EP1668995B1 - Method and apparatus for the graphic representation of the filling profile of a cigarette - Google Patents

Abstract

The method involves developing a sinusoidal mathematical model representing a density with respect to an axial position, using parameters, phase and two constants. Density and humidity in several points of a cigarette are measured to find a regression determination coefficient. A shift of a reinforced tip from a position calculated from the phase and parameters, is calculated. An index of reinforcement is calculated from the constants. The parameters are lengths of a tobacco section (L), a cigarette and a filter. An independent claim is also included for a device implementing a cigarette filling profile graphical representation method.

Description

The present invention relates to a method and a device for graphically representing the filling profile of a cigarette, in particular with a view to controlling the amplitude of reinforcement and the position of the reinforced ends relative to the section of the rod.

In general, we know that for economic reasons, cigarette manufacturers have been led to reduce the density of tobacco in cigarettes.

• comment conserver une bonne tenue des bouts,
• comment conserver une bonne qualité d'assemblage.

The following two questions were then asked:

• how to keep a good behavior of the ends,
• how to maintain a good quality of assembly.

The solution adopted to solve these two problems was to maintain the initial density for the ends (or even to strengthen it) and to reduce the density only in the middle of the tobacco section.

It then became necessary to control the amount of reinforcement and the position of the reinforced ends relative to the cut.

The Applicant has therefore developed a cigarette filling analyzer apparatus called ARC answering this need.

• un premier orifice d'émission d'un rayonnement radioactif (rayonnement β) provenant d'une source radioactive au strontium 90, et
• un orifice de réception de ce rayonnement situé en regard d'une chambre d'ionisation connecté à un circuit de mesure permettant de mesurer l'atténuation du rayonnement β après passage au travers du tabac, étant entendu que cette atténuation est fonction de la densité de matière traversée.

This apparatus was designed to move the cigarettes axially in a tubular element comprising two diametrically opposed coaxial orifices, namely:

• a first orifice for emitting radioactive radiation (β radiation) from a strontium 90 radioactive source, and
• an orifice for receiving this radiation situated opposite an ionization chamber connected to a measuring circuit making it possible to measure the attenuation of the β radiation after passing through the tobacco, it being understood that this attenuation is a function of the density of the material crossed.

In this apparatus, a step-by-step drive system causes the cigarette to move within the tubular member. The measuring circuit is then controlled so as to record at each step the density of the material traversed by the radiation in the axis of the two orifices.

This technology was subsequently abandoned because of the stringent regulations governing the handling of radioactive elements.

The Applicant then developed another solution consisting in passing the cigarettes through a tuned microwave cavity having a relatively low active thickness, for example 3 mm. The combination of the offset of the tuning frequency and the attenuation of the radiated signal as the cigarette passes through the cavity allows the density profile of the tobacco section of the cigarette to be plotted.

In either case, the measured density values are used to plot the density profile of the cigarette.

Nevertheless, the visual interpretation of the density profile plot to determine with sufficient accuracy the position of the reinforced ends with respect to the section of the stem and the amplitude of the reinforcement is difficult and uncertain because it is operator dependent.

The invention therefore more particularly aims to automatically determine these parameters.

It proposes, for this purpose, in a general way, a process based on the observation that the shape of the density profile of the tobacco section of a cigarette, as well with two symmetrical reinforced ends as one reinforced end or two asymmetrical reinforced ends, is periodic and can be modeled in a sinusoidal form.

• • l'élaboration d'un modèle mathématique sinusoïdal représentant la densité y en fonction de la position axiale x, ce modèle prenant en compte des paramètres tels que la longueur du tronçon de tabac L, la longueur totale de la cigarette LT, la longueur du filtre LF et utilisant au moins trois constantes A0, A1 et ϕ à déterminer expérimentalement,
• • la réalisation de mesures expérimentales de manière à déterminer la densité moyenne D et l'humidité moyenne H en une pluralité de points le long de l'axe longitudinal de la cigarette,
• • le calcul d'un coefficient de détermination de régression R² à partir des valeurs mesurées,
• • le calcul de la position P du bout renforcé à partir de la phase ϕ et des susdits paramètres,
• • le calcul du décalage du bout renforcé par rapport à la coupe à partir de la position P précédemment calculée,
• • le calcul de l'indice de renforcement à partir de la valeur du susdit coefficient A1.

In view of this observation, the process according to the invention comprises the following operating phases:

• The development of a sinusoidal mathematical model representing the density y as a function of the axial position x, this model taking into account parameters such as the length of the section of tobacco L, the total length of the cigarette LT, the length of the LF filter and using at least three constants A0, A1 and φ to be determined experimentally,
• • carrying out experimental measurements in order to determine the average density D and the average humidity H at a plurality of points along the longitudinal axis of the cigarette,
• Calculating a regression determination coefficient R ² from the measured values,
• Calculating the position P of the reinforced end from the phase φ and the aforementioned parameters,
• Calculating the offset of the reinforced tip with respect to the section from the previously calculated position P,
• • the calculation of the reinforcement index from the value of the aforesaid coefficient A1.

• La figure 1 est une représentation schématique d'un appareil pour la mise en oeuvre du procédé selon l'invention ;
• La figure 2 représente deux vues en perspective montrant deux cigarettes présentées selon le sens de confection ;
• La figure 3 est un diagramme densité/position présenté en relation avec une tige incluant deux cigarettes à deux bouts renforcés symétriques ;
• La figure 4 est une représentation similaire à celle de la figure 3 pour des cigarettes à un seul bout renforcé ;
• La figure 5 est une représentation similaire à celles des figures 3 et 4 pour des cigarettes à deux bouts renforcés asymétriques.

Embodiments of the invention will be described below, by way of non-limiting examples, with reference to the accompanying drawings in which:

• The figure 1 is a schematic representation of an apparatus for carrying out the method according to the invention;
• The figure 2 represents two perspective views showing two cigarettes presented according to the direction of making;
• The figure 3 is a density / position diagram presented in relation to a stem including two symmetrical reinforced double-ended cigarettes;
• The figure 4 is a representation similar to that of the figure 3 for cigarettes with a single reinforced tip;
• The figure 5 is a representation similar to those of Figures 3 and 4 for asymmetric reinforced two-ended cigarettes.

• Une trémie 1 associée à un distributeur 2 qui délivre des cigarettes une par une.
• Un module hyperfréquence comprenant un vobulateur 3 et une cavité 4 traversée par un tube de guidage des cigarettes qui mesure la densité ponctuelle et l'humidité des cigarettes 5 passant au travers de la cavité 4.
• Des moyens d'entraînement à vitesse constante des cigarettes lors de leur passage dans la cavité, ces moyens d'entraînement comprenant dans cet exemple une vis sans fin 6 entraînée par un moteur électrique 7 et une noix 8 entraînée en translation par la vis 6, cette noix 8 portant un bras de support basculant 9 dont le basculement est assuré par un actionneur électromécanique 10.
• Un microcontrôleur 11 servant à assurer le contrôle du module hyperfréquence 3 et un prétraitement des informations délivrées par ce module 3.
• Un processeur 12 relié au premier par une liaison 13 par exemple de type RS 232, à un interface d'entrée/sortie 14 connecté à l'actionneur 10 ainsi qu'à des contacts fin de course 15, 16 disposés aux extrémités du trajet de la noix 8, et à un circuit de puissance 17 connecté au moteur du distributeur 2 associé à la trémie 1. Ce processeur 12 est associé à des interfaces classiques (affichage, impression, saisie, ...) qui n'ont pas été représentés. Il assure la gestion de l'appareil et effectue le traitement des informations relatives aux mesures effectuées, délivrées par le microcontrôleur 11.

In the example shown on the figure 1 , the apparatus for the graphical representation of the filling profile and for the determination of the reinforcement amplitude and the position of the reinforced ends with respect to the section of the stem consists of the following main elements:

• A hopper 1 associated with a dispenser 2 which delivers cigarettes one by one.
• A microwave module comprising a vobulator 3 and a cavity 4 crossed by a cigarette guide tube which measures the point density and humidity of the cigarettes passing through the cavity 4.
• Constant speed drive means of the cigarettes during their passage in the cavity, these drive means comprising in this example a worm 6 driven by an electric motor 7 and a nut 8 driven in translation by the screw 6, this nut 8 carrying a tilting support arm 9 whose tilting is provided by an electromechanical actuator 10.
• A microcontroller 11 for controlling the microwave module 3 and preprocessing the information delivered by this module 3.
• A processor 12 connected to the first by a link 13, for example of the RS 232 type, to an input / output interface 14 connected to the actuator 10 as well as end-of-travel contacts 15, 16 arranged at the ends of the path of the the nut 8, and a power circuit 17 connected to the motor of the distributor 2 associated with the hopper 1. This processor 12 is associated with conventional interfaces (display, printing, input, ...) that have not been represented . It manages the device and performs the processing of the information relating to the measurements made, delivered by the microcontroller 11.

By way of example, the instantaneous density and humidity values will be transferred to the processor 12 by the microcontroller 11 every 50 ms, which corresponds to a displacement of 1 mm of the cigarette and at a speed of 20 mm / s. .

• une première famille F₁ dont le filtre est positionné en avant du tronçon tabac par rapport au sens de confection,
• une deuxième famille F₂ dont le filtre est positionné en arrière du tronçon tabac par rapport au sens de confection.

Before carrying out a series of measurements, the cigarettes 5 must be sorted into two families illustrated on the figure 2 , to know :

• a first family F ₁ whose filter is positioned in front of the tobacco section relative to the direction of manufacture,
• a second family F ₂ whose filter is positioned behind the tobacco section relative to the direction of manufacture.

After measuring the two families, filter first, the average results of the family F ₂ are reversed (recovery of the direction of manufacture) to be treated with the family F ₁ .

In the case of symmetrically reinforced double-ended cigarettes BS ₁ , BS ₂ , the density profile is periodic and of period equal to the length of the tobacco section.

This periodicity appears on the figure 3 where a density chart in g / l as a function of the position (in mm) is shown in relation to a rod including two cigarettes in which the filters FR are located opposite each other; the actual cut C ₁ effected (position of the reinforced end BR) as well as the theoretical section C ₂ which extend in the middle of areas denser in scaferlati are indicated respectively in solid lines and in broken lines.

avec

• y = densité
• x = position
• L = longueur de tabac, soit longueur totale LT - longueur filtre LF
• A₀, A₁, ϕ = constantes

This diagram comprises the plot of a sinusoidal model of density MS ₁ and the curve connecting the measured density values MD ₁ . It shows a periodic density profile with a period equal to the length of the tobacco section of a cigarette and satisfies the following equation: $$\mathrm{Y}\mathrm{=}{\mathrm{AT}}_{\mathrm{0}}\mathrm{+}{\mathrm{<figure-callout\; id="1"\; label="AT"\; filenames="imgf0001.png"\; state="\{\{state\}\}">AT</figure-callout>}}_{\mathrm{1}}\mathrm{\times }\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0001.png"\; state="\{\{state\}\}">cos</figure-callout>}\left[\mathrm{2}\mathrm{\times }\mathrm{\pi }\mathrm{\times }\left(\mathrm{x}\mathrm{-}\mathrm{\phi }\right)\mathrm{/}\mathrm{The}\right]$$

with

• y = density
• x = position
• L = length of tobacco, total length LT - LF filter length
• A ₀ , A ₁ , φ = constants

A sinusoidal regression on the measurement points (coefficient of determination R ² ) makes it possible to automatically determine the amplitude of reinforcement and the offset of the reinforced end with respect to the section C ₂ (the actual section C ₁ is in general offset relative to to the theoretical section C ₂ which is in principle located in the middle of a corresponding reinforced zone of the rod T).

• L'humidité moyenne H
• La densité moyenne D
• Le coefficient de détermination de la régression R²

• • La position P du bout renforcé peut être obtenue par exemple par la séquence opératoire suivante :
  • Si A₁ < 0 → ϕ = ϕ + 0,5 × L
  • P = modulo (ϕ/L)
  • Si P < LT - L/2 alors $$\mathrm{Si\; P}\mathrm{<}\mathrm{LT}\mathrm{-}\mathrm{L}\mathrm{/}\mathrm{2}\mathrm{alors\; P}\mathrm{=}\mathrm{P}\mathrm{+}\mathrm{L}\mathrm{\times }\left[\mathrm{ent}\left(\left(\mathrm{LT}\mathrm{-}\mathrm{L}\mathrm{/}\mathrm{2}\mathrm{-}\mathrm{P}\right)\mathrm{/}\mathrm{<figure-callout\; id="1"\; label="L\; +"\; filenames="imgf0001.png"\; state="\{\{state\}\}">L</figure-callout>}\right)\mathrm{+}\mathrm{}\mathrm{1}\right]$$
    
• • Le décalage du bout renforcé BR est par exemple obtenu à l'aide d'une formule du type $$\mathrm{BR}\mathrm{=}\mathrm{P}\mathrm{-}\mathrm{LT}$$
  
• • L'indice de renforcement IR est, quant à lui, obtenu à l'aide d'une relation du type $$\mathrm{IR}\mathrm{=}\mathrm{2}\mathrm{\times }\left|\mathrm{A}\mathrm{1}\right|$$
  

The parameters determined are then:

• The average humidity H
• The average density D
• The coefficient of determination of the regression R ²

• The position P of the reinforced end can be obtained for example by the following operating sequence:
  • If A ₁ <0 → φ = φ + 0.5 × L
  • P = modulo (φ / L)
  • If P <LT - L / 2 then $$\mathrm{If\; P}\mathrm{<}\mathrm{LT}\mathrm{-}\mathrm{The}\mathrm{/}\mathrm{2}\mathrm{then\; P}\mathrm{=}\mathrm{P}\mathrm{+}\mathrm{The}\mathrm{\times }\left[\mathrm{ent}\left(\left(\mathrm{LT}\mathrm{-}\mathrm{The}\mathrm{/}\mathrm{2}\mathrm{-}\mathrm{P}\right)\mathrm{/}\mathrm{The}\right)\mathrm{+}\mathrm{1}\right]$$
    
• • The offset of the reinforced end BR is for example obtained using a formula of the type $$\mathrm{BR}\mathrm{=}\mathrm{P}\mathrm{-}\mathrm{LT}$$
  
• • The IR reinforcement index is, for its part, obtained using a relationship of the type $$\mathrm{IR}\mathrm{=}\mathrm{2}\mathrm{\times }\left|\mathrm{AT}\mathrm{1}\right|$$
  

It appears that two other types of cigarettes are also available on the market, namely: single-end-reinforced cigarettes and symmetrical reinforced two-end cigarettes.

In the first case, the cigarette comprises a single reinforced end BD located on the distal end of the cigarette.

In order to determine the density profile and the position of this reinforced end with respect to the section, the invention is also based on the observation that this profile is always periodic and that, in this case, the period is equal to twice the length. of the tobacco section.

This periodicity appears on the figure 4 on which is shown in a similar way to the figure 3 a density diagram g / l as a function of the position in mm in relation to a rod T including two cigarettes arranged end to end, the filters FR being arranged opposite one another.

Here also, the actual cut C ₁ performed as well as the theoretical cut C ₂ are indicated in solid lines and in broken lines.

This diagram comprises the plot of a sinusoidal model MS ₂ with a period density equal to twice the length of the tobacco section of a cigarette and the MD ₂ curve connecting the density values measured.

avec

• y = densité
• x = position
• L = longueur du tronçon de tabac = longueur totale de la cigarette LT - longueur du filtre LF
• ϕ = phase

ici également, une régression sinusoïdale sur les points de mesure (coefficient de détermination R²) permet de déterminer automatique l'amplitude de renforcement et le décalage du bout renforcé par rapport à la coupe.The sinusoidal model used MS ₂ responds to the following equation: $$\mathrm{there}\mathrm{=}{\mathrm{AT}}_{\mathrm{0}}\mathrm{+}{\mathrm{<figure-callout\; id="1"\; label="AT"\; filenames="imgf0001.png"\; state="\{\{state\}\}">AT</figure-callout>}}_{\mathrm{1}}\mathrm{\times }\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0001.png"\; state="\{\{state\}\}">cos</figure-callout>}\left[\mathrm{2}\mathrm{\times }\mathrm{\pi }\mathrm{\times }\left(\mathrm{x}\mathrm{-}\mathrm{\phi }\right)\mathrm{/}\left(\mathrm{2}\mathrm{\times }\mathrm{The}\right)\right]$$

with

• y = density
• x = position
• L = length of tobacco section = total length of cigarette LT - length of filter LF
• φ = phase

here also, a sinusoidal regression on the measurement points (coefficient of determination R ² ) makes it possible to automatically determine the amplitude of reinforcement and the offset of the reinforced tip with respect to the section.

• • l'humidité moyenne H
• • la densité moyenne D
• • le coefficient de détermination de la régression R²

The parameters determined are then

• • average humidity H
• • the average density D
• The coefficient of determination of the regression R ²

• Si A₁ < 0 alors ϕ = ϕ + L
• P = modulo [ϕ/(2×L)]
• Si P < LT - L alors $$\mathrm{Si\; P}\mathrm{<}\mathrm{LT}\mathrm{-}\mathrm{L\; alors\; P}\mathrm{=}\mathrm{P}\mathrm{+}2\times \mathrm{L}\mathrm{\times }\left[\mathrm{ent}\left(\left(\mathrm{LT}\mathrm{-}\mathrm{L}\mathrm{-}\mathrm{P}\right)\mathrm{/}\left(2\times \mathrm{L}\right)\right)\mathrm{+}\mathrm{1}\right]$$
  

The position P of the reinforced end is then obtained by the following operating sequence:

• If A ₁ <0 then φ = φ + L
• P = modulo [φ / (2 × L)]
• If P <LT - L then $$\mathrm{If\; P}\mathrm{<}\mathrm{LT}\mathrm{-}\mathrm{L\; then\; P}\mathrm{=}\mathrm{P}\mathrm{+}2\times \mathrm{The}\mathrm{\times }\left[\mathrm{ent}\left(\left(\mathrm{LT}\mathrm{-}\mathrm{The}\mathrm{-}\mathrm{P}\right)\mathrm{/}\left(2\times \mathrm{The}\right)\right)\mathrm{+}\mathrm{1}\right]$$
  

The offset of the reinforced tip BR is obtained using a formula of the type $$\mathrm{BR}\mathrm{=}\mathrm{P}\mathrm{-}\mathrm{LT}$$

The reinforcement index is obtained using a formula of the type $$\mathrm{IR}\mathrm{=}\mathrm{2}\mathrm{\times }\left|\mathrm{AT}\mathrm{1}\right|$$

It turns out that the assembly of cigarettes with a reinforced end BD is difficult because of a certain "softness" of the tobacco section filter side.

This is the reason why a conformation of the intermediate cigarettes has been proposed between the cigarette with two symmetrical reinforced ends as illustrated. figure 3 and the cigarette with a reinforced end illustrated figure 4 , by creating BA ₁ , BA ₂ asymmetric reinforced two-ended cigarettes comprising a substantial distal side reinforcement and a FR filter side medium reinforcement.

Here again, the invention is based on the observation that the density profile is periodic and of periodicity equal to twice the length of the tobacco.

It proposes to automatically determine the amplitudes of the reinforcements and the offset of the reinforced tip with respect to the cut by a pair of sinusoidal regression of the second order, with a period equal to twice the length of the tobacco.

avec

• y = densité
• x = position
• L = longueur du tronçon de tabac

The sinusoidal model used satisfies the following equation: $$\mathrm{there}\mathrm{=}{\mathrm{AT}}_{\mathrm{0}}\mathrm{+}{\mathrm{<figure-callout\; id="1"\; label="AT"\; filenames="imgf0001.png"\; state="\{\{state\}\}">AT</figure-callout>}}_{\mathrm{1}}\mathrm{\times }\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0001.png"\; state="\{\{state\}\}">cos</figure-callout>}\left[\mathrm{2}\mathrm{\times }\mathrm{\pi }\mathrm{\times }\left(\mathrm{x}\mathrm{-}\mathrm{\phi }\right)\mathrm{/}\left(\mathrm{2}\mathrm{\times }\mathrm{The}\right)\right]+{\mathrm{<figure-callout\; id="2"\; label="AT"\; filenames="imgf0001.png"\; state="\{\{state\}\}">AT</figure-callout>}}_{\mathrm{2}}\mathrm{\times }\mathrm{<figure-callout\; id="4"\; label="cos"\; filenames="imgf0001.png"\; state="\{\{state\}\}">cos</figure-callout>}\left[\mathrm{4}\mathrm{\times }\mathrm{\pi }\mathrm{\times }\left(\mathrm{x}\mathrm{-}\mathrm{\phi }\right)\mathrm{/}\left(\mathrm{2}\mathrm{\times }\mathrm{The}\right)\right]$$

with

• y = density
• x = position
• L = length of tobacco section

• L'humidité moyenne H
• La densité moyenne D
• Le coefficient de détermination de la régression R²

The determined parameters are also

• The average humidity H
• The average density D
• The coefficient of determination of the regression R ²

• si A₁ < 0 $$\mathrm{\varphi }\mathrm{=}\mathrm{\varphi }\mathrm{+}\mathrm{L}$$
  
  l'expression de la valeur maximum de densité y_F du bout à renforcement fort est $${\mathrm{y}}_{\mathrm{F}}\mathrm{=}{\mathrm{A}}_{\mathrm{0}}\mathrm{+}{\mathrm{A}}_{\mathrm{2}}\mathrm{-}{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="imgf0001.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1}}$$
  

The position P of the reinforced ends is obtained by the following operating sequence:

• if A ₁ <0 $$\mathrm{\phi }\mathrm{=}\mathrm{\phi }\mathrm{+}\mathrm{The}$$
  
  the expression of the maximum value of density y _F of the strong reinforcement tip is $${\mathrm{there}}_{\mathrm{F}}\mathrm{=}{\mathrm{AT}}_{\mathrm{0}}\mathrm{+}{\mathrm{AT}}_{\mathrm{2}}\mathrm{-}{\mathrm{<figure-callout\; id="1"\; label="AT"\; filenames="imgf0001.png"\; state="\{\{state\}\}">AT</figure-callout>}}_{\mathrm{1}}$$
  

si A₁ >0 on a $${\mathrm{Y}}_{\mathrm{F}}={\mathrm{A}}_0+{\mathrm{A}}_1+{\mathrm{A}}_2\left(\mathrm{densité\; maximum\; du\; bout\; à\; renforcement\; Fort}\right)$$

$${\mathrm{y}}_{\mathrm{f}}={\mathrm{A}}_0+{\mathrm{A}}_2-{\mathrm{A}}_1\left(\mathrm{densité\; maximum\; du\; bout\; à\; renforcement\; faible}\right)$$

The expression of the maximum value of density y _f of the weakly reinforced tip is $${\mathrm{there}}_{\mathrm{f}}\mathrm{=}{\mathrm{AT}}_{\mathrm{0}}\mathrm{+}{\mathrm{<figure-callout\; id="1"\; label="AT"\; filenames="imgf0001.png"\; state="\{\{state\}\}">AT</figure-callout>}}_{\mathrm{1}}+{\mathrm{<figure-callout\; id="2"\; label="AT"\; filenames="imgf0001.png"\; state="\{\{state\}\}">AT</figure-callout>}}_{\mathrm{2}}$$

if A ₁ > 0 we have $${\mathrm{Y}}_{\mathrm{F}}={\mathrm{AT}}_0+{\mathrm{<figure-callout\; id="1"\; label="AT"\; filenames="imgf0001.png"\; state="\{\{state\}\}">AT</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="AT"\; filenames="imgf0001.png"\; state="\{\{state\}\}">AT</figure-callout>}}_2\left(\mathrm{maximum\; density\; of\; reinforced\; tip}\right)$$

$${\mathrm{there}}_{\mathrm{f}}={\mathrm{AT}}_0+{\mathrm{AT}}_2-{\mathrm{<figure-callout\; id="1"\; label="AT"\; filenames="imgf0001.png"\; state="\{\{state\}\}">AT</figure-callout>}}_1\left(\mathrm{maximum\; density\; of\; weakly\; reinforced\; tip}\right)$$

Si P < LT - L alors $$\mathrm{Si\; P}\mathrm{<}\mathrm{LT}\mathrm{-}\mathrm{L\; alors\; P}\mathrm{=}\mathrm{P}\mathrm{+}2\times \mathrm{L}\mathrm{\times }\left[\mathrm{ent}\left(\left(\mathrm{LT}\mathrm{-}\mathrm{L}\mathrm{-}\mathrm{P}\right)\mathrm{/}\left(2\times \mathrm{L}\right)\right)\mathrm{+}\mathrm{1}\right]$$

The position P of the reinforced ends is obtained using the following operating sequence: $$\mathrm{P}\mathrm{=}\mathrm{modulo}\left[\mathrm{\phi }\mathrm{/}\left(\mathrm{2}\mathrm{\times }\mathrm{The}\right)\right]$$

If P <LT - L then $$\mathrm{If\; P}\mathrm{<}\mathrm{LT}\mathrm{-}\mathrm{L\; then\; P}\mathrm{=}\mathrm{P}\mathrm{+}2\times \mathrm{The}\mathrm{\times }\left[\mathrm{ent}\left(\left(\mathrm{LT}\mathrm{-}\mathrm{The}\mathrm{-}\mathrm{P}\right)\mathrm{/}\left(2\times \mathrm{The}\right)\right)\mathrm{+}\mathrm{1}\right]$$

$$\mathrm{Mini\; min}\mathrm{=}\mathrm{y}\left(\mathrm{x}\right)\mathrm{pour\; x}\mathrm{=}\mathrm{\varphi }\mathrm{+}\mathrm{L}\mathrm{/}\mathrm{pi}\mathrm{\times }\mathrm{Arccos}\left(\mathrm{-}{\mathrm{A}}_{\mathrm{1}}\mathrm{/}\mathrm{4}\mathrm{/}{\mathrm{A}}_{\mathrm{2}}\right)$$

• Indice de renforcement Fort IR_F = y_F - min
• Indice de renforcement faible IR_f = y_f - min

The offset of the reinforced ends is obtained by the relation: $$\mathrm{BR}\mathrm{=}\mathrm{P}\mathrm{-}\mathrm{LT}$$

$$\mathrm{Mini\; min}\mathrm{=}\mathrm{there}\left(\mathrm{x}\right)\mathrm{for\; x}\mathrm{=}\mathrm{\phi }\mathrm{+}\mathrm{The}\mathrm{/}\mathrm{pi}\mathrm{\times }\arccos \left(\mathrm{-}{\mathrm{<figure-callout\; id="1"\; label="AT"\; filenames="imgf0001.png"\; state="\{\{state\}\}">AT</figure-callout>}}_{\mathrm{1}}\mathrm{/}\mathrm{4}\mathrm{/}{\mathrm{<figure-callout\; id="2"\; label="AT"\; filenames="imgf0001.png"\; state="\{\{state\}\}">AT</figure-callout>}}_{\mathrm{2}}\right)$$

• Reinforcement index Strong IR _F = y _F - min
• IR weak reinforcement index _f = y _f - min

The execution modes illustrated on the Figures 3 to 5 allow to obtain excellent results as part of the measurements carried out by the apparatus represented figure 1 .

Nevertheless, density measurements could be made using other techniques such as, for example, ionizing radiation (the β-ray technique has been ruled out only for regulatory reasons).

Claims (10)

1. A method for graphically illustrating the filling profile of a cigarette, with control of the strengthening amplitude and of the position of the strengthened tip(s) relatively to the cut of the stem performed during the manufacturing of the cigarette,
   characterized in that it comprises the following operating phases:

   • elaborating a sinusoidal mathematical model representing density y versus axial position x, this model taking parameters into account such as the length of the tobacco section L, the total length of the cigarette LT, the length of the LF filter and by using at least three constants A0, A1 and ϕ to be determined experimentally,

   • achieving experimental measurements so as to determine the average density D and the average moisture H at a plurality of points along the longitudinal axis of the cigarette,

   • calculating a regression determination coefficient R² from the measured values,

   • calculating the position P of the strengthened tip from the phase ϕ and the aforesaid parameters,

   • calculating the shift of the strengthened tip relatively to the cut from the position P calculated earlier,

   • calculating the strengthening index from the value of said constants.
2. The method according to claim 1,
   characterized in that, in the case of cigarettes with two symmetrical strengthened tips, the model of the sinusoidal plot is periodic, with a period equal to the length of tobacco section and fits the following equation: $$\mathrm{Y}\mathrm{=}{\mathrm{A}}_{\mathrm{0}}\mathrm{+}{\mathrm{A}}_{\mathrm{1}}\mathrm{\times }\cos \left[\mathrm{2}\mathrm{\times }\mathrm{\pi }\mathrm{\times }\left(\mathrm{x}\mathrm{-}\mathrm{\varphi }\right)\mathrm{/}\mathrm{L}\right]$$

   

   with

   y = density

   x = position

   L = tobacco length, i.e., total length LT - filter length LF

   A₀, A₁, ϕ = constants
3. The method according to claim 2,
   characterized in that:

   • the position P of the strengthened tip is for example obtained by the following operating sequence:

   if A₁ < 0 → ϕ + 0,5 × L $$\mathrm{P}\mathrm{=}\mathrm{modulo}\left(\mathrm{\varphi }\mathrm{/}\mathrm{L}\right)$$

   

   if P < LT - L T/2 then $$\mathrm{P}=\mathrm{modulo}\left(\mathrm{\varphi }/\mathrm{L}\right)$$

   

   • the shift of the strengthened tip BR is obtained by a formula of the type $$\mathrm{BR}\mathrm{=}\mathrm{P}\mathrm{-}\mathrm{LT}$$

   

   • the strengthening index IR as for it, is obtained by a relationship of the type $$\mathrm{IR}\mathrm{=}\mathrm{2}\mathrm{\times }\left|\mathrm{A}\mathrm{1}\right|$$

   
4. The method according to claim 1,
   characterized in that, in the case when the cigarette comprises a single strengthened tip BD located on the distal end of the cigarette, the sinusoidal model MS₂ used fits the following equation: $$\mathrm{y}\mathrm{=}{\mathrm{A}}_{\mathrm{0}}\mathrm{+}{\mathrm{A}}_{\mathrm{1}}\mathrm{\times }\cos \left[\mathrm{2}\mathrm{\times }\mathrm{\pi }\mathrm{\times }\left(\mathrm{x}\mathrm{-}\mathrm{\varphi }\right)\mathrm{/}\left(\mathrm{2}\mathrm{\times }\mathrm{L}\right)\right]$$

   

   with

   y = density

   x = position

   L = length of the tobacco section = total length of cigarette - filter length LT

   ϕ = phase
5. The method according to claim 4,
   characterized in that the position P of the strengthened tip is obtained by the following operating sequence:

   if A₁ < 0 then ϕ = ϕ + L $$\mathrm{P}\mathrm{=}\mathrm{modulo}\left[\mathrm{\varphi }\mathrm{/}\left(\mathrm{2}\mathrm{\times }\mathrm{L}\right)\right]$$

   

   if P < LT - L then $$\mathrm{if\; P}\mathrm{<}\mathrm{LT}\mathrm{-}\mathrm{L\; then\; P}\mathrm{=}\mathrm{P}\mathrm{+}2\times \mathrm{L}\mathrm{\times }\left[\mathrm{int}\left(\left(\mathrm{LT}\mathrm{-}\mathrm{L}\mathrm{-}\mathrm{P}\right)\mathrm{/}\left(2\times \mathrm{L}\right)\right)\mathrm{+}\mathrm{1}\right]$$

   

   the shift of the strengthened tip BR is obtained by a formula of the type $$\mathrm{BR}\mathrm{=}\mathrm{P}\mathrm{-}\mathrm{LT}$$

   

   the strengthening index is obtained by a formula of the type $$\mathrm{IR}\mathrm{=}\mathrm{2}\mathrm{\times }\left|\mathrm{A}\mathrm{1}\right|$$

   
6. The method according to claim 1,
   characterized in that, in the case when the cigarette comprises significant strengthening on the distal side and medium strengthening on the filter side FR, the sinusoidal module used fits the following equation: $$\mathrm{y}\mathrm{=}{\mathrm{A}}_{\mathrm{0}}\mathrm{+}{\mathrm{A}}_{\mathrm{1}}\mathrm{\times }\cos \left[\mathrm{2}\mathrm{\times }\mathrm{\pi }\mathrm{\times }\left(\mathrm{x}\mathrm{-}\mathrm{\varphi }\right)\mathrm{/}\left(\mathrm{2}\mathrm{\times }\mathrm{L}\right)\right]+{\mathrm{A}}_{\mathrm{2}}\mathrm{\times }\cos \left[\mathrm{4}\mathrm{\times }\mathrm{\pi }\mathrm{\times }\left(\mathrm{x}\mathrm{-}\mathrm{\varphi }\right)\mathrm{/}\left(\mathrm{2}\mathrm{\times }\mathrm{L}\right)\right]$$

   

   with

   y = density

   x = position

   L = length of the tobacco section
7. The method according to claim 6,
   characterized in that:

   the position P of the strengthened tips is obtained by the following operating sequence:

   if A₁ < 0 $$\begin{array}{cc}\mathrm{if}{\mathrm{A}}_{\mathrm{1}}\mathrm{<}\mathrm{0}& \mathrm{\varphi }\mathrm{=}\mathrm{\varphi }\mathrm{+}\mathrm{L}\end{array}$$

   

   the expression of the maximum density value y_F of the high-strength tip is $${\mathrm{y}}_{\mathrm{F}}\mathrm{=}{\mathrm{A}}_{\mathrm{0}}\mathrm{+}{\mathrm{A}}_{\mathrm{2}}\mathrm{-}{\mathrm{A}}_{\mathrm{1}}$$

   

   
   the expression of the maximum density value y_f of the low-strength tip is $${\mathrm{y}}_{\mathrm{f}}\mathrm{=}{\mathrm{A}}_{\mathrm{0}}\mathrm{+}{\mathrm{A}}_{\mathrm{1}}+{\mathrm{A}}_{\mathrm{2}}$$

   

   if A₁ > 0 one has $${\mathrm{Y}}_{\mathrm{F}}\mathrm{=}{\mathrm{A}}_{\mathrm{0}}\mathrm{+}{\mathrm{A}}_{\mathrm{1}}+{\mathrm{A}}_{\mathrm{2}}\left(\mathrm{maximum\; density\; of\; the\; high}-\mathrm{strength\; tip}\right)$$

   

   $${\mathrm{y}}_{\mathrm{f}}\mathrm{=}{\mathrm{A}}_{\mathrm{0}}\mathrm{+}{\mathrm{A}}_{\mathrm{2}}-{\mathrm{A}}_{\mathrm{1}}\left(\mathrm{maximum\; density\; of\; the\; low}-\mathrm{strength\; tip}\right)$$

   

   
   the position P of the strengthened tips is obtained by the following operating sequence: $$\mathrm{P}\mathrm{=}\mathrm{modulo}\left[\mathrm{\varphi }\mathrm{/}\left(\mathrm{2}\mathrm{\times }\mathrm{L}\right)\right]$$

   

   if P < LT - L then $$\mathrm{if\; P}\mathrm{<}\mathrm{LT}\mathrm{-}\mathrm{L\; then\; P}\mathrm{=}\mathrm{P}\mathrm{+}2\times \mathrm{L}\mathrm{\times }\left[\mathrm{int}\left(\left(\mathrm{LT}\mathrm{-}\mathrm{L}\mathrm{-}\mathrm{P}\right)\mathrm{/}\left(2\times \mathrm{L}\right)\right)\mathrm{+}\mathrm{1}\right]$$

   

   
   the shift of the strengthened tips is obtained by the relationship : $$\mathrm{BR}\mathrm{=}\mathrm{P}\mathrm{-}\mathrm{LT}$$

   

   $$\mathrm{Minimum\; min}\mathrm{=}\mathrm{y}\left(\mathrm{x}\right)\mathrm{for\; x}\mathrm{=}\mathrm{\varphi }\mathrm{+}\mathrm{L}\mathrm{/}\mathrm{pi}\mathrm{\times }\mathrm{Arccos}\left(\mathrm{-}{\mathrm{A}}_{\mathrm{1}}\mathrm{/}\mathrm{4}\mathrm{/}{\mathrm{A}}_{\mathrm{2}}\right)$$

   

   High strengthening index IR_F = y_F - min

   Low strengthening index IR_f = y_f - min
8. A device for applying the method according to any of the preceding claims,
   characterized in that it comprises:

   - a hopper (1) associated with a distributor (2) which delivers cigarettes one-by-one,

   - an hyper frequency module comprising an electronic rack (3) (wobbulator) and a cavity (4) crossed by a tube for guiding the cigarettes, which measures the point density and the moisture of the cigarettes (5) passing through the cavity (4),

   - constant speed driving means for the cigarettes during their passing in the cavity.
9. The device according to claim 8,
   characterized in that the aforesaid driving means comprise a worm screw (6) driven by an electric motor (7) and a sprocket wheel (8) driven into translation by the screw (6), this sprocket wheel (8) bearing a pivoting supporting arm (9), the pivoting of which is provided by an electromechanical actuator (10).
10. The device according to claim 9,
    characterized in that it further comprises a microcontroller (11) used for providing the control of the hyper frequency module (3) and pre-processing of the information delivered by this module (3) and a processor (12) connected to the former via a link (13) for example of the RS 232 type, to an input/output interface (14) connected to the actuator (10) as well as to end-of-travel contacts (15, 16) positioned at the ends of the travel of the sprocket wheel (8), and to a power circuit (17) connected to the motor of the distributor (2) associated with the hopper (1).

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