Abstract:
A method of providing tolerancing of an assembly of parts comprising the steps of querying and storing in a processor storage a mean dimension of the parts of the assembly, a sensitivity for each mean dimension, a fixed tolerance for the parts for which the user cannot change and a standard deviation for which the user can change. The method further includes the step of processing said mean dimension, said sensitivity, said tolerances, and said standard deviation to provide projected defects per unit and directions to or other information to achieve design goals.

Description:
STATEMENT OF THE INVENTION 
     This invention relates to tolerance analysis and more particularly to an automated analysis system and method. 
     BACKGROUND OF THE INVENTION 
     In traditional mechanical tolerance analysis, mechanical engineers and designers assign tolerances to dimensions and analyze the effectiveness of meeting performance requirements such as clearance around a module. It was an iterative process, with the number of steps determined by the skill of the engineer to define or modify the design. In addition, the tolerance chosen was based on perceptions the individual engineer possessed regarding the ability of machine tools to perform a particular operation, e.g., what is the best tolerance to apply to a part that will be machined on lathe? 
     In an effort for manufacturers to achieve higher quality, goals are set to have failure of parts down to certain limits. One such limited failure goal is called &#34;Six Sigma&#34; goal. 
     Known tolerancing software tools on the market or privately owned: 
     VSA (Variation Simulation Analysis )--Applied Computer Solutions; 
     CATS (Computer Aided Tolerancing Software)--Brigham Young University 
     available with Autocad 
     working on implementation with CATHA and others; 
     GEOS--Renssalaer Polytechnic Institute 
     Dimensional Management Software--Trikon 
     TI/TOL--Texas Instruments and BYU 
     Cognition 
     CATS has some form of Motorola Six Sigma capability. TI/TOL has some Six Sigma capability. 
     SUMMARY OF THE INVENTION 
     In accordance with one preferred embodiment of the present invention, an automated spreadsheet is provided that aids design engineers to assign tolerances to mechanical components and to predict their effect on the function of an assembly. The equations used in the system and method reduce the iterations required to choose dimensions and tolerances, and utilize process capability data to establish tolerances based on history, not perception. They are for one example focused on helping the engineer to achieve Six Sigma goals, and provide guidance about what could be changed in the design to meet these goals. 
    
    
     DESCRIPTION OF THE DRAWING 
     FIG. 1 is a system block diagram. 
     FIG. 2 illustrates a bearing assembly for which the present design provides analysis. 
     FIG. 3 is a sketch of the bearing assembly mean dimensions. 
     FIG. 4 illustrates the fields of the spreadsheet. 
     FIG. 5A and 5B are flow charts of the logic of the system and method. 
     FIG. 6 illustrates the spreadsheet with the mean dimensions, sensitivity, and tolerances for performing a Classical method of analysis and resizing. 
     FIG. 7 illustrates the spreadsheet with mean dimension, sensitivity, tolerance and standard deviation for performing statistical method of analysis. 
     FIG. 8 illustrates the spreadsheet with calculated DPU. 
    
    
     DESCRIPTION OF PREFERRED EMBODIMENT 
     In accordance with one embodiment of the present invention, the system comprises a computer system as illustrated in FIG. 1, for example, including a processor 10a, with a keyboard 10b, a mouse 10d, and a screen or monitor 10c. The processor system 10a may include a floppy disk load system or a hard drive. In accordance with the present invention and a preferred embodiment, the system 10 uses an Excel spreadsheet, Version 4.0. The tolerance analysis spreadsheet is an Excel file, which is then loaded via a floppy disk, or hard drive, into the processor 10a. The worksheet file (template) that performs basic tolerance analysis for one dimensional stack-ups. This tool is a generic tool that can quickly and efficiently assign mechanical tolerances for simple models. The tool has six major functions: 
     Classical tolerance analysis 
     (1) Worst Case Analysis 
     (2) Root Sum of Squares (RSS) Analysis 
     (3) Modified RSS Analysis 
     The classical models feature a &#34;resizing&#34; function that directly calculates the tolerances required to meet traditional performance goals (as opposed to several iterations to get the answer). The system also includes a Six Sigma tolerance allocation/analysis with 
     (4) Worst Case Allocation 
     (5) Statistical Allocation 
     (6) Statistical Analysis 
     The Six Sigma models assign and evaluate tolerances based on capabilities of the processes that are used to make the parts. These models automatically assign tolerances so that each component is equally producible. The spreadsheet also calculates an estimate of the assembly defect rate that will occur. 
     Advantages: 
     1) This tool gives the user 11 several analysis or allocation options at the click of a mouse as illustrated at 10d. 
     2) The user 11 can get an estimate of defect data by taking advantage of process capabilities instead of choosing a traditional method which relied on user expertise. 
     3) Automatically resizes tolerances if one of the classical methods is used. 
     4) Automatically allocates tolerances if one of the Six Sigma methods is used. 
     5) Includes both fixed and variable inputs to accommodate purchased and internally fabricated parts. 
     6) Allows for any sensitivity value, not just +/-1. 
     7) Output is the form of handy worksheet for future reference. 
     8) Provides guidance to meet Six Sigma productivity and performance goals. 
     9) Calculates an estimate of the defect rates for assemblies. 
     Referring to FIG. 2, for example, a bearing assembly 13 is illustrated with indicated tolerances. A sketch of the mean dimensions is shown in FIG. 3. The bearing assembly comprises the following parts: (a shaft 15, two bearings 17, a spacer 19, and a retaining ring 21). In accordance with the present invention, an auto tolerancing spreadsheet, or worksheet, is created using, for example, Excel Spreadsheet Version 4.0. The fields have the layout shown in FIG. 4. Table 1 below is a description of the six models solved on by the spreadsheet. The description is with respect to solving the gap marked in FIG. 2. 
     
                       TABLE 1______________________________________Model Name    Description      Notes______________________________________Worst Case    Range at the gap is                     Simplest and most(WC)     considered to be equal to                     conservative of    the numeric sum of all the                     traditional approaches.    tolerances of the included    dimensions.Root Sum of    Range at the gap is                     Least conservative ofSquares  considered to be equal to                     traditional approaches.(RSS)    the square root of the sum    of the squares of all the    tolerances in the stack-up.Modified Range at the gap is                     More conservativeRoot Sum of    considered to be equal to                     than RSS, but lessSquares  the RSS value times a                     than Worst Case.(MRSS)   correction factor.A resize feature is included for each of the above models that willmodify tolerances so that the total will equal the nominal gap forwhichever of the three models is chosen. Each tolerance isincreased by the same factor so that relative productivity ofevery dimension will be preserved.Worst Case    A technique that uses                     Assembly is assuredAllocation    available standard                     with worst case(WC      deviations to assign                     combinations ofALLOC)   tolerances to each                     tolerances, and each    dimension. The tolerances                     tolerance will have a    are assigned so that each                     Sigma of a least 6.0.    will be equally producible    (same Sigma). A value is    provided as a guideline as    to what should be changed    to meet Six Sigma    guidelines.Statistical    Is similar to RSS model.                     If the assembly doesAllocation    Tolerances are assigned to                     not meet Six Sigma(Stat    each dimension so that it                     requirements, aALLOC.)  has a Sigma of 6.0. The                     value is provided as    expected defects per unit                     a guideline to    (DPU) and Sigma of the                     improve the design.    gap is provided.Statistical    This is used on designs that                     It provides aAnalysis already have tolerances                     guideline as to what(STAT    assigned, but a DPU and                     can be changed toANALYSIS)    Sigma of the gap is                     achieve Six Sigma    desired.         interchangeability at                     the gap.______________________________________ 
    
     The mechanical tolerancing worksheet fields of FIG. 4 are defined as charted below in Table 2: 
     
                       TABLE 2______________________________________Fields     Definitions______________________________________ASSY NAME/ Name of assembly or part number.PART #PREPARED BY:      YourselfINTERFACE  Description of the assembly tolerance stackupDESC       to be analyzed.DATE       Date you perform the analysis. It is auto-      matically updated by the computer, or can be      altered by user.MEAN DIM   The mid-dimension of the tolerance limitsPLUS +     Positive dimensions follow from left to right      (or bottom to top) on the loop diagram. Enter      as positive numbers.MINUS -    Negative dimensions follow from left to right      (or bottom to top) on the loop diagram. Enter      as positive numbers.SENS       Sensitivity is a factor that defines direction and      magnitude for a dimension. Sensitivities are      entered as positive numbers for &#34;plus&#34; mean      dimensions, and as negative numbers for      &#34;minus&#34; mean dimensions. Example: A      diameter term may be modified by -0.5 to      indicate that a radius is a negative contributing      factor in the stackup.F/V        Fixed or Variable tolerance. F is a fixed input,      such as a vendor part dimension. The user      cannot change these inputs. V is a variable      input. The user can change these inputs.+/- TOL    This is the equal bilateral tolerance that the      user assigns to each dimension when using the      WC, RSS, or MRSS method of analysis.RESIZED TOL      This is the dimension tolerance that will give a      gap performance equal to,      the sum of the positive mean dimensions,      minus the sum of the negative mean      dimensions, minus the distance to the nearest      spec. limit.      using the WC ALLOC or STAT ALLOC      method.STANDARD   A number that is a measure of the dispersionDEVIATION  of the actual values of the variable from the      menu.SIGMA      A measure of the width of a process      distribution as compared to the specification      limits. there are two Sigma on the spreadsheet.      Cell I7 (next to STANDARD DEVIATION)      refers to the Sigma for each tolerance. Cell      M31 (under SH and ZN columns) refers to the      Sigma for the assembly.DRAWING #  The drawing from which the dimension and      tolerance are obtained.ZN         The zone reference number and letter on the      drawing where you find the dimension and      tolerance.UPPER SPEC This is the largest gap that the user will allow.LIMIT      Default is zero.LOWER SPEC This is the smallest gap that the user willLIMIT      allow. The default is zero.TOTALS     The first box (under Mean Dim) is the sum of      each dimension multiplied by its sensitivity.      The totals under the &#34;+/- TOL&#34;, the      &#34;RESIZED TOL&#34;, and the &#34;ALLOCATED      +/- TOL&#34; columns are the expected ranges      using the method selected.DPU        Defects Per Unit. The average number of      defects that is expected to be found during      assembly.METHOD     The method used to perform the analysis/USED       allocation. These are listed below.WC ALLOC   Check this box if you want to allocate      tolerance based on 100% interchangeability.      This method will calculate the Sigma for each      piece part, given process standard deviations.      WC ALLOCSTAT ALLOC Check this box if you want to allocate      tolerances based on probability. This method      will calculate the Sigma and DPU for the      assembly, given process standard deviations.      This method will also assign a dimension      tolerance based on a Sigma of 6.0.WC         Check this box if you want to do a worst case      analysis based on 100% interchangeabiltiy.RSS        Check this box if you want to do a statistical      analysis based on the Root Sum of Squares      method.STAT       Check this box if you want to calculate theANALYSIS   assembly DPU and Sigma.MRSS       Check this box if you want to do a statistical      analysis based on the Modified Root Sum of      Squares method.______________________________________ 
    
     Methods of analysis/allocation 
     There are six methods of analysis and allocation calculated by this spreadsheet. The first three methods of Worst Case, Root Sum of Squares, and Modified Sum of Squares follow one procedure. The last three methods, Statistical Analysis, Worst Case Allocation, and Statistical Allocation, follow the second procedure. Throughout both procedures, the spreadsheet by embedded logic will prompt the user for needed information. 
     First Procedure 
     This procedure is used for Worst Case, Root Sum of Squares, and Modified Sum of Squares as illustrated in Table 3. 
     
                       TABLE 3______________________________________Step What to do______________________________________1.   Choose the method of analysis you want to perform.2.   Input mean dimensions.3.   The spreadsheet will prompt you for sensitivities. You caninput these after you are finished with the dimensions.4.   Input +/- tolerances. The spreadsheet will prompt as towhether the tolerances are Fixed or Variable (F/V).Spreadsheet will NOT resize fixed tolerances.5.   Change upper spec limit and lower spec limit as needed.Value will default to zero.______________________________________ 
    
     Depending on the method used, you will get the results in Table 4: 
     
                       TABLE 4______________________________________Method               Results Calculated______________________________________Worst Case (WC)      WC Tolerances                Resized Tolerances                Nominal gapRoot Sum of Squares (RSS)                RSS totals                Resized Tolerances                Nominal gapModified RSS         RSS totals                Resized Tolerances                Nominal gap______________________________________ 
    
     Second Procedure 
     This procedure is used for Statistical Analysis, Worst Case Allocation, and Statistical Allocation as indicated in Table 5 below. 
     
                       TABLE 5______________________________________Step What to do______________________________________1.   Choose the method of analysis you want to perform.2.   Input mean dimensions.3.   The spreadsheet will prompt you for sensitivities. You caninput these after you are finished with the dimensions.4.   The spreadsheet will prompt as to whether the tolerancesare Fixed or Variable (F/V).If V, input the standard deviation.If F, input +/- tolerances.______________________________________ 
    
     Depending on the method used, you will get the indicated results in Table 6: 
     
                       TABLE 6______________________________________   ResultsMethod  Calculated    Notes______________________________________Statistical   DPUAnalysis   SigmaWorst Case   Allocated +/- TolAllocation   SigmaStatistical   DPU           Assigns Allocated Tol so thatAllocation   Sigma         Sigma = 6.0 for each   Allocated +/- Tol                 dimension______________________________________ 
    
     Error Messages 
     The error messages are indicated in Table 7 below: 
     
                       TABLE 7______________________________________Message     Meaning______________________________________RSS not     This message warns the user that he/recommended for       she should not use the RSS method if there&lt;4 dimensions       are fewer than four dimensions in the       stackup.MRSS not    This message warns the user that he/recommended for       she should not use the MRSS method if&lt;4 dimensions       there are fewer than four dimensions in the       stackup.Fixed tolerances &gt;       This message appears in the WC mode if thegap, WC resizing       fixed tolerances use up all of the tolerancewill not work       that is available to allocate.       Example: You are performing a worst case       analysis. You have .04 to allocate. You have       two fixed tolerances (.03 and .04). Since the       expected range of the fixed tolerances is .07,       the variable tolerances cannot be &#34;resized&#34;       to give a total tolerance equal to .04.Fixed tolerances &gt;       This message appears in the RSS mode if thegap, RSS resizing       fixed tolerances use up all of the tolerancewill not work       that is available to allocate.       Example: You are performing an RSS       analysis. You have .04 to allocate. You have       two fixed tolerances (.03 and .04). Since the       expected range of the fixed tolerances is .05,       the variable tolerances cannot be &#34;resided&#34;       to give a total tolerance equal to .04.Choose only one       This message appears if you select moremethod      than one method of analyzing/allocating       tolerances. Deselect one method to get rid       of error message.There must be a       This message appears if there is not a valuenumber in both spec       in cells C31 and C32 (under the Senslimit boxes column). The default value is zero.Increase (Decrease)       Using the worst case allocation method, thisUSL (LSL) a message appears if any of the dimensionsminimum of .sub.--  for       have a Sigma of less than 6.0.Six Sigma   Using the statistical allocation method or theproductivity (or       statistical method, this message appears ifreduce standard       the assembly Sigma is less than 6.0.deviations) The user can achieve a Sigma of 6.0 by       adjusting the mean or spec limit by the       amount shown. The user can adjust the       mean gap by increasing/decreasing one or       more mean dimensions. If this is not       possible, the user can achieve a high Sigma       by choosing processes with smaller standard       deviations.Fixed tolerances &gt;       This message appears in the MRSS mode ifgap, MRSS residing       the fixed tolerances use up all of thewill not work       tolerance that is available to allocate.       Example: You are performing an MRSS       analysis. You have .04 to allocate. You have       two fixed tolerances (.03 and .04) and three       variable tolerances (.02, .02, and .02). Since       the expected range of the fixed tolerances is       .058, the variable tolerances cannot be       &#34;resided&#34; to give a total tolerance equal       to .04.______________________________________ 
    
     In accordance with one embodiment of the present invention, embedded logic is placed in the spreadsheet. The system could be implemented in a conventional Fortran or C program. In either case, the system would follow the logic of the flow chart of FIG. 5. In the case of the spreadsheet, this is by placing an x next to WC, RSS, MRSS, WC ALLOC., STAT ALLOC. or STAT. ANALYSIS in FIG. 4. The user inputs the method of analysis (Step 102) as indicated in the flow chart of FIG. 5. The mean dimensions are then queried and entered by the user (Step 103) for each mean dimension. The query may be started by an &#34;IF&#34; statement in response to an x in one of the squares listed above. The sensitivity is prompted by the logic (Step 104) in response to the mean dimensions, and then also the Fixed (F) or Variable (V) tolerances are prompted (Step 105). FIG. 6 illustrates in columns 1 and 2 the mean dimensions entered for the assembly of FIG. 2 in response to WC selected. Columns 3, 4, and 5 indicate the sensitivity, the F/V, and the ±TOL inputs where fixed (F), represents the tolerance of the vendor part and V, or Variable, are those that can be changed by the user. The fixed are those the spreadsheet will not resize and the variable are those the user can resize. For classical analysis (WC, RSS or MRSS selected), the logic will then ask for upper and lower spec limits (Step 109) as represented in FIG. 5 and entered at the lower left of FIG. 6, and then based on the selected analysis of Worst Case (WC) will (Step 100) calculate WC tolerances using ##EQU1## where n=the number of dimensions in the stack; 
     j=the tolerance of the jth dimension; 
     T j  =the tolerance of the jth dimension in the stack; and 
     S j  =the sensitivity factor denoting magnitude and direction impact of the jth dimension in the stack. 
     T WC  gives expected tolerance range using the worst case method. Root Sum of Squares (RSS) total using: ##EQU2## T RSS  gives the expected tolerance range using the root sum of squares method, or modified RSS totals using: ##EQU3## where C f  is the correction factor. T MRSS  gives the expected tolerance range using the modified root sum of squares method. The value C f  is calculated first according to the following equation. ##EQU4## The design goal or performance requirement P is the minimum of U G  -LSL (lower spec. limit) or USL (upper spec. limit)-U G . U G  is the mean value of the performance parameter and is calculated by: ##EQU5## where U j  is the mean value of the jth dimension 
     The resize tolerance j·th dimension or T j ,rs is determined by F·T j  where F is the resize factor. The resize factor (F) equation for resize for worst case is: ##EQU6## where T j ,f is the fixed tolerance and k is the number of fixed tolerances in the stack. 
     The resize factor (F) equation for RSS is: ##EQU7## where T j ,v is the variable tolerance. 
     The resize factor for modified RSS uses equation ##EQU8## 
     The embedded program for these solutions would look to the pertinent fields and given input and calculate the solution and put that in the appropriate fields for the worksheet. Resizing is automatically done and the resize factor (F) equation is applied and the resized value placed in the appropriate resized field in the &#34;RESIZED TOL&#34; column (column 6 on the left) in FIG. 6. Note resized in FIG. 6 is for WC or worst case. 
     When the user 11 selects as the method of analysis to be the statistical method of analysis (Step 102) as indicated by the right portion of the flow chart of FIG. 5, again the input mean dimensions are prompted and entered (Step 111) as shown in Table 5 and the spreadsheet prompts for the sensitivities (112) and for the fixed or variable tolerances (Step 113). The fixed tolerances are those predetermined as by vendor parts. For the variable tolerances, the standard deviations (Step 114) as determined by historical data are entered in the eighth column from the left. This is a measure of the dispersion of the actual values of the variable. When all mean dimensions are entered, the screen prompts by way of the embedded program to request the user to supply the upper and lower spec limits (Step 117). If the selected field is worst case allocation, then for each of the dimensions in the stack the tolerance T j  is determined by the equation: ##EQU9## where σ j  =process standard deviation of the jth dimension of the stack. This is entered at the appropriate T j  field in the column called &#34;Allocated +/-TOL.&#34; This may be done by an embedded program for that field on the worksheet with the equation stated above. Guidance for Six Sigma goals are achieved using the equation: ##EQU10## 
     FIG. 7 illustrates for WC allocation and gives Sigma for each piece part given process standard deviations. Sigma is a measure of the width of a process distribution as compared to the specification limits. The Sigma, or field column, refers to the Sigma for each tolerance. The cell at the lower right labeled Sigma refers to the Sigma for the entire assembly. 
     FIG. 8 illustrates the calculated DPU (Defects Per Unit), which for the example calculates 1.5462E04 and when compared to nearer specification limit suggest increasing the upper specification limit a minimum of 9E-04, or reduce standard deviations. 
     The above is for when there is not the worst case allocation, but is operated on the statistical allocation and using the equation of T j  =6σ j  to calculate the tolerance for each dimension to ensure Six Sigma productivity for DPU: 
     
         DPU=(((((((1+0.049867347*Z.sub.LT)+0.0211410061*Z.sub.LT.sup.2 +0.0032776263*Z.sub.LT.sup.3 +0.00003870036* Z.sub.LT.sup.4)+0.00004889606*Z.sub.LT.sup.5)+0.000005383*Z.sub.LT.sup.6).sup.-16 /2 
    
     The short term Z ST  and long term Z LT  standard transform is calculated using the equation: ##EQU11## 
     The spreadsheet guidance to modify the design is given by the equation: ##EQU12##