CN102581384A - Gear shaping method based on equal cutting area - Google Patents

Abstract

The invention relates to a gear shaping method based on the equal cutting area, which is characterized in that gear shaping of a gear aims to realize shaping with equal cutting force by means of gear shaping with equal cutting area. The gear shaping method has the advantages that the method can be used only by adding corresponding numerical control codes without changing a main structure of a machine tool, main driving force of the machine tool can be fully used in a rough shaping phase, instability of the machine tool is reduced, shaping time is shortened, shaping cost is reduced, and shaping efficiency is improved.

Description

A kind of based on etc. the Gear Shaping method of the area of cut

Technical field

The invention belongs to the gear machining technology field, particularly relate to a kind of based on etc. the Gear Shaping method of the area of cut.

Background technology

At present, gear is the crucial transmission parts in the machinery manufacturing industry, wherein uses the most extensive with roller gear again.Gear shaping is one of main mode of roller gear processing.During Gear Shaping, pinion cutter is parallel with axis of workpiece, and pinion cutter and workpiece are with fixing rolling than doing generating motion, and pinion cutter is done reciprocal cutting movement simultaneously, thereby on workpiece, processes the teeth groove with pinion cutter profile of tooth conjugation.

In the conventional Gear Shaping, pinion cutter and workpiece are done generating motion with constant rotational speed separately, cause in the process of teeth groove, and the gear shaping area of cut changes and constantly changes with the Working position of teeth groove in the unit interval, causes the cutting force cyclic fluctuation.In a cutting cycle, gear shapping machine has only the very short period can be operated in rated load, and the live load of most of period is far below rated value.The Gear Shaping mode of this routine can not make full use of the gear shapping machine load-bearing capacity, and working (machining) efficiency is low.In addition, the cyclic fluctuation of cutting force also possibly excite the vibration of gear shapping machine multiband, and workpiece crudy and gear shapping machine are produced ill effect.

Summary of the invention

The present invention for solve the technical problem that exists in the known technology provide a kind of based on etc. the Gear Shaping method of the area of cut; This method does not change the gear shapping machine agent structure; Only need in the gear shapping machine digital control system, to add the load-bearing capacity that corresponding numerical control code can make full use of gear shapping machine; Improve the roller gear working (machining) efficiency, reduce production costs.

The technical scheme that the present invention takes for the technical problem that exists in the solution known technology is:

A kind of based on etc. the Gear Shaping method of the area of cut, it is characterized in that: to the Gear Shaping of gear for waiting cutting force processing.

The present invention can also adopt following technical scheme:

Saidly wait that cutting force processing is passed through etc. area of cut processing realizes.

Should based on etc. the Gear Shaping method of the area of cut, may further comprise the steps:

A: set initial parameter, set up pinion cutter flank profil Mathematical Modeling, and calculate the Mathematical Modeling of two processed teeth;

B: calculate pinion cutter machining locus in the conventional method, and extract the machining locus discrete data point.

C: establishment computer aided design software secondary development program, conventional processing method process is carried out reconstruct, and simulate the Boolean calculation in the process, and then try to achieve the area of cut in the required moment, draw area of cut Changing Pattern in the conventional processing method.

D: the above-mentioned area of cut variation rule curve in the C step is carried out adaptive analysis.

E: convert the analysis result in the D step into cutter rotation speed change rule.

F: the cutter rotation speed change rule of correspondence when gained cutter rotation speed change rule is the feeding of cutting force such as realization self adaptation.

G: the response speed that combines machine tool numerical control system; From cutter rotation speed change law curve, choose some crucial rotating speed points; And confirm the time that each rotating speed continues according to the lathe stroke time; Make numerical control program repeat desired rotating speed, need measuring system constructing to measure main shaft cutting force in real time simultaneously, selected rotating speed point is suitably adjusted.

Advantage and good effect that the present invention has are:

After the present invention has adopted above technical scheme, utilize adaptive method with cutting force processing such as constant speed processing change into, need not to change the machine tool main body structure, only needing to add corresponding numerical control code can use.Adopt this method to make full use of the lathe main driving force, slow down not stationary vibration of lathe, shorten process time, cut down finished cost, improve working (machining) efficiency in the roughing stage.

Description of drawings

The n time area of cut sketch map when Fig. 1 adopts the conventional method Gear Shaping;

The n+1 time area of cut sketch map when Fig. 2 adopts the conventional method Gear Shaping;

Fig. 3 adopts the area of cut sketch map of method Gear Shaping of the present invention the n time;

Fig. 4 adopts the area of cut sketch map of method Gear Shaping of the present invention the n+1 time;

The flow chart of Fig. 5 the inventive method;

Fig. 6 gear pair coordinate system sketch map;

Fig. 7 pinion cutter tooth curve figure;

Each movement relation sketch map in Fig. 8 Gear Shaping process;

Fig. 9 involute profile gear tooth slot forming process sketch map;

Figure 10 simulates Boolean calculation and finds the solution area of cut process sketch map;

Figure 11 routine based on etc. the area of cut block diagram of Gear Shaping method of the area of cut;

Figure 12 routine based on etc. the area of cut variation rule curve of Gear Shaping method of the area of cut;

Total area cut variation rule curve after Figure 13 stack;

Figure 14 process waits the area of cut Changing Pattern behind the cutting force adaptive analysis;

Figure 15 satisfies the cutter rotation speed change rule that waits the feeding of cutting force self adaptation;

The specific embodiment

For further understanding summary of the invention of the present invention, characteristics and effect, the following examples of giving an example now, and conjunction with figs. specifies as follows:

See also Fig. 1 to Figure 15, a kind of based on etc. the Gear Shaping method of the area of cut, wait the adaptive algorithm block diagram of cutting force as shown in Figure 2.A is the area of cut among Fig. 2, A _mBe the maximum area of cut, X is the area of cut coefficient of variation of confirming according to the lathe load capacity.

For ease of explanation, set up gear pair coordinate system as shown in Figure 3.Wherein, (O-x y) is inertial coodinate system; (O ₁-x ₁, y ₁) be tool coordinate system, connect firmly with pinion cutter; (O ₂-x ₂, y ₂) be the wheel blank coordinate system, connect firmly with processed gear; α is a pressure angle of graduated circle; α _kBe arbitrarily round pressure angle; I is the gear pair gearratio; r _A1Be the pinion cutter radius of addendum; r _A2Be processed gear teeth tips radius of circle; r _B2Be processed rolling circle radius; z ₁Be the cutter number of teeth; z ₂Be the processed gear number of teeth; φ is the corresponding central angle of cutter teeth tip circle arc; n ₁Be the cutter rotating speed; n ₂Be processed gear rotational speed.

(1) sets up pinion cutter flank profil Mathematical Modeling

According to the gears engaged theory pinion cutter tooth curve is carried out mathematical modeling, tooth curve is by two sections involutes, two sections epicycloids, and one section circular arc is formed, and is as shown in Figure 4.

Involute equation under the tool coordinate system is following:

$\left\{\begin{array}{c}{x_1}^{\left(1\right)}=\frac{{\mathrm{<figure-callout\; id="2"\; label="r\; b"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">r</figure-callout>}}_b\sin (i(\mathrm{\&alpha;}-\tan {\mathrm{\&alpha;}}_k)+\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_k)}{\cos {\mathrm{\&alpha;}}_k}-a\sin \left(i(\mathrm{\&alpha;}-\tan {\mathrm{\&alpha;}}_k)\right)\\ {y_1}^{\left(1\right)}=\frac{{\mathrm{<figure-callout\; id="2"\; label="r\; b"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">r</figure-callout>}}_b\cos (i(\mathrm{\&alpha;}-\tan {\mathrm{\&alpha;}}_k)+\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_k)}{\cos {\mathrm{\&alpha;}}_k}-a\cos \left(i(\mathrm{\&alpha;}-\tan {\mathrm{\&alpha;}}_k)\right)\end{array}\right.---\left(1\right)$

$\left\{\begin{array}{c}{x_2}^{\left(1\right)}=\frac{{\mathrm{<figure-callout\; id="2"\; label="r\; b"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">r</figure-callout>}}_b}{\cos {\mathrm{\&alpha;}}_k}\sin (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan {\mathrm{\&alpha;}}_k+\frac{\mathrm{\&pi;}}{z_2})+{\mathrm{\&alpha;}}_k-\mathrm{\&alpha;})-a\sin (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan {\mathrm{\&alpha;}}_k+\frac{\mathrm{\&pi;}}{z_2})\\ {y_2}^{\left(1\right)}=\frac{{\mathrm{<figure-callout\; id="2"\; label="r\; b"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">r</figure-callout>}}_b}{\cos {\mathrm{\&alpha;}}_k}\cos (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan {\mathrm{\&alpha;}}_k+\frac{\mathrm{\&pi;}}{z_2})+{\mathrm{\&alpha;}}_k-\mathrm{\&alpha;})-a\cos (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan {\mathrm{\&alpha;}}_k+\frac{\mathrm{\&pi;}}{z_2})\end{array}\right.---\left(2\right)$

Epicycloid equation under the tool coordinate system is following:

$\left\{\begin{array}{c}{x_3}^{\left(1\right)}=r_{a2}\sin (i(\mathrm{\&alpha;}-\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right))+\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_k)-a\sin \left(i(\mathrm{\&alpha;}-\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right))\right)\\ {y_3}^{\left(1\right)}=r_{a2}\cos (i(\mathrm{\&alpha;}-\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right))+\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_k)-a\cos \left(i(\mathrm{\&alpha;}-\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right))\right)\end{array}\right.---\left(3\right)$

$\left\{\begin{array}{c}{x_4}^{\left(1\right)}=r_{a2}\sin (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right)+\frac{\mathrm{\&pi;}}{z_2})+\left(\arccos \frac{r_{b2}}{r_{a2}}\right)-\mathrm{\&alpha;})\\ -a\sin (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right)+\frac{\mathrm{\&pi;}}{z_2})\\ {y_4}^{\left(1\right)}=r_{a2}\cos (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right)+\frac{\mathrm{\&pi;}}{z_2})+\left(\arccos \frac{r_{b2}}{r_{a2}}\right)-\mathrm{\&alpha;})\\ -a\cos (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right)+\frac{\mathrm{\&pi;}}{z_2})\end{array}\right.---\left(4\right)$

Circular arc equation under the tool coordinate system is following:

$\left\{\begin{array}{c}{x_5}^{\left(1\right)}=r_{a1}\cos \mathrm{\&phi;}\\ {y_5}^{\left(1\right)}=r_{a1}\sin \mathrm{\&phi;}\end{array}\right.---\left(5\right)$

When setting up the cutter Mathematical Modeling, need confirm to calculate the minimum number n of cutter tooth ₁, basis principle is in the analysis of cutter machining locus, to guarantee can cut out at least two complete profiles of tooth, and combines registration ε to choose according to formula (6).

${\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">n</figure-callout>}}_1=\left\{\begin{array}{cc}2& 1\&le;\mathrm{\&epsiv;}<2\\ 3& 2\&le;\mathrm{\&epsiv;}<3\end{array}\right.---\left(6\right)$

Can set up the Mathematical Modeling [x of one of them tooth according to formula (1)-(5) _my _m1]

$\left[\begin{array}{ccc}{x}_m& y_{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">m</figure-callout>}}& 1\end{array}\right]=\left[\begin{array}{ccc}{x}_1^{\left(1\right)}& y_1^{\left(1\right)}& 1\\ x_2^{\left(1\right)}& y_2^{\left(1\right)}& 1\\ x_3^{\left(1\right)}& y_3^{\left(1\right)}& 1\\ x_4^{\left(1\right)}& y_4^{\left(1\right)}& 1\\ x_5^{\left(1\right)}& y_5^{\left(1\right)}& 1\end{array}\right]---\left(7\right)$

The number of teeth model on the left side is [x _Ly _L1]

$\left[\begin{array}{ccc}{x}_{\mathrm{<figure-callout\; id="1"\; label="L\; y\; L"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">L</figure-callout>}}& y_L{}_{}& 1\end{array}\right]=\left[\begin{array}{ccc}{x}_m& y_{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">m</figure-callout>}}& 1\end{array}\right]\left[\begin{array}{ccc}\cos (2\mathrm{\&pi;}-\frac{2\mathrm{\&pi;}}{z_1})& \sin (2\mathrm{\&pi;}-\frac{2\mathrm{\&pi;}}{z_1})& 0\\ -\sin (2\mathrm{\&pi;}-\frac{2\mathrm{\&pi;}}{z_1})& \cos (2\mathrm{\&pi;}-\frac{2\mathrm{\&pi;}}{z_1})& 0\\ 0& 0& 1\end{array}\right]---\left(8\right)$

The number of teeth model on the right is [x _Ry _R1]

$\left[\begin{array}{ccc}{x}_{\mathrm{<figure-callout\; id="1"\; label="R\; y\; R"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">R</figure-callout>}}& y_R{}_{}& 1\end{array}\right]=\left[\begin{array}{ccc}{x}_m& y_{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">m</figure-callout>}}& 1\end{array}\right]\left[\begin{array}{ccc}\cos (2\mathrm{\&pi;}+\frac{2\mathrm{\&pi;}}{z_1})& \sin (2\mathrm{\&pi;}+\frac{2\mathrm{\&pi;}}{z_1})& 0\\ -\sin (2\mathrm{\&pi;}+\frac{2\mathrm{\&pi;}}{z_1})& \cos (2\mathrm{\&pi;}+\frac{2\mathrm{\&pi;}}{z_1})& 0\\ 0& 0& 1\end{array}\right]---\left(9\right)$

(2) calculate pinion cutter machining locus in the conventional processing method

The digital control gear shaper process is respectively the straight reciprocating motion of Z axle, cutter shaft Z by the motion realization of 3 axles ₁Axle is with angular velocity omega ₁Carry out the constant speed rotation, workbench Z ₂With angular velocity omega ₂Carry out the constant speed rotation, the movement relation between each is as shown in Figure 5.

Suppose that processed gear rotation crosses an angular pitch required time

T ₁=0, so at [T ₁, T ₂] calculate machining locus in the time period, process constantly index suc as formula shown in (10).

$t={\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">T</figure-callout>}}_1+(T_2-T_1)\frac{j-1}{59},$ t∈[T ₁，T ₂] (10)

J=1 wherein, 2 ..., 60.

All need cutter be transformed to workpiece coordinate system from tool coordinate system at each moment t, the coordinate transform formula that realizes this conversion is suc as formula shown in (11).

$\left[\begin{array}{c}{x}^{\left(2\right)}\\ y^{\left(2\right)}\\ 1\end{array}\right]=M_{21}\left[\begin{array}{c}{x}^{\left(1\right)}\\ y^{\left(1\right)}\\ 1\end{array}\right]---\left(11\right)$

By tool coordinate system (O ₁-x ₁, y ₁) transform to workpiece coordinate system (O ₂-x ₂, y ₂) transformation matrix be M ₂₁

$M_{21}={\left(M_{02}\right)}^{-1}\&CenterDot;M_{01}=\left[\begin{array}{ccc}\cos (\frac{t\&CenterDot;n_1}{i}+t\&CenterDot;n_1)& -\sin (\frac{t\&CenterDot;n_1}{t}+t\&CenterDot;n_1)& -a\sin \frac{t\&CenterDot;n_1}{i}\\ \sin (\frac{t\&CenterDot;n_1}{i}+t\&CenterDot;n_1)& \cos (\frac{t\&CenterDot;n_1}{i}+t\&CenterDot;n_1)& a\cos \frac{t\&CenterDot;n_1}{\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="HDA0000144685330000032.png,HDA0000144685330000061.png"\; state="\{\{state\}\}">i</figure-callout>}}\\ 0& 0& 1\end{array}\right]---\left(12\right)$

Wherein by tool coordinate system (O ₁-x ₁, y ₁) (O-x, transformation matrix y) are M to transform to inertial coodinate system ₀₁

$M_{01}=\left(\begin{array}{ccc}\cos t\&CenterDot;n_1& -\sin t\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">n</figure-callout>}}_1& 0\\ \sin t\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">n</figure-callout>}}_1& \cos t\&CenterDot;n_1& a\\ 0& 0& 1\end{array}\right)---\left(13\right)$

By wheel blank coordinate system (O ₂-x ₂, y ₂) (O-x, transformation matrix y) are M to transform to inertial coodinate system ₀₂

$M_{02}=\left(\begin{array}{ccc}\cos \frac{t\&CenterDot;n_1}{i}& \sin \frac{t\&CenterDot;n_1}{i}& 0\\ -\sin \frac{t\&CenterDot;n_1}{i}& \cos \frac{t\&CenterDot;n_1}{\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="HDA0000144685330000032.png,HDA0000144685330000061.png"\; state="\{\{state\}\}">i</figure-callout>}}& 0\\ 0& 0& 1\end{array}\right)---\left(14\right)$

By formula (11), at t ∈ [T ₁, T ₂] interior each moment; Can the pinion cutter tooth curve be transformed to the wheel blank coordinate system by tool coordinate system, promptly obtain a series of positions of pinion cutter flank profil in the wheel blank coordinate system, i.e. machining locus; The envelope of position formation is teeth groove---the involute profile of gear thus, and is as shown in Figure 6.

(3) area of cut Changing Pattern of pinion cutter in the analytic routines Gear Shaping process

Digital control gear shaper pinion cutter in process not only has the constant speed revolution, and back and forth cutting is also arranged axially, so this method is only derived in any tooth base cross section.The Gear Shaping process is seen as a series of Boolean calculations that cutter and wheel blank are done from geometric angle, and finally the envelope by a series of positions that obtained of pinion cutter flank profil in the wheel blank coordinate system is the involute profile that is cut into.Choosing a cutter tooth finds the solution the area of cut and describes; At first each the bar tooth curve in this cutter tooth machining locus is dispersed respectively and be some spots; Utilize the aforementioned discrete data point of computer aided design software secondary development routine call then, machining locus is carried out reconstruct, and then through secondary process simulation Boolean calculation process; Can try to achieve the area of cut of current pinion cutter slotting, the analog approach process is as shown in Figure 7.Utilize this method iterative solution, just can try to achieve all areas of cut, area of cut block diagram is as shown in Figure 8.

Gained area of cut variation rule curve is carried out match, can find that the area of cut is cyclically-varying rule (as shown in Figure 9) in the gear shaping process.

(4) to routine based on etc. the Gear Shaping method area of cut Changing Pattern of the area of cut carry out adaptive analysis, and the cutter rotating speed law curve of the cutting force self adaptation feedings such as realization of deriving

The area of cut law curve reflection that (3) step drew be the area change rule of slotting each time, so the Changing Pattern (shown in figure 10) of the total area cut will convert into this curve from initial time to slotting each time the time.After converting law curve is carried out match, utilize formula (15) to analyze afterwards, establish A _mBe the maximum area of cut, a ₁T ⁿ+ a ₂T ^N-1+ ... + a _nT+a _N+1Be the fit equation of law curve, a ₁... A _nCoefficient for variable in the fit equation.

$\left\{\begin{array}{c}{A}_m\&CenterDot;1=\&Integral;\left(\mathrm{\&Sigma;aT}\right)\mathrm{dt}=a_1{T}_1^n+a_2{T}_1^{n-1}+...a_{\mathrm{<figure-callout\; id="1"\; label="n\; T"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">n</figure-callout>}}{T}_{}{}_1+a_{n+1}\\ A_m\&CenterDot;2=\&Integral;\left(\mathrm{\&Sigma;aT}\right)\mathrm{dt}=a_1{T}_2^n+a_2{T}_2^{n-1}+...+a_{\mathrm{<figure-callout\; id="2"\; label="n\; T"\; filenames="HDA0000144685330000032.png,HDA0000144685330000042.png"\; state="\{\{state\}\}">n</figure-callout>}}{T}_{}{}_2+a_{n+1}\\ .\\ .\\ .\\ A_m\&CenterDot;n=\&Integral;\left(\mathrm{\&Sigma;aT}\right)\mathrm{dt}=a_1{T}_n^n+a_2{T}_n^{n-1}+...+a_n{T}_n+a_{n+1}\end{array}\right.---\left(15\right)$

Separate formula (15) and can obtain T ₁..., T _nSeries of points, repeating step (2), (3) can be obtained the corresponding area of cut of each point, and whether checking is positioned at A _mWithin ± 5%,, need carry out local correction if the data point that exceeds deviation is arranged.If promptly this puts the corresponding area of cut greater than A _m± 5%, explain that this point value is bigger than normal, need suitably reduce; If this puts the corresponding area of cut less than A _m± 5%, explain that this point value is less than normal, need suitably to increase.Repeating step (2), (3) once more after the local correction all are positioned at A until the corresponding area of cut of all T points so repeatedly _mWithin ± 5% (shown in figure 11).

With revised T point by formula (T _i-T _I-1) n ₁Convert the cutter rotating speed into, obtain cutter rotation speed change law curve then, be and satisfy the pinion cutter rotation speed change rule (shown in figure 12) that waits the feeding of cutting force self adaptation.

(5) generate new numerical control code

After the pinion cutter rotation speed change rule of cutting force self adaptation feedings such as being met, can write new numerical control code.The key that numerical control code is write is how to make the cutting of pinion cutter variable speed; At first from rotation speed change law curve shown in Figure 12, choose some crucial rotating speed points, the principle of choosing is to take into account the response speed of machine tool control system and improve working (machining) efficiency to greatest extent; Confirm the time of implementation of all crucial rotating speed points then, definite principle is to take into account the time of each stroke and the effect of practical application.

Although combine accompanying drawing that the preferred embodiments of the present invention are described above; But the present invention is not limited to the above-mentioned specific embodiment, and the above-mentioned specific embodiment only is schematically, is not restrictive; Those of ordinary skill in the art is under enlightenment of the present invention; Not breaking away under the scope situation that aim of the present invention and claim protect, can also make a lot of forms, these all belong within protection scope of the present invention.

Claims (7)

1. One kind based on etc. the Gear Shaping method of the area of cut, it is characterized in that: to the Gear Shaping of gear for waiting cutting force processing.
2. 2. according to claim 1 a kind of based on etc. the Gear Shaping method of the area of cut, it is characterized in that: saidly wait that cutting force processing is passed through etc. area of cut processing realizes.
3. 3. according to claim 2 a kind of based on etc. the Gear Shaping method of the area of cut, may further comprise the steps:

   A: set initial parameter, set up pinion cutter flank profil Mathematical Modeling, and calculate the Mathematical Modeling of two processed teeth;

   B: calculate pinion cutter machining locus in the conventional method, and extract the machining locus discrete data point.

   C: establishment computer aided design software secondary development program, conventional processing method process is carried out reconstruct, and simulate the Boolean calculation in the process, and then try to achieve the area of cut in the required moment, draw area of cut Changing Pattern in the conventional processing method.

   D: the above-mentioned area of cut variation rule curve in the C step is carried out adaptive analysis.

   E: convert the analysis result in the D step into cutter rotation speed change rule.

   F: the cutter rotation speed change rule of correspondence when gained cutter rotation speed change rule is the feeding of cutting force such as realization self adaptation.

   G: the response speed that combines machine tool numerical control system; From cutter rotation speed change law curve, choose some crucial rotating speed points; And confirm the time that each rotating speed continues according to the lathe stroke time; Make numerical control program repeat desired rotating speed, need measuring system constructing to measure main shaft cutting force in real time simultaneously, selected rotating speed point is suitably adjusted.
4. 4. according to claim 3 a kind of based on etc. the Gear Shaping method of the area of cut, (O-x y) is inertial coodinate system; (O ₁-x ₁, y ₁) be tool coordinate system, connect firmly with pinion cutter; (O ₂-x ₂, y ₂) be the wheel blank coordinate system, connect firmly with processed gear; α is a pressure angle of graduated circle; α _kBe arbitrarily round pressure angle; I is the gear pair gearratio; r _A1Be the pinion cutter radius of addendum; r _A2Be processed gear teeth tips radius of circle; r _B2Be processed rolling circle radius; z ₁Be the cutter number of teeth; z ₂Be the processed gear number of teeth; φ is the corresponding central angle of cutter teeth tip circle arc; n ₁Be the cutter rotating speed; n ₂Be processed gear rotational speed;

   Wherein in the A step, the Mathematical Modeling of setting up the pinion cutter flank profil is:

   The involute equation of tool coordinate system is following:

   $\left\{\begin{array}{c}{x_1}^{\left(1\right)}=\frac{r_{b2}\sin (i(\mathrm{\&alpha;}-\tan {\mathrm{\&alpha;}}_k)+\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_k)}{\cos {\mathrm{\&alpha;}}_k}-a\sin \left(i(\mathrm{\&alpha;}-\tan {\mathrm{\&alpha;}}_k)\right)\\ {y_1}^{\left(1\right)}=\frac{r_{b2}\cos (i(\mathrm{\&alpha;}-\tan {\mathrm{\&alpha;}}_k)+\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_k)}{\cos {\mathrm{\&alpha;}}_k}-a\cos \left(i(\mathrm{\&alpha;}-\tan {\mathrm{\&alpha;}}_k)\right)\end{array}\right.---\left(1\right)$

   $\left\{\begin{array}{c}{x_2}^{\left(1\right)}=\frac{r_{b2}}{\cos {\mathrm{\&alpha;}}_k}\sin (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan {\mathrm{\&alpha;}}_k+\frac{\mathrm{\&pi;}}{z_2})+{\mathrm{\&alpha;}}_k-\mathrm{\&alpha;})-a\sin (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan {\mathrm{\&alpha;}}_k+\frac{\mathrm{\&pi;}}{z_2})\\ {y_2}^{\left(1\right)}=\frac{r_{b2}}{\cos {\mathrm{\&alpha;}}_k}\cos (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan {\mathrm{\&alpha;}}_k+\frac{\mathrm{\&pi;}}{z_2})+{\mathrm{\&alpha;}}_k-\mathrm{\&alpha;})-a\cos (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan {\mathrm{\&alpha;}}_k+\frac{\mathrm{\&pi;}}{z_2})\end{array}\right.---\left(2\right)$

   Epicycloid equation under the tool coordinate system is following:

   $\left\{\begin{array}{c}{x_3}^{\left(1\right)}=r_{a2}\sin (i(\mathrm{\&alpha;}-\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right))+\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_k)-a\sin \left(i(\mathrm{\&alpha;}-\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right))\right)\\ {y_3}^{\left(1\right)}=r_{a2}\cos (i(\mathrm{\&alpha;}-\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right))+\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_k)-a\cos \left(i(\mathrm{\&alpha;}-\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right))\right)\end{array}\right.---\left(3\right)$

   $\left\{\begin{array}{c}{x_4}^{\left(1\right)}=r_{a2}\sin (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right)+\frac{\mathrm{\&pi;}}{z_2})+\left(\arccos \frac{r_{b2}}{r_{a2}}\right)-\mathrm{\&alpha;})\\ -a\sin (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right)+\frac{\mathrm{\&pi;}}{z_2})\\ {y_4}^{\left(1\right)}=r_{a2}\cos (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right)+\frac{\mathrm{\&pi;}}{z_2})+\left(\arccos \frac{r_{b2}}{r_{a2}}\right)-\mathrm{\&alpha;})\\ -a\cos (i(\mathrm{\&alpha;}-2\tan \mathrm{\&alpha;}+\tan \left(\arccos \frac{r_{b2}}{r_{a2}}\right)+\frac{\mathrm{\&pi;}}{z_2})\end{array}\right.---\left(4\right)$

   Circular arc equation under the tool coordinate system is following:

   $\left\{\begin{array}{c}{x_5}^{\left(1\right)}=r_{a1}\cos \mathrm{\&phi;}\\ {y_5}^{\left(1\right)}=r_{a1}\sin \mathrm{\&phi;}\end{array}\right.---\left(5\right)$

   Choose the minimum number n of confirming to calculate cutter tooth according to formula (6) in conjunction with registration ε ₁

   $n_1=\left\{\begin{array}{cc}2& 1\&le;\mathrm{\&epsiv;}<2\\ 3& 2\&le;\mathrm{\&epsiv;}<3\end{array}\right.---\left(6\right)$

   Set up the model [x of a processed tooth according to above formula (1)～(5) _my _m1]

   $\left[\begin{array}{ccc}{x}_m& y_m& 1\end{array}\right]=\left[\begin{array}{ccc}{x}_1^{\left(1\right)}& y_1^{\left(1\right)}& 1\\ x_2^{\left(1\right)}& y_2^{\left(1\right)}& 1\\ x_3^{\left(1\right)}& y_3^{\left(1\right)}& 1\\ x_4^{\left(1\right)}& y_4^{\left(1\right)}& 1\\ x_5^{\left(1\right)}& y_5^{\left(1\right)}& 1\end{array}\right]---\left(7\right)$

   The model of a tooth on the left side is [x _Ly _L1],

   $\left[\begin{array}{ccc}{x}_L& y_L& 1\end{array}\right]=\left[\begin{array}{ccc}{x}_m& y_m& 1\end{array}\right]\left[\begin{array}{ccc}\cos (2\mathrm{\&pi;}-\frac{2\mathrm{\&pi;}}{z_1})& \sin (2\mathrm{\&pi;}-\frac{2\mathrm{\&pi;}}{z_1})& 0\\ -\sin (2\mathrm{\&pi;}-\frac{2\mathrm{\&pi;}}{z_1})& \cos (2\mathrm{\&pi;}-\frac{2\mathrm{\&pi;}}{z_1})& 0\\ 0& 0& 1\end{array}\right]---\left(8\right)$

   The number of teeth model on the right is [x _Ry _R1]

   $\left[\begin{array}{ccc}{x}_R& y_R& 1\end{array}\right]=\left[\begin{array}{ccc}{x}_m& y_m& 1\end{array}\right]\left[\begin{array}{ccc}\cos (2\mathrm{\&pi;}+\frac{2\mathrm{\&pi;}}{z_1})& \sin (2\mathrm{\&pi;}+\frac{2\mathrm{\&pi;}}{z_1})& 0\\ -\sin (2\mathrm{\&pi;}+\frac{2\mathrm{\&pi;}}{z_1})& \cos (2\mathrm{\&pi;}+\frac{2\mathrm{\&pi;}}{z_1})& 0\\ 0& 0& 1\end{array}\right]---\left(9\right).$
5. 5. according to claim 4 a kind of based on etc. the Gear Shaping method of the area of cut, calculate in the conventional method in the pinion cutter machining locus definition cutter shaft Z described in the B step ₁Axle is with angular velocity omega ₁Be rotated workbench Z ₂With angular velocity omega ₂Be rotated, process index constantly is shown below.

   $t=T_1+(T_2-T_1)\frac{j-1}{59},$ t∈[T1，T2] (10)

   J=1 wherein, 2 ..., 60.

   All need cutter be transformed to workpiece coordinate system from tool coordinate system at each moment t, the coordinate transform formula that realizes this conversion is suc as formula shown in (11).

   $\left[\begin{array}{c}{x}^{\left(2\right)}\\ y^{\left(2\right)}\\ 1\end{array}\right]=M_{21}\left[\begin{array}{c}{x}^{\left(1\right)}\\ y^{\left(1\right)}\\ 1\end{array}\right]---\left(11\right)$

   By tool coordinate system (O ₁-x ₁, y ₁) transform to workpiece coordinate system (O ₂-x ₂, y ₂) transformation matrix be M ₂₁

   $M_{21}={\left(M_{02}\right)}^{-1}\&CenterDot;M_{01}=\left[\begin{array}{ccc}\cos (\frac{t\&CenterDot;n_1}{i}+t\&CenterDot;n_1)& -\sin (\frac{t\&CenterDot;n_1}{t}+t\&CenterDot;n_1)& -a\sin \frac{t\&CenterDot;n_1}{i}\\ \sin (\frac{t\&CenterDot;n_1}{i}+t\&CenterDot;n_1)& \cos (\frac{t\&CenterDot;n_1}{i}+t\&CenterDot;n_1)& a\cos \frac{t\&CenterDot;n_1}{i}\\ 0& 0& 1\end{array}\right]---\left(12\right)$

   Wherein by tool coordinate system (O ₁-x ₁, y ₁) (O-x, transformation matrix y) are M to transform to inertial coodinate system ₀₁

   $M_{01}=\left(\begin{array}{ccc}\cos t\&CenterDot;n_1& -\sin t\&CenterDot;n_1& 0\\ \sin t\&CenterDot;n_1& \cos t\&CenterDot;n_1& a\\ 0& 0& 1\end{array}\right)---\left(13\right)$

   By wheel blank coordinate system (O ₂-x ₂, y ₂) (O-x, transformation matrix y) are M to transform to inertial coodinate system ₀₂

   $M_{02}=\left(\begin{array}{ccc}\cos \frac{t\&CenterDot;n_1}{i}& \sin \frac{t\&CenterDot;n_1}{i}& 0\\ -\sin \frac{t\&CenterDot;n_1}{i}& \cos \frac{t\&CenterDot;n_1}{i}& 0\\ 0& 0& 1\end{array}\right)---\left(14\right)$

   By formula (11), at t ∈ [T ₁, T ₂] interior each moment; Can the pinion cutter tooth curve be transformed to the wheel blank coordinate system by tool coordinate system, promptly obtain a series of positions of pinion cutter flank profil in the wheel blank coordinate system, i.e. machining locus; The envelope of position formation is the teeth groove of gear, i.e. involute profile thus.
6. 6. according to claim 5 a kind of based on etc. the Gear Shaping method of the area of cut, said C step is accomplished through following method: selected cutter tooth,

   At first each the bar tooth curve in this cutter tooth machining locus being dispersed respectively is some spots, calls aforementioned discrete data point then, and machining locus is carried out reconstruct, and then through simulation Boolean calculation process, tries to achieve the area of cut of current pinion cutter slotting; With the said process iterative solution, try to achieve all areas of cut;

   And gained area of cut variation rule curve carried out match.
7. 7. according to claim 6 a kind of based on etc. the Gear Shaping method of the area of cut; The Changing Pattern of the total area cut when area of cut Changing Pattern is from initial time to slotting each time in the conventional processing method of C step gained; After converting law curve is carried out match; And utilize following formula analysis, wherein, establish A _mBe the maximum area of cut, a ₁T ⁿ+ a ₂T ^N-1+ ... + a _nT+a _N+1Be the fit equation of law curve, a ₁... A _nCoefficient for variable in the fit equation:

   $\left\{\begin{array}{c}{A}_m\&CenterDot;1=\&Integral;\left(\mathrm{\&Sigma;aT}\right)\mathrm{dt}=a_1{T}_1^n+a_2{T}_1^{n-1}+...a_n{T}_1+a_{n+1}\\ A_m\&CenterDot;2=\&Integral;\left(\mathrm{\&Sigma;aT}\right)\mathrm{dt}=a_1{T}_2^n+a_2{T}_2^{n-1}+...+a_n{T}_2+a_{n+1}\\ .\\ .\\ .\\ A_m\&CenterDot;n=\&Integral;\left(\mathrm{\&Sigma;aT}\right)\mathrm{dt}=a_1{T}_n^n+a_2{T}_n^{n-1}+...+a_n{T}_n+a_{n+1}\end{array}\right.---\left(15\right)$

   Separate formula (15) and can obtain T ₁..., T _nSeries of points, repeating step (2), (3) can be obtained the corresponding area of cut of each point, and whether checking is positioned at A _mWithin ± 5%,, need carry out local correction if the data point that exceeds deviation is arranged.If promptly this puts the corresponding area of cut greater than A _m± 5%, explain that this point value is bigger than normal, need suitably reduce; If this puts the corresponding area of cut less than A _m± 5%, explain that this point value is less than normal, need suitably to increase.Repeating step (2), (3) once more after the local correction all are positioned at A until the corresponding area of cut of all T points so repeatedly _mWithin ± 5% (shown in figure 11).

   With revised T point by formula (T _i-T _I-1) n ₁Convert the cutter rotating speed into, obtain cutter rotation speed change law curve then, be and satisfy the pinion cutter rotation speed change rule (shown in figure 12) that waits the feeding of cutting force self adaptation.

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