this area of soil (7), and is compared with a lowest measured sub-harmonic (f/[2·n]) during a new run over, and a new run over is set up if no lower sub-harmonic (f/[2·n]) is reached after a predefined number of runs, since no further soil compaction can be achieved with the set machine data.
5. Method according to one of Claims 1 to 4, characterized in that amplitude values of the vibrations of the sub-harmonics over a respective area of soil (7) are stored associated with this area of soil (7) and are compared with the amplitude values during a new run over, and a further run over is set up if an increased amplitude value of the lowest sub-harmonic is reached after a predefined number of runs, since no further soil compaction can be achieved with the set machine data.
6. Method according to one of Claims 1 to 5, characterized in that the amplitude (A₀) of the soil compaction excitation force (F_B) immediately after the determination of the respectively lowest sub-harmonic (f/[2·n]) is set back to a value until a stable position of the soil compaction device is reached.
7. Soil compaction device (1; 12; 14) for compacting an area of soil (7) to a defined measure for the soil rigidity (k_B) or level compaction, having a soil contact unit (5; 11; 17) acting on the area of soil (7), having a drive for at least one vibrating mass (m_d) which exerts a periodically changing soil compaction force (F_B) on the soil contact unit (5; 11; 17), and having at least one sensor (21) for determining the vibration of a vibratory system which contains the soil compaction device (1; 12; 14) with the soil contact unit (5; 11; 17) and the area of soil (7), characterized by an evaluation unit (20) that is connected to the at least one sensor (21), with which, on the basis of excitation vibration or excitation vibrations acting on the soil contact unit (5; 11; 17) with a frequency (f) or frequencies of action, a vibration mode can be picked up and stored and, from the vibration mode, from machine parameters of the soil compaction device (1; 12; 14) and from a position in time of the soil compaction force (F_B), the measure of the soil rigidity (k_B) or the level of compaction can be determined by the evaluation unit (20), wherein, for this purpose, a plurality of sub-harmonics (f/2, f/4, f/8 and so on) of the frequency of action (f) of the at least one vibrating mass (m_d) can be determined by the evaluation unit (20) and, from these sub-harmonics (f/2, f/4, f/8 and so on), the one having the lowest frequency (f/[2·n]) can be determined as a measure of the soil rigidity (k_B) or the level of compaction, and the soil rigidity (k_B) that is achieved is higher, the lower the frequency of the lowest sub-harmonic frequency (f/[2·n]).
8. Soil compaction device (1; 12; 14) according to Claim 7, characterized in that by using the evaluation unit (20), maximum amplitude values (A(f), A(f/[2·n]) of the sub-harmonics (f/[2·n]) from the vibration mode and the frequency of action (f) are placed in a mutual relationship with one another for the purpose of more accurate determination of the measure of the soil rigidity (k_B) or the level of compaction.
9. Soil compaction device (1; 12; 14) according to Claim 7 or 8, characterized in that the at least one sensor is connected to the drive, and the frequency of the at least one vibrating mass can be adjusted by the drive in such a way that a maximum vibration amplitude can be achieved, which indicates a resonance of a vibrating system.
10. Soil compaction device (1; 12; 14) according to one of Claims 7 to 9, characterized by a second sensor, with which the time of a preferably maximum force of the at least one vibrating mass in the soil compaction device can be recorded, the first sensor being formed in such a way that it can additionally record a predefined, preferably a maximum, vibration amplitude of the soil contact unit in the soil compaction direction, and by a comparator unit that is connected to the two sensors and the drive and adjusts the drive frequency in such a way that, between the two maximum amplitude values, there is a leading phase angle of the excitation mass vibration of between 90° and 180°, preferably between 95° and 130°.
11. Soil compaction device (1; 12; 14) according to one of Claims 7 to 10, characterized in that the at least one vibrating mass has a variable imbalance and the imbalance moment of the imbalance can be reduced in such a way that the measured sub-harmonics still fall just within the measurement sensitivity of the first sensor.

Images