The hob tooth form of workpiece of rolling cut regular polygon is designed

Summary: The hob that introduced work of tooth form of rolling cut random is general devise a method, accordingly derivation gives workpiece of rolling cut regular polygon to use the formula of tooth form computation of hob, gave out to devise example. Keyword: 　 of 　 of Tooth Profile Design Of Hobs For Hobbing Regular Polygon WorkpiecesZhang Baoming of hob of regular polygon of aleatoric tooth form Abstract: An Universal Method Of Designing Hobs For Hobbing Arbitrary Tooth Profiles Is Introduced. The Calculating Formulas Of Tooth Profiles For Hobbing Regular Polygon Workpieces Are Deduced, and A Design Example Is Given. Keywords: Regular polygon spare parts of 　 of Hob of 　 of Regular Polygon of Arbitrary Profile 　 is the commonly used workpiece on the project, general plant all uses milling craft treatment, manufacturing efficiency is low, goods precision is poor. When large quantities of quantities are produced, can consider to use boil cut craft to manufacture efficiency in order to rise. One, design principle seeks a rack tooth form with conjugate of photograph of workpiece tooth form by principle of planar clench the teeth, the law that regards hob as this rack tooth form to tooth form. Workpiece tooth form is aleatoric tooth form (blame involute tooth form) when, hob law to dentiform general beg a law to be able to undertake by undermentioned measure (refer to a graph 1, graph 2) : Graph 1 graph 2 　 　 (1) building workpiece coordinate to fasten Xoy and cutting tool coordinate is X0o0y0; (2) the Rj of pitch circle radius when affirmatory conjugate; (3) the F of ＝ of Y of tooth form expression that keeps a work (X) ; (4) draw up the law of hob to tooth form (fiducial rack tooth form) ／ of π of ＝ of the φ in expression type 2 - α - δ (3) ＝ of α of Cos of 　 　 　 (δ of Ysin of Xcos δ ＋ ) ／ Rj (4) δ ＝ of Tg of 　 　 　 , xoy is workpiece coordinate department, along with workpiece roll. X0o0y0 is department of cutting tool coordinate, along with cutting tool translation. X1o1y1 is referenced coordinate department, fall asleep. Graph 2 in, what M dot is workpiece tooth form to go up is a bit more aleatoric, a nods the node of the normal that nods for M and pitch circle, the corner that φ nods for M (had turned MA of the normal after φ will pass node P) , α is change horn, be equal to ∠ AOB, δ is the included angle of the tangent that M nods and X axis. 2, design stage 　 1. Introduce each coordinate to fasten each coordinate department to see the graph is shown 3 times. Graph 3 　 　 2. The option of radius of pitch circle of 　 of Rj of radius of affirmatory pitch circle is very important, the choice is undeserved, what beg conjugate tooth form to be able to appear to lose sharp drop instead, arise to be cut to the root cuts workpiece dentiform or supporting thereby; Pitch circle radius has been obtained small, what beg conjugate tooth form to have one share the likelihood is nonexistent. To tooth form of straight edge workpiece, its are the most nodular round radius is (6) in type, ra is radius of the circle outside workpiece, it is namely right now the circumscribed circle radius of N edge form; A is form round radius, it is namely right now the inscribed circle radius of N edge form. Go to the lavatory for computation, can take pitch circle commonly go up in the circle outside its, ra of reason Rj ＝ (7) 　 　 3. Draw up equation of workpiece tooth form pursues 3 in, CD is an edge of N edge form, e is the midpoint of CD, EO is the inscribed circle radius of N edge form, a of your EO ＝ , criterion the tooth form expression of workpiece is Y ＝ A (8) 　 　 4. Beg ① of 　 of formula of cutting tool tooth form to press type (5) ② of the 　 that get 　 presses type (4) get Cos α ＝ (δ of Ysin of Xcos δ ＋ ) Ra of ／ of X of ＝ of Rj of ／ of X of ／ Rj ＝ , namely Ra of ／ of X of Cos α ＝ (9) 　 　 ③ presses type (3) must (10) 　 general (7) , (8) , (10) type takes the place of (1) , (2) type is gotten (11) (12) , reason is when α when D dot, according to type (9) get ＝ of Ra of ／ of ED of ＝ of Ra of ／ of XD of ＝ of Cos α Min (L ／ 2) ／ Ra (13) the L in 　 type is growing by the side of N edge form. It is when α when E dot, according to type (9) 0 α of ＝ of Ra of ／ of XE of ＝ of Max of α of the Cos that get 　 90 ° of Max ＝ 　 such, in α Min ～ inside 90 ° limits, make choice of can decide different X after different α , era enters type (1) , (2) can reach the law of whole hob to tooth form coordinate. The place on put together is narrated, when foregone N is being counted by the side of N edge form, the edge grows L, ra of circumscribed circle radius, a of inscribed circle radius, criterion the law of hob of N edge form can press to tooth form the following each formula begs piece: α of X0 ＝ Xsin - Ra of Acos α ＋ (90 ° - α ) 180 ° of π ／ (14) Y0 ＝ Ra - Xcos α - Asin α (15) 　 of Ra of ／ of X of Cos α ＝ (α of X ＝ Racos, x ＝ ／ of 0 ～ L 2) (16) Arccos of α Min ＝ (L ／ 2ra) (17) 90 ° of α Max ＝ (18) law to pitch Pn ＝ N of ／ of 2 π Ra (19) 3, hob computation example is foregone hexagon workpiece. Graph 4 　 criterion 20 　 of Ra ＝ 　 A ＝ 35. 2 ＝ of 47 ／ 17. 735 (calculate by intermediate estimation) ＝ of α Min of Arccos of 　 of 　 　 　 (L ／ 2) ／ Ra ＝ 62. 90 ° of ＝ of Max of α of 　 of 46765222 ° 　 0 ～ of ＝ of 　 　 X 9. 244986479 　 are in α α Min ～ begs a X offspring that answers relatively to enter type inside 90 ° limits (14) , (15) , can reach cutting tool law to tooth form coordinate (see next tables) pursue with the tooth form of hob (see a picture 5) . ° of Min64 of the α that express α 65. 5 ° ... 71. 5 ° ... 86. 88 ° of 5 ° 90 ° of 89 ° X ＝ (15) type 9. 2458. 7678. 294... 6. 346... 1. 2210. 6980. 3490x0 ＝ (13) type 9. 6109. 1818. 745... 6. 848... 1. 3580. 7770. 3880y0 ＝ (14) type 00. 2170. 422... 1. 168... 2. 2242. 2512. 2622. 265 hob law to pitch Pn ＝ 2 π of ＝ of N of ／ of 2 π Rj 2 π of ＝ of Ra ／ N 20 ／ of × 6 ＝ 20. 944 graphs 5 　 pursue 5 in, line of section of X0 axis above is curvilinear tooth form, section line takes linear tooth form under X0 axis (do not attend exhibit cutting) , its are approximate the X0 that β of tooth form horn can press α Min and adjacent α point, y0 coordinate computation reachs. This exemple takes α Min and α ＝ 65.

The coordinate of 5 ° is worth, criterion ＝ of Y0 of Δ of ／ of X0 of Δ of Arctg β ／ 9.

610 - 8.

745 ／ 0.

Complete tine of 64 ° 　 is in 422 ＝ greatly add on foundation of Max of Y0, α on 0.

The clearance with 2 right amount ～ is measured (in order to make sure tooth of hob tine bottom is wide unapt too pointed for the principle) , this exemple is added 0.

25mm, reason complete tine is taken greatly 2.

265 ＋ 0. 25 ＝ 2.

515mm. Because craft needs, must give out substitute circular arc parameter, because tooth form is symmetrical at Y0 axis, reason is replaced be located in with circular arc the centre of a circle on Y0 axis, make substitute circular arc radius is Ra, coordinate distance is Xa, ya, can get arched tall EO0 to be according to geometrical relation get via arranging namely (20) Min of α of Xa ＝ X0 (21) Ya ＝ Ra - Y0 α Max (22) ＝ of Max of α of the Y0 in this 　 exemple 2. 265, ＝ of X0 α Min 9. 610, era enters type (20) with type (21) , the relevant parameter that reach is: Ra ＝ 21. 519mm, xa ＝ 9. 610, ya ＝ 19. 254. CNC Milling