proe tol组装公差分析

組裝公差分析

公差分析主要是探討一個描述工件組合後，其公差變動模式，一個好的公差

分析模式可以預測組件公差能吻合實際組件公差界限有多少，其預測之機率

愈大愈好。組裝公差分析可分成三種模式：最壞狀況模式(Worst-case model)、統計模式(Statistical model)和蒙地卡羅模式(Monte Carlo model).

概念

Dimension chain (sometimes called tolerance chain) is a closed loop of interrelated dimensions. It consists of increasing, decreasing links and a single concluding link. In figures 2-4 and 2-5, link i is the increasing link, d is a decreasing link and c is the concluding link.

Apparently, the concluding link c is the one whose tolerance is of interest and which is produced indirectly. Increasing and decreasing links (both called contributing links) are the ones that by increasing them, concluding link increases and decreases; respectively.

Figure 1. Dimension Chain of c, 2 links, 1D Figure 2.: Dimension Chain of c, 4 links, 1D The equation for evaluating the concluding link dimension is [Lin and

Zhang (2001)]:

---------(1)

Where:

Σi: The summation of the increasing link dimensions.

Σd: The summation of the decreasing link dimensions.

j: increasing links index.

k: decreasing links index.

l: number of increasing links.

m: number of decreasing links.

For figure 1 ,c can be found as:

c = i -

d ------(2)

As for chain in figure 2, c can be found as:

c = (i1 + i2)-( d1 + d2) ------(3)

1. 最壞狀況模式(Worst-case model)

最壞狀況模式又稱上下偏差模式、極限模式、完全互換模式，此模式是以工件的最大及最小狀況組合，可以滿足完全互換性、組件公差最大.

In worst-case method, the concluding dimension’s tolerance Δc can be found as following:

------(4)

Referring to figure 2 and equations (3 and 4), the deviation of the concluding link is:

Δc = Δi1 + Δi2 + Δd1 + Δd2------(5)

T0: 總公差

m: 零件之數目

T i: 各零件之公差

2. 統計模式(Statistical model)

大量生產的產品，其零組件因為生產過程的變異所造成的公差呈統計分布，統計公差分析雖然可以估算結果尺寸公差的特性，但實際的分布情形還是無法掌握，統計模擬即是透過隨機取樣的原理

統計模式又稱均方根和模式(Root sum squared model)，假設各零件公差都依據本身的特徵或加工條件會符合常態之鐘型曲線分佈，且分佈中心與公差帶中心值相同,分佈範圍與公差範圍也相同,組合公差為

--------(6)

m: 零件個數 , Ti :各零件之尺寸公差

另一種堆疊統計公差觀念如下

In statistical method, the concluding dimension’s tolerance Δc can be found as following:

--------(7)

Referring to figure 2 and equations (5 and 7), the deviation of the concluding link is:

------------------(8) Reduction if eliminated (貢獻度)

1. Statistical Contribution

= ------------------------(9)

2. Worst Case Contribution

-------------------------------------------(10)

?

其中 Ci : Worst Case Clearance

蒙地卡羅模式(Monte Carlo model)

「蒙地卡羅方法」是一種數值方法，利用亂數取樣(Random sampling) 模擬來解決數學問題。在數學上，產生亂數，就是從一給

定的數集合中選出的數，若從集合中不按順序隨機選取其中數字,稱為亂數,如果選到的機率相同,視為均勻亂數,凡是所有具有隨機效應的過程,均可能以蒙地卡羅方法來大量模擬單一事件，藉統計上平均值獲得某設定條件下實際最可能測量值。

蒙地卡羅方法的基本原理是將所有可能結果發生的機率，定義出一機率密度函數。將此機率密度函數累加成累積機率函數，調整其值最大值為1，此稱