Comprehensive analysis of the hottest machining er

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Comprehensive analysis of machining error (Part 1)

in production practice, the factors affecting machining error are often complex, and sometimes it is difficult to analyze its causal relationship with a single factor, but it is necessary to use mathematical statistical methods for comprehensive analysis to find out the way to solve the problem

I. the nature of processing errors

various single factor processing errors can be divided into systematic errors and random errors according to their statistical laws. Systematic errors are divided into constant systematic errors and variable systematic errors

(I) systematic error

l. constant systematic error

sequential processing should consider not only China's environment, but also the impact of the world's environment and other technological innovation, industry changes on itself. The error whose size and direction remain unchanged after a batch of workpieces is called constant systematic error. For example, the machining principle error and the manufacturing error of machine tools, fixtures and cutters are constant system errors. In addition, the wear rate of machine tools, fixtures and measuring tools is slow, which can also be regarded as a constant systematic error within a certain period of time

2. variable value system error

in the sequential processing of a batch of workpieces, the error whose size and direction change according to a certain law is called variable value system error. For example, the thermal deformation error and tool wear of machine tools, fixtures and tools before thermal balance are all variable value system errors

(II) random error

when a batch of workpieces are processed in sequence, the processing errors with different sizes and directions and irregular changes are called random errors. For example, the re mapping of blank errors (different sizes of allowances, uneven hardness, etc.), positioning errors (different accuracy of reference planes, the influence of gaps between TPO compounds used in automotive interiors), clamping errors (different sizes of clamping forces), errors of multiple adjustments, deformation errors caused by residual stresses, etc., are random errors

the random error seems to have no law on the surface, but the application of mathematical statistics can find out the overall law of the processing error of a batch of workpieces, and then take measures to control it in the process

II. Statistical analysis of machining error (distribution diagram analysis)

statistical analysis is an analysis method based on the data observed on the production site and the actual inspection of the workpiece, which uses mathematical statistics to analyze and process these data, so as to reveal the comprehensive impact of various factors on machining error and obtain the way to solve the problem, mainly including distribution diagram analysis method and point diagram analysis method. This section mainly introduces the distribution map method. Please refer to relevant materials for other methods

1. Histogram of actual distribution diagram

in the processing process, the processing size of a process is analyzed by taking limited sample data. the quality grade of each batch of ex factory products is expressed in the form of a square diagram according to the comprehensive judgment theorem of the inspection results of ex factory inspection items and the frost resistance inspection results, which is called histogram analysis method to facilitate the analysis of processing quality and its stability

in the extracted limited sample data, the change of processing size is called size dispersion; The number of parts in the same size interval is called frequency; The ratio of frequency to the total number of samples in this batch is called frequency; The ratio of frequency to group spacing (size interval) is called frequency density

the actual distribution diagram that takes the size of the workpiece (a small size interval) as the abscissa and the frequency or frequency as the ordinate to represent the processing size of the process is called the histogram, as shown in the figure

the area of the rectangle on the histogram = frequency density group spacing (size interval) = frequency

since the sum of the frequencies of all groups is equal to 100%, the sum of the areas of all rectangles on the histogram is equal to L

the method of histogram is illustrated by examples:

for example, grinding a batch of workpieces with shaft diameter of mm, and the measured dimensions are shown in the table

the measured value of shaft diameter (m)

the steps of histogram are as follows:

(1) collect data. Generally, take about 100 pieces and find out the maximum value La = 54 m and the minimum value SM = 16 m (see table)

(2) divide 100 sample data into several groups, and the grouping number can be determined by table

selection of table samples and group numbers

in this case, the number of groups k = 8. Experience has proved that too few groups will cover up the changes of data within the group, and too many groups will make the height of each group uneven, so that the change law cannot be seen. Usually, the number of groups should be determined so that each group can average at least 4 ~ 5 data

(3) calculate the group distance h, that is, the interval between groups

h = = =4.75 M 5 m

(4) calculate the upper and lower limits of the first group


the upper limit of the first group is s M + = (16+) M = 18.5 m

the lower limit is SM - (16 -) M = 13.5 M

(5) calculate the upper and lower limits of other groups. The upper limit of the first group is the lower limit of the second group. The lower limit value of the second group plus the group distance is the upper limit value of the second group, and so on

(6) calculate the center value x I of each group. The center value is the value in the middle of each group

xi = (upper limit value of a group + lower limit value of a group)/2

central value of the first group xi= xi= m=16 m

(7) record the data of each group and sort it into a frequency distribution table, as shown in the table

(8) count the size frequency, frequency and frequency density of each group and fill them in the table

(9) take the frequency density as the ordinate according to the data listed in the table; The histogram can be drawn when the group distance (size interval) is the abscissa, as shown in the figure

table frequency distribution table the computer screen displays the experimental force and experimental curve

from the figure, it can be seen that the size dispersion range of this batch of workpieces is mostly in the middle, and the ones that are larger or smaller are less

size dispersion range = maximum diameter minimum diameter = 60.054 60.016 = 0.038mm

size dispersion range Center:


tolerance zone center of diameter = 60+ = 60.025 mm

standard deviation: =

= mm

it can be seen from the figure that the dispersion range of this batch of workpieces is 0.038, which is smaller than the tolerance zone, but the center of size dispersion range does not coincide with the center of the tolerance zone, If we try to adjust the center of the dispersion range to coincide with the tolerance zone, that is, as long as the radial feed of the machine tool is increased by 0.012 mm, the constant systematic error can be eliminated

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