两维公差_RSS_叠加法
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GD&T Tolerance Stack-Up Analysis
尺寸链公差叠加分析
There are two major types of Tolerance Analysis
1. Worst-case (arithmetic) straight stack or limit stack: 极限法 Worst-case tolerance analysis represent the largest (worstcase) possible variation 得出可能最大的误差
2. DEFINE THE DIRECTION OF THE STUDY. X, Y, OR Z ?
3. DEFINE THE PATH OF ENABLERS.
4. RETRIEVE THE ITEMS NECESSARY TO DO THE STUDY.
ITEMS NEEDED
1. GD&T DWGS FOR ALL PARTS RELATED TO STUDY.
Normal distribution: +/-3 σ = 6 σ = Tolerance range
正态分布
σ = range/6
Uniform +/-(square root3) σ = 2(Square Root3)σ
均匀分布
=Tolerance range
σ = range/2(square root)
零部件总成装配分析（1D ANALYSIS － RSS ）
GETTING STARTED
1. DEFINE THE STUDY OBJECTIVE. EXAMPLES: a. ANALYSIS OF DTS. b. CALCULATION OF ASSEMBLY TOLERANCE. c. HOLE/PIN CLEARANCE STUDY.
same time. The example shown on the next page demonstrates the chances of this occurring.极限法叠加公差是假设尺寸链上的公差将 会在+3σor -3σ点上同时产生.下页的案例将会展现得出这种结果的 概率．
Limit Stack – Example 极限法 – 案例 Determine the probability that all of the tolerances in a five (5) tolerance stack-up will each be at or beyond the +3 σ point of inflection at the same time ( assumes normal distributions for each tolerance) 确定叠加五个公差时所有公差同时在+3 σ 点上产生的概率（假定正态分布） Probability Total = ( 0.00135)x(0.00135)x(0.00135)x(0.00135)x(0.00135)
Statistics Stack – Example
Find the RSS result for the following input tolerance
( +/-1.0 nuniform, +/-2.0 uniform
In this example, the extra step required is to convert all of the tolerances into +/- 1 σ. This is required because for a normal distribution the range equals +/-3 σ but for a uniform distribution, the range equals +/σ(square root 3). First convert all values to 1 σ, the 4 values are:
3. ASSEMBLY PROCESS INFORMATION a. ASSEMBLY SEQUENCE. b. ASSEMBLY FIXTURE INFORMATION AND TOLERANCING. c. OPERATOR PROCEDURE FOR INSTALLATION OF PARTS.
2. Statistics Tolerance Analysis：统计公差法 For a Tolerance Stackup with many dimensions and tolerances, statistical tolerance analysis may be more appropriate. 统计公差法叠加处理许多尺寸公差可得出更合适 的结果.
4. 1D ANALYSIS SPREADSHEET.
Float Calculation
Non-Gravity Biased Definition: Part Shift due to the positioning of the part/assembly on the tooling pins/fasteners where there is the equal likelihood that the positioning of the part can be anywhere within the allowable float zone The distribution type for this float calculation will be normal
1-0.9973 = 0.0027 or 0.27% 如正态分布所示，公差值产生在+/-3 σ 或以外的概率为0.27%
Straight stacking the tolerances assumes that all of the tolerances in the stack will be at either +3 σ or -3 σ point of inflection at the
不论公差分布型态如何, RSS法是有效的.然而当计算叠加公差分布 型态多于一种时则需要额外的步骤．
If more than one distribution type exist, The RSS requires to calculate the equivalent σ 如存在多于一种分布型态，RSS要求 计算等值σ
Calculation:10.2 - 9.7 = 0.5 Nominal Shift = 0.5/2 or 0.25
Note: to determine shift direction based on application
Note: All pin floats are to be calculated from the process utilizing the smallest pins I.E… Weld tools typically utilize smaller pins than gages to minimize or eliminate part binding in the welders. You should be calculating your floats based on these pin sizes.
Gravity Biased Definition: Part Shift due to the positioning of the part/Assembly on the tooling pins/fasteners where gravity will shift the part totally to one side of the tooling/attachment feature.
Combining Tolerance – Limit Stack 极限法
T = T1 + T2 + T3 + T4 + T5 …..
公式
A Straight stack or limit stack is a method of combining contributing tolerances by summing the tolerance as shown above
Application: Applied at the end of the study as a mean shift (See example) I.E…Hole 10.1+0.1/0 Pin 0.4 under nominal (Based on program tooling Reqt's)
1D Study Practice
The attached sheets reflect the GD&T for the Fender Assembly Door Assembly Bodyside With the information 1D study can be created for the Door to
极限法用上述公式
Why don’t we use straight stacks when adding normally distributed tolerances? 为什么不用极限法去叠加正态分布的公差？
As can be seen from normal distribution, the probability that a given tolerance will be at or beyond its +/- 3σvalue is:
(0.333), (0.333), (1/square root 3), 2/square root 3 )
Perform the RSS σ = square root { 0.333^2 + 0.333^2 + (1/square root 3)^2 +
(2/square root3)^2}
= 1.37 +/-3 σ = +/-4.12
Application: Calculated from the Largest hole minus the smallest pin I.E…Hole 10.1+0.1/0 Pin 0.4 under nominal (Based on program tooling Reqt's) Calculation:10.2 - 9.7 = 0.5 or +/-0.25 float
= 4.48 x 10^15 = 1 in 223,000,000,000,000
RSS Stack up – Root of Sum of Squares ＲＳＳ叠加法（统计公差法 ） It requires that : 要求
1. each of the tolerances are indipendent 各公差相互独立 2. each tolerance acts in the same direction 各公差作用在同一方向
2. DWGS OR DETAILED INFORMATION ON ALL FASTENERS RELATED TO THE STUDY. a. SIZE OF FASTENER. b. SIZE TOLERANCE OF FASTENER. c. HOW THE FASTENER FUNCTIONS.
Combining Tolerances – ＲＳＳ Stack ＲＳＳ叠加法
T = square root (T1^2 + T2^2 + T3^2 + T4^2 + T5^2 ….. )
The R.S.S method is valid regardless of the distribution type of the tolerances. However, extra steps are required when calculating the result when more than one distribution type is present. This method assumes the tolerances are independent.
尺寸链公差叠加分析
There are two major types of Tolerance Analysis
1. Worst-case (arithmetic) straight stack or limit stack: 极限法 Worst-case tolerance analysis represent the largest (worstcase) possible variation 得出可能最大的误差
2. DEFINE THE DIRECTION OF THE STUDY. X, Y, OR Z ?
3. DEFINE THE PATH OF ENABLERS.
4. RETRIEVE THE ITEMS NECESSARY TO DO THE STUDY.
ITEMS NEEDED
1. GD&T DWGS FOR ALL PARTS RELATED TO STUDY.
Normal distribution: +/-3 σ = 6 σ = Tolerance range
正态分布
σ = range/6
Uniform +/-(square root3) σ = 2(Square Root3)σ
均匀分布
=Tolerance range
σ = range/2(square root)
零部件总成装配分析（1D ANALYSIS － RSS ）
GETTING STARTED
1. DEFINE THE STUDY OBJECTIVE. EXAMPLES: a. ANALYSIS OF DTS. b. CALCULATION OF ASSEMBLY TOLERANCE. c. HOLE/PIN CLEARANCE STUDY.
same time. The example shown on the next page demonstrates the chances of this occurring.极限法叠加公差是假设尺寸链上的公差将 会在+3σor -3σ点上同时产生.下页的案例将会展现得出这种结果的 概率．
Limit Stack – Example 极限法 – 案例 Determine the probability that all of the tolerances in a five (5) tolerance stack-up will each be at or beyond the +3 σ point of inflection at the same time ( assumes normal distributions for each tolerance) 确定叠加五个公差时所有公差同时在+3 σ 点上产生的概率（假定正态分布） Probability Total = ( 0.00135)x(0.00135)x(0.00135)x(0.00135)x(0.00135)
Statistics Stack – Example
Find the RSS result for the following input tolerance
( +/-1.0 nuniform, +/-2.0 uniform
In this example, the extra step required is to convert all of the tolerances into +/- 1 σ. This is required because for a normal distribution the range equals +/-3 σ but for a uniform distribution, the range equals +/σ(square root 3). First convert all values to 1 σ, the 4 values are:
3. ASSEMBLY PROCESS INFORMATION a. ASSEMBLY SEQUENCE. b. ASSEMBLY FIXTURE INFORMATION AND TOLERANCING. c. OPERATOR PROCEDURE FOR INSTALLATION OF PARTS.
2. Statistics Tolerance Analysis：统计公差法 For a Tolerance Stackup with many dimensions and tolerances, statistical tolerance analysis may be more appropriate. 统计公差法叠加处理许多尺寸公差可得出更合适 的结果.
4. 1D ANALYSIS SPREADSHEET.
Float Calculation
Non-Gravity Biased Definition: Part Shift due to the positioning of the part/assembly on the tooling pins/fasteners where there is the equal likelihood that the positioning of the part can be anywhere within the allowable float zone The distribution type for this float calculation will be normal
1-0.9973 = 0.0027 or 0.27% 如正态分布所示，公差值产生在+/-3 σ 或以外的概率为0.27%
Straight stacking the tolerances assumes that all of the tolerances in the stack will be at either +3 σ or -3 σ point of inflection at the
不论公差分布型态如何, RSS法是有效的.然而当计算叠加公差分布 型态多于一种时则需要额外的步骤．
If more than one distribution type exist, The RSS requires to calculate the equivalent σ 如存在多于一种分布型态，RSS要求 计算等值σ
Calculation:10.2 - 9.7 = 0.5 Nominal Shift = 0.5/2 or 0.25
Note: to determine shift direction based on application
Note: All pin floats are to be calculated from the process utilizing the smallest pins I.E… Weld tools typically utilize smaller pins than gages to minimize or eliminate part binding in the welders. You should be calculating your floats based on these pin sizes.
Gravity Biased Definition: Part Shift due to the positioning of the part/Assembly on the tooling pins/fasteners where gravity will shift the part totally to one side of the tooling/attachment feature.
Combining Tolerance – Limit Stack 极限法
T = T1 + T2 + T3 + T4 + T5 …..
公式
A Straight stack or limit stack is a method of combining contributing tolerances by summing the tolerance as shown above
Application: Applied at the end of the study as a mean shift (See example) I.E…Hole 10.1+0.1/0 Pin 0.4 under nominal (Based on program tooling Reqt's)
1D Study Practice
The attached sheets reflect the GD&T for the Fender Assembly Door Assembly Bodyside With the information 1D study can be created for the Door to
极限法用上述公式
Why don’t we use straight stacks when adding normally distributed tolerances? 为什么不用极限法去叠加正态分布的公差？
As can be seen from normal distribution, the probability that a given tolerance will be at or beyond its +/- 3σvalue is:
(0.333), (0.333), (1/square root 3), 2/square root 3 )
Perform the RSS σ = square root { 0.333^2 + 0.333^2 + (1/square root 3)^2 +
(2/square root3)^2}
= 1.37 +/-3 σ = +/-4.12
Application: Calculated from the Largest hole minus the smallest pin I.E…Hole 10.1+0.1/0 Pin 0.4 under nominal (Based on program tooling Reqt's) Calculation:10.2 - 9.7 = 0.5 or +/-0.25 float
= 4.48 x 10^15 = 1 in 223,000,000,000,000
RSS Stack up – Root of Sum of Squares ＲＳＳ叠加法（统计公差法 ） It requires that : 要求
1. each of the tolerances are indipendent 各公差相互独立 2. each tolerance acts in the same direction 各公差作用在同一方向
2. DWGS OR DETAILED INFORMATION ON ALL FASTENERS RELATED TO THE STUDY. a. SIZE OF FASTENER. b. SIZE TOLERANCE OF FASTENER. c. HOW THE FASTENER FUNCTIONS.
Combining Tolerances – ＲＳＳ Stack ＲＳＳ叠加法
T = square root (T1^2 + T2^2 + T3^2 + T4^2 + T5^2 ….. )
The R.S.S method is valid regardless of the distribution type of the tolerances. However, extra steps are required when calculating the result when more than one distribution type is present. This method assumes the tolerances are independent.