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

Patent metadata

Field	Value
Publication number	US-9314954-B2
Application number	US-201013513922-A
Country	US
Kind code	B2
Filing date	Dec 3, 2010
Priority date	Dec 8, 2009
Publication date	Apr 19, 2016
Grant date	Apr 19, 2016

Abstract

The invention relates to a method for constructing bodies which, while rotating codirectionally about axes arranged in parallel, constantly touch one another at at least one point.

First claim

The invention claimed is:

1. A method for generating a profile of bodies K 1 and K 2 which, while rotating codirectionally at a same rotational speed about two axes of rotation A 1 with regard to body K 1 and A 2 with regard to body K 2 arranged parallel to one another at a distance a, constantly touch one another at at least one point, said method comprising as a first step forming a cross-sectional profile of the body K 1 in a plane E perpendicular to axes of rotation by a constant, segmentally constantly differentiable, closed convex curve {right arrow over (p)}, and as a second step, forming a cross-sectional profile of the body K 2 from the curve {right arrow over (p)}, according to
{right arrow over (q)}={right arrow over (p)}+a·{right arrow over (n)} ({right arrow over ( p )})+ a   (1),

said {right arrow over (q)} being a curve describing the cross-sectional profile of the corresponding body K 2 ,
said curve {right arrow over (p)}, having at any point a radius of curvature p which is smaller than or equal to distance a,
for each point of said curve {right arrow over (p)}, within a constantly differentiable segment, there being a standardized normal vector {right arrow over (n)}({right arrow over (p)}) of length l which at each point is perpendicular to a tangent to said curve {right arrow over (p)}, and points in a direction of a centre portion of a circle of curvature belonging to the respective point of said curve {right arrow over (p)},
{right arrow over (a)} being a vector which leads in a direction from an intersection point S 1 of the axis of rotation A 1 with the plane E to an intersection point S 2 of the axis of rotation A 2 with the plane E and possesses a length equal to the distance a, and
in a case of a kink in said cross-sectional profile of the body K 1 , said cross-sectional profile of the body K 2 having an arc of a circle, the radius of which corresponds to the distance a and an angle of which corresponds to an angle at which tangents to curve segments of said curve {right arrow over (p)}, abut one another at a kink point wherein

said curve {right arrow over (p)} is described by a single mathematical function, the said single mathematical function being selected from the series consisting of the following members:
B-spline function, Bézier function, rational Bézier function, non-uniform rational B-spline function,
or wherein
said curve {right arrow over (p)} is described segmentally by various mathematical functions, at least one of these said various mathematical functions is selected from the series consisting of the following members:
B-spline function, Bézier function, rational Bézier function, non-uniform rational B-spline function.

2. The method according to claim 1 , wherein said point S 1 lies outside said curve {right arrow over (p)}.

3. The method according to claim 1 , wherein said point S 1 lies on or inside said curve {right arrow over (p)}.

4. The method according to claim 3 , wherein said intersection point S 1 lies on an intersection point of at least two axes of symmetry of said curve {right arrow over (p)} or said intersection point S 1 lies at a symmetry point of said curve {right arrow over (p)} or said intersection point S 1 lies on a centre of rotation of said curve {right arrow over (p)}.

5. The method according to claim 1 , wherein said curve {right arrow over (p)}, has one or more kinks.

6. The method according to claim 5 , wherein said curve {right arrow over (p)}, is described at kink points by an arc of a circle with radius eps which merges tangentially into two adjacent curves, eps being a very small positive real number which tends towards 0 (eps<<1, eps→0).

7. The method according to claim 1 , wherein bodies K 1 and K 2 are screw elements.

8. The method according to claim 1 , wherein said cross-sectional profiles are continued helically in an axial direction, the bodies generated in this way being right-handed or left-handed, and a pitch standardized to the distance a lying in a range of 0.1 to 10, and lengths, standardized to the distance a, of bodies K 1 and K 2 lying in a range of 0.1 to 10.

9. The method according to claim 1 , wherein said cross-sectional profiles are segmentally continued linearly in an axial direction, and a length, standardized to the distance a, of the bodies K 1 and K 2 lies in a range of 0.05 to 10.

10. A method for generating screw elements, wherein said, in a first step, generating by a method of claim 1 cross-sectional profiles of bodies which, while rotating codirectionally at the same rotational speed about axes of rotation arranged parallel to one another at a distance a, constantly touch one another at at least one point and, in a second step, introducing plays between the bodies K 1 and K 2 .

11. A computer system for executing a method according to claim 1 .

12. A computer system according to claim 11 , associated with a machine tool for generating calculated bodies.

Assignees

• König Thomas
• Bierdel Michael
• Bayer Ip Gmbh

Inventors

• König Thomas
• Bierdel Michael

Classifications

• B29C48/402

  the screws having intermeshing parts · CPC title

• B29C48/2517

  of intermeshing screws · CPC title

• B29C48/2513

  in the plasticising zone · CPC title

• B29B7/483 Primary

  the other mixing parts being discs perpendicular to the screw axis · CPC title

• B29C48/03

  characterised by the shape of the extruded material at extrusion · CPC title