Mechanical product precision optimizes the research that designs a model
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source:GERHOLD CNC Machining
The summary carries the significance between public errand of analytic spare parts and finished cost, the point of view that makes from the product sets out, the interest of the person that at the same time product of give attention to two or morethings is used, derivation the computation that allocates spare parts public errand by design product precision is formulary, get mechanical product precision optimizes the mathematical model of the design. Finished cost of public errand of keyword product precision optimizes 1 cost of design - the correlation that tolerancepublic errand model describes cost and public errand for thorough, accurate ground, often need to use mathematical method, because the influencing factor of product finished cost is very much, use different process instrumentation, guide necessarily to finished cost disparate. Although use same treatment technology, because different maker produces the difference of the element such as technology and level of management, the manufacturing finished cost of end item has very big discrepancy possibly also. Because this is hard to decide a current cost truly quite - tolerancepublic errand relation. As a result of cost - the relation of tolerancepublic errand, depend on specific treatment target and treatment process, machine object and treatment process differently, likelihood more suit to be planted at some specific mathematical model. At present foreign investigator raised multiform cost respectively on experimental foundation - tolerancepublic errand model [1] [2] , the research that home already also began to pay close attention to this one problem [4] . But no matter show some which kind of model plan, all increase to follow independent variable and hasten is bordering on one constant fall inside the first quadrant sunken drab decrease function, the appearance of its theory curve all is shown 1 times like the graph. Among them, the commonnest pour several models for square [3] (in 1 style of 1) drawing: C -- the finished cost of face of shape of spare parts function; A -- change with tolerancepublic errand the cost that have nothing to do is invariable; B -- change with tolerancepublic errand coefficient of concerned cost curve feature. Through choosing example of many observation statistic, use a least square method to undertake recursive an analysis to statistical example data, can get cost - greatly the output function index such as the working precision with the product contacts the parameter of tolerancepublic errand model is worth public errand of following 2 spare partses to optimize the quality that designs mechanical product together. Be in usually, the output character parameter of the product is the map of the component geometry parameter that makes a product, accordingly, the output character of the product can use parameter of its component geometry to describe. Apparent, the extraction that outputs characteristic change and geometrical parameter is worth limits, corresponding mathematical expression also can be built between product precision and hardware design public errand namely, this maths expression calls functional equation, can convey for T ＝ F (T1, t2, ... , tn) (in 2) type: T -- the product outputs characteristic public errand; Ti -- the spare parts designs tolerancepublic errand. Functional equation is the main basis that undertakes tolerancepublic errand is designed. Tolerancepublic errand design includes noncombatant duty analysis and public errand are integrated two content. Tolerancepublic errand analysis is the Ti of design public errand of spare parts of foregone product composition, according to functional equation computational product outputs characteristic variation T0, examine whether does T of products plan precision get satisfaction. The purpose with integrated public errand is allocate T of products plan precision Ti of public errand of relevant spare parts by certain regulation, make product production cost is the smallest. Accordingly, best public errand allocates criterion is the production cost of the spare parts. The route is delivered in what decided the product outputs characteristic error, after the part that decided to obtain a product working precision should include namely designs tolerancepublic errand and public errand to deliver coefficient, can use two kinds of models to build functional equation commonly: Model of extreme difference public errand and model of statistical public errand. Model of extreme difference public errand (model of 3) statistic public errand (4) among them: ξ I -- I tolerancepublic errand delivers coefficient; K0 -- output character public errand divides cloth coefficient relatively; Ki -- I coefficient of cloth of bisect of tolerancepublic errand photograph. When distributinging curve of spare parts dimension is normal school, ki value is 1. All follow normal distribution when dimension of each spare parts when, no matter how much does spare parts dimension count and the ratio between magnitude of each size distributinging scope how, output character cost is sure follow normal distribution; Have the distributinging curve of respective and aleatoric form when dimension of each spare parts, want measure only number is not quite little (5) of general N , magnitude of each size distributinging scope differs not quite big when, the product exports characteristic worth still incline to normal school, at this moment, all can take K0 ＝ 1. If always make cost be stated with C ∑ , criterion by type (2) is gotten (5) is research premise with model of statistical public errand suppose, functional equation is (6) with ∑ of C of totle drilling cost the smallest allocate criterion for tolerancepublic errand, this is problem of extreme value of a condition that seek solution, can seek solution with Lagrange multiplier law. Introduce a new function (7) the λ in the type on is Lagrange multiplication, it is one waits for calm coefficient. To make function F is the smallest, your F is right of Ti first-order slant derivative is 0, must get from this (8) general type (8) generation enters type (6) is gotten namely (9) again type (9) generation enters type (8) , must devise general formula of tolerancepublic errand computation namely (10) sees not hard, by the design affirmatory product outputs T of characteristic public errand, when T of of T0 of contented tie condition, by type (10) computation gives common difference of each spare parts, optimize those who achieve tolerancepublic errand allocate a design. type (10) generation enters type (5) gets totle drilling cost (11) 3 products precision optimizes design Japan famous quality to manage Tian Kouxuan learning the home one doctor thinks: "After the product appears on the market, alleged quality gives social loss namely. But, as a result of the loss except that functional itself place produces. " [6] this shows, no matter after any product range city, can produce different rate as a result of product function (also say the product outputs character) the loss that fluctuate and causes. The product with alleged good quality, it is the product with the little loss that after appearing on the market, brings to the society. Quality gives a society brought losing consequence, on the desire that is reflected in the user to buy a product above all, and immediate impact is had to the market of the product lead, also want finally to bring a loss to generator. Accordingly, quality loss also can serve as measure product maker to be in index of market reputation losing. The quality loss function that Tian Kouxuan puts forward, described a product to output the L of mensurable relation between character and quality loss (Y) ＝ K (Y - M) in 2 type: M -- the good cause cost with product characteristic output; K -- quality loss efficiency, lose functional loss F and product function dividing line by the product (output characteristic public errand) T decision, with product output characteristic Y has nothing to do. Curve of quality loss function is shown 2 times like the graph. Graph 2 output Y of ｜ of ＝ of T of characteristic public errand as a result of the product - M ｜ , reason has L (Y) ＝ KT2 (12) generally speaking, the spare parts precision that comprises a product is tall, conduce to the quality that improves a product, reduce quality loss thereby. But the spare parts with tall precision, want to raise the manufacturing cost of the product necessarily. Reduce the production precision of the spare parts, to the product although maker reduced cost loss, but make the quality of the product drops, increased the quality loss of the product again, also will cause finally to product maker damage. Apparent, make quality loss and cost loss integrated the loss is the smallest, it is the level that chooses optimal precision. Your L ∑ is total loss, have L of ＝ of L ∑ (Y) of ＋ C ∑ by type (11) and type (12) can be gotten (13) if curve of function of total loss pursues show 3 times. Graph 3 by before be narrated, ai, bi, ξ I and K0, ki all is the parameter that T of as characteristic as output public errand has nothing to do, might as well make a type (13) can be stated for (14) the objective presence that makes consider the product outputs characteristic public errand, abandon go be worth insignificantly, attainable the value of optimal public errand that is product precision namely, build mechanical product precision to optimize the mathematical model of the design. The article connects 4 last words to analyse the relationship between spare parts public errand and finished cost too, derivation the computation that allocates spare parts public errand by design product precision is formulary, set out from the angle of product maker, the interest of the person that at the same time product of give attention to two or morethings is used, loss of integrated product quality and cost losing are academic, get the optimization model of products plan precision. 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