CN104407569B - Cutter advancing and retreating path planning method in numerically controlled grinding and polishing - Google Patents

Abstract

The invention provides a cutter advancing and retreating path planning method in numerically controlled grinding and polishing, relates to a grinding and polishing path planning method, and solves a problem of appearance of cutter advancing and retreating traces in the existing grinding and polishing process caused by the fact that a linear cutter advancing and retreating mode is adopted a grinding and polishing tool. The cutter advancing and retreating path planning method in numerically controlled grinding and polishing comprises the steps that a starting point and a terminal point of an effective grinding and polishing path and a normalized direction vector are calculated firstly; then total time of cutter advancing and retreating and a second safety height position vector of the cutter advancing and retreating path are calculated according to a given safety height value and cutter advancing and retreating speed; furthermore, position vectors and direction vectors of all the cutter position points of the spiral cutter advancing and retreating path; moreover, directions of the spiral cutter advancing and retreating path and the effective polishing path are adjusted so as to be maintained to be consistent; and finally the position vector of the first safety height is calculated. The invention is suitable for the field of numerically controlled grinding and polishing so that uniform removal caused by partial contact of a grinding and polishing mould and a processed piece can be avoided and thus avoidance of the cutter advancing and retreating traces is facilitated.

Description

Advance and retreat knife paths planning method in numerical control polishing

Technical field

The present invention relates to a kind of paths planning method of grinding and polishing, polishing in more particularly, to a kind of CNC Lapping ＆ Polishing Instrument enters the spiral path planing method of withdrawing.

Background technology

CNC Lapping ＆ Polishing is a kind of manufacturing procedure obtaining high-precision surface quality, the wherein path planning of polishing instrument It is a key technology in whole process.The path of polishing instrument mainly entering by effective machining path and polishing instrument Withdrawing path two parts are constituted.Effectively machining path is the path realizing the removal of material certainty, the effective processing commonly used at present There are spiral path, raster scanning path and pseudorandom path etc. in path.Advance and retreat cutter track footpath refers to start in polishing or terminate In the stage, polishing instrument is toward or away from surface to be machined and then beginning or the path terminating surface polishing process.Generally for reality The polishing instrument that removes of existing material needs to apply certain pressure by certain mode to surface of the work.In addition, polishing instrument needs To carry out rotating with certain rotating speed and to be moved relative to surface to be machined with certain feed speed simultaneously.At present, effective polishing road Footpath is the situation of spiral path is the polishing work after the completion of feed along beeline approaching surface to be machined while polishing instrument rotation Press spiral path while tool rotation to move with respect to workpiece.Withdrawing process is just contrary with this process.For entirely polished The basic demand of journey is that polished die can keep coincideing with the machined surface moment, to ensure the removal for material for the polished die each point Can be homogenized well, it is to avoid remain the surface defects such as obvious cut.

But, due to the reason such as the alignment error of foozle, rigging error and workpiece of polishing instrument itself, polishing Instrument polished die subregion when being toward or away from surface to be machined can not be coincide well with polished surface, and polished die is indivedual Fitted with machined surface first in region.Because this inconsistent laminating leads to polished die respective regions first during entering withdrawing First create material to remove.The presence of this problem causes bistrique uneven in feed point or withdrawing point removal amount, thus in work The advance and retreat tool marks mark of part remained on surface annular affects the quality of entire surface.

Content of the invention

The present invention enters withdrawing mode using straight line and advance and retreat tool marks mark for polishing instrument during solving existing polishing Problem, there is provided the advance and retreat knife paths planning method in a kind of numerical control polishing.

Advance and retreat knife paths planning method in numerical control polishing, the method is realized by following steps:

Step one, determine the end points p of effective machining path_s(x, y, z), end points p_sThe normalization direction vector at (x, y, z) placeAnd calculate described end points p_sThe direction angle alpha of (x, y, z) direction vector and end points p_s(x, y, z) corresponding polar diameter ρ and polar angle θ_s；

Step 2, according to the second safe altitude value h " and spiral enters withdrawing speed v and calculates into withdrawing time t, and according to The angular velocity omega that workpiece rotates calculates the total angle rotating into during withdrawing

Step 3, differential of the arc segment length l according to setting_t, the end points p of acquisition in step one_s(x, y, z) corresponding polar diameter ρ, Calculate the corresponding angle of differential of the arc sectionAnd calculate between spiral advance and retreat cutter track footpath cutter spacing points n and every section of differential of the arc corresponding time Every τ, τ=t/n；

Step 4, the end points p being obtained according to step one_s(x, y, z) corresponding polar diameter ρ, polar angle θ_s, direction angle alpha, step 2 In the cutter location p entering withdrawing speed v, calculating spiral advance and retreat cutter track footpath_i(x, y, z) position and cutter location pi (x, y, z) are right The direction vector answeredIt is expressed as with formula one and formula two respectively:

Formula one, $\left\{\begin{array}{c}{x}_i=(\mathrm{\ρ}+v\·t\·\tan \left(\mathrm{\α}\right))\·\cos ({\mathrm{\θ}}_s+\mathrm{\θ})\\ y_i=(\mathrm{\ρ}+v\·t\·\tan \left(\mathrm{\α}\right))\·\sin ({\mathrm{\θ}}_s+\mathrm{\θ})\\ z_i=z+v\·t\end{array}\right.$

In formula, t=(i+1) τ, i are the positive integer being less than or equal to n more than or equal to 1, and t is the cutter location corresponding time, θ=2 πωt；

Formula two, $\left\{\begin{array}{c}{e}_{\mathrm{ix}}=e_{\mathrm{sx}}\·\cos ({\mathrm{\θ}}_s+\mathrm{\θ})-e_{\mathrm{sy}}\·\sin ({\mathrm{\θ}}_s+\mathrm{\θ})\\ e_{\mathrm{iy}}=e_{\mathrm{sx}}\·\sin ({\mathrm{\θ}}_s+\mathrm{\θ})+e_{\mathrm{sy}}\·\cos ({\mathrm{\θ}}_s+\mathrm{\θ})\\ e_{\mathrm{iz}}=e_{\mathrm{sz}}\end{array}\right.$

In formula, e_sx、e_sy、e_szIt is respectively the corresponding direction vector of end pointsX, y, z durection component, e_ix、 e_iy、e_izIt is respectively the corresponding direction vector of cutter locationX, y, z durection component；

Step 5, by the terminal p in spiral advance and retreat cutter track footpath_n(x, y, z) is designated as the second safe altitude position p ", according to effective The hand of spiral of machining path adjusts to feed or withdrawing spiral path travel direction；And according to the second safe altitude position p " with And corresponding direction vector e " (x, y, z) calculates the first safe altitude position p ', completes the planning in advance and retreat cutter track footpath.

Beneficial effects of the present invention: the present invention adopts spiral advance and retreat cutter track footpath, can disperse polishing instrument feed or move back The material that during knife, polishing mould regional area produces removes, it is to avoid advance and retreat tool marks mark in surface to be machined, is conducive to carrying High crudy.

Brief description

Fig. 1 is the principle front view of advance and retreat knife paths planning method in numerical control polishing of the present invention；

Fig. 2 is the principle top view of advance and retreat knife paths planning method in numerical control polishing of the present invention.

Specific embodiment

Specific embodiment one, combine Fig. 1 and Fig. 2 illustrate present embodiment, advance and retreat knife path planning side in numerical control polishing Method, for realizing the feed path of polishing instrument and the planning in withdrawing path during numerical control polishing, the method includes:

The first step, determine effective machining pathEnd points p_s(x, y, z), the normalization side at end points To vectorAnd then calculate the direction angle alpha of end points direction vector；

Second step, calculating end points p_s(x, y, z) corresponding polar diameter ρ and polar angle θ_s；

3rd step, " and enter withdrawing speed v and calculate into withdrawing time t, and then according to work according to the second safe altitude value h The angular velocity omega that part rotates calculates the total angle rotating into withdrawing process

4th step, differential of the arc segment length l according to setting_tAnd corresponding polar diameter ρ of end points calculates the corresponding angle of differential of the arc section And then calculate the spiral advance and retreat cutter track footpath cutter spacing points n and corresponding time interval τ=t/n of every section of differential of the arc；

5th step, the end points p being obtained according to step one_s(x, y, z) corresponding polar diameter ρ, polar angle θ_s, direction angle alpha, step 2 In enter withdrawing speed v, successively calculate spiral advance and retreat cutter track footpath cutter location p_i(x, y, z) position:

$\left\{\begin{array}{c}{x}_i=(\mathrm{\ρ}+v\·t\·\tan \left(\mathrm{\α}\right))\·\cos ({\mathrm{\θ}}_s+\mathrm{\θ})\\ y_i=(\mathrm{\ρ}+v\·t\·\tan \left(\mathrm{\α}\right))\·\sin ({\mathrm{\θ}}_s+\mathrm{\θ})\\ z_i=z+v\·t\end{array}\right.$

T=(i+1) τ in formula, i=1 ... n, θ=ω t, t are the cutter location corresponding time.

6th step, calculate spiral advance and retreat cutter track footpath cutter location p successively according to following formula_i(x, y, z) corresponding direction vector

$\left\{\begin{array}{c}{e}_{\mathrm{ix}}=e_{\mathrm{sx}}\·\cos ({\mathrm{\θ}}_s+\mathrm{\θ})-e_{\mathrm{sy}}\·\sin ({\mathrm{\θ}}_s+\mathrm{\θ})\\ e_{\mathrm{iy}}=e_{\mathrm{sx}}\·\sin ({\mathrm{\θ}}_s+\mathrm{\θ})+e_{\mathrm{sy}}\·\cos ({\mathrm{\θ}}_s+\mathrm{\θ})\\ e_{\mathrm{iz}}=e_{\mathrm{sz}}\end{array}\right.$

E in formula_sx、e_sy、e_szIt is respectively direction vectorX, y, z durection component e_ix、e_iy、e_izIt is respectively side To vectorX, y, z durection component.

7th step, the terminal p in helix advance and retreat cutter track footpath_n(x, y, z) is designated as the second safe altitude position p "；

8th step, according to the hand of spiral of effective machining path, feed or withdrawing spiral path travel direction are adjusted；

9th step, according to the second safe altitude position p " and corresponding direction vector e " (x, y, z) calculate the first safety Height and position p ', realizes advance and retreat knife path planning.

Enter withdrawing speed v, the second safe altitude value h in present embodiment ", the first safe altitude value h ' can set respectively Put.The terminal in spiral advance and retreat cutter track footpath is the second safe altitude position p ".

Specific embodiment two, combine Fig. 1 and Fig. 2 illustrate present embodiment, present embodiment be specific embodiment one The embodiment of advance and retreat knife paths planning method in described numerical control polishing:

(1) the end points p of effective machining path 2 is determined according to the surface profile 1 of work piece_s(x, y, z), returning at end points One change direction vectorAnd then the direction angle alpha of calculating end points direction vector:

α=arccos (e_sz)

(2) calculate end points p_s(x, y, z) corresponding polar diameter ρ and polar angle θ_s:

$\left\{\begin{array}{c}\mathrm{\ρ}=\sqrt{x_s^2+y_s^2}\\ {\mathrm{\θ}}_s=\arctan \left(\frac{y_s}{x_s}\right)\end{array}\right.$

(3) according to the second safe altitude value h " and enter withdrawing speed v and calculate into withdrawing time t, and then turned according to workpiece Dynamic angular velocity omega calculates the total angle rotating into withdrawing process

(4) differential of the arc segment length l according to setting_tAnd corresponding polar diameter ρ of end points calculates the corresponding angle of differential of the arc section

Further, calculating spiral advance and retreat cutter track footpath cutter spacing points n:

Correspondingly, the corresponding time interval of every section of differential of the arc is:

$\mathrm{\τ}=\frac{t}{n};$

(5) calculate the cutter location p in spiral advance and retreat cutter track footpath successively_i(x, y, z) position:

$\left\{\begin{array}{c}{x}_i=(\mathrm{\ρ}+v\·t\·\tan \left(\mathrm{\α}\right))\·\cos ({\mathrm{\θ}}_s+\mathrm{\θ})\\ y_i=(\mathrm{\ρ}+v\·t\·\tan \left(\mathrm{\α}\right))\·\sin ({\mathrm{\θ}}_s+\mathrm{\θ})\\ z_i=z+v\·t\end{array}\right.$

T=(i+1) τ in formula, i=1 ... n, θ=ω t, t are the cutter location corresponding time, collated can obtain:

$\left\{\begin{array}{c}{x}_i=(\mathrm{\ρ}+v\·(i+1)\mathrm{\τ}\·\tan \left(\mathrm{\α}\right))\·\cos ({\mathrm{\θ}}_s+\mathrm{\ω}\·(i+1)\mathrm{\τ})\\ y_i=(\mathrm{\ρ}+v\·(i+1)\mathrm{\τ}\·\tan \left(\mathrm{\α}\right))\·\sin ({\mathrm{\θ}}_s+\mathrm{\ω}\·(i+1)\mathrm{\τ})\\ z_i=z+v\·(i+1)\mathrm{\τ}\end{array}\right.$

(6) calculate spiral advance and retreat cutter track footpath cutter location p_i(x, y, z) corresponding direction vector

$\left\{\begin{array}{c}{e}_{\mathrm{xi}}^{\′}=e_{\mathrm{sx}}\·\cos ({\mathrm{\θ}}_s+\mathrm{\θ})-e_{\mathrm{sy}}\·\sin ({\mathrm{\θ}}_s+\mathrm{\θ})\\ e_{\mathrm{yi}}^{\′}=e_{\mathrm{sx}}\·\sin ({\mathrm{\θ}}_s+\mathrm{\θ})+e_{\mathrm{sy}}\·\cos ({\mathrm{\θ}}_s+\mathrm{\θ})\\ e_{\mathrm{zi}}^{\′}=e_{\mathrm{sz}}\end{array}\right.$

E in formula_sx、e_sy、e_szIt is respectively direction vectorX, y, z durection component, e_ix、e_iy、e_izIt is respectively side To vectorX, y, z durection component.

(7) the terminal p in helix advance and retreat cutter track footpath_n(x, y, z) is designated as two safe altitude position p ", i.e. p "=p_n(x,y, Z), corresponding direction vector e " (x, y, z)=e_n(x,y,z).

(8) hand of spiral according to effective machining path adjusts to feed or withdrawing spiral path travel direction；

(9) according to the second safe altitude position p, " (x, y, z) and corresponding direction vector e " (x, y, z) calculates the first peace Full-height position p ' (x, y, z), is expressed as with following formula:

$\left\{\begin{array}{c}{x}^{\′}=x^{\′\′}+e_{\mathrm{nx}}\·h^{\′}\\ y^{\′}=y^{\′\′}+e_{\mathrm{ny}}\·h^{\′}\\ z^{\′}=z^{\′\′}+e_{\mathrm{nz}}\·h^{\′}\end{array}\right.$

X ' in formula, y ', z ' are respectively the first safe altitude position, the x, y, z durection component of p ' (x, y, z), x ", y ", z " It is respectively the second safe altitude position p " the x, y, z durection component of (x, y, z), e_nx、e_ny、e_nzIt is respectively direction vectorX, y, z durection component, h ' be the first safe altitude value, so far complete the planning in spiral advance and retreat cutter track footpath, obtain Spiral advance and retreat cutter track footpath 3.

Claims (1)

1. the advance and retreat knife paths planning method in numerical control polishing, for realizing the feed path of polishing instrument during numerical control polishing And the planning in withdrawing path, it is characterized in that, the method comprises the following steps:

Step one, determine the end points p of effective machining path_s(x, y, z), end points p_sThe normalization direction vector at (x, y, z) placeAnd calculate described end points p_sThe direction angle alpha of (x, y, z) direction vector and end points p_s(x, y, z) corresponding polar diameter ρ and polar angle θ_s；

Step 2, according to the second safe altitude value h, " and spiral enters withdrawing speed v and calculates into withdrawing time t, and according to workpiece The angular velocity omega rotating calculates the total angle rotating into during withdrawing

Step 3, differential of the arc segment length l according to setting_t, the end points p of acquisition in step one_s(x, y, z) corresponding polar diameter ρ, calculates The corresponding angle of differential of the arc sectionAnd calculate spiral advance and retreat cutter track footpath cutter spacing points n and corresponding time interval τ of every section of differential of the arc, τ =t/n；

Step 4, the end points p being obtained according to step one_s(x, y, z) corresponding polar diameter ρ, polar angle θ_s, direction angle alpha, in step 2 Enter withdrawing speed v, calculate the cutter location p in spiral advance and retreat cutter track footpath_i(x, y, z) position and cutter location p_i(x, y, z) corresponding side To vectorIt is expressed as with formula one and formula two respectively:

Formula one,

In formula, x_i,y_i,z_iIt is respectively the cutter location p in spiral advance and retreat cutter track footpath_i(x, y, z) is in x, the coordinate value in y, z direction, t=(i + 1) τ, i are the positive integer being less than or equal to n more than or equal to 1, and t is the cutter location corresponding time, θ=ω t；

Formula two,

In formula, e_sx、e_sy、e_szIt is respectively the corresponding direction vector of end pointsX, y, z durection component, e_ix、e_iy、e_iz It is respectively the corresponding direction vector of cutter locationX, y, z durection component；

Step 5, by the terminal p in spiral advance and retreat cutter track footpath_n(x, y, z) is designated as the second safe altitude position p ", processed according to effective The hand of spiral in path adjusts to feed or withdrawing spiral path travel direction；And according to the second safe altitude position p " and right " (x, y, z) calculates the first safe altitude position p ' to the direction vector e answering, and completes the planning in advance and retreat cutter track footpath.