CN106845117A - Guide pair of machine tool linearity decline computational methods under a kind of random wear working condition - Google Patents

Abstract

The present invention discloses guide pair of machine tool linearity decline computational methods under a kind of random wear working condition, and the method includes, based on Archard abrasion principles, calculating guide pair of machine tool single-point wearing depth equation when considering load, speed chance mechanism；Based on random principle, the guide pair of machine tool greatest wear depth model for considering feeding length change at random is calculated；Guide pair of machine tool single-point wearing depth equation during according to the consideration load, speed chance mechanism, substitute into the guide pair of machine tool greatest wear depth model for considering feeding length change at random, guide pair of machine tool linear precision decline computation model is calculated, and influence of the lathe operating mode to guideway precision is considered according to the precision degenerated mode.Consider the insufficient deficiency of influence supplemented with existing computational methods, be conducive to optimizing guideway accuracy computation result, deeply understand guideway contact surface abrasion form and its evolutionary process, so as to preferably instruct the design and application of machine tooling technique.

Description

Guide pair of machine tool linearity decline computational methods under a kind of random wear working condition

Technical field

The invention provides guide pair of machine tool linearity decline computational methods under a kind of random wear working condition, belong to numerical control machine Bed accuracy Design field.

Background technology

The calculating for studying numerical control machine slide rail precision has very with prediction to improving Digit Control Machine Tool global reliability level Important meaning, it is research main in recent years that Digit Control Machine Tool operational reliability is studied from the angle of numerical control precision deterioration law One of direction.In expected life period, can the machining accuracy of Digit Control Machine Tool be kept, and the precision with its critical component is protected Holding property has direct relation, and the precision stability for studying associated components is the necessary ways for improving Digit Control Machine Tool global reliability One of.Abrasion is the main cause of machine tool guideway component failure, and the significance for studying tribology is saving energy consumption, reduces material Material loss, the service life and raising functional reliability of prolonged mechanical equipment.Existing computational methods parameter ranges span is larger, Lack and the details of actual condition stochastic behaviour is considered.For example, under lathe actual condition, the feed speed during time processing Excursion is larger, should not be substituted into according to a definite value and calculated.Therefore, how from abrasion principle, for lathe operating mode Stochastic behaviour carries out the calculating of guide precision, as problem demanding prompt solution.

The content of the invention

The object of the invention provides guide pair of machine tool linearity decline computational methods under a kind of random wear working condition.Can calculate Guide pair of machine tool linear precision change caused by surface abrasion, while considering random load influence, random velocity influence, Yi Jijin To the influence of length change at random, the insufficient deficiency of influence is considered supplemented with existing computational methods, be conducive to optimizing guideway Accuracy computation result, deeply understands guideway contact surface abrasion form and its evolutionary process, so as to preferably instruct machine tooling The design of technique and application.Described the method includes：

S1, principle of being worn and torn based on Archard, calculate guide pair of machine tool single-point when considering load, speed chance mechanism Wearing depth equation；

S2, based on random principle, calculate the guide pair of machine tool greatest wear depth mould for considering feeding length change at random Type；

S3, according to the consideration load, speed chance mechanism when guide pair of machine tool single-point wearing depth equation, substitution examines Consider the guide pair of machine tool greatest wear depth model of feeding length change at random, calculate guide pair of machine tool linear precision decline meter Model is calculated, and influence of the lathe operating mode to guideway precision is considered according to the precision degenerated mode.

Brief description of the drawings

The schematic flow sheet of guide pair of machine tool linearity decline computational methods under a kind of random wear working condition of Fig. 1 present invention.

Specific embodiment

To make the purpose, technical scheme and advantage of the embodiment of the present invention clearer, below in conjunction with the embodiment of the present invention In accompanying drawing, the technical scheme in the embodiment of the present invention is explicitly described, it is clear that described embodiment be the present invention A part of embodiment, rather than whole embodiments.Based on the embodiment in the present invention, those of ordinary skill in the art are not having The every other embodiment obtained under the premise of creative work is made, the scope of protection of the invention is belonged to.

Step one is based on Archard abrasion principles, calculates guide pair of machine tool list when considering load, speed chance mechanism Point wearing depth equation

It is former based on Archard to consider that guide pair of machine tool contact load and influence of the contact velocity to guide rail are starting point Reason and guide rail loaded state, calculate stand under load way rub depth equation；With the increase of contact load and contact velocity, guideway The wearing depth of upper contact point can increase.

Step 1.1 is based on the guideway single-point wearing depth equation of the consideration load of Archard abrasion principles

Selected guide rail is research object, can be obtained based on Archard abrasions principle：

In formula, V is the wear extent of certain arbitrfary point on guideway, and K is the coefficient of waste of the arbitrfary point, and P is the arbitrfary point Load, L is the sliding distance of the arbitrfary point, and H is the hardness of the arbitrfary point；

The wear point differential character for analyzing guide rail is obtained：

Obtained by Differential Geometry relation, dV=dhdA_C, P=σ dA_C, dL=vdt, h is same formula on guideway in formula (1) wearing depth of arbitrfary point described by, σ is the contact stress of the arbitrfary point, A_CIt is the contact area of the arbitrfary point, v is should The contact velocity of arbitrfary point, t is represented since guideway starts the time slided occur；Substitute into：

Consider that contact stress is changed over time：

T is integrated, guide pair of machine tool single-point wearing depth equation during load chance mechanism must be considered：

Make a period of time Δ t_jInterior, contact stress σ is definite value, asks for this section of wearing depth Δ h of time_j,n,；J is represented This section of time Δ t_jGeneration jth time is slided, and n represents n-th contact point, and summation draws the wearing depth of this slip；Then obtain Δ t_j Wearing depth Δ h in time_j,n：

In formula, σ_j,nThe contact for representing that the wear point experience jth time of n-th consideration on guide pair of machine tool is relative when sliding should Power；

Guide pair of machine tool single-point wearing depth h during load chance mechanism must be considered_k,n：

In formula, k represents that the guide pair of machine tool of consideration is relative and slides total degree, h_k,nRepresent n-th consideration on guide pair of machine tool Wear point experience the wearing depth after k relative slip；

Step 1.2 considers the guideway single-point wearing depth equation of load and speed influence

With step 1.1, it is considered to which contact velocity is changed over time：

In formula, dh represents the differential of the wearing depth h to time t of arbitrfary point described by same formula (1) on guide pair of machine tool, K The coefficient of waste of the arbitrfary point is represented, H represents the hardness of the point, and v represents the contact velocity of the point, and σ represents connecing for the arbitrfary point Stress is touched, t is represented since guideway starts the time slided occur；

T is integrated, guide pair of machine tool single-point wearing depth equation when load, speed chance mechanism must be considered：

Make a period of time Δ t_jInterior, contact velocity v and contact stress σ is definite value, asks for this section of wearing depth Δ of time h_j,n, j represented in this section of time Δ t_jGeneration jth time is slided, and n represents n-th contact point, and summation draws the abrasion of this slip Depth；Then obtain Δ t_jWearing depth Δ h in time_j,n：

In formula, v_j,nThe contact speed for representing that the wear point experience jth time of n-th consideration on guide pair of machine tool is relative when sliding Degree, σ_j,nThe contact stress for representing that the wear point experience jth time of n-th consideration on guide pair of machine tool is relative when sliding；

Guide pair of machine tool single-point wearing depth h when load, speed chance mechanism must be considered_k,n：

In formula, k represents that the guide pair of machine tool of consideration is relative and slides total degree, h_k,nRepresent n-th consideration on guide pair of machine tool Wear point experience the wearing depth after k relative slip.

Step 2 is based on random principle, calculates the guide pair of machine tool greatest wear depth for considering feeding length change at random Model

The whole service process of guide pair of machine tool, including to knife, feeding and withdrawing process, load is relatively during feeding High and long operational time, feeding pixel accuracy decay most serious.Now consider the abrasion in guide pass feeding region to guide precision Influence, and think that the abrasive action of feeding process and withdrawing process in the region is suitable.

Step 2.1 considers feeding length random distribution, the length Random Effect factor

Consider feeding length change at random, introduce length Random Effect factor r.

Guide rail surface cumulative volume wear extent is made for V, the volume wear in heavy wear area is V_S, it is considered to geometrical relationship, by It is proportional in perfect condition wear extent and sliding stroke, thus V_SBy total sliding distance L and heavy wear area sliding distance L_SRepresent For：

Make l_maxRepresent maximum feeding length, l_minMinimum feeding length is represented, N represents feeding number of times, by geometrical relationship, and Guide rail kinetic characteristic understands：

L_S=Nl_min (13)

L=Nl_min+Nr(l_max-l_min) (14)

Thus：

R represents the length Random Effect factor, relevant with actual feeding technical process, is a stochastic variable, 0≤r≤1, r Show that feeding length distribution is intended near 0 small, it is big that r shows that feeding length distribution is intended near 1.In practical engineering application In, r is estimated using normal distribution, then r=0.5.

Step 2.2 considers feeding length change at random, calculates guide pair of machine tool greatest wear depth model

Make h_maxGreatest wear depth is represented, b represents guideway contact width, obtained by Differential Geometry relation：

dV_S=dl_min·db·dh_max (16)

σ is made to represent contact stress, P represents contact load, it is considered to Archard wear modelsP=σ dl_minDb, dL=vdt are obtained：

Above formula is integrated to t, must consider the guide pair of machine tool greatest wear depth model of feeding length change at random：

Wherein, h_maxRepresent the greatest wear depth for feeding the guide pair of machine tool after terminating, l_maxRepresent guide pair of machine tool Maximum feeding length, l_minThe minimum feeding length of guide pair of machine tool is represented, r represents the length Random Effect factor.K represents abrasion Coefficient, H represents hardness, and v represents the contact velocity of guide pair of machine tool, and σ represents the contact stress of guide pair of machine tool.

Guide pair of machine tool single-point wearing depth equation when step 3 is according to the consideration load, speed unit effect, generation Enter to consider the guide pair of machine tool greatest wear depth model of feeding length change at random, calculate guide pair of machine tool linear precision and decline Computation model is moved back, and influence of the lathe operating mode to guideway precision is considered according to the precision degenerated mode.

Consider guide pair of machine tool linear precision principle, make lathe straightness error for A, substitute into and consider that load, speed are random The guide pair of machine tool greatest wear of guide pair of machine tool single-point wearing depth equation and consideration feeding length change at random during effect Depth model, obtains：

Make a period of time Δ t_jInterior, contact velocity v and contact stress σ is definite value, asks for this section of straightness error of time ΔA_j, sue for peace and draw the wearing depth of this slip；Then obtain Δ t_jStraightness error Δ A in time_j：

In formula, v_jThe contact velocity for representing that guide pair of machine tool experience jth time is relative when sliding, σ_jRepresent guide pair of machine tool jth Contact stress during secondary relative slip；

Obtain the guide pair of machine tool linear precision decline computation model A under random operating mode_k：

In formula, k represents that the guide pair of machine tool of consideration is relative and slides total degree.

It will thus be seen that with the increase of abrasion number of times, guide pair of machine tool straightness error will be continuously increased, and increased Amplitude can be proportionate with contact stress with contact velocity, meanwhile, the Random Effect of feeding length can be subject to.Thus, judge To reduce the degeneration of guide rail linear precision when lathe is used, should try one's best and avoid excessive contact stress and contact velocity, while logical Cross and the maximum amount of feeding be rationally set so that feeding length distribution be intended to maximum feeding.

Although being described in conjunction with the accompanying embodiments of the present invention, those skilled in the art can not depart from this hair Various modifications and variations are made in the case of bright spirit and scope, such modification and modification are each fallen within by appended claims Within limited range.

Claims (2)

1. under a kind of random wear working condition guide pair of machine tool linearity decline computational methods, it is characterised in that：The method includes：

S1, principle of being worn and torn based on Archard, calculate guide pair of machine tool single-point abrasion when considering load, speed chance mechanism Depth equation；

S2, based on random principle, calculate the guide pair of machine tool greatest wear depth model for considering feeding length change at random；

S3, according to the consideration load, speed chance mechanism when guide pair of machine tool single-point wearing depth equation, substitution takes into account To the guide pair of machine tool greatest wear depth model of length change at random, calculate the decline of guide pair of machine tool linear precision and calculate mould Type, and influence of the lathe operating mode to guideway precision is considered according to the precision degenerated mode.

2. guide pair of machine tool linearity decline computational methods under a kind of random wear working condition according to claim 1, it is special Levy and be：Step one is based on Archard abrasion principles, calculates guide pair of machine tool list when considering load, speed chance mechanism Point wearing depth equation

To consider that guide pair of machine tool contact load and influence of the contact velocity to guide rail are starting point, based on Archard principles with Guide rail loaded state, calculates stand under load way rub depth equation；With the increase of contact load and contact velocity, connect on guideway The wearing depth of contact can increase；

Step 1.1 is based on the guideway single-point wearing depth equation of the consideration load of Archard abrasion principles

Selected guide rail is research object, can be obtained based on Archard abrasions principle：

$\frac{V}{L}=K\frac{P}{H}---\left(1\right)$

In formula, V is the wear extent of certain arbitrfary point on guideway, and K is the coefficient of waste of the arbitrfary point, and P is the load of the arbitrfary point, L is the sliding distance of the arbitrfary point, and H is the hardness of the arbitrfary point；

The wear point differential character for analyzing guide rail is obtained：

$\frac{dV}{dL}=K\frac{P}{H}---\left(2\right)$

Obtained by Differential Geometry relation, dV=dhdA_C, P=σ dA_C, dL=vdt, h is same formula (1) institute on guideway in formula The wearing depth of arbitrfary point is described, σ is the contact stress of the arbitrfary point, A_CIt is the contact area of the arbitrfary point, v is the arbitrfary point Contact velocity, t represent since guideway start occur slide time；Substitute into：

$dh=\frac{Kv}{H}\mathrm{\σ}\·dt---\left(3\right)$

Consider that contact stress is changed over time：

$dh=\frac{Kv}{H}\mathrm{\σ}\left(t\right)\·dt---\left(4\right)$

T is integrated, guide pair of machine tool single-point wearing depth equation during load chance mechanism must be considered：

$h=\frac{Kv}{H}{\∫}_0^t\mathrm{\σ}\left(t\right)\·dt---\left(5\right)$

Make a period of time Δ t_jInterior, contact stress σ is definite value, asks for this section of wearing depth Δ h of time_j,n,；J is represented in the section Time Δ t_jGeneration jth time is slided, and n represents n-th contact point, and summation draws the wearing depth of this slip；Then obtain Δ t_jTime Interior wearing depth Δ h_j,n：

${\mathrm{\Δh}}_{j,n}=\frac{Kv}{H}{\mathrm{\σ}}_{j,n}{\mathrm{\Δt}}_j---\left(6\right)$

In formula, σ_j,nThe contact stress for representing that the wear point experience jth time of n-th consideration on guide pair of machine tool is relative when sliding；

Guide pair of machine tool single-point wearing depth h during load chance mechanism must be considered_k,n：

$h_{k,n}=\underset{j=1}{\overset{k}{\Σ}}\frac{Kv}{H}{\mathrm{\σ}}_{j,n}{\mathrm{\Δt}}_j---\left(7\right)$

In formula, k represents that the guide pair of machine tool of consideration is relative and slides total degree, h_k,nRepresent n-th mill of consideration on guide pair of machine tool Damage the wearing depth after the k relative slip of point experience；

Step 1.2 considers the guideway single-point wearing depth equation of load and speed influence

With step 1.1, it is considered to which contact velocity is changed over time：

$dh=\frac{K}{H}v\left(t\right)\mathrm{\σ}\left(t\right)\·dt---\left(8\right)$

In formula, dh represents the differential of the wearing depth h to time t of arbitrfary point described by same formula (1) on guide pair of machine tool, and K is represented The coefficient of waste of the arbitrfary point, H represents the hardness of the point, and v represents the contact velocity of the point, and σ represents that the contact of the arbitrfary point should Power, t is represented since guideway starts the time slided occur；

T is integrated, guide pair of machine tool single-point wearing depth equation when load, speed chance mechanism must be considered：

$h=\frac{K}{H}{\∫}_0^{t}v\left(t\right)\mathrm{\σ}\left(t\right)\·dt---\left(9\right)$

Make a period of time Δ t_jInterior, contact velocity v and contact stress σ is definite value, asks for this section of wearing depth Δ h of time_j,n, j Represent in this section of time Δ t_jGeneration jth time is slided, and n represents n-th contact point, and summation draws the wearing depth of this slip； Then obtain Δ t_jWearing depth Δ h in time_j,n：

${\mathrm{\Δh}}_{j,n}=\frac{K}{H}{v}_{j,n}{\mathrm{\σ}}_{j,n}{\mathrm{\Δt}}_j---\left(10\right)$

In formula, v_j,nThe contact velocity for representing that the wear point experience jth time of n-th consideration on guide pair of machine tool is relative when sliding, σ_j,nThe contact stress for representing that the wear point experience jth time of n-th consideration on guide pair of machine tool is relative when sliding；

Guide pair of machine tool single-point wearing depth h when load, speed chance mechanism must be considered_k,n：

$h_{k,n}=\underset{j=1}{\overset{k}{\Σ}}\frac{K}{H}{v}_{j,n}{\mathrm{\σ}}_{j,n}{\mathrm{\Δt}}_j---\left(11\right)$

In formula, k represents that the guide pair of machine tool of consideration is relative and slides total degree, h_k,nRepresent n-th mill of consideration on guide pair of machine tool Damage the wearing depth after the k relative slip of point experience；

Step 2 is based on random principle, calculates the guide pair of machine tool greatest wear depth model for considering feeding length change at random

The whole service process of guide pair of machine tool, including to knife, feeding and withdrawing process, during feeding load it is of a relatively high and Long operational time, feeding pixel accuracy decay most serious；Now consider influence of the abrasion in guide pass feeding region to guide precision, And think that the abrasive action of feeding process and withdrawing process in the region is suitable；

Step 2.1 considers feeding length random distribution, the length Random Effect factor

Consider feeding length change at random, introduce length Random Effect factor r；

Guide rail surface cumulative volume wear extent is made for V, the volume wear in heavy wear area is V_S, it is considered to geometrical relationship, due to ideal State wear extent is proportional with sliding stroke, thus V_SBy total sliding distance L and heavy wear area sliding distance L_SIt is expressed as：

$V_S=\frac{L_S}{L}V---\left(12\right)$

Make l_maxRepresent maximum feeding length, l_minMinimum feeding length is represented, N represents feeding number of times, by geometrical relationship, and guide rail Kinetic characteristic understands：

L_S=Nl_min (13)

L=Nl_min+Nr(l_max-l_min) (14)

Thus：

$V_S=\frac{l_{min}}{l_{min}+r(l_{max}-l_{min})}V---\left(15\right)$

R represents the length Random Effect factor, relevant with actual feeding technical process, is a stochastic variable, and 0≤r≤1, r is close to 0 to show that feeding length distribution is intended to small, and it is big that r shows that feeding length distribution is intended near 1；In practical engineering application, r is adopted Estimated with normal distribution, then r=0.5；

Step 2.2 considers feeding length change at random, calculates guide pair of machine tool greatest wear depth model

Make h_maxGreatest wear depth is represented, b represents guideway contact width, obtained by Differential Geometry relation：

dV_S=dl_min·db·dh_max (16)

${\mathrm{dV}}_S=\frac{L}{L_S}{\mathrm{dV}}_S=(1+r(\frac{l_{max}}{l_{min}}-1)){\mathrm{dl}}_{min}\·db\·{\mathrm{dh}}_{max}---\left(17\right)$

σ is made to represent contact stress, P represents contact load, it is considered to Archard wear modelsP=σ dl_min· Db, dL=vdt are obtained：

${\mathrm{dh}}_{max}=\frac{KP\·dL}{(1+r(\frac{l_{\max }}{l_{\min }}-1\left)\right)H\·l_{min}\·db}=\frac{K\mathrm{\σ}v\·dt}{(1+r(\frac{l_{\max }}{l_{\min }}-1\left)\right)H}---\left(18\right)$

Above formula is integrated to t, must consider the guide pair of machine tool greatest wear depth model of feeding length change at random：

$h_{max}={\∫}_0^t\frac{K\mathrm{\σ}v}{(1+r(\frac{l_{\max }}{l_{\min }}-1\left)\right)H}dt---\left(19\right)$

Wherein, h_maxRepresent the greatest wear depth for feeding the guide pair of machine tool after terminating, l_maxRepresent the maximum of guide pair of machine tool Feeding length, l_minThe minimum feeding length of guide pair of machine tool is represented, r represents the length Random Effect factor；K represents the coefficient of waste, H represents hardness, and v represents the contact velocity of guide pair of machine tool, and σ represents the contact stress of guide pair of machine tool；

Guide pair of machine tool single-point wearing depth equation when step 3 is according to the consideration load, speed unit effect, substitution is examined Consider the guide pair of machine tool greatest wear depth model of feeding length change at random, calculate guide pair of machine tool linear precision decline meter Model is calculated, and influence of the lathe operating mode to guideway precision is considered according to the precision degenerated mode；

Consider guide pair of machine tool linear precision principle, make lathe straightness error for A, substitute into and consider load, speed chance mechanism When guide pair of machine tool single-point wearing depth equation and consider feeding length change at random guide pair of machine tool greatest wear depth Model, obtains：

$A={\∫}_0^t\frac{K\mathrm{\σ}\left(t\right)v\left(t\right)}{H(1+r(\frac{l_{\max }}{l_{\min }}-1))}dt---\left(20\right)$

Make a period of time Δ t_jInterior, contact velocity v and contact stress σ is definite value, asks for this section of straightness error Δ A of time_j, Summation draws the wearing depth of this slip；Then obtain Δ t_jStraightness error Δ A in time_j：

${\mathrm{\ΔA}}_j=\frac{{\mathrm{K\σ}}_j{v}_j}{H(1+r(\frac{l_{\max }}{l_{\min }}-1))}{\mathrm{\Δt}}_j---\left(21\right)$

In formula, v_jThe contact velocity for representing that guide pair of machine tool experience jth time is relative when sliding, σ_jRepresent guide pair of machine tool jth time phase Contact stress during to sliding；

Obtain the guide pair of machine tool linear precision decline computation model A under random operating mode_k：

$A_k=\underset{j=1}{\overset{k}{\Σ}}\frac{{\mathrm{K\σ}}_j{v}_j}{H(1+r(\frac{l_{\max }}{l_{\min }}-1))}{\mathrm{\Δt}}_j---\left(22\right)$

In formula, k represents that the guide pair of machine tool of consideration is relative and slides total degree.