CN103551674A - Pre-grinding hob for machining micro-segment gears - Google Patents

Abstract

The invention relates to a pre-grinding hob for micro-segment gear processing. The normal tooth profile of the cutting edge of the pre-grinding hob is composed of a main cutting edge section, an addendum arc section, and a characteristic curve connection section, wherein the main cutting edge section is used to process the normal meshing contact tooth profile of the micro-line segment gear pair The curved section is formed by the smooth connection of micro-segment curves or micro-segment straight lines, and the length is not more than 1 micron; the characteristic curve connection section is the connection curve section between the hob tooth top arc section and the micro-segment tooth profile section before grinding. The direction and length are related to the modulus, initial pressure angle, pressure angle increment, grinding allowance, and the distribution form of the grinding allowance of the micro-segment gear to be processed. According to the theoretical calculation and experience of the direction and length of the undercut circular arc segment and the characteristic transition curve segment, the present invention proposes to make the high-precision micro-segment gear meet the specific use requirements and mass production conditions as much as possible.

Description

Pre-grinding hob for microsegment gear processing

Technical field

The invention belongs to machining tool technical field, be specifically related to the front gear hobbing cutter of a kind of microsegment gear mill, especially for the front gear hobbing process tool of a kind of mill that adopts the hard flank of tooth microsegment gear of forming grinding wheel roll flute fine finishining mode.

Background technology

Gear drive is as a kind of important kind of drive in machine driving, and in Practical Project, application is extremely extensive.Microsegment gear (patent No. ZL2004100656163.3) has than the better teeth bending strength of involute gear and contact strength of tooth surface, but because profile of tooth flank profil is different from common involute profile, therefore can not process by the method for existing processing involute gear.In addition, the hobboing cutter of the microsegment gear proposing in CN200820034342.5 utility model patent can only be processed the microsegment gear of general precision, cannot require high accuracy microsegment gear processing high, at a high speed, under case of heavy load for transmission accuracy.When the processing number of teeth is less than 17 non-profile modified gear, if gear tooth root does not produce undercut, for the microsegment gear that needs later stage fine finishining roll flute, roll flute hour wheel tooth root portion there will be grinding step, generation stress is concentrated, and owing to not occurring that therefore undercut can not produce the effect of cutter relieving groove, be easy to destroy Gear Root, the counter-bending fatigue strength that is unfavorable for the gear teeth, and cause emery wheel edge overheated, wearing and tearing, this grinding step has not only reduced the transmission efficiency of gear, has increased noise when gear meshes, and has also shortened the service life of emery wheel; If tooth root undercut is excessively dark, gear teeth root thickness can reduce, and is unfavorable for the teeth bending strength of gear, and has shortened the length of the effective engaged section of gear, thereby has reduced gear-driven registration, has reduced meshing efficiency.Micro-line segment hobboing cutter that patent CN200820034342.5 proposes cannot guarantee that microsegment gear flank profil contact-segment is connected with the round and smooth of tooth top circular arc after not leaving grinding allowance and grinding, also cannot be suitable for the front processing of mill of microsegment gear.

The high accuracy of gear is processed with various ways, and is based on following reason for the combination processing mode of the selected gear hobbing of microsegment gear and moulding roll flute.1. gear hobbing working (machining) efficiency is high.The same with other gear, cutting working method is still a kind of most important method of microsegment gear processing, and wherein conventional with rolling cut processing, all the more so when batch is larger.2. gear hobbing processing and manufacturing is simple, cost is low.Adopt gear hobbing processing can utilize existing lathe, only need to change corresponding hobboing cutter tool, so cost reduces greatly.3. current, gear-grinding process remains the most important means of gear fine finishining, its great advantage is can process quenching hard gear and machining accuracy is high, special for domestic due to the impact of factor on gear member precision such as material, forging normalizing and heat treatment deformations, by gear-grinding process, eliminate the distortion producing after heat treatment, major reason that gear-grinding process more and more attracts people's attention that Here it is.But, at present for processing the pre-grinding hob of conventional involute gear, because its cutter tooth cutting edge shape and microsegment gear flank profil do not match, the micro line segment gear cutter hob that this external Chinese patent CN200820034342.5 proposes, owing to not leaving grinding allowance, cannot produce suitable undercut, and after grinding, cannot guarantee that microsegment gear flank profil contact-segment is connected with the round and smooth of tooth top circular arc, also cannot be suitable for the front processing of mill of microsegment gear.

Summary of the invention

In order to overcome the problem existing in the microsegment gear finishing step described in above-mentioned background technology, the invention provides and a kind ofly can process microsegment gear flank profil and can make processed microsegment gear produce suitable undercut, leave special-purpose micro-line segment pre-grinding hob before the mill of grinding allowance.In actual production, identical for modulus, grinding allowance distribution form is identical and the pre-grinding hob of the same batch of gear that grinding allowance is different, can provide technical support for easily manufactured and batch production.

Concrete technical solution is as follows:

Pre-grinding hob for microsegment gear processing, comprise hobboing cutter, uniform cutter tooth on the base cylinder 11 of described hobboing cutter, on each cutter tooth, be respectively equipped with rake face 1, top sword 2, right side sword 3, left side sword 4, back of the body shovel top below 5, knife face 7 behind knife face 6 and left side behind right side, wherein the middle hypomere of right side sword 3 and the middle hypomere of left side sword 4 are main cutting edge, between top sword 2 and the main cutting edge of both sides, be respectively equipped with feature easement curve 8, right side sword 3, left side sword 4 and top sword 2 extend back and form respectively knife face 6 behind right side along hobboing cutter helix, behind left side, knife face 7 and back of the body shovel top below 5, described top sword 2, right side sword 3, left side sword 4 and feature transition curve 8 form the normal profile of hobboing cutter, described top sword 2 is circular arc, behind the normal direction of rake face 1 and right side, behind knife face 6 or left side, between knife face 7, form side edge relief angle α _c, and the side edge relief angle α of both sides _cangle identical, the normal direction of rake face 1 and back of the body shovel top form top relief angle α below between 5 _e, the gap on the circumference of base cylinder 11 between adjacent cutter tooth is chip pocket 10,

The shape of main cutting edge is similar to the shape of the tooth curve of processed microsegment gear, the normal profile curve of hobboing cutter is to be to be not more than the micro-section of curve of 1 micron or micro-section of straight line to be smoothly connected and to form by length, gap between main cutting edge and the tooth curve of processed microsegment gear is exactly the grinding allowance of later stage roll flute processing, and grinding allowance reduces to tooth root gradually from the tooth top of processed gear;

The radius of curvature rt of described feature transition curve 8 is circular arcs of 0.82～0.85m, and the position relationship between top sword 2 centers of circle of the position in feature transition curve 8 centers of circle and circular arc is y _t=y _{tooth top circular arc}-(0.9～0.94) m, x _t=-(1.08～1.02) m, wherein y _tand x _trespectively ordinate and the abscissa in feature transition curve 8 centers of circle, y _{tooth top circular arc}and x _{tooth top circular arc}be respectively ordinate and the abscissa in top sword 2 centers of circle of circular arc, m is the modulus of processed gear;

The circular arc radius of curvature r of described top sword 2 _j=min (r _j1, r _j2), r _j1and r _j2can calculate according to following formula, ${\mathrm{<figure-callout\; id="1"\; label="r\; j"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">r</figure-callout>}}_j=(\frac{s_{n0}}{2}-x_c)/\cos {\mathrm{\&alpha;}}_c,{\mathrm{<figure-callout\; id="2"\; label="r\; j"\; filenames="131021160923.png"\; state="\{\{state\}\}">r</figure-callout>}}_j=\frac{{0.5s}_0\cos {\mathrm{\&alpha;}}_c}{1-\sin {\mathrm{\&alpha;}}_c},$ $s_0=2[\frac{s_{n0}}{2}-x_c-(h_{a0}-h_c)\mathrm{tg}{\mathrm{\&alpha;}}_c],$ Wherein, r _j1for unit header tooth top arc radius, r _j2for two round end tooth top arc radius, s _n0for thickness on pitch circle, s ₀tooth top is not thick when making transition arc, x _cfor this abscissa, α _cfor this some place pressure angle, h _cfor effective engaging tooth is risen, h _a0for working addendum;

Described side edge relief angle α _cspan be 1.8 °～2.2 °, described top relief angle α _eshould be within the scope of 17 °～19 °, selection principle is: higher cutting speed and the less amount of feeding are selected larger top relief angle and side edge relief angle;

The effective length of action l of rolling cut of described hobboing cutter _mwith the required hobboing cutter length l of metal in excision teeth groove _ccan be calculated as follows l _m=| ρ _mkcos α _k| _max, wherein, ρ _mkfor the radius of curvature at this some place, α _kfor the pressure angle at this some place,

r _afor processed microsegment gear radius of addendum, h is processed microsegment gear fully teeth height, λ ₀for pre-grinding hob lead angle;

Described chip pocket 10 directions are consistent with the axis direction of hobboing cutter, and its shape is circular-arc.

The structural design of pre-grinding hob of the present invention comprises the designing and calculating of pre-grinding hob cutter tooth profile of tooth, flank profil and the designing and calculating of pre-grinding hob contour length.

With pre-grinding hob processing microsegment gear of the present invention, be equivalent to the engagement of spatial intersecting axle helical gear, namely pre-grinding hob basic worm and processed microsegment gear are made the process of spatially spiral engagement.

1. microsegment gear pre-grinding hob (chip pocket is straight trough) cutter tooth tooth Shape Design is calculated

1) space medium tooth bar method

Fig. 4 (b) is depicted as the engagement situation of engagement pre-grinding hob rack cutter 12 and processed microsegment gear 14, Fig. 4 (a) is depicted as engagement pre-grinding hob rack cutter 12 and the engagement situation that meshes helical rack II13, Fig. 4 (c) is depicted as processed microsegment gear 14 and the engagement situation that meshes helical rack I15, and the axis of processed microsegment gear 14 is perpendicular to the end face of engagement helical rack II13 and engagement helical rack I15.

As shown in Fig. 4 (d), because engagement helical rack I 15, the normal tooth profile of engagement helical rack II 13 is identical and all equal the profile of tooth of space medium spur rack I-II 16, therefore this space medium spur rack I-II 16 just can mesh with processed microsegment gear 14 and engagement pre-grinding hob rack cutter 12 simultaneously, as space medium spur rack I-II 16 is taken out, mesh pre-grinding hob rack cutter 12 and processed microsegment gear 14 with regard to each around the rotation of its oneself axle center, this is just equivalent to helical gear drive, correctly engagement continuously while only having them to there is equal initial parameter and normal circular pitch.

The space medium spur rack I-II 16 above proposing, makes space engagement problem to be converted in this way plane engagement problem.

Due to discussion of the present invention be the micro-segment Tooth Profile Gears of straight-tooth, so in application during the method, processed microsegment gear 14 be spur gear, meshes helical rack I15 consistent with space medium spur rack I-II 16.

2) with the profile of tooth of the engagement helical rack I 15 of processed microsegment gear 14 profile of tooth conjugation

By the aufbauprinciple of microsegment gear, can try to achieve the micro-line segment curve of rack tooth profile of linear of standard equation, it is exactly the space medium spur rack I-II 16 in above-mentioned medium tooth bar method and the profile of tooth that meshes helical rack I 15.

If the form of gear tooth coordinate of processed microsegment gear 14 is x ₁o ₁y ₁, the coordinate of engagement helical rack I 15 is x _t1o _t1y _t1, x _t1o _t1y _t1plane is vertical with the axis of processed microsegment gear 14, in this plane, with the engagement helical rack I 15 normal tooth profile equations of processed microsegment gear 14 profile of tooth conjugation is:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="x\; t"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">x</figure-callout>}}_t=\&PlusMinus;(\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}\frac{r_{\mathrm{bi}}(\sin \mathrm{\&delta;}-\sin {\mathrm{\&delta;}}_i)}{\cos ({\mathrm{\&alpha;}}_{i-1}+\mathrm{\&delta;})}-{\mathrm{\&rho;}}_{\mathrm{mk}}\cos {\mathrm{\&alpha;}}_k)\\ y_{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">t</figure-callout>}1}=\&PlusMinus;{\mathrm{\&rho;}}_{\mathrm{mk}}\sin {\mathrm{\&alpha;}}_k\end{array}\right.k=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n---\left(1\right)$

In formula, ρ _mkbe m _kthe radius of curvature of point;

δ _iit is the central angle of i basic circle;

α _kfor corresponding k point pressure angle.

3) ask engagement helical rack II 13 profiles of tooth in the plane vertical with pre-grinding hob axis

Engagement helical rack II 13, engagement helical rack I 15 is involutory, therefore the profile of tooth equation of engagement helical rack I 15 is exactly the normal tooth profile equation of engagement helical rack II 13.

As shown in Figure 5, T-T cross section is vertical with pre-grinding hob axis, sets up engagement helical rack II 13 coordinate system x in this cross section _to _ty _t, the lead angle of establishing on pre-grinding hob base cylinder 11 is λ, in T-T cross section, meshes helical rack II 13 profiles of tooth to be

$\left\{\begin{array}{c}{x}_t=x_{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">t</figure-callout>}1}/\sin \mathrm{\&lambda;}\\ y_t=-y_{t1}\end{array}\right.---\left(2\right)$

4) ask the contrate tooth profile of pre-grinding hob basic worm

Because known with engagement helical rack II 13 profiles of tooth in pre-grinding hob axis vertical cross-section T-T, therefore, can obtain the pre-grinding hob basic worm contrate tooth profile equation of conjugation with it.

Shown in Fig. 6 (a), set up engagement helical rack II 13 coordinate system x _to _ty _tand pre-grinding hob end face coordinate system x ' ₀o ' y ' ₀, x _taxle overlaps with engagement helical rack II 13 nodel lines, and o ' is positioned on pre-grinding hob axial line, r ' ₀for pre-grinding hob pitch radius, during beginning, y _taxle and y ' ₀axle overlaps, and p is working pitch point, M (x _t, y _t) be any point in engagement helical rack II 13 profiles of tooth, cross M point profile of tooth normal and hand over x _taxle, in p ' point, is established its coordinate for (l, 0), and γ was M point profile of tooth tangent line and x _taxle clamp angle.Can write out the equation of straight line Mp '

$Y-y_t=-\frac{1}{\mathrm{tg\&gamma;}}(X-x_t)---\left(3\right)$

In formula:

$\mathrm{tg\&gamma;}=\frac{{\mathrm{dy}}_t}{{\mathrm{dx}}_t}=\frac{d(-y_{t1})}{d(x_{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">t</figure-callout>}1}/\sin \mathrm{\&lambda;})}=-\frac{{\mathrm{dy}}_{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">t</figure-callout>}1}}{{\mathrm{<figure-callout\; id="1"\; label="dx\; t"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">dx</figure-callout>}}_t}\sin \mathrm{\&lambda;}---\left(4\right)$

Because p ' (l, 0) is a bit on straight line, Y=0 substitution above formula can be obtained

l＝X＝y _ttgγ+x _t （5）

When engagement helical rack II 13 is moved to the left after l, as shown in Fig. 6 (b), p ' overlaps with p point, and now M becomes contact point, establishes pre-grinding hob rotational angle to be

therefore:

According to principle of coordinate transformation, can try to achieve pre-grinding hob basic worm contrate tooth profile

By formula (1)～formula (6) substitution formula (7),

In above formula, contain differential expression because micro-segment Tooth Profile tooth curve is not a Hypothesis of Single Curve Build Up, therefore, be difficult to obtain

explicit expression, but can, according to the definition numerical calculations of differential, according to the definition of differential, have

$\frac{{\mathrm{dy}}_{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">t</figure-callout>}1}}{{\mathrm{<figure-callout\; id="1"\; label="dx\; t"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">dx</figure-callout>}}_t}=\underset{\mathrm{\&Delta;}{x}_i\&RightArrow;0}{\lim }\left(\frac{\mathrm{\&Delta;}{y}_i}{\mathrm{\&Delta;}{x}_i}\right)---\left(9\right)$

Because microsegment gear between adjacent two zero points line segment very short, can think and go to zero, therefore

$\frac{{\mathrm{dy}}_{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">t</figure-callout>}1}}{{\mathrm{<figure-callout\; id="1"\; label="dx\; t"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">dx</figure-callout>}}_t}=\underset{\mathrm{\&Delta;}{x}_i\&RightArrow;0}{\lim }\left(\frac{\mathrm{\&Delta;}{y}_i}{\mathrm{\&Delta;}{x}_i}\right)\&ap;\frac{y_i-y_{i-1}}{x_i-x_{i-1}},i=\mathrm{0,1,2},\&CenterDot;\&CenterDot;\&CenterDot;---\left(10\right)$

Formula (10) is the contrate tooth profile of pre-grinding hob basic worm.

5) ask the profile of tooth of the front rake face (1) of mill

After obtaining pre-grinding hob basic worm contrate tooth profile, can each point on contrate tooth profile is for the helical movement to rake face (1), form the profile of tooth on pre-grinding hob rake face (1).

In Fig. 7, establish M point on contrate tooth profile (x ' ₀, y ' ₀, 0) radius vector r _y0with reference axis y ₀angle is θ _t, rake face (1) is apart from y ₀wheelbase is from being e,

$\left\{\begin{array}{c}\sin {\mathrm{\&theta;}}_0=e/r_{y0}\\ r_{y0}=\sqrt{x_0^{\&prime;2}+y_0^{\&prime;2}}\\ \cos {\mathrm{\&theta;}}_t=y_0^{\&prime;}/r_{y0}\\ \sin {\mathrm{\&theta;}}_t=-x_0^{\&prime;}/r_{y0}\end{array}\right.---\left(11\right)$

The M point M ' point to pre-grinding hob rake face (1) for the helical movement, establishing its coordinate is (x _0e, y _0e, z _0e), if the pitch of screw is p,

$\left(\begin{array}{c}{x}_{0e}\\ y_{0e}\\ z_{0\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">e</figure-callout>}}\\ 1\end{array}\right)=\left(\begin{array}{cccc}\cos ({\mathrm{\&theta;}}_0+{\mathrm{\&theta;}}_t)& \sin ({\mathrm{\&theta;}}_0+{\mathrm{\&theta;}}_t)& 0& 0\\ -\sin ({\mathrm{\&theta;}}_0+{\mathrm{\&theta;}}_t)& \cos ({\mathrm{\&theta;}}_0+{\mathrm{\&theta;}}_t)& 0& 0\\ 0& 0& 1& -\frac{2\mathrm{\&pi;}}{p}({\mathrm{\&theta;}}_0+{\mathrm{\&theta;}}_t)\\ 0& 0& 0& 1\end{array}\right)\left(\begin{array}{c}{x}_0^{\&prime;}\\ y_0^{\&prime;}\\ 0\\ 1\end{array}\right)---\left(12\right)$

Above formula is launched, make triangular transformation, and by relational expression (10) substitution wherein,

$\begin{array}{c}{x}_{0e}=e\\ y_{0e}=r_{y0}\cos {\mathrm{\&theta;}}_0\\ z_{0e}=-\frac{2\mathrm{\&pi;}}{p}({\mathrm{\&theta;}}_0+{\mathrm{\&theta;}}_t)\end{array}---\left(13\right)$

Notice in pre-grinding hob basic worm, a minute radius of circle is r ' ₀, lead angle is λ, in formula (12), pitch p is

$p=\frac{2\mathrm{\&pi;}{r}_0^{\&prime;}}{\sin \mathrm{\&lambda;}}---\left(14\right)$

Formula (13) is the equation of pre-grinding hob rake face (1).

2. microsegment gear pre-grinding hob structural design

2.1 tooth top relief angles

If pre-grinding hob tooth top relief angle is α _e, at pre-grinding hob radius, be r _y0the normal direction side edge relief angle at place is α _c, this place's profile angle is α _y, as shown in Figure 7.Have following relational expression to set up:

tgα _c＝tgα _eysinα _y (15)

If pre-grinding hob per tooth back-off amount is K, the circumference number of teeth is Z _k, there is relational expression:

$\mathrm{tg}{\mathrm{\&alpha;}}_e=\frac{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="131021160923.png"\; state="\{\{state\}\}">K</figure-callout>}}{2\mathrm{\&pi;}{r}_{a0}/Z_k}---\left(16\right)$

$\mathrm{tg}{\mathrm{\&alpha;}}_{\mathrm{ey}}=\frac{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="131021160923.png"\; state="\{\{state\}\}">K</figure-callout>}}{2\mathrm{\&pi;}{r}_{y0}/Z_k}---\left(17\right)$

By relational expression (16), (17) substitution (15)

$\mathrm{tg}{\mathrm{\&alpha;}}_c=\frac{r_{a0}}{r_{y0}}\mathrm{tg}{\mathrm{\&alpha;}}_e\sin {\mathrm{\&alpha;}}_y---\left(18\right)$

Pre-grinding hob tooth top relief angle α _edetermine, should be able to guarantee the relief angle that its side edge is necessary, and in microsegment gear flank profil, the profile angle of each point changes, and profile angle minimum is at reference circle place, be selected initial pressure angular dimensions α ₀, generally speaking, the initial pressure angle α of microsegment gear ₀less, compare involute gear much smaller, so when selecting the basic parameter of microsegment gear, for the microsegment gear that need process by generation, general recommendations α ₀be not less than 6 °.From formula (18), can find out, for guaranteeing that side edge has necessary relief angle α _c, must adopt larger top relief angle α _e.Usually, side edge relief angle α _cspan be 1.8 °～2.2 °, top relief angle α _eshould be within the scope of 17 °～19 °, profile angle α _yby formula (18), calculated.Concrete numerical value will be selected according to Tool in Cutting speed and the amount of feeding, is generally that higher cutting speed and the less amount of feeding is selected larger top relief angle and side edge relief angle.

2.2 pre-grinding hob length

The minimum length of pre-grinding hob should meet two requirements:

1, the complete envelope of energy goes out the flank profil of gear.

2, the edge cutter tooth of pre-grinding hob is not answered overload.

(1) the required pre-grinding hob length of envelope gear-profile

As shown in Figure 9, the engagement of pre-grinding hob and processed microsegment gear 14 is regarded approx as to the engagement of imaginary pinion rack 18 and imaginary meshing gear 17, in Fig. 9, A ₁pB ₁for the path of contact of right side flank profil, A ₂pB ₂for the path of contact of left side flank profil, the length of region of engagement, left and right is

for asking

length, should first obtain Equation of engaged line, for left side flank profil, Equation of engaged line is:

In above formula, ρ _mk, α _kradius of curvature and pressure angle for this place.

Region of engagement, left and right length

be the tooth top part of two path of contacts in the projection sum of pre-grinding hob axis direction,

$l_{\stackrel{\&OverBar;}{B_1{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="131021160923.png"\; state="\{\{state\}\}">B</figure-callout>}}_2}}=2l_m=2{\left|{\mathrm{\&rho;}}_{\mathrm{mk}}\cos {\mathrm{\&alpha;}}_k\right|}_{\max }---\left(20\right)$

As can be seen here, effective length of action of rolling cut microsegment gear is decided by the basic parameter of pre-grinding hob, and irrelevant with the processed microsegment gear number of teeth.

Effective length of action (the unit: mm) of table 1 rolling cut microsegment gear

Modulus m	Effective length of action l m
		1	4.64
2	8.448
		3	11.979
4	15.461
		5	18.838

On

Table 1 has been listed effective length of action value of rolling cut microsegment gear under part modulus.

(2) the required pre-grinding hob length of metal in excision teeth groove

As shown in Figure 10 (a), at the incision end of pre-grinding hob, at length of action l _mthough outside pre-grinding hob cutter tooth do not participate in the work of generated profile, from the teeth groove of microsegment gear blank, excise metal, this part must have enough length, otherwise the Load on Cutting Teeth that makes to start incision is overweight, causes the damage of cutter tooth.For simplify calculating, can think that pre-grinding hob cutter tooth is that A point from Figure 10 (b) starts to cut tooth base, do so content to retain sovereignty over a part of the country entirely.Therefore, pre-grinding hob incision part should have

length:

$l_{\stackrel{\&OverBar;}{\mathrm{AB}}}=\sqrt{{r_a}^2-{(r_a-h)}^2}=\sqrt{2r_{a}h-h^2}---\left(21\right)$

In formula: r _a: processed microsegment gear radius of addendum;

H: processed microsegment gear fully teeth height.

Will

be reflected to pre-grinding hob axis direction, its length is

$l_c=\frac{l_{\stackrel{\&OverBar;}{\mathrm{AB}}}}{\cos {\mathrm{\&lambda;}}_0}=\frac{\sqrt{2r_{a}h-{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="131021160923.png"\; state="\{\{state\}\}">h</figure-callout>}}^2}}{\cos {\mathrm{\&lambda;}}_0}---\left(22\right)$

As can be seen from the above equation, l _cirrelevant and only relevant with fully teeth height with three basic parameters of microsegment gear, thereby this part length of microsegment gear pre-grinding hob can be determined by the data of involute gear cutter.

The end that cuts out at pre-grinding hob, pre-grinding hob mainly completes the work of envelope profile of tooth, cutting out end length should calculate by formula (20), incision end at pre-grinding hob, pre-grinding hob mainly completes the task of rejecting metal from processed microsegment gear teeth groove, therefore incision end length should be calculated by formula (22), like this, the required total length of pre-grinding hob is l _m+ l _c.

From the above analysis, the length of the microsegment gear pre-grinding hob of making by the initial parameter of recommending can be chosen by standard by corresponding involute gear data, be partial to like this safety, but when the number of teeth of initial parameter change or processed microsegment gear 14 is larger, must calculate or verification pre-grinding hob length by formula (20) and formula (22).

2.3 pre-grinding hob tooth top circular arcs

Whether the tooth top circular arc of pre-grinding hob correctly has important impact to the durability of pre-grinding hob and processed microsegment gear 14 profiles of tooth.The greatest wear of pre-grinding hob is created in tooth top circular arc place, and tooth top circular arc is less, more easily wearing and tearing.Therefore, tooth top circular arc should do bigger as far as possible, meanwhile, studies and also shows, the tooth root knuckle of microsegment gear is larger on the bending fatigue strength impact of the gear teeth, for improving gear quality, increases the service life, and should increase the root fillet of gear.When with pre-grinding hob processing microsegment gear, the easement curve that forms processed microsegment gear 14 root fillets is formed by pre-grinding hob outside circle arc, from improving the angle of gear performance, also should increase pre-grinding hob tooth top arc radius, but it is subject to easement curve at the bottom of gear teeth to allow the restriction of height.

During gear hobbing, we are similar to pre-grinding hob to regard as engagement pre-grinding hob rack cutter 12, the equal space line that is fillet centrode (prolate involute) by the formed easement curve track of engagement pre-grinding hob rack cutter 12 tooth top circular arc.And the maximum tooth tip circle arc of pre-grinding hob is the circular arc that is cut in its top sword and two side edges.As shown in figure 11.

Restriction pre-grinding hob tooth top circular arc radius r _jcondition be: whether the microsegment gear processed with this pre-grinding hob 14 can produce easement curve during with coupling gear 20 engagement is interfered, and checks easement curve starting point place radius r on tooth root _cwhether be less than microsegment gear and effectively mesh starting point radius r _g, otherwise just need reduce r _jvalue.

(1) ask the radius of the effective starting point of meshing G of processed microsegment gear.

As shown in figure 12, establish processed microsegment gear 14 and be meshed with coupling gear 19, curve EPG is its path of contact, and wherein P is node.The intersection point G of the outside circle of coupling gear 19 and path of contact is the effective starting point of meshing in processed microsegment gear 14 flank profils, connect PG, GP direction is the flank profil normal at coupling gear 19 outside circle places, cross the tangent line that G makes coupling gear 19 outside circles, according to the definition of pressure angle, know: ∠ BGC is coupling gear 19 outside circle pressure angle α _a2.At Δ O ₂in PG:

$O_{2}P={\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="131021160923.png"\; state="\{\{state\}\}">r</figure-callout>}}_2,O_{2}G=r_{a2},\&angle;{\mathrm{<figure-callout\; id="2"\; label="PGO"\; filenames="131021160923.png"\; state="\{\{state\}\}">PGO</figure-callout>}}_2=\frac{\mathrm{\&pi;}}{2}-{\mathrm{\&alpha;}}_{a2}$

$\stackrel{\&CenterDot;}{\&CenterDot;\&CenterDot;}\&angle;{\mathrm{<figure-callout\; id="2"\; label="O"\; filenames="131021160923.png"\; state="\{\{state\}\}">O</figure-callout>}}_2\mathrm{PG}=\frac{\mathrm{\&pi;}}{2}+\mathrm{<figure-callout\; id="2"\; label="arcsin\; r"\; filenames="131021160923.png"\; state="\{\{state\}\}">arcsin</figure-callout>}\frac{r_{}}{}\frac{{}_2\cos {\mathrm{\&alpha;}}_{a2}}{r_{a2}}---\left(23\right)$

$\stackrel{\&CenterDot;}{\&CenterDot;\&CenterDot;}\&angle;{\mathrm{PO}}_{2}G={\mathrm{\&alpha;}}_{a2}-\mathrm{<figure-callout\; id="2"\; label="arcsin\; r"\; filenames="131021160923.png"\; state="\{\{state\}\}">arcsin</figure-callout>}\frac{r_{}}{}\frac{{}_2\cos {\mathrm{\&alpha;}}_{a2}}{r_{a2}}---\left(24\right)$

At Δ O ₁o ₂in G, O ₁o ₂=r ₁+ r ₂, O ₂g=r _a2, ∠ PO ₂g is by formula (24) definition:

$r_G=O_{1}G=\sqrt{{({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2)}^2+{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="131021160923.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}^2\text{-2}({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2){\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="131021160923.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos ({\mathrm{\&alpha;}}_{a2}-\mathrm{<figure-callout\; id="2"\; label="arcsin\; r"\; filenames="131021160923.png"\; state="\{\{state\}\}">arcsin</figure-callout>}\frac{r_{}}{}\frac{{}_2\cos {\mathrm{\&alpha;}}_{a2}}{r_{a2}})}---\left(25\right)$

(2) there is not easement curve interference condition

Referring to Figure 11, the coordinate of establishing active profile (being the part of side edge below height of teeth top ha) the peak c of engagement pre-grinding hob rack cutter 12 is (x _c, y _c), the conjugate point of c point in processed microsegment gear 14 flank profils is c ', its coordinate be (x ' _c, y ' _c).For avoiding easement curve to interfere, processed microsegment gear 14 easement curve starting points should be lower than effective starting point of meshing G,

$r_c^{\&prime;}=\sqrt{x_c^{\&prime;2}+y_c^{\&prime;2}}\&le;r_G---\left(26\right)$

In formula, x ' _c, y ' _ccan be according to x _c, y _cvalue is calculated according to the tooth profile curve equation of the microsegment gear in ZL2004100656163.3 patent of invention.

(3) ask possible maximum tooth top arc radius

Tooth top circular arc has two kinds of forms, and a kind of is to be tangential on d point (as shown in Figure 13 a) with top sword, is unit header tooth top circular arc; Another kind is to be cut in c point (as shown in Figure 13 b) with side edge, be two round end tooth top circular arcs, flank profil feature for microsegment gear " epirelief is recessed ", in order to guarantee the bending strength of tooth root portion, the design of the general recommend adoption list of pre-grinding hob round end formula tooth top circular arc, in addition, possible maximum tooth tip circle arc is the smaller in both.

In coordinate system shown in Figure 13, c point coordinates (x _c, y _c), pressure angle α _c, x _cand y _cshould be able to meet formula (26).In Figure 13, effectively engaging tooth is risen h _cbe its ordinate y _c, establish the thick s of being of tooth top while not making transition arc ₀,, to helicla flute zero anterior angle pre-grinding hob, have

$s_0=2[\frac{s_{n0}}{2}-x_c-(h_{a0}-h_c)\mathrm{tg}{\mathrm{\&alpha;}}_c]---\left(27\right)$

For situation shown in Figure 13 (a), have

$r_{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="131021160929.png,131021160933.png"\; state="\{\{state\}\}">j</figure-callout>}1}=(\frac{s_{n0}}{2}-x_c)/\cos {\mathrm{\&alpha;}}_c---\left(28\right)$

For situation shown in Figure 13 (b), have

$r_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="131021160923.png"\; state="\{\{state\}\}">j</figure-callout>}2}=\frac{0.5s_0\cos {\mathrm{\&alpha;}}_c}{1-\sin {\mathrm{\&alpha;}}_c}---\left(29\right)$

Tooth top arc radius is:

r _j＝min(r _j1,r _j2) (30)

R _j1for unit header tooth top arc radius, r _j2for two round end tooth top arc radius, s _n0for thickness on pitch circle, s ₀tooth top is not thick when making transition arc, x _cfor this abscissa, α _cfor this some place pressure angle, h _cfor effective engaging tooth is risen, h _a0for working addendum.

Wherein:

Table 2 microsegment gear pre-grinding hob tooth top circular arc calculated value (unit: mm)

Modulus m	r	jmax
			1	0.5762（0.5762m）
2	1.1302(0.5651m)
		3	1.6814(0.5605m)
4	2.2203(0.5551m)
		5	2.7604(0.5521m)
6	3.2809(0.5468m)
		8	4.39(0.5488m)
10	5.2033(0.5203m)

In table, m represents modulus

The one group calculated value of upper table 2 for obtaining according to above method, show that optimum pre-grinding hob tooth top circular arc radius of curvature is for (0.52～0.58) m, the modulus that wherein m is pre-grinding hob.

The useful technique effect of pre-grinding hob of the present invention embodies in the following areas:

1, patent of the present invention can realize processing before the mill that the patent No. is the microsegment gear that proposes in the patent of invention of ZL2004100656163.3, for follow-up grinding lays the foundation, to realize production and the manufacture of the hard flank of tooth microsegment gear of high accuracy;

2, the present invention can realize the efficient rolling cut processing of microsegment gear under the prerequisite that does not change traditional hobbing machine structure, can realize the front roughing microsegment gear of batch production mill, can effectively improve the front gear hobbing working (machining) efficiency of mill, improve service life, transmission efficiency and the serviceability of processed microsegment gear simultaneously;

3, take the microsegment gear minimum teeth number of the invention process rolling cut processing is only 8 teeth, and conventional involute gear not the minimum teeth number of undercut be 17;

Owing to being subject to the impact of gear own characteristic, the circular arc tooth top that the undercut that existing gear hob is difficult to process generation does not affect the little number of teeth gear of use and reach gear after using forming grinding wheel to grind away given surplus is with contact flank profil smooth connection excessive, accurately transmission again simultaneously, do not affect gear serviceability, comprise noise and efficiency.The in the situation that of undercut not, if get addendum coefficient, be 1, tip clearance coefficient is 0.25, and pressure angle is 20o, and the minimum teeth number of existing involute hob processing is 17; And be still 1 when getting addendum coefficient, top coefficient is still 0.25, and get initial pressure angle while being 6o, it is 8 gear that the microsegment gear pre-grinding hob proposing in the present invention can process the number of teeth, thereby can realize larger gearratio, export larger moment, improve the bearing capacity of gear train, or reduce the volume of gear train, and then reduce the quality of transmission system;

4, the present invention is set to (0.52～0.58) m by the tooth top circular arc radius of curvature of pre-grinding hob, and m is processed module, makes processed gear have stronger bending strength bearing capacity.

The tooth top circular arc of pre-grinding hob has direct impact to the gear easement curve cutting out.Tooth top circular arc radius of curvature is less, the counter-bending ability of processed gear is out stronger, feature easement curve and gear-profile are more not easy to occur interfering, on the contrary, the feature easement curve of the gear processing is more level and smooth, be not prone to stress concentration phenomenon, therefore tooth top circular arc radius of curvature has a upper limit value and lower limit value.In the present invention, the radius of curvature of pre-grinding hob tooth top circular arc is set to (0.52～0.58) m, can guarantee correct profile of tooth, can obtain again stronger bending strength bearing capacity;

5, make the sheet iron filings of processing hardened face gear generation better be gathered in chip pocket with the circular-arc chip pocket of this pre-grinding hob axially parallel, under quick rolling cut, can large area, the degree of depth scratches machined surface, in addition the stress that circular-arc chip pocket also can reduce cutting edge root is concentrated, and improves the service life of pre-grinding hob;

6, this pre-grinding hob is similar to microsegment gear pitch curve section shape in main cutting edge shape, by formula 13, tried to achieve, distance difference between the two is the thickness of grinding allowance, and the grinding allowance distribution form on main cutting edge is and increases progressively trend from top to bottom, reach the little surplus of the important engaged section of gear-profile, fine grinding, the large surplus of the non-important engaged section of the portions such as tooth root, the effect of corase grind, when guaranteeing grinding accuracy, be lowered into like this stock removal at abrasive wheel edge as far as possible, and then the wearing and tearing of minimizing emery wheel, improve grinding efficiency, guarantee the bending strength that tooth root portion is stronger simultaneously,

7, adopt the mode that gear engagement is assumed to be to the engagement of rack-and-pinion, ask for the pre-grinding hob minimum length of the complete envelope gear-profile of energy, and determine and not occur that edge cutter tooth overload obtains phenomenon, can determine the minimum rolling cut length of pre-grinding hob, otherwise suitably strengthen pre-grinding hob length until meet instructions for use, pre-grinding hob volume be can reduce, material and unnecessary processing cost saved;

8, chip pocket direction is consistent with pre-grinding hob azimuth axis direction, and its shape is circular-arc, convenient manufacture, measurement, and guarantee that chip removal is normal, reduce the stress concentration phenomenon of pre-grinding hob cutter tooth and base cylinder junction.

Accompanying drawing explanation

Fig. 1 is pre-grinding hob structural representation.

Fig. 2 is pre-grinding hob rake face flank profil schematic diagram.

Fig. 3 is a cutter tooth on pre-grinding hob.

Fig. 4 is the space medium tooth bar method schematic diagram during pre-grinding hob Theoretical Design calculates.

Fig. 5 meshes helical rack II normal direction and contrate tooth profile schematic diagram in Fig. 4.

Fig. 6 (a) meshes helical rack II coordinate system schematic diagram in Fig. 4.

Fig. 6 (b) is pre-grinding hob end face coordinate system schematic diagram in Fig. 4.

Fig. 7 is pre-grinding hob tooth profile of rake face coordinate system schematic diagram.

Fig. 8 is the location drawing that is related to of pre-grinding hob side edge relief angle, tooth top relief angle and profile angle.

Fig. 9 is effective region of engagement schematic diagram of engagement pre-grinding hob rack cutter and the approximate engagement of processed microsegment gear.

Figure 10 (a) is the envelope length of pre-grinding hob rolling cut and the front view of cut-in length schematic diagram.

Figure 10 (b) is the envelope length of pre-grinding hob rolling cut and the top view of cut-in length schematic diagram.

Figure 11 is engagement pre-grinding hob rack cutter tooth top circular arc schematic diagram.

Figure 12 is effective starting point of meshing schematic diagram of processed microsegment gear and coupling gear.

Figure 13 (a) is the excessive single head fillet of pre-grinding hob tooth top schematic diagram.

Figure 13 (b) is the excessive double end fillet of pre-grinding hob tooth top schematic diagram.

Sequence number in upper figure: after 1 rake face, 2 top swords, 3 right side swords, 4 left side swords, 5 back of the body shovel tops, behind 6 right sides, behind knife face, 7 left sides, knife face, 8 feature transition curves, 9 basic spiral table lines, 10 chip pockets, 11 base cylinders, 12 engagement pre-grinding hob rack cutters, 13 mesh helical rack II, 14 processed microsegment gears, 15 engagement helical rack I, 16 space medium spur rack I-II, 17 imaginary meshing gears, 18 imaginary pinion racks, 19 these gears of pairing.

The specific embodiment

Below in conjunction with concrete processed microsegment gear parameter, by embodiment, further the present invention will be described.

In the middle of practical operation, select suitable pre-grinding hob characteristic parameter according to pre-grinding hob material, pre-grinding hob Technology for Heating Processing, the number range calculated by gear cutting machine material, pre-grinding hob cutting linear velocity and the condition binding isotherm such as lubricated.

Embodiment 1:

The processed microsegment gear parameter of table 3

Modulus/mm	The number of teeth	Initial pressure angle/degree	Pressure angle increment/degree	Initial basic circle/mm	Addendum coefficient	Tip clearance coefficient
							3	30	10.6	0.00085	818611.14	1.05	0.375

Suppose that the basic parameter of the microsegment gear that plan is processed is as above shown in table 3.

As shown in Figure 1, pre-grinding hob for microsegment gear processing, uniform cutter tooth on the base cylinder of described pre-grinding hob, on each cutter tooth, be respectively equipped with rake face 1, top sword 2, right side sword 3, left side sword 4, back of the body shovel top below 5, knife face 7 behind knife face 6 and left side behind right side, wherein right side sword 3 and left side sword 4 are main cutting edge, between top sword 2 and the main cutting edge of both sides, be respectively equipped with feature easement curve 8, right side sword 3, left side sword 4 and top sword 2 extend back and form respectively knife face 6 behind right side along the basic spiral table of pre-grinding hob line 9, behind left side, knife face 7 and back of the body shovel top below 5, described top sword 2, right side sword 3, left side sword 4 and feature transition curve 8 form the normal profile of pre-grinding hob, behind the normal direction of rake face 1 and right side, behind knife face 6 or left side, between knife face 7, form side edge relief angle α _c, and the side edge relief angle α of both sides _cangle identical, the normal direction of rake face 1 and back of the body shovel top form top relief angle α below between 5 _e, the gap on the circumference of base cylinder 11 between adjacent cutter tooth is chip pocket 10, described chip pocket 10 directions are consistent with the axis direction of pre-grinding hob, and its shape is circular-arc.

The shape of main cutting edge is similar to the shape of the gear tooth profile curve of processed microsegment gear, between described top sword 2 and the main cutting edge of both sides, be respectively equipped with feature easement curve 8, the normal profile curve of pre-grinding hob is to be to be not more than the micro-section of curve of 1 micron or micro-section of straight line to be smoothly connected and to form by length; Gap between main cutting edge and processed microsegment gear 14 tooth curves is exactly the grinding allowance of later stage roll flute processing, and grinding allowance reduces to tooth root gradually from the tooth top of processed gear;

In the present embodiment, for the moulding of microsegment gear pre-grinding hob, be to take micro-segment Tooth Profile as cross section, for the helical movement to form cutter tooth and basic spiral table line 9 along base cylinder 11 surfaces; Axial direction along base cylinder 11 mills out groove to form chip pocket 10 and rake face 1; Make base cylinder 11 make vertically High Rotation Speed, on relevant position on basic spiral table line 9, form respectively top sword 2 and back of the body shovel top 5 below, take micro-segment Tooth Profile as cross section, along basic helix 9 both sides that extend back, form respectively knife face 7 after the right side sword of knife face 6 after the left side sword of cutter tooth, left side sword 3 and cutter tooth, right side sword 4.

The radius of curvature r of described feature transition curve 8 _tscope is the circular arc of 0.82～0.85m, and m is the modulus of processed gear, and what in the present embodiment, process is that modulus m is 3 microsegment gear, and rolling cut speed is 65r/min, the radius of curvature r of feature transition curve 8 _tbe chosen as 2.48mm;

The radius of curvature r of the circular arc of described top sword 2 _jaccording to formula (27～30), in conjunction with the initial parameter of processed microsegment gear 14, try to achieve as 1.6814mm;

Described side edge relief angle α _cspan be 1.8 °～2.2 °, described top relief angle α _e17 °～19 ° of spans, the present embodiment cutting speed is 65r/min, initial pressure angle α ₀be 10.6 °, the pre-grinding hob radius r of design _a0for 40mm, top relief angle α _ewith side edge relief angle α _caccording to formula (18), trying to achieve is respectively 17.6 ° and 1.92 °;

The effective length of action l of described pre-grinding hob _maccording to formula (20), try to achieve the non-generated profile rolling cut of pre-grinding hob length l _caccording to formula (22), try to achieve.

Table 4 pre-grinding hob parameter

The characteristic parameter of corresponding pre-grinding hob is tried to achieve according to above-mentioned calculating, according to processed microsegment gear 14

Definite pre-grinding hob cutter tooth parameter sees the above table 4.

Embodiment 2:

The processed microsegment gear parameter of table 5

Modulus/mm	The number of teeth	Initial pressure angle/degree	Pressure angle increment/degree	Initial basic circle/mm	Addendum coefficient	Tip clearance coefficient
							2.0	23	10.329	0.00065	796385.14	1.0	0.25

Suppose that the basic parameter of the microsegment gear that plan is processed is as above shown in table 5.

Table 6 pre-grinding hob parameter

The pre-grinding hob parameter of respective design sees the above table 6.

Embodiment 3:

The processed microsegment gear parameter of table 7

Modulus/mm	The number of teeth	Initial pressure angle/degree	Pressure angle increment/degree	Initial basic circle/mm	Addendum coefficient	Tip clearance coefficient
							1.15	19	10.178	0.000632	812568.32	1.0	0.25

Suppose that the basic parameter of the microsegment gear that plan is processed is as above shown in table 7.

Table 8 pre-grinding hob parameter

The pre-grinding hob parameter of respective design sees the above table 8.

Claims (1)

1. The pre-grinding hob used for micro-segment gear processing, including the hob, the base cylinder (11) of the hob is evenly distributed with cutter teeth, and each cutter tooth is respectively provided with a rake face (1), a top edge (2), right edge (3), left edge (4), back blade top back (5), right flank (6) and left flank (7), of which the right edge ( 3) and the middle and lower sections of the left edge (4) are main cutting edges, and there are characteristic transition curves (8) between the top edge (2) and the main cutting edges on both sides, and the right edge (3) ), the left edge (4) and the top edge (2) extend backward along the helix of the hob to form the right flank (6), the left flank (7) and the back of the back shovel top (5), respectively, The top edge (2), the right edge (3), the left edge (4) and the characteristic transition curve (8) constitute the normal tooth profile of the hob, and the top edge (2) is arc-shaped; the front The side edge relief angle α _c is formed between the normal direction of the cutter face (1) and the right flank (6) or left flank (7), and the angle of the flank relief angle α _c on both sides is the same ; The top edge relief angle α _e is formed between the normal direction of the rake face (1) and the rear surface of the back shovel top (5), and the gap between adjacent teeth on the circumference of the base cylinder (11) is a chip pocket ( 10); It is characterized in that: the shape of the main cutting edge is similar to the shape of the tooth profile curve of the machined micro-segment gear, and the normal tooth profile curve of the hob is smoothly connected by a micro-segment curve or a micro-segment straight line with a length not greater than 1 micron. As a result, the gap between the main cutting edge and the tooth profile curve of the machined micro-segment gear is the grinding allowance of the later grinding process, and the grinding allowance gradually decreases from the tooth top to the tooth root of the machined gear; The radius of curvature r _t of the characteristic transition curve (8) is a circular arc of 0.82-0.85m, and the positional relationship between the position of the center of the characteristic transition curve (8) and the center of the arc-shaped top edge (2) is y _t = y _{addendum arc-} (0.9～0.94) m, x _t =-(1.08～1.02) m, where y _t and x _t are the ordinate and abscissa of the center of the characteristic transition curve (8), respectively, y _{Addendum arc} and x _{addendum arc} are the ordinate and abscissa of the center of the arc-shaped top edge (2), respectively, and m is the modulus of the processed gear; The radius of curvature of the arc of the top edge (2) r _j = min(r _j1 , r _j2 ), r _j1 and r _j2 can be calculated according to the following formula, $r_{j1}=(\frac{{\mathrm{the\; s}}_{\mathrm{no}0}}{2}-x_c)/\cos {\mathrm{\&alpha;}}_c,r_{j2}=\frac{{0.5\mathrm{the\; s}}_0\cos {\mathrm{\&alpha;}}_c}{1-\sin {\mathrm{\&alpha;}}_c},$ ${\mathrm{the\; s}}_0=2[\frac{{\mathrm{the\; s}}_{\mathrm{no}0}}{2}-x_c-(h_{a0}-h_c)\mathrm{tg}{\mathrm{\&alpha;}}_c],$ Among them, r _j1 is the radius of the addendum arc of the unit head, r _j2 is the radius of the addendum arc of the double round head, s _n0 is the pitch thickness of the tooth, s ₀ is the thickness of the addendum without transition arc, x _c is the The abscissa of the point, α _c is the pressure angle at this point, h _c is the effective meshing addendum height, h _a0 is the pitch circle addendum height; The value range of the side edge relief angle α _c is 1.8° to 2.2°, and the top edge relief angle α _e should be in the range of 17° to 19°; The hobbing effective meshing length l _m of the hob and the hob length l _c required to remove the metal in the alveolar can be calculated according to the following formula, l _m =|ρ _mk cosα _k | _max , where ρ _mk is the The radius of curvature at the point, α _k is the pressure angle at the point,

r _a is the radius of the addendum circle of the processed micro-segment gear, h is the full tooth height of the processed micro-segment gear, and _λ0 is the helix angle of the hob before grinding; The direction of the chip flute is consistent with the axial direction of the hob, and its shape is arc-shaped.

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