CN104985260A - Continuous hobbing method for straight bevel gear - Google Patents

Abstract

The invention discloses a continuous hobbing method for a straight bevel gear. The continuous hobbing method is based on a special hypocycloid approximating a straight line. A cutterhead rotates at the speed being omega t, a gear rotates at the speed being omega g, and at the moment, relative movement of the gear and a cutter is equivalent to pure rolling engagement movement of cutter rolling and gear rolling. When the rolling radius and the reference radius of the cutter are the same or equal to one half of the gear rolling radius, the track formed by cutter noses of cutter teeth on the gear is an approximate straight line, and therefore the cutter and the gear can be used for continuous hobbing of the straight bevel gear. The continuous hobbing method has the advantages that the continuous hobbing technology is adopted, and therefore production efficiency and precision are high; both wet hobbing and dry hobbing can be achieved, the dry hobbing efficiency is higher, the tooth surface finish degree is better, the requirement for the cutter and a machine tool is higher, and wet hobbing just gets the opposite results; the machined straight bevel gear is in a slight drum shape instead of a strict straight line shape in the tooth length direction. The drum-shaped size can be controlled by adjusting machine tool parameters, so that the contact area of the gear is changed to enable the gear to have the better transmission performance, and gears with constant-depth teeth and shrinkage teeth can be machined.

Description

The continuous Rolling-cut shear method of straight bevel gear

Technical field

The present invention relates to the processing method of straight bevel gear, particularly a kind of continuous Rolling-cut shear method of straight bevel gear.

Background technology

Straight bevel gear due to its design and installation convenient, the advantages such as transmission performance is good, are applied in all trades and professions in a large number at present.Current processing method has forging, gear-shaping, double-cutterhead milling teeth etc.

Forging is only applicable to produce in enormous quantities, is not well positioned to meet the Production requirement of flexible production and single and mini-batch production day by day.Gear-shaping technique and Double-cutter Milling Process efficiency low, machining accuracy is low, processing versatility bad.Therefore high in the urgent need to a kind of working (machining) efficiency, the processing method that versatility is good.

Summary of the invention

The object of this invention is to provide a kind of Gear milling process method of straight bevel gear, the method has following features:

Its Cutting Process is continuous rolling cut (face-hobbing), has higher production efficiency machining accuracy; Can wet and cut also ability and cut, dry working (machining) efficiency of cutting is higher, and flank of tooth fineness is better, but higher to the requirement of cutter and lathe, wet cut just the opposite.

The technical scheme that the present invention realizes above-mentioned purpose is:

General principle of the present invention is the hypocycloid based on a kind of special near linear, and cutterhead is with ω _tspeed rotate, gear is then with ω _gspeed rotate, the now relative motion of gear and cutter is equivalent to cutter, and round as a ball (radius is R _v) and gear round as a ball (radius is R _g) do pure rolling mesh motion.As rolling circle radius and the reference radius r of cutter _vconsistent and equal a half of gear rolling circle radius, i.e. R _v=r _v=R _g/ 2, then the track that the point of a knife of cutter tooth is formed on gear is near linear, thus can be used for the continuous Rolling-cut shear of straight bevel gear.

Technical process of the present invention and parameter calculate is undertaken by following steps:

One, cutting parameter is determined: according to the drawing requirement of straight bevel gear, and the dry processing request cut of cutting or wet, select suitable lathe, clamping mode, the type of cooling, feed speed ω _f, speed of mainshaft ω _c.

Two, the parameter of cutterhead is calculated:

A) number of teeth of cutterhead: by the number of teeth z of gear to be processed _gand root angle δ determines, is calculated as follows: z _t/ z _g=2sin (δ);

B) cutter radius: the first spherical radius R of selected theoretical contact point ₀, be generally in the mid point of tooth surfaces of bevel gears, i.e. R ₀=R _d-B/2, in formula, R _dfor the large end radius of bevel gear, B is the face width of tooth of bevel gear, its radius r _vscope be about:

C) pressure angle of blade: the tough pressure angle of flank of tooth form-cutting is calculated as follows:

α _c＝atan(2r _vtanα/R ₀)，

Wherein α is the pressure angle of gear to be processed, is generally 20 degree.According to twice cutting method, then do not participate in that the tough pressure angle of the shaping cutting of the flank of tooth is desirable is less than α _cvalue with avoid interfere, according to cutting at one time method, then inside and outside cutter be the flank of tooth be shaped tough, its pressure angle is equal to α _c.

D) inside and outside point width: general inside and outside, point width determines according to the modulus of gear and the tough position of the actual cut of cutting, needs in theory repeatedly to calculate, to ensure that a pair gear has good contact zone and sideshake.

Three, cutter spacing parameter:

A) calculate without generate cutter spacing: according to product shape principle and the corresponding Mathematical Modeling of cycloid, calculate the cutter spacing without generate: if lathe is cage chair type lathe, without generate cutter spacing be then:

$\left\{\begin{array}{c}{r}_i=r\\ {\mathrm{\θ}}_i=acos(R_0/2r_v)\end{array}\right.$

Wherein r _ifor radial without generate cutter spacing, θ _ifor angle is without generate cutter spacing

If lathe is cartesian co-ordinate type lathe, without generate cutter spacing be then:

$\left\{\begin{array}{c}{H}_i=r_{c}sin\left({\mathrm{\θ}}_i\right)\\ V_i=R_0/2\end{array}\right.$

Wherein, H _ifor vertical without generate cutter spacing, V _ifor level is without generate cutter spacing.

B) initial cutter spacing is calculated: its start angle relatively increases without the angle of generate or reduces by a generate angle θ _k(by the direction of generate, namely climb cutting and upmilling determine), this angle machining gears gear teeth such as to be from the engaging-in angle to nibbling out cage chair and turning.For cage chair type lathe, initial cutter spacing is calculated as follows:

$\left\{\begin{array}{c}{r}_{i0}=r_c\\ {\mathrm{\θ}}_{i0}=acos(R_0/2r_v)\±{\mathrm{\θ}}_k\end{array}\right.$

Wherein, r _c0for initial radial cutter spacing, θ _i0for initial angle is to cutter spacing.

For cartesian co-ordinate type lathe, then initial cutter spacing is:

$\left\{\begin{array}{c}{H}_{i0}=r_{c}sin({\mathrm{\θ}}_i\±{\mathrm{\θ}}_k)\\ V_{i0}=r_{c}cos({\mathrm{\θ}}_i\±{\mathrm{\θ}}_k)\end{array}\right.$

Wherein, H _i0for initial perpendicular cutter spacing, V _i0for initial level cutter spacing.

Four, position of wheel parameter: determined by the installation of gear, revise the adjustment that this position is conducive to Gear Contact district.

Five, machine root angle parameter: this parameter is determined by the tapered tooth system of gear, to processing equal-depth teeth straight bevel gear, then this parameter is the pitch cone angle of straight bevel gear, and to processing tapered tooth straight bevel gear, then this parameter is the root angle of gear.

Six, the movement relation of each axle: if lathe is the lathe of cage chair type, now the movement relation equation of each axle of lathe is

$\left\{\begin{array}{c}{\mathrm{\ω}}_g={\mathrm{\ω}}_t{z}_t/z_g\\ {\mathrm{\ω}}_c={\mathrm{\ω}}_f\\ r_c=r_v\end{array}\right.$

Wherein ω _gfor gear rotational speed, ω _cfor the rotating speed of cage chair.

If lathe is cartesian co-ordinate type lathe, need by virtual for cutterhead horizontal and vertical axle (being generally X-axis and Y-axis) be a cage chair axle, the amount of feeding of this cage chair axle is the amount of feeding of gear generating motion.But because cutter shaft its angle in right angle motion does not change, so also need an additional differential motion, now, the movement relation equation of each axle of lathe is:

$\left\{\begin{array}{c}{\mathrm{\ω}}_g={\mathrm{\ω}}_t{z}_t/z_g+{\mathrm{\ω}}_c/sin\mathrm{\δ}\\ v_H={\mathrm{\ω}}_c{r}_{v}cos({\mathrm{\ω}}_{c}t+{\mathrm{\θ}}_k)\\ v_V=-{\mathrm{\ω}}_c{r}_v\sin ({\mathrm{\ω}}_{c}t+{\mathrm{\θ}}_k)\end{array}\right.$

Wherein, H and V is respectively the displacement of machine tool horizontal axle and vertical axis, and t is time parameter.

Seven, cutting process: according to the processing of cutting at one time method, then can machine the processing of straight bevel gear according to the lathe setting of the 3rd step; Or adopt the processing of secondary cutting method, then after above-mentioned generating motion completes, by initial cutter spacing mirror image along the horizontal plane, obtain new initial cutter spacing as follows:

$\left\{\begin{array}{c}{r}_{i1}=r_{i0}\\ {\mathrm{\θ}}_{i1}=-{\mathrm{\θ}}_{i0}\end{array}\right.$

$\left\{\begin{array}{c}{H}_{i1}=H_{i0}\\ V_{i1}=-V_{i0}\end{array}\right.$

Above formula is corresponding cage chair type lathe and cartesian co-ordinate type lathe respectively

Then the invariant position (avoiding processing random tooth) of workpiece is ensured, cutter shaft is reversed, once generating motion fast (because this cutter cutting output is very little, the speed mainly optimizing the adjustment contact area event generate of profile of tooth can be quite fast) is carried out again by the movement relation of each axle in the 6th step.

Eight, the adjustment of lathe parameter: due to lathe, cutterhead, the composition errors such as frock, the contact area of the bull wheel that actual cut goes out and steamboat is often inconsistent with theory calculate, can finely tune to reach best contact condition to the movement relation of the workpiece spindle of cutter spacing and machine tool chief axis.

The present invention has following features: its Cutting Process is continuous rolling cut (face-hobbing), has higher production efficiency machining accuracy; Can wet and cut also ability and cut, dry working (machining) efficiency of cutting is higher, and flank of tooth fineness is better, but higher to the requirement of cutter and lathe, wet cut just the opposite; Process the straight bevel gear obtained not be strict straight line at its tooth length direction but have the cydariform of trace, and adjustment lathe state modulator cydariform amount can be passed through, thus the contact area of profile shifted gear, make it have better transmission performance; The straight bevel gear of equal-depth teeth and tapered tooth two kinds of teeth can be processed.

Accompanying drawing explanation

Fig. 1 is basic process principle schematic diagram of the present invention.

Fig. 2 is cutter head structure schematic diagram used in the present invention.

Fig. 3 is that the present invention carries out cutting at one time cutter head structure front view used.

Fig. 4 is that the present invention carries out cutting at one time cutter head structure top view used.

Fig. 5 is that the present invention carries out cutting at one time cutter head structure left view used.

Fig. 6 is that the present invention carries out secondary cutting cutter head structure front view used.

Fig. 7 is that the present invention carries out secondary cutting cutter head structure top view used.

Fig. 8 is that the present invention carries out secondary cutting cutter head structure left view used.

Fig. 9 is that the present invention finally processes the structural representation obtaining straight bevel gear.

In figure: 1. cutter is round as a ball, 2. outer cutter, cutter 3., 4. workpiece gear, 5. straight-side profile, 6. cutterhead, 7. gear is round as a ball.

Detailed description of the invention

As shown in Figure 1, general principle of the present invention is the hypocycloid based on a kind of special near linear, and cutterhead is with ω _tspeed rotate, gear is then with ω _gspeed rotate, the now relative motion of gear and cutter is equivalent to cutter round as a ball 1, and (radius is R _v) and gear round as a ball 7 (radius is R _g) do pure rolling mesh motion.As round as a ball 1 radius of cutter and reference radius r _vconsistent and equal a half of round as a ball 7 radiuses of gear, i.e. R _v=r _v=R _g/ 2, then the track that the point of a knife of cutter tooth is formed on gear is near linear, thus can be used for the continuous Rolling-cut shear of straight bevel gear.

In reality processing, because cutterhead and gear and the number of teeth can not strictly meet above-mentioned theory requirement, therefore the profile of tooth of processing is difficult to accomplish absolute straight line.True this absolute straight line is also unfavorable to transmission properties, therefore will adjust location parameter in right amount, thus is formed with the straight line flank of tooth of micro-cydariform.

The gear of side can be made to meet the requirement of cydariform according to above optimization, but the curved surface formed due to outer cutter 2 and interior cutter 3 does not have symmetry on the gear teeth.If only use cutting at one time, some difference permitted of left and right profile of tooth of gear can be made.Therefore cutting at one time method and twice cutting method can be divided into: cutting at one time method only carries out cutting at one time, and the gear teeth and the left and right sides flank of tooth are once formed by the inside and outside cutter of cutter is tough, and the benefit of this processing method is that working (machining) efficiency is high.But shortcoming is the left and right flank of tooth the asymmetric of trace, contact zone is difficult to adjustment; Secondary cutting method is on the basis of cutting at one time, use that reverse cutter is tough to be cut once again, two lateral tooth flanks of gear are formed by the outer cutter 2 (or interior cutter 3) of cutter, two lateral tooth flanks absolute symmetry in theory, its benefit is flank profil full symmetric, and contact zone easily adjusts.

Process tool

In order to avoid cutterhead is interfered and secondary cutting, utilize the present invention to cut cutterhead 6 shape of straight bevel gear as shown in Figure 2, cutterhead 6, regardless of rotation direction, can fill left-handed cutterhead, also can fill dextrorotation cutterhead.Cutting at one time method adopts the cutter head of different rotation direction when processing large steamboat, tip shapes is as shown in Fig. 3, Fig. 4, Fig. 5; Secondary cutting method adopts cutter head as shown in Fig. 6, Fig. 7 Fig. 8, and this cutter head, therefore can twice cutting regardless of rotation direction.Machining tool

This process is cut straight bevel gear and can be realized on the lathe that can realize generation processing spiral bevel gear.The structure of lathe can be cage chair formula and Cartesian coordinate type.

A pair straight bevel gear can be processed by identical cutterhead or process separately with different cutterheads, obtains best lathe adjusting parameter by theory calculate, finally revises lathe adjusting parameter according to reality contact situation, to optimize the contact situation of gear.

Use the present invention namely can process tapered tooth straight bevel gear and also can process equal-depth teeth straight bevel gear, during processing tapered tooth straight bevel gear, the root angle adjustment parameter of lathe is determined by the root angle of gear, and when processing equal-depth teeth straight bevel gear, the root angle of lathe adjusts parameter and determined by the pitch cone angle of gear.

Tapered tooth straight bevel gear to be processed, its basic parameter is as shown in the table:

Form 1 Basic parameters of gear

According to above parameter, 6 axle Cartesian coordinate type spiral bevel gear milling machines are processed, use the processing of secondary cutting method, its step is as follows:

1, as follows according to the basic cutting parameter of processing conditions determination gear

The basic processing conditions of form 2

2, cutter basic parameter is calculated according to said method as shown in the table:

Form 3 cutterhead and insert parameters

3, calculate initial cutter spacing according to said method, obtain the basic adjustment parameter following (because the large steamboat of a pair gear is just the same, therefore machined parameters is completely the same) of lathe

4, the equation of motion calculating lathe is as follows:

$\left\{\begin{array}{c}{\mathrm{\ω}}_g=152.358r/min\\ v_H=7.98\cos (0.105t+0.419)\\ v_V=-{7.98}_{v}sin(0.105t+0.419)\end{array}\right.$

According to above parameter, can process the straight-side profile 5 obtaining workpiece gear 4, finally processing obtains the structure of straight bevel gear as shown in Figure 9.

Claims (1)

1. a continuous Rolling-cut shear method for straight bevel gear, is characterized in that: based on a kind of hypocycloid of special near linear, cutterhead is with ω _tspeed rotate, gear is then with ω _gspeed rotate, the now relative motion of gear and cutter is equivalent to cutter, and round as a ball (radius is R _v) and gear round as a ball (radius is R _g) do pure rolling mesh motion; As cutter rolling circle radius and reference radius r _vconsistent and equal a half of gear rolling circle radius, i.e. R _v=r _v=R _g/ 2, then the track that the point of a knife of cutter tooth is formed on gear is near linear, thus can be used for the continuous Rolling-cut shear of straight bevel gear;

Technical process and parameter calculate is undertaken by following steps:

One, cutting parameter is determined: according to the drawing requirement of straight bevel gear, and the dry processing request cut of cutting or wet, select suitable lathe, clamping mode, the type of cooling, feed speed ω _f, speed of mainshaft ω _c;

Two, the parameter of cutterhead is calculated:

A) number of teeth of cutterhead: by the number of teeth z of gear to be processed _gand root angle δ determines, is calculated as follows: z _t/ z _g=2sin (δ);

B) cutter radius: the first spherical radius R of selected theoretical contact point ₀, be generally in the mid point of tooth surfaces of bevel gears, i.e. R ₀=R _d-B/2, in formula, R _dfor the large end radius of bevel gear, B is the face width of tooth of bevel gear, its radius r _vscope be about:

C) pressure angle of blade: the tough pressure angle of flank of tooth form-cutting is calculated as follows:

α _c＝atan(2r _vtanα/R ₀)，

Wherein α is the pressure angle of gear to be processed, is generally 20 degree; According to twice cutting method, then do not participate in that the tough pressure angle of the shaping cutting of the flank of tooth is desirable is less than α _cvalue with avoid interfere, according to cutting at one time method, then inside and outside cutter be the flank of tooth be shaped tough, its pressure angle is equal to α _c;

D) inside and outside point width: general inside and outside, point width determines according to the modulus of gear and the tough position of the actual cut of cutting, needs in theory repeatedly to calculate, to ensure that a pair gear has good contact zone and sideshake;

Three, cutter spacing parameter:

A) calculate without generate cutter spacing: according to product shape principle and the corresponding Mathematical Modeling of cycloid, calculate the cutter spacing without generate: if lathe is cage chair type lathe, without generate cutter spacing be then:

$\left\{\begin{array}{c}{r}_i=r\\ {\mathrm{\θ}}_i=acos(R_0/2r_v)\end{array}\right.$

Wherein r _ifor radial without generate cutter spacing, θ _ifor angle is without generate cutter spacing

If lathe is cartesian co-ordinate type lathe, without generate cutter spacing be then:

$\left\{\begin{array}{c}{H}_i=r_{c}sin\left({\mathrm{\θ}}_i\right)\\ V_i=R_0/2\end{array}\right.$

Wherein, H _ifor vertical without generate cutter spacing, V _ifor level is without generate cutter spacing;

B) initial cutter spacing is calculated: its start angle relatively increases without the angle of generate or reduces by a generate angle θ _k(by the direction of generate, namely climb cutting and upmilling determine), this angle machining gears gear teeth such as to be from the engaging-in angle to nibbling out cage chair and turning; For cage chair type lathe, initial cutter spacing is calculated as follows:

$\left\{\begin{array}{c}{r}_{i0}=r_c\\ {\mathrm{\θ}}_{i0}=acos(R_0/2r_v)\±{\mathrm{\θ}}_k\end{array}\right.$

Wherein, r _c0for initial radial cutter spacing, θ _i0for initial angle is to cutter spacing;

For cartesian co-ordinate type lathe, then initial cutter spacing is:

$\left\{\begin{array}{c}{H}_{i0}=r_{c}sin({\mathrm{\θ}}_i\±{\mathrm{\θ}}_k)\\ V_{i0}=r_{c}cos({\mathrm{\θ}}_i\±{\mathrm{\θ}}_k)\end{array}\right.$

Wherein, H _i0for initial perpendicular cutter spacing, V _i0for initial level cutter spacing;

Four, position of wheel parameter: determined by the installation of gear, revise the adjustment that this position is conducive to Gear Contact district;

Five, machine root angle parameter: this parameter is determined by the tapered tooth system of gear, to processing equal-depth teeth straight bevel gear, then this parameter is the pitch cone angle of straight bevel gear, and to processing tapered tooth straight bevel gear, then this parameter is the root angle of gear;

Six, the movement relation of each axle: if lathe is the lathe of cage chair type, now the movement relation equation of each axle of lathe is

$\left\{\begin{array}{c}{\mathrm{\ω}}_g={\mathrm{\ω}}_t{z}_t/z_g\\ {\mathrm{\ω}}_c={\mathrm{\ω}}_f\\ r_c=r_v\end{array}\right.$

Wherein ω _gfor gear rotational speed, ω _cfor the rotating speed of cage chair;

If lathe is cartesian co-ordinate type lathe, need by virtual for cutterhead horizontal and vertical axle (being generally X-axis and Y-axis) be a cage chair axle, the amount of feeding of this cage chair axle is the amount of feeding of gear generating motion; But because cutter shaft its angle in right angle motion does not change, so also need an additional differential motion, now, the movement relation equation of each axle of lathe is:

$\left\{\begin{array}{c}{\mathrm{\ω}}_g={\mathrm{\ω}}_t{z}_t/z_g+{\mathrm{\ω}}_c/sin\mathrm{\δ}\\ v_H={\mathrm{\ω}}_c{r}_{v}cos({\mathrm{\ω}}_{c}t+{\mathrm{\θ}}_k)\\ v_V=-{\mathrm{\ω}}_c{r}_v\sin ({\mathrm{\ω}}_{c}t+{\mathrm{\θ}}_k)\end{array}\right.$

Wherein, H and V is respectively the displacement of machine tool horizontal axle and vertical axis, and t is time parameter;

Seven, cutting process: according to the processing of cutting at one time method, then can machine the processing of straight bevel gear according to the lathe setting of the 3rd step; Or adopt the processing of secondary cutting method, then after above-mentioned generating motion completes, by initial cutter spacing mirror image along the horizontal plane, obtain new initial cutter spacing as follows:

$\left\{\begin{array}{c}{r}_{i1}=r_{i0}\\ {\mathrm{\θ}}_{i1}=-{\mathrm{\θ}}_{i0}\end{array}\right.$

$\left\{\begin{array}{c}{H}_{i1}=H_{i0}\\ V_{i1}=-V_{i0}\end{array}\right.$

Above formula is corresponding cage chair type lathe and cartesian co-ordinate type lathe respectively

Then the invariant position (avoiding processing random tooth) of workpiece is ensured, cutter shaft is reversed, once generating motion fast (because this cutter cutting output is very little, the speed mainly optimizing the adjustment contact area event generate of profile of tooth can be quite fast) is carried out again by the movement relation of each axle in the 6th step;

Eight, the adjustment of lathe parameter: due to lathe, cutterhead, the composition errors such as frock, the contact area of the bull wheel that actual cut goes out and steamboat is often inconsistent with theory calculate, can finely tune to reach best contact condition to the movement relation of the workpiece spindle of cutter spacing and machine tool chief axis.