JPH0771773B2 - How to chamfer gear tooth edges - Google Patents

Description

TECHNICAL FIELD The present invention relates to chamfering a side surface (end surface) of a tooth of a gear, and more particularly to a method for chamfering a side surface of a spur gear.

BACKGROUND OF THE INVENTION It has been well recognized for many years that chamfering the sharp edges of teeth, such as gears, splines, provides the benefits of robustness and ease of engagement. For example, the tedious method of manually chamfering with a file has been overcome by the introduction of a dedicated gear chamfering machine.

Of course, there are many chamfers that could be used to create the desired uniform chamfers on the gear teeth. In some cases, the desired chamfer has been achieved by cold working. More preferably, the chamfering is accomplished by a chamfering disk that utilizes the circular motion of a planar cutting tool. One chamfer related to the present invention is U.S. Pat. No. 3,286,593.
No. Another chamfering machine is called a Sheffield machine. Such a chamfering machine is configured to use a cutting tool (or cutter) that makes a reciprocating arc motion. In such a chamfering machine, a chamfer is formed in each forward stroke of the cutting tool and the gears are set so that during each retraction step the gears direct new parts of the teeth towards the cutter. The present invention is particularly adapted to a chamfering machine of the type in which a tool oscillates in an arc in a plane substantially perpendicular to the side surface of the chamfered tooth. Since the gear teeth have a slightly complicated involute shape and the movement of the cutting tool is a lateral circular movement, the geometry of such a tool is not easily determinable. Therefore, the production of cutting tools for chamfering machines is left to the skilled tool / die manufacturer. Skilled techniques for manufacturing cutting tools are based on the experience and judgment of seniors and self. When making a cutting tool, essentially a "trial and error" procedure is used. That is, the technician relies on his experience to make the first tool. For example, a 45 ° projection of the gear shape may be used because the tangent to the circular motion of the cutting tool is inclined 45 ° to the plane of the tooth tip. The tool manufacturer then mounts the tool on the actual chamfering machine and tests its cutting action on the actual gear. Observe the chamfer formed and if the result is incomplete, iteratively modify the contour of the tool until the chamfer with the desired specifications is obtained.

Precision and high performance machines can have relatively tight specifications regarding chamfer width. For example, a typical gear chamfer with a diameter of about 11 inches (28 cm) and 69 teeth is 0.040
It would be required to have a chamfer width of ± 0.010 inches (0.102 ± 0.025 cm). Typically, the chamfer is set on the gear prior to hardening. When the gear is subsequently finished by further removing material in the gear, a relatively small chamfer remains. Therefore, the position of the chamfer must be precisely set to achieve the desired purpose. Manufacture of tools is a tedious and labor intensive process, even if the technician is skilled. By the time the tool geometry is determined, the actual gear must be manufactured, which leads to production delays. Expensive gear parts must be consumed during the trial and error tool manufacturing process. Also, perfect chamfers are rarely achieved. Even if the quality of chamfering is incomplete to some extent, it must be allowed in consideration of economical efficiency.

DISCLOSURE OF THE INVENTION It is an object of the present invention to form more precise and uniform chamfers in gears and to determine the dimensions of gear chamfering tools directly without the need to experiment with actual gear parts and tools. To provide the means.

According to the invention, the tool dimensions are determined and optimized through a procedure involving the use of the s dimension. The s dimension is a function measured from one or both of the opposite edges of the chamfer formed by the tool as the tool moves along its curved cutting path. The s dimension is equal to the radius of the inscribed circle located on the chamfer and is therefore the minimum distance across the chamfer at the measurement point. Preferably, the s dimension is referenced to both opposite edges of the chamfer.
The s dimension is determined as a pair where the curved path of the cutting edge point of the tool intersects the chamfer edge. In the preferred embodiment of the invention, an iterative optimization process is used to match the s-dimensions obtained with different tool profile shapes to the chamfer width tolerance and the normal or average chamfer width. As a starting point, it is preferable to take the dimension of the tool profile that makes the chamfer width zero and then repeat in the direction of increasing the chamfer width.

By practicing the present invention, a tool that produces a very precisely uniform chamfer is manufactured without trial and error testing or compensation by the tool manufacturer. Not only are the tolerances met, but the desired regular dimensions are essentially achieved.

The above and other objects, features and advantages of the present invention will become more apparent in the following detailed description of the preferred embodiments thereof with reference to the drawings.

BEST MODE FOR CARRYING OUT THE INVENTION The present invention is described for the case of cutting a normal spur gear on a Schufffield model (380 Deburring Machine (Cheffield Company, formerly Dayton, Ohio). However, it will be appreciated that the present invention is applicable to chamfering other types of gears, splines, etc. where the relationship between the tool, tool motion and work piece creates problems similar to those described above.

The following description is given in mathematical description, and the method according to the invention is most easily implemented using a digital computer. Although the iterative optimization is efficiently performed only by a computer, it will be appreciated that the method according to the invention can also be performed manually if it does not require efficiency and highest precision. Once the mathematical description of the present invention is understood, it will also be understood that it involves the use of measurements and parameters not used in conventional empirical and empirical methods.

FIG. 1 shows a spur gear 20 having Cartesian axes x, y and z.
It is shown. The spur gear 20 has side surfaces (or end surfaces) 22 and 23 that intersect the teeth 24. Referring to both FIGS. 1 and 2, each tooth has an involute shape characteristic of its effective profile surface 100, 100 '. The profile surface of each of the teeth has transitioned to the corner surface 102. Adjacent teeth have root surface 1
Connected by 04. Tooth tip 32 of each tooth has a tooth tip surface 106
Exists. The profile surface 100, the corner surface 102, and half of the root surface 104 (sometimes including a portion of the addendum surface 106) are collectively referred to below as the tooth flank 26. The present invention relates to the processing of the chamfered portion 48 of the edge 108 formed by the intersection of the flank and the side surface of the gear. When using the chef field board, flanks of adjacent teeth facing each other 26,
The edges formed on 26 'are chamfered by the movement of a cutting tool (or cutter) 28, as shown in FIGS.

Referring to FIG. 1, the tool performs a cutting motion that describes a circular path 30 to progressively remove material from the flanks of adjacent teeth from tip 32 to root 34. When the cutting operation is completed, the position of the center of rotation of the tool bit changes with respect to the position when the tool is installed in the chamfering machine, so that the cutter returns on a slightly different path 36.

Referring to FIG. 3, the gear 20 is shown mounted to a pocket-shaped fixture 41 attached to the chamfering base 39 so that it can rotate about its centerline 37.
The gear has a tool 28 so that all of its teeth are chamfered.
It rotates by stepping motion that is linked to the motion of. As can be seen in FIG. 3, the movement of the cutting tool is such that the lower side 22 of the gear mounted on the chamfer is chamfered. To chamfer the opposite side 23, the gear is removed and attached to the fixture with side 23 facing the base of the chamfering machine.

The tool 28 is a holder for allowing various movements with respect to the gear.
Held in 38. First, the tool 28 is configured to be movable axially along its longitudinal axis L by an adjusting nut 40. Second, the tool holder 38
Is configured to be movable with respect to the slide 42 in a direction perpendicular to the plane of the drawing in order to position the tool axis on a line along the diameter of the gear wheel 20 (y axis). Third, slide 42
Is configured to be movable by a screw 44 to move the arcuate path 30 away from or closer to the gear.
Fourth, the tool is configured to be able to move in the plane of the paper along a path of rotation by rotation about the pivots 45,46. By adjusting the pivot point, the tool can move the eccentric path 30,
Can exercise along 36. Such eccentric circular motion mechanisms are well known to those skilled in the field of machine tools.

FIGS. 4-8 show some of the terms used to describe the present invention. FIG. 4 is another view showing the relationship between the gear 20 and the cutting tool 28, which is also shown in FIG. A longitudinal axis L is set on the tool 28. The longitudinal axis L is the tool 28 and the gear 20 on the arc path 30 of the tool 28.
It is parallel to the tangent line of the path 30 at the portion where and meet or intersect. A surface perpendicular to the axis L is a vertical surface N. The front face F of the tool 28 is inclined with respect to the vertical face N by an angle α. The shape of the tool 28 when projected onto the vertical plane N of the contour is defined as the "tool profile" described in this specification. The path 30 of the point P (,,) is drawn by a curve of radius ri around the pivot point (, ya, za). Gear 20 has principal axes x, y and z, where x is the direction perpendicular to the plane of the paper of FIG. The tool bit also has axes x, y and z. Here, the axis x of the tool bit is defined to be parallel to the axis x of the gear. The tool axis y (yf and yn) and axis z are tilted with respect to the principal axes y and z.

FIGS. 5 and 6 show views of the gear and the tool bit shown in FIG. 4 in the directions of arrows A and B, respectively. 5 and 6 are intentionally aligned vertically in the drawings to show that the axes y of the gears and tool bits are in the same plane and the axes x are parallel. FIG. 6 shows a shape defined as a "tool profile". A point Pi on the surface of the cutting tool can only cut the material at a position having the same coordinates of the gear, dx. With this promise, it's Frank 26 'first
The position of the point P can be defined on reaching, then as it penetrates the side 22 of the gear.

FIG. 7 shows a chamfer 48 having a width c at the tooth root surfaces 104 and 34 of the gear, which chamfer is in the x-yn coordinate system at coordinates (i, i) (i. = 1,2 ..., n)
It is cut by a cutting tool having a vertical section defined by the set of i. Since the surface F of the cutting tool makes an angle α with the vertical surface N, the point of the surface of the cutting tool has the coordinates (i, i · secα) in the x-yf coordinate system of the surface F.
It is assumed that the chamfered portion 48 formed on the root surface of the adjacent tooth 24 is desired to have the width c as shown in the drawing. Therefore, the point coordinates (i, i, i) on the cutter surface F in the x, y, z coordinate system satisfy the following equation.

i = xi = ii + c * cos? = yi * cos? = i * sec? * cos? i = yi * sin? =-i * sec? * sin? Where β = (? / 2)-?-? i = i i = isecαsin (α + θ) -ccosθ i = -isecαcos (α + θ) Therefore, for the face F of the cutting tool, these equations are used for the side face 22 (here, z = 0 ) And gear flank 26,
Can solve the relationship with 26 '. Since the cutting tool moves by rotation around the axes y = ya and z = za,
The distance ri to the point Pi is expressed by the following equation.

ri = [(ya-yi) ² + (za-zi) ² ] ^1/2 Therefore, the following equation is obtained for the intersection of the point Pi and the side surface 22 of the gear.

xi = xi yi = ya ± (ri ² −za ² ) ^1/2 zi = 0 where the sign of yi is consistent with the physical problem shown in the drawing and avoids inappropriate solutions Like, yi
Is chosen to be closer to zero.

Similarly, when considering the intersection of the face F of the cutting tool with the gear flanks 26, 26 ', for x = xi, If is the coordinates of the points on the teeth of the gear (determined by partial linear interpolation for some data points on the teeth of the consecutive gear), then the flank forms for z> 0. It can be seen that it includes the point. The point Pi on the surface of the cutting tool is Intersect with Frank, where the distance ri to the point Pi is expressed by the following equation.

Similar to the above, the smaller value of zi is selected.

At this point, a set of cutting tool intersections with the flanks and flanks of the gear are defined, and by partial linear interpolation, the facing edges 5 of the chamfers on each of the flanks and flanks are defined.
Two spatial curves are obtained that define 0,52. As a result, it becomes possible to evaluate the parameter indicating the variation of the chamfer width c. For simplification, the intersection 50 for a typical flank is Ui = (xi, yi, 0), and the intersection 52 for a typical flank is Indicated by. Therefore, the distance between Ui and Vj is expressed by the following equation.

A minimum value of dij can be found for j. That is, Is found. Thus ui is the shortest distance across the chamfer surface measured from the side of the gear at (xi, yi, 0).

Similarly, the points along the intersection Vi for Frank The width vi of the chamfered portion measured from is expressed by the following equation.

Considering further, the chamfer width functions (hereinafter referred to as s length or s dimension) u (x) and v (x) are not necessarily the same, and the center extending along the length direction of the chamfered portion. It will be appreciated that the dimensions perpendicular to the axis are not necessarily the same. This is clarified schematically in the example of FIG. The point P on the cutting tool moving on the path 30 'of the cutting tool is the edge of the chamfer of the flank.
52, V to contact the teeth, and finally the side edge 50, U
Comes into contact with the teeth. Both points are located at the same x-direction distance 54, 56 from the y-axis. The s dimension 58, 60 from the facing edge appears to be off. It will also be understood that, as they are inscribed circle radii, the s dimension will be non-parallel for chamfers that are more uneven than shown. Of course, they are physically measurable on a given chamfer because they are referenced to corresponding opposite edges of the chamfer. It is advisable to use them for achieving the object of the present invention, if the object is limited to the chamfer width, particularly the chamfer width near the tips 32 and roots 34 of the gear teeth. If the s dimension is within the desired chamfer tolerance range, then the tool can be satisfactory for that gear. If this is not the case, the tool will be changed until the necessary conditions are met. That is, at least one of the conditional expressions c _min ≤ u (x) ≤ c _max and c _min ≤ v (x) ≤ c _max (where c _min and c _max are defined minimum and maximum chamfer widths, respectively) If not satisfied, the cutter geometry has to be modified.

Several ways to improve the shape of the cutter are possible, depending on the situation. For example, if u (x) and v
If both (x) are greater than c _max for x = xi for some i, then the chamfer width or apparently is too large in xi, the cutter geometry is modified to cut less material. There must be. That is, corresponding
yi is reduced.

A better solution is to treat all yi as variables and treat the problem as one of the optimization problems. That is, yi is selected so that the following function has the minimum value.

here Is. Since f is the sum of squares, f ≧ 0. u
When both (x) and v (x) are within the specified or desired chamfer width tolerances, none of the terms in square brackets are positive, so f is zero.

The most sophisticated procedure is to determine the minimum f by considering all yi as variables and solving an unconstrained minimization problem. However, using a smaller set of data points (eg 50 points), and parametrically fitting this reduced set of points to produce a spline fit to describe the surface F of the cutting tool, It is computationally more efficient to determine the function f corresponding to the set of data points (xi, yi) interpolated to the spline fit, and to modify this reduced set of variables to minimize f .

The process according to the invention for achieving the above fit is
A flowchart suitable for programming a digital computer is shown in FIGS. 9 and 10. Referring to the chart, the starting steps 62-66 include the generation of the first cutting tool that produces a zero s length (and zero chamfer width). Although other starting points based on tool designer experience or other calculations may be used, a zero s-length profile surface is
A particularly convenient starting point. The procedure described here allows its easy determination, and this approach does not require the toolmaker's judgment. Optimization step 68 ~
At 86, in addition to ensuring that the chamfer has a width within a tolerance in the substep of determining the "goodness" f of step 72, the chamfer is smoothed along edges and surfaces to Allows the width to be close to the normal (ie maximum and minimum average) width. Therefore, substantially better tools are produced than those that could be produced by trial and error methods. Incremental iterative steps 74-82
Is repeated for the desired number of points along the vertical profile plane of the cutter. The present inventor has used 50 points and found satisfactory results by repeating the updating of 5 to 10 openings in step 84. However, different values may be used, depending on the available calculation time and the quality of the results obtained. At step 86, the results are output and the tooling and gear chamfering can be performed accordingly. Of course, additional outputs and visual displays other than the output results may be used at various steps in the procedure. Also, if desired, to allow the tool designer to manipulate the steps to allow optimization of a particular area of the tool's profile surface prior to obtaining a complete solution. Means may be provided.

Although the present invention has been described in detail above with respect to specific preferred embodiments, the present invention is not limited to these embodiments, and various embodiments are possible within the scope of the present invention. It will be apparent to those skilled in the art.

[Brief description of drawings]

FIG. 1 is a perspective view of a gear having coordinate axes defined in the description of the present invention. FIG. 2 is a perspective view showing some of the teeth of the gear in FIG. 1 in more detail. FIG. 3 is a simplified view of the gear chamfering disk and a part of the gear, and together with FIG. 1, shows how to chamfer the gear by the reciprocating circular motion of the tool. FIG. 4 is a diagram showing the relationship between the gear and the cutter in FIG. 3 in more detail. 5 and 6 are views showing the relationship between the side surface of the gear and the vertical plane of the cutter, respectively, showing that the y-axis is in the same plane and the x-axis dimension is the same for both. . FIG. 7 is a sectional view of the gear along the yz plane, showing a chamfered portion formed by a cutter at the tooth base. FIG. 8 is a perspective view of a gear showing a chamfered portion and physically showing the s dimension facing each other at one point. 9 and 10 are flow charts showing the steps for manufacturing a tool according to the present invention. 20 …… Gear, 22, 23 …… Gear side, 24 …… Gear tooth, 2
6, 26 ′ …… Gear flank, 28 …… Tool, 30 …… Circular path of tool, 32 …… Tooth tip, 34 …… Root of tooth, 36 …… Tool path, 38 ……
Retainer, 39 …… Chamfer base, 40 …… Adjusting nut, 41…
… Mounting fixture, 42 …… Slide, 44 …… Screw, 45,46 …… Pivot, 48 …… Chamfer, 50,52 …… Chamfer edge, 54,56
…… x distance, 58, 60 …… s dimension, 100, 100 ′ …… Effective profile surface, 102 …… Corner surface, 104 …… Root surface, 106 …… Tooth surface, 1
08: Edge

Claims (1)

[Claims] 1. Substantially xy at each of the gear teeth.
On the edge of the tooth of the gear formed by the intersection of the side of the gear in the plane and the flank of the gear extending substantially perpendicular to it in the z-axis, y
A width that falls within the range between the desired maximum chamfer width and the minimum chamfer width along the length of the edge, using a cutting tool that makes a circular movement about an axis perpendicular to the x-plane. A method of forming a chamfer having dimensions, comprising the steps of selecting a profile of a first tool and a number of points along the length of the chamfer to be formed by the profile of the first tool. Determining the s dimension defined as the distance across the chamfer from one edge of the chamfer to the closest point on the opposite edge, and the desired chamfer at each of the plurality of points. A process of comparing the width and the s dimension and a profile of another tool different from the profile of the tool before that are selected, and the length of the chamfered part to be formed for the selected tool profile. It is within the range between the desired maximum chamfer width and the minimum chamfer width to determine the s dimension at a number of points along the direction and to compare the s dimension with the desired chamfer width s. An iterative process until the dimensioning tool profile (final tool profile) is determined,
A gear tooth edge characterized by including the steps of manufacturing a tool having substantially the profile of the final tool, and chamfering the teeth of the gear using the tool thus manufactured. Chamfer method.