Abstract
A method of grinding 3-face ground cutting blades for producing gears by a face hobbing cutting process wherein the correct initial blade spacing angle is achieved while providing the desired values for the effective cutting edge hook angle and the effective side rake angle as well as providing a complete cutting blade front face clean-up.
Claims
1. A method of grinding 3-face ground cutting blades for producing gears by a face hobbing cutting process, said method comprising: providing an inside cutting blade and an outside cutting blade wherein each of said inside and outside cutting blades comprises a plurality of grinding surfaces including at least a cutting side surface, a clearance side relief surface and a front face, said inside cutting blade and said outside cutting blade being positionable in consecutive blade mounting slots of a face hobbing cutter head, grinding at least one of said cutting side surface, said clearance side relief surface and said front face on each of said inside cutting blade and said outside cutting blade to produce at least a predetermined effective cutting edge hook angle and a predetermined effective cutting side rake angle on each of said inside cutting blade and said outside cutting blade, grinding the front face of at least one of said inside cutting blade and said outside cutting blade whereby when positioned in said consecutive blade mounting slots of said face hobbing cutter head, the front face of said inside cutting blade and the front face of said outside cutting blade defining an initial blade spacing angle .
2. The method of claim 1 wherein the front face of said inside cutting blade and the front face of said outside cutting blade are each ground to effect a clean-up of each front face.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) FIG. 1(a) shows a 2-face ground blade and FIG. 1(b) shows a 3-face ground blade. Both Figures are labeled with the blade parameter definitions and include the blade related coordinate system.
(2) FIG. 2(a) shows a two-dimensional view of a blade in a cutter head with low slot inclination angle of 4.42. The blade hook angle .sub.min delivers in this cutter a maximal top rake angle of 0.
(3) FIG. 2(b) shows a blade in a cutter head with a high slot inclination angle of 12. The blade hook angle .sub.min delivers in this cutter a maximal top rake angle of 7.58.
(4) FIG. 3(a) illustrates a blade in a cutter head with a low slot inclination angle. A front face grind off of s causes a large loss of blade length I.sub.1.
(5) FIG. 3(b) illustrates a blade in a cutter head with a high slot inclination angle. The blade shows only a small loss of blade length I.sub.2 with the same front grind off amount s as in FIG. 3(a).
(6) FIG. 4 shows a three-dimensional view of a face hobbing cutter head with the cutting plane drawn in front of one outside blade.
(7) FIG. 5 shows a view onto the side of an inside blade. The cutting plane is indicated and contains the blade reference point.
(8) FIG. 6(a) is a front view of a blade which has a ground front face (3-face blade) which is completely cleaned up.
(9) FIG. 6(b) is a front view of a blade which also has a ground front face (3-face blade) but is only partially cleaned up on the front face.
(10) FIG. 7 shows a simplified two-dimensional view of two proceeding blades in a cutter head having a linear blade spacing of S.sub.x which is larger than the theoretical spacing S of a reference cutter.
(11) FIG. 8 illustrates how a blade spacing error of F.sub.d causes a radial error of N.sub.e in face hobbing.
(12) FIG. 9 shows a flank deviation plot wherein the deviations represent the errors of a real flank form versus a theoretically calculated flank form.
(13) FIG. 10(a) shows a reference cutter head with 2-face blades wherein only one blade group (outside and inside blades) is represented.
(14) FIG. 10(b) shows a cutter head with high angle slot inclination and 3-face blades wherein only one blade group (outside and inside blades) is represented.
(15) FIG. 11 represents five imbedded loops for 3-face blade determination.
(16) FIG. 12 is a bevel gear cutting blade which illustrates the blade front clean-up of Loop No. 2 in FIG. 11.
(17) FIG. 13 is a blade grinding summary output section for 3-face blades showing the effective blade geometry.
(18) FIG. 14 shows measurement results of a pinion cut with 4.42 cutter slot inclination and a 2-face blade (equal reference blade and reference cutter) that was measured with a coordinate file which reflects the reference blade and the reference cutter.
(19) FIG. 15 shows measurement results of a pinion cut with a 3-face ground blade which was built in a cutter head with 12 slot inclination.
(20) FIG. 16 shows measurement results of a pinion cut with a 3-face ground blade which was built in a cutter head with 12 slot inclination.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
(21) The terms invention, the invention, and the present invention used in this specification are intended to refer broadly to all of the subject matter of this specification and any patent claims below. Statements containing these terms should not be understood to limit the subject matter described herein or to limit the meaning or scope of any patent claims below. Furthermore, this specification does not seek to describe or limit the subject matter covered by any claims in any particular part, paragraph, statement or drawing of the application. The subject matter should be understood by reference to the entire specification, all drawings and any claim below. The invention is capable of other constructions and of being practiced or being carried out in various ways. Also, it is understood that the phraseology and terminology used herein is for the purposes of description and should not be regarded as limiting.
(22) The details of the invention will now be discussed with reference to the accompanying drawings which illustrate the invention by way of example only. In the drawings, similar features or components will be referred to by like reference numbers.
(23) The use of including, having and comprising and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. The use of letters to identify elements of a method or process is simply for identification and is not meant to indicate that the elements should be performed in a particular order.
(24) Although references may be made below to directions such as upper, lower, upward, downward, rearward, bottom, top, front, rear, etc., in describing the drawings, there references are made relative to the drawings (as normally viewed) for convenience. These directions are not intended to be taken literally or limit the present invention in any form. In addition, terms such as first, second, third, etc., are used to herein for purposes of description and are not intended to indicate or imply importance or significance.
(25) In the context of the invention, the term bevel gears is understood to be of sufficient scope to include those types of gears known as bevel gears, hypoid gears, as well as those gears known as crown or face gears.
(26) The problem to be solved is to find a blade geometry where the following blade geometry parameters are preferably determined in parallel: Effective cutting edge hook angle Front clean-up amount Effective cutting side rake angle Calculations for outside and inside blade in parallel Blade spacing
(27) Face hobbing cutter blades are positioned in a particular cutter head with a certain blade slot offset. The face hobbing motion causes the relative velocity vector between cutting blade and work piece to point in a direction that is not coincident with one of the axis directions of the cutting blade. As a result, the angles ground on the blade are not the angles that make a blade sharp or dull with respect to a workpiece during cutting. In the cutting process, it is not the actual angles on the blade, but the effective angles of side rake, top rake and cutting edge hook angles of the blades, realized as a result of the face hobbing motion between tool and work piece, that are relevant and which determine if the cutting is optimal. The effective angles are the angles realized as a result of being in the cut. The angles ground on a blade, the orientation of the blade positioned in a certain cutter head, and the face hobbing motion between work piece and cutter all contribute to the effective angles between the cutting edge and the material of the work piece.
(28) Because of the cross influences between the parameters which are present in the inventive solution, a closed analytical solution of the 3-face blade geometry is not practical. The approach of the inventive idea is a combination of imbedded iterations and single direction step approximations, preferably with certain abort criteria or maximum number of steps, in order to achieve a sufficient front clean-up and realize the effective input values. The preferred calculation scheme which is represented in FIG. 11 achieves a stable and convergent behavior of the calculations while maintaining a fast algorithm.
(29) Loop No. 1 (inner iteration loop) shown in FIG. 11 influences the top rake angle on the blade front face in order to achieve the given effective cutting edge hook angle. At the end of each calculation step, the effective cutting edge hook angle is determined and the difference between this number and the desired input value is preferably multiplied by a damping factor (e.g. 0.5) and then subtracted from the top rake angle used in the last step. After that, Loop No. 1 is repeated until the deviation between the actual and the nominal value is below a predetermined limit. Use of a dampening factor reduces or eliminates the possibility of a deviation that may be too large for the iteration to function properly, resulting in a more stable iteration.
(30) Loop No. 2 in FIG. 11 is preferably a single direction step approximations. The lead parameter of this iteration is the grind depth (see FIG. 12). The calculation begins with the minimally required grind depth. This loop preferably accomplishes two things at the same time. First, the front clean-up has to cover the entire length of the cutting edge in order to correctly cut the whole depth of the gear. Secondly, the clean-up thickness at the tip of the blade has to be equal or above a given minimal value. FIG. 12 shows 9 steps, starting at the minimal grind depth to the final grind depth. After each step, the clean-up thickness is checked to determine if it is still below the target value. If so, another step is performed at an incrementally increased grind depth. When the clean-up thickness, calculated at the end of Loop No. 2, passes the target value for the first time, the front clean-up loop ends and Loop No. 3 in FIG. 11 finishes the first step of calculating the effective cutting side rake angle for a blade geometry which already shows the correct effective cutting edge hook angle as well as the correct front clean-up.
(31) The result of the effective side rake after finishing the first step of the Loop No. 3 iteration may not deliver the desired effective side rake angle because the two inner loops in FIG. 11 will change the cutting direction relative to the blade coordinate system enough that several corrective repetitions of this loop are required. Corrective input is the deviation (with negative sign) between actual and nominal effective side rake angle. Although this procedure makes this loop an iteration, the loop ends if either the deviation limit is satisfied or after a maximum number (e.g. 5) of steps.
(32) The algorithm of iterations and correction loops in FIG. 11 includes two additional loops (No. 4. and No. 5.) in order to achieve the desired goal of re-establishing the original blade spacing. Loop No. 4 repeats all previously discussed loops for both blades involved in cutting one pinion or gear slot. The outer loop (Loop No. 5) will determine the actual blade spacing angle (which requires that both inside and outside-blade calculations have been finished at this point) and processes this value in order to decide which blade (inside or outside) has to receive a certain amount of additional front clean-up thickness S.sub.x. The corrective repetition of all four inner loops uses a dampened amount of S.sub.x (reduced amount). All inner loops are repeated until their abort criteria are reached. The outer blade spacing iteration loop repeats until the actually achieved blade spacing deviation from the original (desired) spacing is below a defined iteration limit, or if the deviation value changes its sign (or it aborts after a maximum number (e.g. 6) of steps). The dampening factor (e.g. 0.5) and the number of steps may be adjusted such that the overall system of loops functions in a stable manner and the final results in all evaluated cases are within acceptable accuracy limits.
(33) FIG. 13 is the blade grinding summary output section with the effective blade geometry. Lines 02 and 05 show the effective cutting edge hook angle of 1.00 and the effective cutting side rake angle of 4.50 respectively. Those values are identical with the input values of the calculation algorithm where the correct values have been achieved by the algorithm. In the output in FIG. 13, the blade spacing correction is evident in the fact that the effective tip clean up thickness of 1.32 mm for the outside blade (line No. 07) varies from the target value of 1.00 mm (line No. 06).
(34) Face milling designs do not require the outer iteration loop No. 5 (FIG. 11) because the tooth thickness is independent from the blade spacing.
(35) The iteration loops may be carried out utilizing commercially available blade grinding software as is known to the skilled artisan, such as, for example, CAGE Blade Grinding Software available from The Gleason Works, Rochester, N.Y.
(36) The flank form measurement results in FIG. 14 are the baseline for a pinion cut with a 2-face ground blade built in a cutter head with 4.42 slot inclination (equal reference blade and reference cutter) and measured with a coordinate file which reflects exactly the reference blade and the reference cutter. The corner point deviation of less than 4 m in FIG. 14 leads to a Sum of Errors Squared of 0.00000040 inch.sup.2, which is a very good result for cutting before heat treatment.
(37) The measurement results in FIG. 15 also use the standard coordinate file which is based on reference blades in a reference cutter. The measured pinion was cut with a 3-face ground blade which was built in a cutter head with 12 slot inclination. The measurement was conducted with the standard coordinate file which is based on reference blades in a reference cutter (2-face blades and cutter with 4.42 slot inclination). The blade grinding summary for this test was determined with an algorithm which did not include the inventive method. FIG. 15 shows the deviations of the cut pinion, which are nearly 14 m. The Sum of Errors Squared is 0.00000231 inch.sup.2 which is still acceptable for a soft cut pinion before heat treatment but the surface deviations are significantly larger than the ones in FIG. 14. The R.sub.w blade point radii correction to maintain the correct tooth thickness, which was used to prepare the cutting blades, causes the length crowning which is more visible on the convex flank.
(38) The results obtained with 3-face blades which have been ground according to the inventive method are shown in the flank deviation graphic in FIG. 16. The 3-face blade calculation was repeated utilizing the inventive method. A pinion manufactured with the new 3-face blade geometry in a cutter head with 12 slot inclination angle was measured with a coordinate file, based on a reference blade in a reference cutter (2-face blades with 12 blade side rake angle used in a cutter with 4.42 slot inclination) and shows a single micron flank form deviation with an Sum of Errors Squared of 0.00000046 inch.sup.2.
(39) 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 without deviating from the spirit and scope of the appended claims.
