The statistic of machining error is analysed
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02mm, the dimension of a batch of aperture after treatment also slants big 0.
02mm. Characteristic: ① and handling time (ordinal) have nothing to do; ② can estimate beforehand; ③ is eliminated completely more easily; ④ won't cause work measure to fluctuate (the influence that often is worth systematic error to approve work to be the same as is consistent, won't cause the difference between each workpiece) ; ⑤ does not affect figure of dimension distributinging curve. (2) change value system error: Definition: In processing a batch of work continuously, the size of its machining error and direction press the systematic error that definite pattern changes, call change value system error. For example: Of cutting tool wear away normally the machining error that cause, its size lets handling time and have regular ground change, belong to change value system error. Characteristic: ① and handling time (ordinal) about; ② can estimate beforehand; ③ is eliminated completely harder; The accretion that ④ can create work measure or reduce (change although value system error can be caused approve the difference between workpiece together, but of according to definite pattern ordinal change, won't cause fluctuate smally suddenly greatly suddenly) ; ⑤ affects figure of dimension distributinging curve. Notice the heat of 1 machining complex is out of shape, in temperature rise process, will cause commonly change value system error, after achieving hot balance, cause error of constant value system again. 2, random error: Definition: In processing a batch of work continuously, the size of its machining error and direction are worn without regular change, such error calls random error. For example: Semifinished product error (mental allowance is inhomogenous, material hardness is inhomogenous etc) answer mirror, fixed position error, clamp error (clamping force size) , the element such as workpiece internal stress is metabolic adventitious, it is the cause that causes random error. Characteristic: ① cannot estimate beforehand (∵ is random) , but have, decided statistical rule; ② is eliminated completely harder, can reduce only minimal; ③ work measure ignore big ignore small, the measure that creates a batch of work is dispersive (the numerical value of random below certain treatment condition error always is inside certain limits fluctuant) . Those who notice error of system of 2 random sum of errors differentiating also is not absolutely, there is distinction to have connection again already between them. For example: When machining a batch of spare partses, if be,adjust in the machine tool in finish, criterion the adjustment of the machine tool the error causes error of constant value system; If be a course a certain number of second adjust finish, adjust an error to cause random error. Notice 3 errors property is different, settlement approach is different also. To often be worth systematic error error, if can master its size and direction, can eliminate through adjusting; Be worth systematic error to changing, if can grasp the pattern that its size and direction change along with time, can eliminate through automatic compensation; To random error, can use statistic to analyse a way, contractible their fluctuant limits. 2, the statistical analysis law with the statistical commonly used analysis of machining error has two kinds: Distributinging curve law and point attempt law. (one) distributinging curve law (see P206) 1, distributing actually curve (histogram) 1) example and sample size: Use setting method to machine some kind of spare parts group by group, random and draw-out among them a certain quantity of undertake metrical, this batch of draw-out spare partses call sample book. A number of example call sample size, express with N. 2) dimension is dispersive with dispersive limits: Because random sum of errors changes,be worth the existence of systematic error, the real numerical value of dimension of these spare parts treatment is each are not identical, this kind of phenomenon calls dimension to disperse. The difference of the maximum Xmax of sample size and Xmin of the least value, call dispersive range. 3) reach in group group be apart from D: Arrange sample size by size order, cent becomes K group, criterion group be apart from D to be: D= (Xmax-Xmin) / K, the make choice of that counts K in group expresses as follows: Sample size N50 is the following 250250 above count 100100 ～ of 50 ～ in group 76 ～ of K6 ～ 1210 ～ of 107 ～ 204) frequency M: The spare parts amount of same size interval, weigh frequency, express with M. 5) frequency F and frequency density: Of frequency M and sample size N than, weigh frequency, express with F. Namely: F=m/n. Frequency F is divided with group be apart from D place business calls frequency density (F/d) . 6) distributing actually curve (histogram) : With work measure (or error) for the abscissa, make ordinate with frequency or frequency density, can make what should approve a spare parts to machine dimension wait for wide histogram. Join again the midpoint of every square all the time width in histogram (group median) get a broken line, distributing actually namely curve, see figure below. Distributing actually curve (histogram) scale measure: Sampling, > measure, > in group, > nod surely, > even the line. Curve of Nextpage2, normal school (1) the curvilinear equation of normal school: Practice and theoretical analysis make clear, when processing a batch of work with setting method, its on size error is the result that the collaboration of element put together that becomes independent by very polyphase each other uses, if be done not have among them, action of the decision since the element, the dimension of the spare parts after be being machined distributings curve of obedient normal school (call gauss curve) again, see figure below. The Y in type of normal school curve -- the probability density of normal school; α -- of normal school curve all be worth; σ -- the standard deviation of normal school curve (deviation of root mean square) (2) the characteristic of normal school curve: 1) the central position that all is worth α to decide normal school curve, and semmetry is controlled in its. When X= α , it is the maximum of curvilinear Y, namely: ; In σ of X= α ± place curve has inflection point; The curve is asymptote with X axis, the curve becomes bell entity. The characteristic of normal school curve 2) the parameter that standard deviation σ is decision curve appearance. σ value increases, criterion Ymax is reduced, the curve will tend evenness, dimension is dispersive the gender is bigger; Contrary, σ value is less, criterion the curve is thin tall, dimension is dispersive the gender is smaller. The discretion that reason σ value made clear to a batch of workpiece machine precision (σ value is little, ymax value is great, machine precision tall) . 3) the whole area that includes below distributinging curve machines a spare parts on behalf of a batch, namely the real measure of 100% spare partses is inside this one distributinging limits. If right graph is medium, the Xmin of size of the smallest maximum that C dot delegate sets, CD represents the tolerancepublic errand area of the spare parts, below the curve two area delegate machines C, D the percent of pass of the spare parts. Below the curve the area of others (the part that shadow line does not have on the graph) it is percent defective. When the circle outside treatment, part of the left hatching that do not have shade is equivalent to on the graph not repairable reject, the part of the hatching that do not have shade of right is repairable reject; In the Kong Shi inside treatment, apropos and contrary. Use percent of pass of product of computation of normal school curve to normal school curve, the area that leaves to X curve by α decides by next type: When σ of X- α =3, criterion: 2A=2 × 0.
49865=0.
9973=99.
73% , namely work measure in ± the frequency beyond 3 σ is occupied only 0.
27 ％ , can ignor. The area function below normal school curve because this, the dispersive range that takes normal school curve commonly is earth 3 σ . So, if workpiece public errand is δ , criterion ① is like distributinging center and public errand to take central coincide, the condition that does not produce waste product is δ ≥ 6 σ , have reject generation conversely. Percent defective: Q abandons =0.
5-A ② is like distributinging center and public errand to head a center not coincide, the condition that does not produce waste product is: 6 σ of δ ≥ 10 2 △ constant theoretic normal school curve is to both sides infinite and outspread, and the measure value of the product in be being produced actually is finite however. The estimation that because this uses finite example average X and S of example standard deviation,serves as theory to all be worth α and standard deviation σ is worth. Its computation formula is as follows: The X in type -- example average, namely the average size of workpiece. It basically decides the size at adjusting dimension and error of constant value system; Xi -- I the dimension of workpiece; S -- example standard deviation, its are worth the dispersive rate that shows work measure, it by change random error decides value system sum of errors; N---Sample size. 3, the application of distributinging curve 1) the property of differentiate machining error: If change without △ in treatment process, so its dimension distributings should be subject to normal school, this is the basic method of property of differentiate machining error. ① distributings actually curve and normal school curve are basic conform to, explain to in machining a process, change without △ ; Whether does ② take central coincide with tolerancepublic errand according to average X, will judge whether to put in △ constant: Average X and public errand take central coincide, show nonexistent △ constant; Average X and public errand head a center not coincide, demonstrative existence △ constant. ③ △ often affects average X only, affect the position of distributinging curve only namely. Citing accords with normal school; 6 σ of δ ≥ ; And dimension distributinging center and public errand take central coincide. Accord with normal school; 6 σ of δ ≥ ; But dimension distributinging center and public errand head a center not coincide, existence △ constant. Accord with normal school, 6 σ of δ ＜ , and dimension distributinging center and public errand head a center not coincide. Explain: Department of normal, △ does not have treatment condition almost, △ is followed small, in machining a process, appear without reject, working procedure precision satisfies a requirement. Explain: △ changes to be not had almost, △ is followed small, outstanding △ often exists. Because cutting tool installation adjusts what forbid and cause,it basically is. Below this kind of circumstance, although appeared,reject also is OK try to avoid through adjusting (adjust cutting tool initiative treatment position, eliminate △ constant) . Explain: △ changes to be not had almost, the △ with outstanding existence constant, △ is followed bigger. Although pass cutting tool to adjust,eliminated △ constant, also cannot avoid the generation of reject completely. Working procedure precision cannot satisfy workpiece to machine the requirement of precision, should change with a kind of more accurate than using process now treatment the method completes treatment (reduce working procedure σ to be worth) namely. Change turning treatment grinding treatment for example, reaming treatment changes aperture of bore with a reamer to wait. ④ distributings actually when the curve does not accord with normal school, show like occurrence distributinging curve flat-roofed distributing, Shuang Feng distributings or slant when voice distributings, there is outstanding △ to change in showing treatment process existence. Machine machining error distributinging rule is flat-roofed distributing in the element of a lot of error in affecting machining, if cutting tool is linear tatty effect is distinct, criterion the on size error of workpiece will appear flat-roofed distributing. The result that distributinging curve combines the error of numerous normal state that flat-roofed error distributinging curve can regard along with time translation as. Shuang Feng distributings in the treatment content of same process, will be finished at the same time by two machine tools, the adjustment as a result of these two machine tools size is endless and same, the precision condition of two machine tools also has difference, be like the workpiece lump that machines place of these two machine tools, criterion the on size error of workpiece shows Shuang Feng to distributing. Slant voice distributings using when trying diameter of axis of the turning that cut a way or aperture, arise to avoid as far as possible as a result of handlers not repairable reject, subjective (is not random ground) make journal is machined peace is greatly not small, criterion they get on size error to be shown slant voice distributings. 2) certain technology ability and its grade Ⅰ ) craft ability: Be when showing working procedure is in steady state, the extent that machining error fluctuates normally. For example: When machining dimension obedience normal school, its dimension is dispersive limits should be 6 σ , the size of 6 σ represented some to plant treatment method falls in formulary condition (wait like dosage of semifinished product surplus, cutting, normal machine tool, clamping apparatus, cutting tool) the treatment precision that can achieve, namely craft ability. Ⅱ ) craft ability grade: Express in order to be versed in Cp of skill force coefficient comes, cp represented craft ability to satisfy the degree that tolerancepublic errand asks. Its value presses type calculates: Cp = δ / in 6 σ type: δ---For work measure public errand. According to the size of craft ability coefficient, craft ability cent becomes 5 form: Cp ＞ 1.
67 for fancy, explain craft ability is exorbitant, not certain economy; 1.
＞ of 67 ≥ Cp 1.
33 for one class, explain craft capacity is sufficient, can allow constant wave motion; 1.
＞ of 33 ≥ CP 1.
00 for 2 class, explain craft ability is loath, must pay close attention; 1.
＞ of 00 ≥ Cp 0.
67 for 3 class, explain craft ability is insufficient, the possibility arises a few reject; Cp ≤ 0.
67 for 4 class, the specification is versed in skill force is no good, must try to improve. Note: Usually, craft ability do not answer under 2 class. Nextpage3) estimation percent of pass or fraction defective: Q abandons =0.
The statistic of 5-A5, machining error analyses citing 6, distributinging curve law belongs to the problem ① that distributinging curve law exists analysis of after the event, the generation of reject cannot prevent in machining a process; ② cannot change △ and △ is followed divisional come out; ③ take time, wasteful. Use the law that choose a plan to be able to offset these weakness. (2) the sample book that the analysis choosing a plan of process orders a graph to analyse law place to use is ordinal galley proof this, smoke sampling at regular intervals namely this capacity N ＝ 5 ～ a little sample book of 10, computation gives each arithmetical average X of little sample book and extreme difference R. 1, a few kinds of forms of the law that choose a plan (1) is odd point attempt is the size that by treatment ground of ordinal one by one measures a batch of workpiece, with the treatment of workpiece ordinal number is the abscissa, with work measure (on size error or form error) a kind of dot picture that as ordinate scale gives. Odd a change that ordered a graph to mirror a spare parts to machine dimension and treatment are ordinal (or handling time) relation. (2) chooses a plan in group is a batch of spare partses ordinal by every M cent undertakes for a group in group, with the abscissa the delegate arranges serial number in group, the point that with ordinate on behalf of the real measure of the spare parts scale gives pursues. The length that chooses a plan in group follows sheet the photograph that choose a plan is compared shorten greatly, the measure that can see each moments from which is dispersive circumstance. (3)X point attempt is it is the abscissa with arranging serial number in group, be ordinate scale with the average size X of every groups of spare partses. The metabolic trend that it can see work measure average (the influence) that highlighted △ to change. (R of 4) extreme difference chooses a plan with in group ordinal date is the abscissa, the difference of the largest size of the workpiece of inter block of extreme difference R(with every groups of spare partses and the smallest size) the dot picture that gives for ordinate scale, abbreviation R chooses a plan. It is main the dimension in process of indication treatment of in order to is dispersive the metabolic circumstance of limits. X nods a graph to control the change of distributinging center of process quality target, index of quality of process of control of R point attempt is dispersive the change of limits, when analysing real problem, r point attempt and X point attempt often rise jointly use, because this calls X-R plan. 2. The applied point attempt of the law that choose a plan can observe piece change value system sum of errors the size of random error and metabolic rule; Still can use the stability that judges process, offer control to process the data of precision in machining a process. Judge the stability of process, want to pursue according to X-R, in needing to go up to draw its respectively in X-R graph at the same time, heart line reachs fluctuation control line, and the bounds line that control line judges process stability namely. The position of each line can press following formula to calculate: X-R nods the normal wave motion of the graph to state process is stable, can protect let machine quality to ask; X-R nods a graph to appear unusual wave motion (be like: The wave motion of drop is very big, have rise continuously or drop the tendency, appear seasonal trend) when, answer to prove a cause in time, readjust, in order to avoid the happening of reject. CNC Milling