WO2011069896A1 - Procédé de construction de corps corotatifs entrant en contact et système informatique pour la mise en oeuvre dudit procédé - Google Patents

Procédé de construction de corps corotatifs entrant en contact et système informatique pour la mise en oeuvre dudit procédé Download PDF

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Publication number
WO2011069896A1
WO2011069896A1 PCT/EP2010/068794 EP2010068794W WO2011069896A1 WO 2011069896 A1 WO2011069896 A1 WO 2011069896A1 EP 2010068794 W EP2010068794 W EP 2010068794W WO 2011069896 A1 WO2011069896 A1 WO 2011069896A1
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WO
WIPO (PCT)
Prior art keywords
curve
point
cross
rotation
bodies
Prior art date
Application number
PCT/EP2010/068794
Other languages
German (de)
English (en)
Inventor
Thomas König
Miachel Bierdel
Original Assignee
Bayer Technology Services Gmbh
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Bayer Technology Services Gmbh filed Critical Bayer Technology Services Gmbh
Priority to BR112012013714A priority Critical patent/BR112012013714A2/pt
Priority to RU2012128348/05A priority patent/RU2554647C9/ru
Priority to IN5079DEN2012 priority patent/IN2012DN05079A/en
Priority to ES10787746.6T priority patent/ES2450942T3/es
Priority to CA2783124A priority patent/CA2783124A1/fr
Priority to EP10787746.6A priority patent/EP2509765B1/fr
Priority to US13/513,922 priority patent/US9314954B2/en
Priority to MX2012006432A priority patent/MX2012006432A/es
Priority to JP2012542463A priority patent/JP5645958B2/ja
Priority to SG2012038568A priority patent/SG181063A1/en
Priority to CN201080055860.5A priority patent/CN102725119B/zh
Priority to KR1020127014667A priority patent/KR101773635B1/ko
Publication of WO2011069896A1 publication Critical patent/WO2011069896A1/fr

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Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29B—PREPARATION OR PRETREATMENT OF THE MATERIAL TO BE SHAPED; MAKING GRANULES OR PREFORMS; RECOVERY OF PLASTICS OR OTHER CONSTITUENTS OF WASTE MATERIAL CONTAINING PLASTICS
    • B29B7/00—Mixing; Kneading
    • B29B7/30—Mixing; Kneading continuous, with mechanical mixing or kneading devices
    • B29B7/34—Mixing; Kneading continuous, with mechanical mixing or kneading devices with movable mixing or kneading devices
    • B29B7/38—Mixing; Kneading continuous, with mechanical mixing or kneading devices with movable mixing or kneading devices rotary
    • B29B7/46—Mixing; Kneading continuous, with mechanical mixing or kneading devices with movable mixing or kneading devices rotary with more than one shaft
    • B29B7/48—Mixing; Kneading continuous, with mechanical mixing or kneading devices with movable mixing or kneading devices rotary with more than one shaft with intermeshing devices, e.g. screws
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29B—PREPARATION OR PRETREATMENT OF THE MATERIAL TO BE SHAPED; MAKING GRANULES OR PREFORMS; RECOVERY OF PLASTICS OR OTHER CONSTITUENTS OF WASTE MATERIAL CONTAINING PLASTICS
    • B29B7/00—Mixing; Kneading
    • B29B7/30—Mixing; Kneading continuous, with mechanical mixing or kneading devices
    • B29B7/34—Mixing; Kneading continuous, with mechanical mixing or kneading devices with movable mixing or kneading devices
    • B29B7/38—Mixing; Kneading continuous, with mechanical mixing or kneading devices with movable mixing or kneading devices rotary
    • B29B7/46—Mixing; Kneading continuous, with mechanical mixing or kneading devices with movable mixing or kneading devices rotary with more than one shaft
    • B29B7/48—Mixing; Kneading continuous, with mechanical mixing or kneading devices with movable mixing or kneading devices rotary with more than one shaft with intermeshing devices, e.g. screws
    • B29B7/482—Mixing; Kneading continuous, with mechanical mixing or kneading devices with movable mixing or kneading devices rotary with more than one shaft with intermeshing devices, e.g. screws provided with screw parts in addition to other mixing parts, e.g. paddles, gears, discs
    • B29B7/483—Mixing; Kneading continuous, with mechanical mixing or kneading devices with movable mixing or kneading devices rotary with more than one shaft with intermeshing devices, e.g. screws provided with screw parts in addition to other mixing parts, e.g. paddles, gears, discs the other mixing parts being discs perpendicular to the screw axis
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25—Component parts, details or accessories; Auxiliary operations
    • B29C48/251—Design of extruder parts, e.g. by modelling based on mathematical theories or experiments
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25—Component parts, details or accessories; Auxiliary operations
    • B29C48/251—Design of extruder parts, e.g. by modelling based on mathematical theories or experiments
    • B29C48/2511—Design of extruder parts, e.g. by modelling based on mathematical theories or experiments by modelling material flow, e.g. melt interaction with screw and barrel
    • B29C48/2513—Design of extruder parts, e.g. by modelling based on mathematical theories or experiments by modelling material flow, e.g. melt interaction with screw and barrel in the plasticising zone
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25—Component parts, details or accessories; Auxiliary operations
    • B29C48/251—Design of extruder parts, e.g. by modelling based on mathematical theories or experiments
    • B29C48/2517—Design of extruder parts, e.g. by modelling based on mathematical theories or experiments of intermeshing screws
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25—Component parts, details or accessories; Auxiliary operations
    • B29C48/36—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die
    • B29C48/395—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die using screws surrounded by a cooperating barrel, e.g. single screw extruders
    • B29C48/40—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die using screws surrounded by a cooperating barrel, e.g. single screw extruders using two or more parallel screws or at least two parallel non-intermeshing screws, e.g. twin screw extruders
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25—Component parts, details or accessories; Auxiliary operations
    • B29C48/36—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die
    • B29C48/395—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die using screws surrounded by a cooperating barrel, e.g. single screw extruders
    • B29C48/40—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die using screws surrounded by a cooperating barrel, e.g. single screw extruders using two or more parallel screws or at least two parallel non-intermeshing screws, e.g. twin screw extruders
    • B29C48/402—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die using screws surrounded by a cooperating barrel, e.g. single screw extruders using two or more parallel screws or at least two parallel non-intermeshing screws, e.g. twin screw extruders the screws having intermeshing parts
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25—Component parts, details or accessories; Auxiliary operations
    • B29C48/36—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die
    • B29C48/395—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die using screws surrounded by a cooperating barrel, e.g. single screw extruders
    • B29C48/40—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die using screws surrounded by a cooperating barrel, e.g. single screw extruders using two or more parallel screws or at least two parallel non-intermeshing screws, e.g. twin screw extruders
    • B29C48/405—Intermeshing co-rotating screws
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25—Component parts, details or accessories; Auxiliary operations
    • B29C48/36—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die
    • B29C48/50—Details of extruders
    • B29C48/505—Screws
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25—Component parts, details or accessories; Auxiliary operations
    • B29C48/36—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die
    • B29C48/50—Details of extruders
    • B29C48/505—Screws
    • B29C48/507—Screws characterised by the material or their manufacturing process
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25—Component parts, details or accessories; Auxiliary operations
    • B29C48/36—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die
    • B29C48/50—Details of extruders
    • B29C48/505—Screws
    • B29C48/59—Screws characterised by details of the thread, i.e. the shape of a single thread of the material-feeding screw
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25—Component parts, details or accessories; Auxiliary operations
    • B29C48/36—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die
    • B29C48/50—Details of extruders
    • B29C48/505—Screws
    • B29C48/64—Screws with two or more threads
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/03—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor characterised by the shape of the extruded material at extrusion
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25—Component parts, details or accessories; Auxiliary operations
    • B29C48/36—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die
    • B29C48/50—Details of extruders
    • B29C48/505—Screws
    • B29C48/56—Screws having grooves or cavities other than the thread or the channel
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25—Component parts, details or accessories; Auxiliary operations
    • B29C48/36—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die
    • B29C48/50—Details of extruders
    • B29C48/505—Screws
    • B29C48/635—Eccentrically rotating screws; Screws revolving around an axis other than their central axis

Definitions

  • the invention relates to a method for the construction of bodies which always touch in at least one point in the same direction rotation at the same speed around parallel axes.
  • FIGS. 1 and 2 can be continued in various ways into the third dimension.
  • a simple possibility is e.g. the linear continuation of the figures in the direction of the axes of rotation, so that disc or rod-shaped body arise, which in a same direction rotation along a line between the centers of rotation, which is parallel to the axes of rotation, strip.
  • helical continue the geometric figures along the axes of rotation, so that helical bodies arise, which touch in the same direction rotation along a curve between the bodies.
  • a Erdmenger type screw element having a cross-sectional profile as in Fig. 2 of the present application may be composed of circular arcs.
  • the task of providing a general method can be constructed with the body, which always touch in at least one point in the same direction rotation at the same speed about two parallel axes arranged.
  • the basic principles were found, which are based on two bodies, which always touch in at least one point in the same direction rotation about two mutually parallel axes.
  • the subject of the present invention is therefore a method according to the independent claim 1 for the construction of bodies which always touch in at least one point in the same direction rotation at the same speed around mutually parallel axes.
  • Preferred embodiments can be found in the dependent claims.
  • the method according to the invention can be applied to two or more bodies.
  • the bodies are arranged side by side on parallel axes of rotation extending in pairs at a distance a.
  • the method is expediently described for two bodies K1 and K2, which rotate about their respective axes at the same speed.
  • the bodies Kl and K2 would always be arranged alternately on adjacent axes of rotation.
  • the bodies K1 and K2 are also referred to as corresponding bodies.
  • the speed is the number of revolutions of a body about its axis of rotation per unit of time (unit hertz).
  • the cross-sectional profiles are the profiles resulting from a section of the bodies K1 and K2 in a plane E which is perpendicular to the axes of rotation AI and A2.
  • the cross-sectional profile of a body can be predetermined and the cross-sectional profile of the other, corresponding body can be easily derived from this predetermined profile.
  • the profile to be specified has to satisfy only a few, easily realizable criteria.
  • the derivation of the profile of the corresponding body is carried out in a simple manner either graphically or by calculation. This allows the construction of an extraordinary variety of corresponding bodies. This makes it possible for the first time to specify an almost arbitrary body and derive the corresponding body in a simple manner from the given.
  • the inventive method is not on Cross-sectional profiles described by circular arcs (as in the case of Erdmenger screw elements, see [1] pages 96 to 98).
  • the method according to the invention is also not limited to the mathematical functions described in [2] for the definition of cross-sectional profiles.
  • the cross-sectional profile to be specified is expediently described as a mathematical curve.
  • a (mathematical) curve is a one-dimensional object that has a curvature.
  • One-dimensional means that you can only move in one direction (or the opposite direction) on the curve.
  • the curve is in a two-dimensional plane E, which is perpendicular to the axes of rotation AI and A2.
  • intersections S l and S2 of the axes of rotation AI and A2 with the plane E are also referred to as fulcrums of the respective axes.
  • the distance of the fulcrums Sl and S2 from each other is a.
  • the curvature of a curve is the change in direction per unit length.
  • the curvature of a straight line is zero everywhere, because its direction does not change.
  • a circle with the radius r has the same curvature everywhere (namely 1 / r), because its direction changes everywhere equally. For all other curves, the curvature usually changes from curve point to curve point.
  • the curvature of a curve at a point P thus indicates how much the curve in the immediate vicinity of the point P deviates from a straight line.
  • the reciprocal of the curvature is called the radius of curvature; this is the radius of the circle (circle of curvature), which is the best approximation in an environment of the contact point (see textbooks of mathematics, especially geometry).
  • a curve can be defined via a parameter representation in a parameter s:
  • x (s) and y (s) are the coordinates of the points of the curve p (s) in the two-dimensional plane E.
  • the following criteria must satisfy the curve which describes the cross-sectional profile of a body Kl, so that a cross-sectional profile of a corresponding body K2 can be generated from the curve:
  • the curve must be steady.
  • the curve must be convex.
  • the curve must be continuously differentiable in sections.
  • the curve p must have a radius of curvature p at each point that is less than or equal to the distance a.
  • a closed, convex curve is known to have the following property: Consider two arbitrary points PI and P2 on the curve. If these points PI and P2 are connected by a straight line, this straight line passes through the points PI and P2 of the curve, but beyond that by no further point on the curve, irrespective of where the points PI and P2 lie on the curve.
  • the curve also has a positive curvature at each point.
  • One way to mathematically describe kinks is listed below.
  • a curve q can be derived from the curve p, which describes the cross-sectional profile of the corresponding body K2.
  • t (p) be a family of normalized tangent vectors of length 1.
  • n (p) - be a family of normalized normal vectors of length 1, each showing t in the direction of the center of the circle of curvature associated with the point of curve p.
  • the circle of curvature has the same radius (the same curvature) as the curve in the respective point.
  • a be a vector with the length a, whose direction leads from the intersection Sl to the intersection S2.
  • Fig. 3 shows schematically the implementation of the method according to the invention with reference to a point on a curve.
  • the points of intersection Sl and S2 of the axes of rotation are shown as small circles. They have a distance a from each other.
  • the vector a has the length a and points from S1 to S2. Above the points of intersection Sl and S2, the section of a curve p is shown. A point on the curve is picked out and marked as a small circle.
  • a point can be generated on the corresponding curve q.
  • the point on the corresponding curve q is obtained by placing a tangent t (p) on the curve at the point of the curve p, forming the normalized normal vectors n (p) to this tangent and extending it by the factor a and finally to this ⁇ vector a n (p) the vector a is added.
  • the curve p can be described throughout by a single mathematical function. Similarly, the curve p sections by different mathematical functions are described
  • the curve p must be continuously differentiable in sections. Thus, at the section boundaries of a sectionally defined curve p, the individual sections do not have to pass into each other in a continuously differentiable manner.
  • the size of a circular arc is given by the indication of its central angle and its radius.
  • the central angle of a circular arc will be referred to briefly as the angle of a circular arc.
  • the position of a circular arc is given by the position of its center and by the position of its two endpoints.
  • a circular arc corresponding to a kink in the cross-sectional profile of the body K1 in the cross-sectional profile of the body K2 always has a radius whose size corresponds to the axial distance a. Furthermore, a circular arc corresponding to a bend always has an angle that corresponds to that angle in which the tangents meet the curve sections in the inflection point.
  • a corresponding profile section of the curve q is a "kink" if a profile section of the curve p is a circular arc with the radius a.
  • a transition of a first curve section takes place by rotation about the angle of the arc of radius zero into a second curve section.
  • a tangent to the first curve portion at the center of the zero-radius arc intersects a tangent to the second curve portion also at the center of the arc at an angle equal to the angle of the arc.
  • FIG. 7 clarifies the described situation.
  • FIG. 7 shows part of a cross-sectional profile of the body K1 and part of the cross-sectional profile of the resulting body K2.
  • the shown part of the cross-sectional profile of the body Kl consists of the curve sections KAI and KA2.
  • the cross-sectional profile of the body Kl has a kink.
  • the kink is preferably described by a circular arc whose radius is zero.
  • the angle of the circular arc is equal to the angle W, in which the tangent TAI to the curve section KAI and the tangent TA2 to the curve section KA2 in the inflection point KP collide.
  • the subject of the present invention is a method for producing two bodies K1 and K2, which, in the case of rotation in the same direction, touch each other at at least one point about two axes of rotation A 1 and A 2 arranged parallel to each other at a distance a, characterized in that in a plane E perpendicular to the axes of rotation a cross-sectional profile of the body Kl is formed by a continuous, sectionally continuously differentiable, closed, convex curve p, and the cross-sectional profile of the body K2 from the curve p according to the relationship
  • the curve p has a radius of curvature p at each point which is less than or equal to the distance a
  • a is a vector which leads in the direction from the point of intersection S 1 of the axis of rotation AI with the plane E to the intersection S2 of the axis of rotation A2 with the plane E and has the length a, at a kink in the cross-sectional profile of the body Kl, the cross-sectional profile of the body K2 a Circular arc whose radius corresponds to the axial distance a and whose angle corresponds to that angle in which the tangents to the curve sections of the curve p abut in the bending point.
  • the intersection S l can be within the closed curve p or outside. Preferably, the intersection Sl lies within the closed curve p.
  • the closed curve p may have a mirror symmetry, a point symmetry or a rotational symmetry. If the closed curve p has a mirror symmetry, the point of intersection S1 is preferably on the axis of symmetry. If the closed curve p has more than one mirror symmetry, the point of intersection S1 is preferably at the intersection of at least two symmetry axes of the curve p. If the closed curve p has a point symmetry, the point of intersection S 1 is preferably at the point of symmetry. If the closed curve p has a rotational symmetry, the point of intersection S 1 is preferably at the pivot point of the profile.
  • the curve p may be described throughout by a single mathematical function. Examples which may be mentioned are functions known to the person skilled in the art, such as circular functions or elliptical functions, parabolic functions or hyperbolic functions. Also is in the form whereby, depending on the shape of the function f (s), a gap of arbitrary shape results in the execution of screw elements between a housing having a radius r 0 and the rotating screw element.
  • f (s) may be a linear function or quadratic function of s, a hyperbolic function, or an exponential function.
  • functions whose values are determined by control points such as B-spline functions, Bezier functions, Bezier rational functions, and non-uniform rational B-splines (NURBS) are called.
  • Bezier functions, Bezier rational functions NURBS are preferred because they are commonly used in CAD (Computer Aided Design) CAD design, where they are used primarily to define arbitrary shapes in geometric visual form by moving control points ,
  • Bezier functions should be mentioned here. Bezier functions are known to have the form where P t is the coordinates of the control points and is an amber polynomial.
  • Rational Bezier functions of degree n which are described, for example, in M.S. Floater, "Derivatives of rational Bezier curves", Comp. Aid., Geom., Design 9, 1992, 161-174 [4], are known to have the form
  • the curve p can be described section by section by various mathematical functions, wherein the section-wise functions preferably correspond to the functions mentioned in the previous paragraph.
  • the corresponding profile sections of the bodies K1 and K2 can also change from section to section.
  • a curve section p n + 1 is specified which transitions tangentially into q n and according to the relationship (1) with interchanged Sl and S2 (ie replacement of a by - a) yields a curve section q n + 1 , which merges tangentially into the previous curve section p n .
  • the method according to the invention can be carried out solely with an angle ruler and compass on paper.
  • the pivot points S 1 and S2 are expediently placed in a plane first.
  • the distance between the pivot points is a.
  • the cross-sectional profile of the body K1 is completely or completely plotted in the plane of the points S1 and S2. The criteria listed above for generating the profile of the body Kl.
  • Each individual point of the cross-sectional profile of a corresponding body K2 can be derived from the individual points of the predetermined cross-sectional profile of a body K1.
  • the cross-sectional profiles of corresponding bodies can be continued in various ways into the third dimension to produce bodies which always touch each other in at least one point when rotating in the same direction at the same speed around mutually parallel axes.
  • screw elements for screw extruders
  • the method according to the invention is preferably used for the production of screw elements.
  • the method according to the invention is not limited to screw elements of the modular design of a screw of screw elements and core shafts which is customary today, but can also be used on screws in solid construction. Therefore, the term screw elements are also to be understood to mean screws of solid construction.
  • Screw elements may e.g. be designed as conveying, kneading or mixing elements.
  • a conveyor element is thereby characterized (see, for example, [1], pages 227-248) that the screw profile is continued to be continuously helically twisted in the axial direction.
  • the conveying element can be right- or left-handed.
  • the slope of the conveyor element is preferably in the range of 0, 1 to 10 times the axial distance, wherein the slope is understood to mean the axial length which is required for a complete rotation of the screw profile, and the axial length of a conveyor element is preferably in Range of 0.1 times to 10 times the center distance.
  • the movement, the pitch and the axial length are the same for adjacent screw elements (corresponding bodies).
  • a kneading element is thereby characterized (see, for example, [1], pages 227-248) that the screw profile is continued in the axial direction in a batchwise manner in the form of kneading disks.
  • the arrangement of the kneading discs can be right- or left-handed or neutral.
  • the axial length of the kneading disks is preferably in the range of 0.05 times to 10 times the center distance.
  • the axial distance between two adjacent kneading disks is preferably in the range of 0.002 to 0.1 times the axial spacing.
  • the mobility and the axial length of the kneading discs are the same for adjacent screw elements (corresponding bodies).
  • the mixing elements are thereby formed (see, for example, [1], pages 227-248) that conveying elements are provided with apertures in the screw flights.
  • the mixing elements can be right- or left-handed.
  • Their pitch is preferably in the range of 0, 1 times to 10 times the axial distance and the axial length of the elements is preferably in the range of 0.1 times to 10 times the axial distance.
  • the apertures preferably have the shape of a u- or v-shaped groove, which are preferably arranged Chrysler Mons or parallel to the axis. The movement, the pitch and the axial length are the same for adjacent screw elements (corresponding bodies).
  • transition elements In order to enable the transition between different screw elements, washers are often used as a spacer sleeve.
  • transition elements are used, which provide a continuous transition between two screw profiles Allow passage number, with a self-cleaning pair of screw profiles present at each point of the transition.
  • Transition elements can be right- or left-handed.
  • Their pitch is preferably in the range of 0.1 times to 10 times the axial distance and their axial length is preferably in the range of 0.1 times to 10 times the axial distance. The movement, the pitch and the axial length are the same for adjacent screw elements (corresponding bodies).
  • the present invention allows the generation of profiles of corresponding bodies ab initio.
  • the prior art method of the invention does not start from existing profiles, but allows the generation of arbitrary profiles step by step, observing simple rules.
  • the process of the invention is general, i. it is not limited to certain types of bodies (e.g., Erdmenger type screw elements).
  • the method according to the invention can be carried out on paper alone with angle ruler and compass.
  • the implementation of the method according to the invention on a computer system is advantageous because the coordinates and dimensions of the profiles are in a form that can be further processed by a computer.
  • the subject of the present invention is therefore also a computer system for carrying out the method according to the invention on a computer.
  • the computer system has a graphical user interface (GUI) that allows a user to easily enter the freely selectable sizes for generating profiles via input devices, such as mouse and / or keyboard.
  • GUI graphical user interface
  • the computer system has a possibility of contours of profiles by means of control points and possibly weights in functions whose values are defined by control points, functions whose values are determined by control points, such as B-spline functions, Bezier functions to specify rational Bezier functions as well as non-uniform rational B-splines (NURBS), in the form of numbers (coordinates), graphically or with a combination of graphical and numerical input.
  • GUI graphical user interface
  • the computer system preferably has a graphical output, by means of which the calculated profiles can be visualized on a graphic output device such as screen and / or printer.
  • the computer system preferably has the possibility of exporting calculated profiles, ie to store them in the form of storable data records, which comprise the geometrical dimensions of the calculated bodies, either on a data carrier for further purposes of use or to transmit them to a connected device.
  • the computer system is preferably designed to be calculate both cross-sectional profiles and bodies generated from the cross-sectional profiles, and output the calculated geometries in a format that can be used by a machine to produce such bodies, eg, a machine tool, such as a milling machine, to make real bodies. Such formats are known to the person skilled in the art.
  • the bodies may be e.g. be produced with a milling machine, a lathe or a whirling machine.
  • Preferred materials for producing such bodies are steels, in particular nitriding steels, chromium, tool and stainless steels, powder metallurgically produced metallic composites based on iron, nickel or cobalt, engineering ceramic materials such as e.g. Zirconia or silicon carbide if the bodies are extruder screws.
  • Screw elements for twin-screw or multi-screw extruders are usually introduced into a housing.
  • screw elements and housing are designed so that not only a pair of Abschabung adjacent screw elements takes place by the rotation of the screw elements, but also a cleaning of the Gescouseinnenwandungen is given by the rotation of the screw elements.
  • the screw elements used in practice do not, strictly speaking, have the property that, in the case of rotation in the same direction, they touch each other about axes arranged parallel to one another in at least one point.
  • bodies are preferably first of all generated virtually, which, in the case of rotation in the same direction, rotate about axes arranged parallel to one another in at least one axis Touch point. Based on these preferably virtual geometries, games are provided which prevent the snail elements used in practice from "eating".
  • housings, games and / or eccentric positioning is correspondingly applicable to corresponding bodies which, when rotating in the same direction about two axes arranged in parallel, always touch each other in at least one point.
  • Another object of the present invention is thus a method for producing screw elements.
  • the method according to the invention for producing screw elements is characterized in that, in a first step, the cross-sectional profiles of bodies which always touch in at least one point in the same direction rotation at the same rotational speed about axes of rotation parallel to one another at a distance a, according to the method described above be generated.
  • games are introduced according to the method of the center distance magnification, the longitudinal section equidistants and / or the room equidistants.
  • the play between the screw elements is preferably in the range of 0.002 to 0, 1 times the axial distance and the clearance between the screw and the housing is preferably in the range of 0.002 to 0.1 times the axial distance.
  • the invention is explained in more detail below by means of examples, without, however, limiting them to them.
  • Example 1 just be an elliptical profile with the parameter representation
  • the center distance is 48, the Drehpu the elliptical profile lie in the coordinate origin and the fulcrum of the second profile at
  • the maximum value of the curve radius is about 44.26, which is smaller than the axial distance. This allows the profile.
  • FIG. 4 shows the two contours, the generating ellipse on the left and the generated contour on the right.
  • Example 2
  • the center distance is 10
  • Fig. 5 shows the curve according to the invention.
  • the points Si and S 2 are the fulcrums of the cross-sectional profiles of the corresponding bodies.
  • the control points PO to P4 are also indicated by circles.
  • the figure shows the contour p and the corresponding contour q.
  • This profile corresponds to a part of the profile from example 1.
  • the center distance is also example 1. Accordingly, then
  • p x is defined as part of an ellipse where d and the profile generated on

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  • Engineering & Computer Science (AREA)
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  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Algebra (AREA)
  • Manufacturing & Machinery (AREA)
  • Extrusion Moulding Of Plastics Or The Like (AREA)
  • Conveying And Assembling Of Building Elements In Situ (AREA)
  • Image Generation (AREA)
  • Preliminary Treatment Of Fibers (AREA)
  • Manufacture Of Motors, Generators (AREA)
  • Processing And Handling Of Plastics And Other Materials For Molding In General (AREA)

Abstract

L'invention concerne un procédé de construction de corps entrant toujours en contact en au moins un point lorsqu'ils tournent dans le même sens autour d'axes parallèles.
PCT/EP2010/068794 2009-12-08 2010-12-03 Procédé de construction de corps corotatifs entrant en contact et système informatique pour la mise en oeuvre dudit procédé WO2011069896A1 (fr)

Priority Applications (12)

Application Number Priority Date Filing Date Title
BR112012013714A BR112012013714A2 (pt) 2009-12-08 2010-12-03 processo para a construção de corpos com rotação na mesma direção e estão em contato entre si e um sistema informático para executar este processo.
RU2012128348/05A RU2554647C9 (ru) 2009-12-08 2010-12-03 Способ конструирования соприкасающихся тел с однонаправленным вращением и компьютерная система для реализации этого способа
IN5079DEN2012 IN2012DN05079A (fr) 2009-12-08 2010-12-03
ES10787746.6T ES2450942T3 (es) 2009-12-08 2010-12-03 Procedimiento para la construcción de cuerpos rotativos en la misma dirección que se tocan
CA2783124A CA2783124A1 (fr) 2009-12-08 2010-12-03 Procede de construction de corps corotatifs entrant en contact et systeme informatique pour la mise en oeuvre dudit procede
EP10787746.6A EP2509765B1 (fr) 2009-12-08 2010-12-03 Procédé de construction de corps corotatifs entrant en contact
US13/513,922 US9314954B2 (en) 2009-12-08 2010-12-03 Method for constructing bodies that rotate in the same direction and are in contact with one another and computer system for carrying out said method
MX2012006432A MX2012006432A (es) 2009-12-08 2010-12-03 Procedimiento para la construccion de cuerpos rotativos en la misma direccion que se tocan y sistema informatico para la realizacion del procedimiento.
JP2012542463A JP5645958B2 (ja) 2009-12-08 2010-12-03 同方向に回転して相互に接触する立体を構築する方法
SG2012038568A SG181063A1 (en) 2009-12-08 2010-12-03 Method for constructing bodies that rotate in the same direction and are in contact with one another and computer system for carrying out said method
CN201080055860.5A CN102725119B (zh) 2009-12-08 2010-12-03 用于构造同向旋转相互接触体的方法以及用于实施该方法的计算机系统
KR1020127014667A KR101773635B1 (ko) 2009-12-08 2010-12-03 동일한 방향으로 회전하며 서로 접촉하는 바디의 제작 방법 및 상기 방법을 수행하기 위한 컴퓨터 시스템

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DE102009057139.6 2009-12-08
DE102009057139A DE102009057139A1 (de) 2009-12-08 2009-12-08 Verfahren zur Konstruktion gleichsinnig rotierender, sich berührender Körper

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CN102717155B (zh) * 2012-06-08 2016-01-20 无锡同联机电工程有限公司 一种不等齿距蜗杆驱动装置的制造方法
JP6513647B2 (ja) * 2013-06-24 2019-05-15 コベストロ、ドイチュラント、アクチエンゲゼルシャフトＣｏｖｅｓｔｒｏ Ｄｅｕｔｓｃｈｌａｎｄ Ａｇ 多軸スクリュー式機械用のスクリューエレメント
DE102013112971B3 (de) * 2013-11-25 2015-02-05 Leistritz Extrusionstechnik Gmbh Einrichtung und Verfahren zur Überprüfung des Aufbaus einer Extruderschnecke
EP2965889A1 (fr) * 2014-07-11 2016-01-13 Covestro Deutschland AG Éléments composé à pouvoir dispersant amélioré
WO2018071041A1 (fr) * 2016-10-14 2018-04-19 Hewlett-Packard Development Company, L.P. Reconstruction de modèles tridimensionnels pour fournir des modèles tridimensionnels simplifiés
US20200039145A1 (en) * 2017-04-13 2020-02-06 Siemens Aktiengesellschaft Powder-Bed-Based Additive Manufacture of a Workpiece
CN108153937A (zh) * 2017-12-03 2018-06-12 长春黄金研究院 一种二叶型转子外形的形线设计及加工方法
CN113892878A (zh) * 2021-09-30 2022-01-07 深圳市杉川机器人有限公司 清洁件、清洁组件和机器人

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US9314954B2 (en) 2016-04-19
CN102725119B (zh) 2015-09-16
EP2509765A1 (fr) 2012-10-17
IN2012DN05079A (fr) 2015-10-09
MX2012006432A (es) 2012-10-15
KR20120123264A (ko) 2012-11-08
RU2554647C2 (ru) 2015-06-27
KR101773635B1 (ko) 2017-08-31
US20120281001A1 (en) 2012-11-08
JP2013513177A (ja) 2013-04-18
SG181063A1 (en) 2012-07-30
RU2012128348A (ru) 2014-01-20
JP5645958B2 (ja) 2014-12-24
BR112012013714A2 (pt) 2017-10-10
EP2509765B1 (fr) 2014-01-22
DE102009057139A1 (de) 2011-06-09
CA2783124A1 (fr) 2011-06-16
ES2450942T3 (es) 2014-03-25
CN102725119A (zh) 2012-10-10
MY161577A (en) 2017-04-28

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