U.S. patent application number 11/543611 was filed with the patent office on 2008-04-10 for manufacturing straight bevel gears.
Invention is credited to Earl D. Ervay, Uwe Gaiser, Theodore J. Krenzer, Hermann J. Stadtfeld.
Application Number | 20080085166 11/543611 |
Document ID | / |
Family ID | 37729876 |
Filed Date | 2008-04-10 |
United States Patent
Application |
20080085166 |
Kind Code |
A1 |
Stadtfeld; Hermann J. ; et
al. |
April 10, 2008 |
MANUFACTURING STRAIGHT BEVEL GEARS
Abstract
A method and tool arrangement for producing straight bevel gears
and the like on a multi-axis computer controlled machine wherein a
single tool is utilized in the machining process.
Inventors: |
Stadtfeld; Hermann J.;
(Rochester, NY) ; Gaiser; Uwe; (Ostfildern,
DE) ; Ervay; Earl D.; (Fairport, NY) ;
Krenzer; Theodore J.; (West Rush, NY) |
Correspondence
Address: |
THE GLEASON WORKS
1000 UNIVERSITY AVENUE, P O BOX 22970
ROCHESTER
NY
146922970
US
|
Family ID: |
37729876 |
Appl. No.: |
11/543611 |
Filed: |
October 4, 2006 |
Current U.S.
Class: |
409/2 ; 409/50;
409/51; 409/55; 700/194 |
Current CPC
Class: |
Y10T 409/10795 20150115;
Y10S 451/90 20130101; B23F 9/08 20130101; B23F 5/207 20130101; Y10T
409/100159 20150115; Y10T 409/108586 20150115; Y10T 409/107791
20150115; B23F 9/02 20130101; B23F 23/006 20130101 |
Class at
Publication: |
409/2 ; 409/51;
409/50; 409/55; 700/194 |
International
Class: |
B23F 17/00 20060101
B23F017/00; B23F 5/20 20060101 B23F005/20 |
Claims
1. A method of machining bevel gears on a multi-axis free-form gear
generating machine, said method comprising: providing axes settings
from a first machine comprising first and second tools each having
stock removing surfaces, said first and second tool each being
positioned in an inclined manner in said first machine whereby upon
rotation during machining an interlocking arrangement of the stock
removing surfaces of the first and second tools is formed to
machine a tooth slot, transforming axes settings of the first
inclined tool of said first machine to axes settings of a basic
gear generating machine, transforming said axes settings of said
basic gear generating machine to the axes settings of said
multi-axis free-form gear generating machine, machining a first
portion of a tooth slot in a workpiece on said multi-axis free-form
machine, said machining being carried out with a tool having the
form of one of said first and second tools.
2. The method of claim 1 further comprising: transforming axes
settings of said second inclined tool of said first machine to axes
settings of a basic gear generating machine, transforming said axes
settings of said basic gear generating machine to the axes settings
of said multi-axis free-form gear generating machine, machining a
remaining portion of said tooth slot in a workpiece, said machining
of said remaining portion being carried out with said tool having
the form of one of said first and second tools.
3. The method of claim 2 wherein said first portion of all tooth
slots in said workpiece are machined followed by machining of said
remaining portion of all tooth slots of said workpiece.
4. The method of claim 1 wherein said tool and said workpiece are
moved relative to one another in a manner wherein said tool is fed
into said workpiece along a vector feed path.
5. The method of claim 1 wherein said tool having the form of one
of said first and second tools is a cutting tool.
6. The method of claim 1 wherein said tool having the form of one
of said first and second tools is a grinding wheel.
Description
[0001] This application claims the benefit of U.S. Provisional
Patent Application No. 60/723,396 filed Oct. 4, 2005, the entire
disclosure of which is hereby incorporated by reference.
FIELD OF THE INVENTION
[0002] The present invention is directed to the manufacture of
bevel gears and in particular, the manufacture of straight bevel
gears.
BACKGROUND OF THE INVENTION
[0003] It is known to produce straight bevel gears, as well as skew
bevel gears, face couplings and splined parts, by providing a pair
of inclined rotary cutting tools whose rotating cutting blades
effectively interlock to simultaneously cut the same tooth space on
a workpiece. Examples of this type of machining can be seen, for
example, in U.S. Pat. No. 2,586,451 to Wildhaber; U.S. Pat. Nos.
2,567,273 and 2,775,921 to Carlsen; U.S. Pat. No. 2,947,062 to
Spear or in the company brochure "Number 102 Straight Bevel
Coniflex.RTM. Generator" published by The Gleason Works.
[0004] Straight bevel gears may be formed by a non-generating
process where the inclined tools are plunged into the workpiece to
form a tooth slot with the profile surface of the tooth being of
the same form as that of the blade cutting edge. Alternatively,
tooth surfaces may be generated wherein the inclined tools are
carried on a machine cradle which rolls the tools together with the
workpiece to form a generated profile surface on the workpiece. In
either instance, the tools may also include cutting edges that are
disposed at a slight angle (e.g. 3.degree.) to the plane of cutter
rotation. Such an angled cutting edge, in conjunction with the
inclination of the tools, removes more material at the ends of a
tooth slot thereby resulting in lengthwise curvature of the tooth
surface (i.e. lengthwise ease-off) for tooth bearing
localization.
[0005] It is also known from U.S. Pat. No. 2,342,129 to Elbertz to
provide a machine and process for cutting straight bevel gears
wherein a single tool is utilized to cut a first portion of a tooth
slot followed by a 180.degree. repositioning of the tool or
workpiece and subsequently utilizing the tool to cut the remainder
of the tooth slot. The path of the tool relative to the workpiece
is controlled by a master surface and guides. Lengthwise crowning
is not possible with the process of Elbertz given a lack of tool
inclination and the cutter would cut shallow at the tooth ends
thereby leaving extra metal at the tooth ends. Also with Elbertz,
repositioning a work head or tool head by 180.degree. is time
consuming and lends itself to machining inaccuracies due to
shifting the large mass of a work head or tool head over a
considerable travel distance in order to machine the entire tooth
slot.
SUMMARY OF THE INVENTION
[0006] The present invention is directed to producing straight
bevel gears and the like on a multi-axis computer controlled
machine wherein a single tool is utilized in the machining
process.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] FIG. 1 shows the interlocking arrangement of a pair of
inclined cutters cutting a tooth slot in a workpiece.
[0008] FIG. 2 is an example of a machine for carrying out the
present inventive method.
[0009] FIG. 3 illustrates a basic bevel gear generating
machine.
[0010] FIG. 4 illustrates the conversion of the upper cutter of an
interlocking cutter arrangement from the summary items of a
mechanical straight bevel generating machine into basic machine
settings.
[0011] FIG. 5 illustrates mounting a cutter disc in a reversed
manner.
[0012] FIG. 6 is a comparison of the generating roll range for a
mechanical machine and a free-form machine.
[0013] FIG. 7 illustrates the set over rotation between the upper
cutting of a tooth flank and the lower cutting of a tooth
flank.
[0014] FIG. 8 shows a vector feed approach for engaging the
workpiece and cutter.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
[0015] The details of the present invention will now be discussed
with reference to the accompanying drawings which represent the
invention by way of example only. In the drawings, like components
will be referred to by the same reference numbers. Although the
preferred embodiments will be discussed with reference to straight
bevel gears, the present invention is not limited thereto but is
intended to include similar types of toothed members, such as, for
example, skew bevel gears, face couplings and splined shafts.
[0016] FIG. 1 illustrates the prior art arrangement of a pair of
inclined rotary disc cutters 2, 4 (commonly referred to and upper
and lower cutters) having cutting blades 6 for cutting a tooth slot
in a workpiece 8. Cutter 2 is rotatable about axis 12 and cutter 4
is rotatable about axis 10. In a generating process on a
conventional mechanical cradle-style machine, the inclined cutters
2, 4 are usually fed into the workpiece to a predetermined depth
and a generating roll of the machine cradle (not shown) is
commenced in a synchronized manner with rotation of the workpiece 8
to generate tooth profile surfaces 14, 16.
[0017] The invention contemplates cutting straight bevel gears on
any of the so-called 6-axis CNC gear manufacturing machines
(commonly referred to as "free-form" machines) such as, for
example, those machines described in U.S. Pat. Nos. 6,712,566;
4,981,402 or U.S. Pat. No. 5,961,260. FIG. 2 shows a machine 20 of
the type disclosed in U.S. Pat. No. 6,712,566, the disclosure of
which is hereby incorporated by reference. While this type of
machine has heretofore been disclosed as producing spiral bevel and
hypoid gears utilizing face milling or hobbing type cutters wherein
cutting blades project from the front surface of a cutter head, the
inventors have now discovered that a single cutting disc, with
radially extending cutting blades, such as cutter 2 or 4 in FIG. 1,
can be positioned on machines such as that of FIG. 2 and
manipulated in such a manner that straight bevel gears can be
produced.
[0018] The machine 20 of FIG. 2 will now be described. For ease in
viewing the various machine components, FIG. 2 illustrates the
inventive machine without doors and exterior sheet metal. The
machine 20 comprises a single stationary column 24 preferably a
monolithic structure such as cast iron or mineral cast but may be
assembled from other elements such as metal plates (e.g. steel or
cast iron) or individual frame elements such as corner posts and
support elements. Column 24 comprises first side 26 and second side
28, being oriented at a desired angle, preferably perpendicular, to
one another. Each of the first and second sides comprises a width
and a height (as viewed in FIG. 2). Alternatively, monolithic
column 24 may comprise a form having non-planar sides such as, for
example, a generally cylindrical column.
[0019] First side 26 includes first spindle 30 rotatable about axis
Q and is preferably driven by a direct drive motor 32, preferably
liquid-cooled, and preferably mounted behind front and rear spindle
bearings (not shown). Spindle 30 is pivotably secured to a spindle
support 31 which, along with spindle 30, is movable in direction Z
along the width of first side 26 on ways 34 attached to column 24.
Movement of spindle 30 in direction Z is provided by motor 36
through a direct-coupled ballscrew (not shown) or by direct
drive.
[0020] A cutting or grinding tool 38 (cutting tool is shown) is
releasably mounted to spindle 30 by mounting equipment 39. The
cutting tool 38 is a single tool and is preferably of the type as
shown by cutter 2 or 4 of FIG. 1 comprising a plurality of cutting
blades projecting radially (with respect to the rotational axis of
the tool) from the periphery of the tool body. FIG. 7 illustrates a
cutting blade 80 comprising cutting edge 82, front surface 84,
clearance edge 86, clearance side surface 88, tip 90 and back
surface 92. FIG. 8 is a back view of FIG. 7 and shows back surface
92, tip 90, cutting edge 82 and cutting side surface 94. The
cutting blades of the tool 38 also preferably include a cutting
edge that is disposed at a slight angle (e.g. 3.degree.-4.degree.)
to the plane of cutter rotation thus giving the cutter a slight
dish shape. This angle is referred to as a "dish angle" and is
illustrated by D in FIG. 8.
[0021] As stated above, first spindle 30 is attached to spindle
support 31 such that any pivoting of the spindle, and hence the
tool 38, may occur about pivot axis F. Spindle bracket 33 is
pivotally attached to support 31 via at least one, and preferably
two, bearing connections 40 and 42, upper bearing connection 40 and
lower bearing connection 42. Pivoting of spindle 30 is effected by
motor 44 and direct-coupled ballscrew 46, or by direct drive,
acting through sleeve portion 48 of yolk 50. Yolk 50 is pivotally
attached to spindle 30 preferably at an upper connection 52 and a
lower connection 54 such that yolk 50 may angularly move relative
to spindle 30 about axis V. Advancing of ballscrew 46, and hence
yolk 50, effectively pushes drive motor 32 angularly away from
column 24 thereby causing a pivot motion about axis F to angularly
move the tool 38 toward the machine column 24. Of course,
retracting ballscrew 46 has the opposite effect. Alternatively, to
effect pivoting of spindle 30, a slide movable on at least one
guideway oriented in the Z direction and positioned on spindle
support 31 may be connected to spindle 30 or motor 42 via a linkage
mechanism. Movement of the slide on the guideway effects pivoting
of spindle 30 about axis F. A further alternative is to include a
motor at one or both of bearing connections 42 and 43 to effect
pivoting of spindle 30.
[0022] Second side 28 includes second spindle 60 which is rotatable
about axis N and is preferably driven by a direct drive motor 62,
preferably liquid-cooled, and preferably mounted behind front and
rear spindle bearings (not shown). Spindle 60 is movable in
direction X along the width of second side 28 on ways 64 attached
to slide 66. Movement of spindle 60 in direction X is provided by
motor 68 through a direct-coupled ballscrew 69 or by direct drive.
Preferably, a workpiece (a pinion 70 in FIG. 2 or a ring gear) is
releasably mounted to spindle 60 by suitable workholding equipment
61 as is known in the art. Spindle 60 is also movable in direction
Y along the height of second side 28 since slide 66 is movable in
the Y direction via ways 72 with movement being provided by motor
74 through a direct-coupled ballscrew 75 or by direct drive.
Directions X, Y and Z are preferably mutually perpendicular with
respect to one another although one or more may be inclined with
respect to its perpendicular orientation. For purposes of
illustration, in all Figures, the Y direction is vertical.
[0023] Movement of first spindle 30 in direction Z, second spindle
60 in direction X, second spindle 60 via slide 66 in direction Y,
pivoting of first spindle 30 about axis F, as well as first spindle
30 rotation and second spindle 60 rotation, is imparted by the
separate drive motors 36, 68, 74, 44, 32 and 62 respectively. The
above-named components are capable of independent movement with
respect to one another or may move simultaneously with one another.
Each of the respective motors is preferably associated a feedback
device such as a linear or rotary encoder, such as pivot axis
encoder 43 (FIG. 2), as part of a CNC system which governs the
operation of the drive motors in accordance with instructions input
to a computer controller (i.e. CNC) such as the Fanuc model 160i or
Siemens model 840D (not shown).
[0024] The machine of the present invention as illustrated by the
embodiments is guided by the controller which preferably
continuously issues positioning and/or velocity commands to the
various drive motors. A set of formulas may be developed for the
configuration of the machine of FIG. 2. However, it is preferable
to use the same input parameters as a conventional mechanical
cradle-style gear generating machine (the "basic" machine as seen
in FIG. 3) for other machines having a different number and/or
configuration of axes. In other words, the positions of the tool
and workpiece axes in the coordinate system of a conventional
mechanical cradle-style bevel gear generating machine are
transformed into the alternative coordinate system of the
multi-axis machine, such as the machine of FIG. 2. Examples of this
type of transformation can be found in previously mentioned and
commonly assigned U.S. Pat. No. 6,712,566 or in commonly assigned
U.S. Pat. No. 4,981,402 the disclosure of which is hereby
incorporated by reference.
[0025] FIG. 3 illustrates a conventional mechanical cradle-style
bevel gear generating machine 160 for producing bevel gears. The
machine generally comprises a machine frame 162, work support
mechanism 164 and a cradle support 166 comprising a cradle
mechanism 168. Traditionally, conventional mechanical cradle-style
bevel gear generating machines are usually equipped with a series
of linear and angular scales (i.e. settings) which assist the
operator in accurately locating the various machine components in
their proper positions. The following is a description of settings
found on a tilt-equipped conventional mechanical cradle-style bevel
gear generating machine such as the machine shown in FIG. 3: [0026]
Eccentric Angle 170 controls the distance between the cradle axis,
A.sub.CR, and the tool axis, T, [0027] Tool Spindle Rotation Angle
172 controls the angle between the cradle axis and the tool axis,
commonly called the tilt angle, * Swivel Angle 174 controls the
orientation of the tool axis relative to a fixed reference on the
cradle 188, [0028] Cradle Angle 176 positions the tool 178 at some
angular position about the cradle axis, [0029] Root Angle 180
orients the work support 164 relative to the cradle axis, [0030]
Sliding Base 182 is a linear dimension which regulates the depth of
tool engagement with the workpiece, [0031] Head Setting 184 is a
linear adjustment of the work support 164 along the workpiece axis,
W, and, [0032] Work Offset 186 controls the offset of the workpiece
axis relative to the cradle axis.
[0033] A final setting, ratio-of-roll, governs the relative
rotational motion between the cradle 168 and workpiece 188. It
should be noted that some of the above machine settings must be
calculated taking into account the following workpiece and tooling
design specifications: [0034] the mounting distance of the blank
workpiece (symbol--M.sub.d), [0035] the overall length of the work
holding equipment (symbol--A.sub.b), and, [0036] the overall height
of the tool (symbol--h).
[0037] The inventors have discovered that straight bevel gears may
be produced on a multi-axis gear generating machine, such as in
FIG. 2, by utilizing a single cutting disc (e.g. either cutter 2 or
4 of FIG. 1), in contrast to the inclined pair of interlocking
cutting discs as seen in the previously mentioned prior art. The
single disc type cutting tool is positioned relative to a workpiece
to cut a first portion of a tooth slot. The tool and workpiece are
then repositioned with respect to one another and the same tool is
utilized to cut the remaining portion of the tooth slot.
[0038] In the present invention, since the conventional mechanical
style straight bevel gear generating machines comprise two skewed
cutter axes, the inventive cutting cycle is preferably split into a
two-cut cycle. Initially, a first transformation is made from the
machine axes settings of one of the skewed cutters of the
conventional mechanical style straight bevel gear generating
machine (the mechanical machine "summary") to the axes settings of
a theoretical cradle-style bevel gear generating machine known as a
"basic" machine (FIG. 3). Such basic settings are then transformed
to the axes arrangement of the multi-axis machine (as discussed in
U.S. Pat. No. 6,712,566 or U.S. Pat. No. 4,981,402 above) for
cutting a first portion of a tooth slot of a straight bevel gear. A
second series of transformations, based on the other of the skewed
axis cutters of the mechanical machine, is similarly made to the
multi-axis machine for cutting the remaining portion of the tooth
slot of the straight bevel gear.
[0039] Straight bevel gear cutting summaries of processes that use
interlocking cutters contain the following gear geometry relevant
settings. The settings of Group 1 are initially identical for the
upper and lower cutters but may be changed in the course of contact
optimizations on the mechanical machine. The settings of Group 2
are always identical for the upper and lower cutters in the
mechanical machine. In the free-form machines, all settings of
Group 1 and Group 2 may be changed in order to optimize a pinion or
ring gear.
[0040] Group 1 [0041] Space Angle [0042] Cutter Offset [0043]
Cutter Cone Distance [0044] Cutter Swing Angle
[0045] Group 2 [0046] Cradle Test Roll [0047] Work Test Roll [0048]
Start Roll Position [0049] End Roll Position [0050] Machine Root
Angle [0051] Sliding Base
[0052] For the correct positioning of the cutter in the mechanical
machine, the tool related dimensions of Group 3 are required:
[0053] Group 3 [0054] Actual Cutter Diameter [0055] Cutter
Reference Height
[0056] In order to convert a summary of a mechanical machine into
basic settings, the machine constants of Group 4 are additionally
required:
[0057] Group 4 [0058] Cutter Tilt Angle [0059] Swing Axis Constant
[0060] Cutter Gage Reference Radius
[0061] FIG. 4 illustrates the conversion of the upper cutter of an
interlocking cutter arrangement from the summary items of a
mechanical straight bevel generating machine into basic machine
settings. With reference to FIG. 4 and the following equations, the
conversion from the conventional mechanical style straight bevel
gear generating machine (upper cutter) to the basic bevel gear
generating machine will be described. The analog approach has to be
performed for the lower cutter, which results in different basic
settings. The portions of each tooth slot (flanks 1) cut with the
free-form machine at an upper position are cut with the basic
settings resulting from FIG. 4. The portions of each tooth slot
(flanks 2) cut with the free-form machine at a lower position are
cut with the basic settings resulting from the analog conversion of
the summary items.
[0062] The initial vector to the center of the workpiece:
R .fwdarw. m 1 = { 0 0 A C } i where A C = cutter cone distance . (
1 ) ##EQU00001##
[0063] Adding cutter offset:
R .fwdarw. m 2 = R .fwdarw. m 1 + { E T 0 0 } where E T = cutter
offset . ( 2 ) ##EQU00002##
[0064] Rotating about the space angle:
R .fwdarw. m 3 = ( cos .theta. S 0 sin .theta. S 0 1 0 - sin
.theta. S 0 cos .theta. S ) R .fwdarw. m 2 where .theta. S = space
angle ( 3 ) ##EQU00003##
[0065] Adding the sliding base position:
R .fwdarw. m 4 = R .fwdarw. m 3 + { 0 X b 0 } where X b = sliding
base ( 4 ) ##EQU00004##
[0066] The initial cutter radius vector:
R .fwdarw. W 0 = { 0 R CP 0 } where R CP = cutter radius ( 5 )
##EQU00005##
[0067] Rotating about the cutter tilt:
R .fwdarw. W 1 = ( cos .phi. X - sin .phi. X 0 sin .phi. X cos
.phi. X 0 0 0 1 ) R .fwdarw. W 0 ( 6 ) ##EQU00006##
[0068] where .phi..sub.x=cutter tilt (inclination of cutter in
mechanical machine)
[0069] Calculating the initial cutter position vector:
{right arrow over (E)}.sub.x1={right arrow over (R)}.sub.m4-{right
arrow over (R)}.sub.w1 (7)
[0070] Rotation about the space angle:
E .fwdarw. X 2 = ( cos .theta. S 0 sin .theta. S 0 1 0 - sin
.theta. S 0 cos .theta. S ) E .fwdarw. X 1 ( 8 ) ##EQU00007##
[0071] A cutter axis matrix is established from j rotation about
Y-axis and i rotation about X-axis:
( T K 1 ) = ( cos j 0 sin j 0 1 0 - sin j 0 cos j ) ( 1 0 0 0 cos i
- sin i 0 sin i cos i ) ( 9 ) ##EQU00008##
i=tilt=90.degree.-.phi..sub.x
j=swivel=90.degree. for upper cutter (-90.degree. for lower
cutter)
[0072] Including rotation about the space angle .theta..sub.S:
( T K 2 ) = ( cos .theta. S 0 sin .theta. S 0 1 0 - sin .theta. S 0
cos .theta. S ) ( T K 1 ) ( 10 ) ##EQU00009##
[0073] Basic settings calculations:
Radial Distance S = ( E X 2 x ) 2 + ( E X 2 z ) 2 ( 11 ) Center
Roll position q 0 = arc tan ( E X 2 x / E X 2 z ) ( 12 ) Swivel
Angle j = - q 0 + arc tan [ ( T K 2 ) 1 , 2 / ( T K 2 ) 3 , 2 ] (
13 ) Tilt Angle i = arc cos [ ( T K 2 ) 2 , 2 ] ( 14 ) Machine Root
Angle .gamma. m = .gamma. m ( mechanical machine ) ( 15 ) Ratio of
Roll R A = WTSTR CTSTR ( 16 ) ##EQU00010##
[0074] where WTSTR=work test roll (job specific) [0075]
CTSTR=cradle test roll (job specific)
[0076] The transformation of the basic-machine settings to the axis
positions of the multi-axis free-form machine is accomplished
according to the method disclosed in previously discussed U.S. Pat.
No. 6,712,566 or U.S. Pat. No. 4,981,402.
[0077] Preferably, the mounting position of a cutter disc on the
free-form machine is reversed with respect to the mounting position
found on the mechanical style straight bevel gear generating
machine. For example, in the free-form machine of FIG. 2, the
mounting position of a cutter disc 2 (shown in FIG. 1) on the tool
spindle would preferably reversed by 180 degrees (i.e. reversed
mounted) such that the visible top portion of cutter disc 2 seen in
FIG. 1 would be positioned adjacent to the tool spindle of the
free-form machine. FIG. 5 illustrates that mounting the cutter disc
in this reversed manner 90 eliminates the need for a negative
machine root angle which would be required if the cutter disc were
mounted to the free-form spindle in the same manner 92 as it is
mounted on the spindle of the mechanical machine. Many machines are
quite limited with respect to the amount of travel in the negative
root angle direction (e.g. minus 3-4 degrees maximum) so reducing
or eliminating the need for negative root angle travel is
advantageous.
[0078] FIG. 6 shows that for the upper cutter in a mechanical
machine, generating the complete involute of flank 1 requires a
generating roll between positions 2U and 3U which in this example
is 40.degree.. The lower cutter in the mechanical machine is
required to roll from position 2L to 1L which in this example is
also 40.degree.. Thus, to fully generate both flanks 1 and 2 in
FIG. 6 with the pair of interlocking type cutters of the
conventional mechanical machine, it is required to perform a
generating roll from position 1L to position 3U which amounts to a
total roll range of 80.degree..
[0079] In a free-form machine, it is only necessary to roll
(generate) either cutter through the required range for the
particular flank. The additional rolling in the mechanical machine
can cause undercut and mutilations and can be avoided in the
free-form machine. The graph portion of FIG. 6 shows different
possibilities of roll ranges:
[0080] Free-Form machine: [0081] Seamless rolling between
-40.degree. to 0.degree. of lower position and 0.degree. to
+40.degree. of upper position [0082] Gap between lower and upper
roll range [0083] Overlap between lower and upper roll range.
[0084] Mechanical Machine [0085] Only one roll range from
-40.degree. to +40.degree. of interlocking cutters
[0086] FIG. 7 shows the upper cutter as positioned in the
mechanical machine and represented by the basic settings in a front
view as well as a top view. A first rotation around the X-axis of
the indicated coordinate system about the machine root angle
.gamma..sub.m lines up the workpiece axis with the Y-axis of the
coordinate system. A second rotation around the Y-axis until the
cutter axis vector is horizontal and does not contain a component
in the X-axis direction is necessary to determine the angle
.DELTA.WZ.sub.U. This is the position cutter and workpiece have in
the free-form machine with respect to the relationship between
workpiece and cutter while the cutter axis is horizontal. In case
of cutting the first (upper) tooth flank, this is not significant.
In the case of cutting the second (lower) tooth flank it is
important in order to achieve the correct tooth slot width to
rotate the workpiece back to the neutral position about
-.DELTA.WZ.sub.U and then it has to be rotated about
.DELTA.WZ.sub.L against the rotation indicated in FIG. 7 to the
lower position. The above may be expressed as:
( T K 3 ) = ( 1 0 0 0 cos .gamma. m - sin .gamma. m 0 sin .gamma. m
cos .gamma. m ) ( T K 2 ) ( 17 ) .DELTA. WZ U = arc tan ( T K 3 ) 1
, 2 ( T K 3 ) 2 , 2 where { ( T K 3 ) 1 , 2 ( T K 3 ) 2 , 2 ( T K 3
) 3 , 2 } ( 18 ) ##EQU00011##
represent the cutter axis vector.
.DELTA.WZ.sub.L is calculated analog using the cutter axis vector
of the basic settings of the lower cutter of the mechanical
machine.
[0087] The set over rotation between the upper cutting of flank 1
and the lower cutting of flank 2 in order to cut the correct tooth
slot width in the correct position is therefore expressed as:
.DELTA.WZ=.DELTA.WZ.sub.U+.DELTA.WZ.sub.L (19)
It should be understood that one cutter in the free-form machine
can represent both cutters of the mechanical machine. The lower
section of the cutter represents the upper cutter and the upper
section of the cutter represents the lower cutter. This is the
reason why the single cutter is moved in the free-form machine
(after conversion to basic settings and transformation of the basic
settings to free-form coordinates) in the upper position, using the
summary of the mechanical machine for the upper cutter, and in the
lower position, using the summary of the lower cutter of the
mechanical machine. Likewise, the correct work rotational position
has to be established with a phase angle rotation of .DELTA.WZ.
[0088] As the upper tooth slot is cut first in the above discussion
it is important to approach the workpiece with the cutter in a
manner to prevent cutting by the clearance side of the cutter
blades. FIG. 8 illustrates the cutter in the start roll position.
The feed vector is derived in the final plunge position at the
start roll position attached to the clearance corner of the cutter
at the center face width such that enough stock is left on the not
yet engaged flank 2. The feed vector is preferably perpendicular to
the root at the mean face width.
[0089] Although discussed with respect to cutting, the present
invention is also applicable to grinding because it converts a
method of using interlocking cutters into a method of cutting with
a single cutter. In a grinding machine, a grinding wheel can be
dressed to duplicate the enveloping surface of the cutting edges
which therefore enables a defined hard finishing of straight bevel
gears preserving the identical flank form.
[0090] It should be understood that the sequence of cutting steps
is not critical. For example, although in the above example a tooth
slot is formed by a first cut at a top position and a second cut at
a bottom position, a tooth slot may instead be first cut at the
bottom position followed by a final cut at the top position.
Alternatively, all slots in a workpiece may be cut at one of the
top or bottom position followed by the remainder of all slots being
cut at the other of the top or bottom position.
[0091] The present method minimizes the amount of machine travel
(and hence time) for repositioning the tool with respect to the
workpiece. With reference to FIGS. 2, it can be seen that
repositioning requires movement essentially in the Y direction only
and for a distance approximately equal to the combined diameters of
the tool and workpiece. Repositioning does not require swinging a
large mass through an arc to a new position. Generation of a tooth
slot does not require a master surface and guides. Furthermore,
with a dish-shaped tool and the combination of machine axes
motions, lengthwise crowning can be produced.
[0092] The present invention also contemplates the transformation
of the settings of the mechanical machine directly into the axis
positions of the free-form machine in a single transformation
step.
[0093] While the invention has been described with reference to
preferred embodiments it is to be understood that the invention is
not limited to the particulars thereof. The present invention is
intended to include modifications which would be apparent to those
skilled in the art to which the subject matter pertains.
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