# Gear hob is the shortest the computation of effective cutting length

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The length of the shortest effective cutting of gear hob is to point to can cut the hob that gear fully teeth height needs length of the shortest axial (L0t)min. In gear cutting, need computation hob is the shortest the circumstance of effective cutting length is very much. When the pinion that is like gear of rolling cut double couplet, if pinion is helical gear and very as close as gear apart, whether can when needing pinion of rolling cut of checking computations hob, touch with gear photograph. Hob external diameter is smaller, axial length is shorter, the possibility that touchs with gear photograph is less. But, the intensity that hob external diameter crosses small conference to affect part of tine root keyway (can consider right now hob and) of an organic whole of cutter shaft make it; In addition, if roll knife axial length too short, the likelihood cannot cut complete pinion. Because this is below this kind of circumstance,need the length of the shortest axial of computational hob. In addition, (L0t)min also is total length of ministry of computational hob tine (the consideration strings together knife length) foundation. Basis of 1 calculation method pursues 1 but when straight gear of rolling cut of derivation plan cipher out (L0t)min. To the hob of common precision, because helix promotes role very small, can think the law is equal to horn of axial tooth form to tooth form horn. The path of contact that has established P of point of tangency and the node that tine teeth of a cogwheel carries round diameter on the head are A, it is B with the node that rolls tooth top line, criterion workpiece tooth form is formed between A of path of contact and B dot. The vertical line that crosses A to nod path of contact and hob tine top line are handed in at C, set C outboard hob to age the top ages horn is C, roll law of tooth ministry edge to most stone's throw (the shortest length that does not need to string together a knife to be able to cut gear fully teeth height namely) for (L0n)min=2(pm/2+CE)=pm+2L3(1) graph takes the place of when 1 computation hob law the half to pitch (Pm/2) , because assume the height of teeth top of hob is equal to its height of teeth root,be. Although do not ask hob height of teeth top is equal to its height of teeth root certainly actually, ask to roll tooth to be more than workpiece completely high to age height of teeth top of completely tall, hob is equal to workpiece height of teeth root only can (workpiece height of teeth root is (Fa1+c1)m, among them Fa1 is coefficient of workpiece height of teeth top, c1 is bottom clearance coefficient, if tine root position pursues 1 in RS place shows) , but era enters workpiece height of teeth root RS undertakes computational comparative a trouble. Calculate to simplify, might as well hypothesis hob height of teeth root is equal to hob height of teeth top, right now RS=pm/2. Because roll knife height of teeth root actually to be less than workpiece height of teeth root normally, because this presses type (the hob of 1) cipher out (L0n)min value has a bit increase, computational result is more safe. By the graph 1 knowable, give complete tooth form to make hob is cut, must satisfy L3 ≥ L2, because need the shortest length of computational hob, reason is desirable L3=L2 of its limit circumstance. L2 is the length that participates in cutting actually, take this length namely when machining double couplet gear to undertake checking computations, its computation formula is L2=L1+Qa=L1+QCtana1=L1+EN Tana1=L1+(NP+ME-PM)tana1=L1+[L1tana1+(fa1+c1)m-x1m]tana1=(tan2a1+1)L1+(fa1+c1-x1)mtana1(2) type in: L1=Ra1sin(aa1-a1) Ra1 -- the tine of workpiece carries round radius Aa1 on the head -- the tine of workpiece carries round pressure angle on the head, after Cosaa1=rb1/Ra1=mz1cosaa1/Ra1 gets L2, take L3 ≥ L2, era enters type (1) can be begged piece (L0n)min, the shortest length is the axial of hob (the G0 in L0t)min=(L0n)min/cosg0(3) type -- as a result of,the helix of hob promotes role G0 normally lesser (about 3 ° , cos3 ° ≈ 0.

9986) , and length of the shortest effective cutting wants hob finally the circle rectifies Mm, accordingly also but direct will (L0n)min serves as (L0t)min. Although afore-mentioned formula age by rolling cut the circumstance derivation of columnar gear goes out continuously, but if will concern parameter to change a way to parameter, replace workpiece with equivalent gear, also can use its at the computation of gear of inclined tine cylinder approximately. If need the pinion when gear of double couplet of checking computations rolling cut to whether be met,touch with gear photograph, answer with type (of the L2 of 2) cipher out double as (L0t)min, namely (L0t)min=2L2 is the hob that participates in cutting the shortest length. Type (the value of 1) cipher out is the shortest length with the due hob when stringing together a knife. Exemple of 2 application example 1: The parameter of workpiece of one straight gear is my factory: Da1=96.

2mm, diameter section P=8(namely M=3.

175mm) , z1=29, a1=20 ° , tine is completely tall H1=5.

733mm, ha1=2 of height of teeth top.

06mm. It is D0=82 of diameter of 90mm, reference circle with external diameter.

The rolling cut of only head hob of 654mm this gear, beg this the shortest length that rolls tooth ministry. Solution: Beg a workpiece tine to carry Aa1 of round pressure angle on the head above all: Cosaa1=mz1cosaa1/Ra1=0.

8993991382aa1=25.

9208 ° L1=Ra1sin(aa1-a1)=4.

Coefficient of 96mm workpiece height of teeth root is Fa1+c1=(h1-ha1)/m=1.

15L2=(tan2a1+1)L1+(Fa1+c1-x1)mtana1=6.

94mm because L3>L2, reason takes L3=7. Criterion the law of hob is to the shortest length (hob of L0n)min=pm+2L3 ≈ 24mm is only head, its helix rises horn to be G0=arcsin(m/D0)=2.

201452653 (L0t)min=(L0n)min/cosg0=24.

01mm is visible, will (L0n)min serves as (the error that L0t)min brings is dinky, can ignor. By afore-mentioned computation knowable, right (L0n)min value impact is bigger is L1=Ra1 Sin(aa1-a1) , bigger to L1 influence is Ra1 and Aa1. Work is greater, ra1 and Aa1 are bigger also, of hob (L0n)min is longer. In addition, by type (2) is knowable, the height of teeth root of workpiece is bigger, its modification coeffication is smaller (the X1=0) in this exemple, of hob (L0n)min is bigger also. Exemple 2: The Mn=3 of helical gear.

5mm, an=20 ° , z1=100, b1=60 ° , h1=7.

875mm, ha1=3.

5mm(is opposite to analyse each parameter (the influence of L0n)min, exaggerate somewhat to the parameter such as B1) . Set workpiece to be double couplet gear, touch with gear photograph to whether be when checking computations is machined, met, seek rolling cut of this gear hob (L0t)min. Solution: The equivalent of helical gear ages number is Z1=z1/cos3b1=181.

The diameter dividing a circle of 182 equivalent gear is 93 ≈ Mnz1=637mm, very round diameter is Mnz1+2ha1=644mm, right now Aa1=arccos[mnz1cosan(/mn Z1+2ha1)]=21.

≈ of 64632097 ° L1=Ra1sin(aa1-a1) 9.

25mmfa1+c1=(h1-ha1)/mn=1.

25L2=(tan2an+1)L1+(fa1+c1-x1)mntanan=12.

067mm criterion the shortest length of hob (L0t)min=2L2 ≈ 24mm. Home's at present commonly used hob design method is to pass the elliptical equation of listed hob inclined section plane to beg its to concern the maximum of coordinate to decide hob is the shortest length. Because involve elliptical equation, beg guide more troublesome, to beg a coordinate maximum to return demand solution surmounts equation, this is quite difficult to manual computation. And use estimation of the biggest coordinate to calculate (L0t)min relatively rough. Under photograph comparing, the method of article introduction is simpler and practical, and the computation of two kinds of methods is close to relatively as a result (exemple 2 get (more elliptical law begs L0t)min ≈ 24mm go out (L0t)min=22.

7mm slightly big, when hob is used more) of on the safe side.