1Cause of positioning error When the workpiece is positioned in the machine tool fixture, the position between the reference is determined because the workpiece positioning reference and the manufacturing error of the fixture positioning component and the matching gap, the positioning reference and the process reference do not coincide, and the workpiece is positioned by multiple bases. The three causes of the error cause the maximum position change amount of the process reference in the process dimension direction, that is, the positioning error.
The positioning error has a great influence on the machining accuracy, so the calculation of the positioning error is especially important in the design of the machine tool fixture. In order to ensure the processing accuracy requirements, the positioning error should be less than or equal to 1/3 to 1/5 of the process dimensional tolerance. Positioning errors are only possible when machining a batch of workpieces using the adjustment method. If the workpiece is processed by trial cutting, the positioning error will not occur.
2 positioning error calculation method The positioning error calculation methods are mainly: formula method, total differential method, graphic method.
2.1 Formula method The positioning error is the comprehensive result of the reference displacement error and the reference non-coincidence error. The formula method is to solve the positioning error by using the positioning error calculation formula. The calculation formula of the positioning error is: ΔD=Δγ+ΔB, ΔD? positioning error, ΔB? The reference does not coincide with the error, Δγ? reference displacement error.
In the specific calculation, Δγ and ΔB are first calculated separately, and then the two are synthesized according to the above formula. The synthesis method is as follows: (1) When ΔB≠0, Δγ=0, ΔD=ΔB when ΔB=0, Δγ≠0 ΔD=Δγ; (2) When ΔB≠0, Δγ≠0, and the process reference is not on the positioning surface, ΔD=Δγ+ΔB; (3) When ΔB≠0, Δγ≠0, and the process reference is on the positioning surface At the time, ΔD = Δγ ± ΔB. This situation can only occur when the workpiece is positioned on the surface, such as the workpiece is positioned in a plane, Δγ=0, so there is no problem of two error synthesis.
The method for determining "+" and "-" in the formula is as follows: (1) First assume that the position of the positioning reference is unchanged, and let the size of the positioning reference surface be changed from small to large (or from large to small), and the process reference position is judged at this time. The change is to make the process size larger or smaller.
(2) When positioning the workpiece, the positioning reference surface should be in contact with the positioning element. When the size of the positioning reference surface changes, the positioning reference surface is separated from the positioning element. Therefore, the position of the positioning reference should be moved to make the positioning reference surface Contact with the positioning element. Since the process reference is on the positioning surface, the position of the process reference also changes, and it is judged whether the process size becomes large or small at this time.
(3) If the process size in the above two steps becomes larger or smaller at the same time, the formula takes "+", otherwise, it takes "-".
This method requires a clearer concept, and it is not so good to determine "+" and "-".
2.2 Total differential method Full differential method to calculate the positioning error, first find the distance from the process reference to a fixed point in the processing dimension direction, establish the relationship between the distance between the two points and the workpiece size, the total differential of the distance between the two points is the positioning error. This method requires the application of advanced mathematics knowledge, which is more complicated, and it is convenient to solve the positioning error with angle size.
2.3 The graphic method uses AUTOCAD to accurately draw the positioning sketch of the workpiece, and enlarges the limit position of the workpiece size change in the figure. The AUTOCAD dimensioning function is used to automatically mark the positioning error of the machine tool fixture. This method is used to solve the positioning error of the machine tool (intuition), which is intuitive, convenient, simple and accurate.
The key to solving the positioning error of the machine tool fixture by the graphic method is to find the two extreme positions that cause the dimensional change of the process.
3 application examples processing keyway as shown in a), known d 1 = φ25-0.021 0 mm, d 2 = φ40-0.025 0 mm, the coaxiality of the two outer cylindrical faces is φ0.02 mm, the angle of the V-shaped block α=90°, the two cylindrical surfaces have been processed, and the keyway depth is A=34.8-0.171 0. The positioning error is calculated and the positioning quality is analyzed.
3.1 Formula method to solve the positioning error First, the dimension is marked, wherein the coaxiality can be marked as e=±0.01mm, R=20-0.0125 0, the positioning reference is the d 1 axis center line, and the process reference is d 2 outer circle lower bus. , the benchmarks do not coincide. It can be seen from Fig. 1b) that the positioning dimension is composed of e and R, so the reference misalignment error is the sum of the dimension and the tolerance, that is, ΔB=T e+T R=0.02+0.0125=0.0325 mm. The reference displacement error is: Δγ=T d 1 (2 sinα2)=0.021/(2×sin 45°)=0.014849 mm Because the process reference is not on the positioning surface, the positioning error is: ΔD=Δγ+ΔB=0.047349mm The positioning error is less than 1/3 of the process dimensional tolerance (0.17/3= 0.056mm), so the positioning scheme is feasible.
3.2 Total differential method for solving positioning error
As shown, O 1 is the center of the d 1 axis, O 2 is the center line of the large outer circle d 2 axis, e is the eccentricity of the two outer circles, and the radius of the small outer circle is γ1 = 12.5-0.0105 0. The radius of the circle γ2=20-0.0125 0, then C=γ2-e-γ1 sinα/2, so the process size A is: A=C+B=γ2-e-γ1 sinα/2+B where the dimension B is the tool size. Regardless of its error, regardless of the angle α error, dAAr 1 dr 1+Ar 2 dr 2+Ae de=0.0105+0.0125+0.02=0.047349mm is obtained by the total differential method with a positioning error of 0.047349 mm.
3.3 Graphic Method Solving Positioning Error Using AutoCAD to accurately map, draw the limit position O 1, O 2 of the positioning reference. When drawing, the deviation is magnified 100 times due to the small deviation value.
Graphic Method Solving Positioning Error When the positioning surface d 1 is the minimum limit size, the axis of d 2 is at the lowest position O 4, and d 2 is the maximum limit size A max , the process size obtains the maximum limit size. When the positioning surface d 1 is the maximum limit size, the axis of d 2 is at the uppermost position O 3, and d 2 is the minimum limit size, the process size A obtains the minimum limit size A min . Use AutoCAD's dimensioning command to directly mark ΔD=4.7349mm, reduce the value of ΔD by 100 times, and ΔD/100=0.047349mm is to position the keyway in the above manner to ensure the positioning error of the process size of 34.8-0.17 0.
4 Conclusions Through the above analysis, the positioning errors obtained by the three analysis methods are the same. AutoCAD accurate drawing, dimensioning function to analyze and solve the machine tool positioning error, intuitive and clear, avoiding cumbersome mathematical operations, and high precision (can determine the number of decimal places according to needs), the key is to find out the process size changes Extreme position. This method not only provides a new method for the calculation of the positioning error of the machine tool fixture, but also provides a new idea for similar calculations in engineering.
(Finish)
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