FR2867543A1 - Gear, has gear section parallel to cycloid at distance, where cycloid corresponds to trajectory of point in location related to toothed unit, when trundle rolls around toothed unit - Google Patents

Abstract

The gear has a toothed unit e.g. pinion, with a succession of tooth gaps that are delimited by a gear section (Cp) and that receive bars (B) of a trundle successively. The gear section is provided which is parallel to a cycloid (Cy) at a distance. The cycloid corresponds to the trajectory of a point (AB) in a location related to the toothed unit, when the trundle rolls around the toothed unit.

Description

DESCRIPTION

    The present invention relates to a lantern gear, that is to say a gear of which one of the inter-geared members comprises, as teeth, circular profile bars which are installed side by side with a certain spacing. between them and which, during the meshing process, are received in tooth recesses defined by the other inter-geared member.

  Typically, the bars are cylindrical, their axes are parallel to each other and distributed along a circular line.

  This type of gear, known for a very long time, finds some particular applications, especially when the bars, instead of being rigidly secured to a lantern body, are supported by a bearing. In this case, there can be rolling contact without sliding between the bar and the hollow of the teeth, while the bar rotates around its bearing relative to the body of the lantern. Such a gear is able to operate in the open air.

  From a theoretical point of view, a gearing problem is a problem of conjugate curves that can be analyzed in the following way. A primitive circle centered on the axis of rotation of the organ is rigidly associated with each of the two intermeshing elements. geared and rotating with it, the two circles being in rolling contact without sliding with each other during the meshing process. The curves defining the gear profiles are curves which slide over each other in at least one point of contact when the pitch circles roll without sliding on top of each other.

  In classical gears, involute geometry has become universal. The two intermeshed members then both have teeth whose flanks are defined by involutes of a respective base circle, which has a diameter smaller than the original circle.

  However, in the case of lantern gears, this geometry is not usable since one of the toothed organs has, by definition, teeth whose profile is circular, and not involute circle.

  The object of the present invention is to provide a lantern gear with good continuity of meshing.

  According to the invention, the lantern gear comprising a first and a second member which have a mutual engagement zone and have, around a first and a second axis, at least one of which is at a distance. finished of the meshing zone, a relative movement substantially corresponding to a rolling without sliding of a first and a second primitive circle on one another, in which: the first member is a lantern comprising bars with a circular contour of radius r, arranged at regular intervals along a line of distribution at a distance h from the first pitch circle, which is centered on the first axis and connected to the lantern; - The second member is a toothed member having a succession of tooth recesses which in each plane perpendicular to the second axis are delimited by a gear profile and successively receive the bars of the lantern, is characterized in that the gear profile is a parallel, at a distance r, of a cycloid described by a point of the distribution line in a reference linked to the toothed member during the rolling without sliding.

  In the context of the present invention, the term cycloid is used to designate generally an epicycloid or a hypocycloid, ordinary, elongated or shortened, or a limit of this kind of curves when one or the other of rays tends to infinity.

  Knowing that we call parallel curves two curves of which all the normals are common to these two curves and whose spacing has the same value along all the normals, the idea which is at the base of the invention is the following: - during the process of meshing, two conjugate surfaces have, at their point of contact, a common normal passing through the point of rotation of the two primitive circles; consequently, the conjugation is a property which is preserved when one passes from given conjugate curves to curves which are respectively parallel to them with the same spacing; it turns out that the center of the circular profile of the bars of radius r is a curve parallel to this circular profile, at a distance r towards the inside of the circle; - if each bar was replaced by its center, in each plane perpendicular to the axis of rotation of the lantern, this point would always be the point of contact during the meshing, in other words the meshing contact points become immobile compared to the lantern; in a reference frame linked to the other toothed member, such a contact point describes a cycloid when the two primitive circles roll on one another, and this cycloid is therefore the conjugate curve of the point; it follows that the conjugate curve of the circle defining the periphery of a bar is a parallel, at a distance r, from the aforesaid cycloid.

  The tooth cavity profiles according to the invention allow embodiments where the lantern and the second toothed member have primitive circles of finite radius external to each other, or one being inside the other.

  When the toothed organ and the lantern are one inside the other, the cycloid is a hypocycloid. In the opposite case, the cycloid is an epicycloid.

  The hollow profile of the teeth according to the invention is also compatible with the embodiments where one of the primitive circle centers is rejected to infinity, ie the case where one or the other of the lantern and toothed organ becomes a rack.

  In the case where the lantern becomes a rack, it can be made in the form of a chain, the bars of the lantern being materialized by the axes of links, preferably surrounded by a cylindrical roller 10 freely rotating around these axes.

  Other features and advantages of the invention will emerge from the description below, relating to non-limiting examples.

  In the accompanying drawings: FIGS. 1 and 2 show, in two different relative positions, a first embodiment of a gear according to the invention, the primitive circles having finite radii and being external to each other, in the case where the line of distribution of the centers of the bars is inside the primitive circle; - Figures 3 and 4 are views similar to Figures 1 and 2, but in a case where the distribution line surrounds the pitch circle.

  FIG. 5 is a diagram illustrating the determination of the profile of a hollow of teeth in the case where the line of distribution of the centers of the bars of the lantern is inside its pitch circle; Figure 6 is a view similar to Figure 5 but in the case where the center line is outside the pitch circle; - Figures 7 to 10 show in four different relative positions, a second embodiment of the case of Figure 5, wherein the lantern is a rack; - Figures 11 to 14 show, in four different relative positions, a third embodiment of the case of Figure 5, wherein the toothed member is a rack; - Figures 15 to 18 show in four different relative positions, a second embodiment of the case of Figure 6, wherein the lantern is a rack; - Figures 19 to 22 show, in four different relative positions, a third embodiment of the case of Figure 6, wherein the toothed member is a rack; and - Figure 23 is a view of a fourth embodiment of the case of Figure 6, forming a captive gear.

  In the example shown in Figures 1 and 2, the lantern L meshes in a meshing zone 1, with a toothed member D, which in this example is a pinion.

  During meshing, the lantern is rotated about an axis AL while the toothed member D is rotated about an axis AD.

  The axes AL and AD are parallel to each other and perpendicular to the plane of Figures 1 and 2.

  The lantern L is represented only by its bars B which are cylindrical with a circular contour around axes of bars AB which are located at equal angular distance around the axis AL of the lantern L and are parallel thereto. The AB axes are located on a distribution line R constituted by a circle centered on the axis AL of the lantern.

  In a manner not shown, the bars B are brought to at least one of their axial ends by a lantern body which may for example take the form of a circular plate.

  The bars B can be massive as shown, or tubular, and be rigidly connected to the lantern body. Preferably, however, the bars comprise a tubular outer body which journalled through a bearing on a central core attached to the lantern body. The bearing between each tubular roll and its core can be lubricated and sealed, allowing the gear of Figure 1 to operate in a poorly protected environment, and typically without being enclosed in a housing.

  The toothed element D has tooth cavities C which are angularly distributed about the axis AD. The transmission ratio between the lantern L and the toothed member D is equal to the ratio between the number of bars B and the number of recesses C, that is, in the example, 7:16.

  The simultaneous rotation movement of the lantern L and the toothed member D is the same as if it were created by rolling without sliding, one on the other, two primitive circles PrL and PrD, namely a circle primitive PrL rigidly connected to the lantern L and centered on the axis AL of the lantern L, and a pitch circle PrD rigidly connected to the toothed member D and centered on the axis AD of the toothed member D. These two circles have a running point PP, located on the line of the centers X, where are the centers of the primitive circles.

  The radii of the primitive circles PrL and PrD are proportional, respectively, to the number of bars B and to the number of tooth cavities C. In the example of Figs. 1 and 2, the pitch circle PrL of the lantern has a slightly larger radius. large than the line R for distribution of the axes AB of the bars B. The cavities C have a vase shape whose angular opening around the axis AD increases steadily when one moves away from the axis AD FIGS. 1 and 2 also show the action curve Ac which is the geometrical locus of each point of contact between a bar B and a tooth cavity C in the plane of the primitive circles. The curve Ac has a loop shape with a double point which coincides with the running point PP. The example of Figures 3 and 4 will be described only for its differences from that of Figures 1 and 2.

  In the example of FIGS. 3 and 4, the distribution line R of the bars B is now located outside the pitch circle of the lantern PrL. For reasons which will be explained in detail below, the tooth cavities C of the toothed member D then assume a configuration which, instead of flaring out permanently from the inside to the outside of the primitive circle PrD, has a neck 2 defined between two angular points 3 located on the opposite sides of the hollow C. the points 3 are located at a certain radial distance beyond the pitch circle PrD.Radially beyond this neck 2, the angular width of the Hollow C increases permanently when moving away from the AD axis.

  Moreover, the action curve Ac no longer has a double point and is subdivided into three segments (see FIG. 4), namely a central segment 4 intersecting the line of the centers X and two marginal segments 6 located symmetrically on the left and right. other of the X axis and radially outside the central segment 4 relative to the axis AD. The marginal segments 6 are separated from each other and separated from the central segment 4.

  The diagram of FIG. 5 is relative to a configuration of the type of FIGS. 1 and 2, that is to say with the primitive circle PrL of the lantern located outside the distribution line R. It is assumed in this figure that an axis of bars AB is on the line of the centers X. If the bar was thinned until its radius is zero, in other words until it is reduced to its axis AB, the line of The action would be a segment of the distribution line R and the conjugate profile linked to the toothed organ would be the cycloid Cy corresponding to the trajectory of the point AB in a reference frame linked to the toothed organ when the lantern rolls around the organ toothed. It is therefore an epicycloid (cycloid generated by rotation of a circle outside another circle), shortened by the distance h (in other words the cycloid is that described by a point situated at a distance h inside the rolling circle). The distance h corresponds to the difference between the radius of the primitive circle PrL and the radius of the distribution line R. As in fact the bar is not a point AB of zero radius but, in each plane, a circle of radius r around this point, in other words a parallel curve at a distance r from this point, the conjugate curve is a parallel at the same distance r, to the cycloid Cy This parallel curve is designated by Cp in FIG.

  As can be understood by observing FIGS. 1 and 2, each parallel curve Cp is extended on either side of its point of greatest depth V until it forms an intersection T with the parallel curve intended to cooperate. with a bar next to the lantern. Each intersection T forms a tooth vertex of the toothed member D. The action curve Ac is the displacement conchoid r and the center PP, of the action curve of the point AB, that is to say the circle R The conchoid of a curve is the transform by which each point is displaced by a given distance, in this case r, along the straight line connecting this point to the center, in this case PP, of the transformation.

  The curve Cy has two points of inversion of curvature (points of inflection) situated on either side of its summit, which coincides with the axis AB of the roll in FIG.

  When the distance h becomes very small, the presence of these curvature inversion points gives rise to a singularity on the parallel curve Cie.

  For this reason when the distribution circle R is inside the primitive circle PrL, we respect the relation: 30 h> p2 + r2 (2P 1) 3 _ 2 + q1q p2 P in which: p = radius of the first primitive circle q = radius of the second primitive circle, counted negative when the primitive circles are external to each other, and positive when one of the primitive circles is inside the other.

  The diagram of FIG. 6, which will be described only for its differences with that of FIG. 5, concerns a configuration such as that of FIGS. 3 and 4, ie with the distribution circle R outside the associated primitive circle PrL.

  In this case, the cycloid Cy is elongated by the distance h. The cycloid no longer has inflection points but forms a loop surrounding the running point PP. In this case, it is impossible to find a profile Cp which would keep a permanent contact with the bar B. The solution is to draw the two parallel curves at + r and -r of the cycloid Cy, and to pass from a parallel curve at the other at the two points of intersection 7 of these parallel curves, so as to choose the three parallel curve segments 8, 9, 11 which are the furthest possible from the cycloid Cy. The remaining two cycloid segments 12 are not used at all. Due to the construction, it is certain that the distance between the two points 7 which define between them the neck 2 and corresponding to the angular points 3 of Figure 3, is always greater than the diameter 2r of the bar B. In operation, the bar B circulates along a radially outer segment such as 8 to the angular point 7, reaches after a short phase of contact break the other angular point 7, then travels through the central segment 9 until it returns to the first angular point 7. At this stage, there is a second contact break, the bar comes into contact with the second angular point 7 and ends its stroke along the second radially outer segment 11. The two contact breaks are illustrated by the constitution in three parts of the action line Ac, described with reference to Figures 3 and 4.

  FIGS. 7 to 10 illustrate the application of the invention to the production of a first type of rack gear, in which the rack corresponds to the lantern L. More particularly, in the example shown, the distribution line R bars B is situated at a distance h from the running point PP towards the outside of the pitch circle PrD of the toothed member D. Thus, we are in a case corresponding to FIG. 5, but where the center of the primitive circle PrL would be rejected to infinity, 10 this circle becoming the Y axis perpendicularly intersecting the X axis at the running point PP. The tooth cavities C thus flare out permanently when moving away from the axis AD from the point of greatest depth V. Assuming that the toothed member D rotates clockwise as illustrated by the arrow 12 in Figure 7, we can follow the course of the meshing by looking successively at Figures 7, 8, 9 and 10 first for the bottom bar, then for the middle one, then finally for the one located the above. The number of driving contacts is always at least equal to one and sometimes equal to two, so that the continuity of the meshing is ensured.

  The example of Figures 11 to 14 will be described only for its differences from the previous.

  In this example, it is the toothed member that is made in the form of a rack, therefore with a pitch circle of infinite radius and constituted by the Y axis. Here again, the distribution line R of the bars B is located inside the primitive circle PrL of the lantern. The troughs of the teeth thus flare out permanently from their bottom V towards their opening.

  The example of Figures 15 to 18 will be described for its differences from that of Figures 7 to 10.

  In this example, the distance h between the rolling point PP and the distribution line R of the centers of the bars is located inside the pitch circle PrD of the toothed member. We are therefore in the case illustrated in Figure 6, and the toothed recesses C of the toothed member D have a neck 2 between two angular points 3.

  The example of Figures 19 to 22 will be described only for its differences from that of Figures 11 to 14.

  The distribution circle R of the bars D is situated radially outside the pitch circle PrL of the lantern L. Consequently, the toothed gear D has toothed cavities having a neck 2 between two angular points 3.

  The example of Figure 23 will only be described for its differences from the previous one.

  In this example, the distance h is chosen large with respect in particular to the diameter 2r of the bars B, and the number of bars B is also chosen relatively large. As a result, there are permanently a large number of bars B (6 bars B in the example) which are in meshing state.

  Given the undercut shape of the hollows C between their point V of greater depth and their neck 2, and the number of bars B which are in contact with various regions around the area behind the neck 2, the lantern L is trapped in the toothed member D, while being perfectly positioned by its contacts with the recesses C as well with regard to the position of its geometric axis AL as regards its angular position about this axis. The lantern L can be made without rotation bearing around the axis AL.

  Of course, the invention is not limited to the examples described and shown.

  The invention is applicable in the case where the lantern engages inside the toothed member made in the form of a ring, and also in the case where the toothed member meshes with the interior of the lantern. In all these configurations, the case where the distribution line R is outside the primitive circle PrL and the case where the repair line R is inside the primitive circle PrL can be made as desired.

  In all these cases, the cycloid such that Cy becomes an elongated hypocycloid when R is outside PrL, shortened in the opposite case.

  The example of FIG. 23, with captive lantern, is not limited to the case where the toothed member D is a rack. The same effect can be obtained with a toothed member D of relatively large diameter compared to that of the lantern L, the toothed member D having a center located outside the pitch circle PrL of the lantern, or in the where the organ D is a crown surrounding the lantern.

Claims (9)

  A lantern gear comprising a first and a second member (L, D) which have a mutual engagement zone (1) and have around a first (AL) and a second (AD) axis , at least one of which is at finite distance from the meshing zone, a relative movement corresponding to a non-slip bearing of first and second primitive circles (PrL, PrD) one over the other , in which: - the first member is a lantern (L) having bars (B) with a circular contour of radius r, arranged at regular intervals along a distribution line (R) located at a distance h from the first circle primitive, which is centered on the first axis (AL) and linked to the lantern; - The second member is a toothed member (D) having a succession of tooth cavities (C) which in each plane perpendicular to the second axis (AD) are delimited by a gear profile (Cp) and successively receive the bars (B). ) of the lantern (L), characterized in that the gear profile (Cp) is a parallel, at a distance r, of a cycloid (Cy) described by a point (AB) of the distribution line (R) in a reference linked to the toothed member (D) during rolling without sliding.   2. Gear according to claim 1, characterized in that the second member (D) is a rack.   3. Gear according to claim 1, characterized in that the first member (L) is a rack.   4. Gear according to claim 1, characterized in that.   the second primitive circle (PrD) is outside the first primitive circle (PrL).   the distribution line (R) is inside the first primitive circle (PrL); the cycloid (Cy) is shortened by the distance h. A gear according to claim 1, characterized in that - the second pitch circle (PrD) is within the first pitch circle (PrL); the distribution line (R) is inside the first primitive circle (PrL); the cycloid (Cy) is shortened by the distance h. 6. Gear according to claim 4 or 5 characterized in that it substantially satisfies the relation 2 + r2 (2p q) 3 p -p 2 + q (qp) 2 in which p = radius of the first pitch circle (PrL) q = radius of the second primitive circle (PrD), counted negative when the primitive circles are external to each other, and positive when one of the primitive circles is inside the other.   7. Gear according to one of claims 1 to 3, characterized in that: - the second pitch circle (PrD) is outside the first pitch circle (PrL); - the distribution line (R) is outside the first primitive circle (PrL); the cycloid (Cy) is extended by the distance h. the parallel (Cp) being formed of a combination of segments (8, 9, 11) of the two parallels to: Er, which are as far as possible from the cycloid. h> \   8. Gear according to claim 1, characterized in that.   the second primitive circle (PrD) is inside the first primitive circle (PrL); - the distribution line (R) is outside the first primitive circle; the cycloid is elongated by the distance h, the parallel being formed of a combination of segments (8, 9, 11) of the two parallel lines at r, which are as far as possible from the cycloid.   9. Gear according to claim 7, characterized in that the value of the distance h and the number of bars (B) in simultaneous meshing state are chosen to be large enough for the lantern (L) to be trapped in the toothed member. (D).