CN107131826A - A kind of lathe translation shaft geometric error method for fast measuring based on laser interferometer - Google Patents

Abstract

The invention discloses a laser interferometer-based rapid measurement method for the geometric error of a translational axis of a machine tool, and relates to the technical field of error measurement and identification of a numerical control machine tool. Determine the initial installation position of the laser interferometer, drive the translation axis, and collect the readings of the laser interferometer on the travel of the translation axis: set n measuring points equally spaced on the travel of the translation axis, where n>2; drive the translation axis to each The measurement point is to collect the readings of laser A and laser B of the laser interferometer. At the measurement point p, adjust the laser interferometer to the second installation position, so that the distance between the second installation position and the initial installation position is L; drive the translation axis, Collect the readings of the laser interferometer on the stroke of the translation axis, and calculate the linear error of the movement direction of the translation axis at each measurement point at the measurement point p; according to the initial installation position, combined with the readings A ₂ and The reading A ₁ of the laser interferometer laser A at the initial installation position, and calculate the linear error of the translation axis direction at each measurement point.

Description

A Rapid Measurement Method of Geometric Error of Translational Axis of Machine Tool Based on Laser Interferometer

technical field

The invention relates to the technical field of error measurement and identification of numerical control machine tools.

Background technique

Geometric error is the main error source affecting the machining accuracy of machine tools, and compensating for geometric errors of machine tools has become an important means to improve the machining accuracy of machine tools. The measurement and identification of geometric error elements is the basis of geometric error compensation technology and one of the prerequisites for accuracy improvement.

The existing technology needs to be further improved in terms of speed and completeness when measuring and identifying the geometric error elements of the motion axis. In practice, the 9-line method and 12-line method based on laser interferometers are mostly used to measure the errors of multiple lines in the workspace to solve the geometric error elements of the translation axis, which requires multiple installations of equipment. The whole process requires multiple installations and multiple measurements of laser interferometers and other equipment to obtain error elements, and the preparation time for finding and installing auxiliary devices often accounts for more than 80% of the overall measurement time. However, there is a calibration error between the laser and the reflector in the step-by-step body diagonal method, and it is difficult to install the laser head and the reflector.

In addition, the integrity of error element identification is related to the accuracy of the precision model of the CNC machine tool workspace, and it is related to the effect of the precision improvement method. Therefore, the rapid measurement and complete identification of error elements can be a step forward in the research on online real-time detection of axis CNC machine tool errors, and it is one of the foundations to ensure the realization of machining accuracy improvement technology research.

Contents of the invention

The purpose of the present invention is to provide a laser interferometer-based rapid measurement method for the geometric error of the translational axis of a machine tool, which can effectively solve the problem of rapid measurement of the geometric error of the translational axis.

The object of the present invention is achieved through the following technical solutions: a method for quickly measuring the geometric error of the translational axis of a machine tool based on a laser interferometer, comprising the following steps:

Step 1. Determine the initial installation position of the laser interferometer according to the type of translation axis of the machine tool to be tested, and determine the relative positions of laser A and laser B of the laser interferometer;

Step 2, drive the translation axis, and collect the readings of the laser interferometer on the travel of the translation axis, including steps:

Step 2.1, setting n measurement points equidistantly distributed on the stroke of the translation axis, where n>2;

Step 2.2, drive the translation axis to each measurement point, collect the readings of laser A and laser B of the laser interferometer, at the measurement point p, the reading of laser A is A ₁ (p), and the reading of laser B is B ₁ ( p);

Step 3. Adjust the laser interferometer to the second installation position, so that the distance between the second installation position and the initial installation position is L;

Step 4, drive the translation axis, and collect the readings of the laser interferometer on the stroke of the translation axis. At the measurement point p, the reading of laser A is A ₂ (p), and the reading of laser B is B ₂ (p);

Step 5. According to the reading of the laser interferometer laser A at the initial installation position, calculate the linear error δ _ii of the movement direction of the translation axis at each measurement point, where i=x, y, z;

Step 6. According to the relative position of laser A and laser B at the initial installation position, combined with the reading A ₁ of laser interferometer and the reading B ₁ of laser B, calculate the angular error ε _ik in the direction of translation axis k at each measurement point and Linear error δ _ij in j direction, where j,k=x,y,z, and i≠j≠k;

Step 7. According to the distance between the second installation position and the initial installation position, combined with the reading A ₂ of the laser interferometer laser A at the second installation position and the reading A ₁ of the laser interferometer laser A at the initial installation position, calculate the translation axis at each measurement point j-direction angle error ε _ij and k-direction linear error δ _ik ;

Step 8. According to the readings A ₁ , B ₁ and A ₂ , B ₂ of the laser interferometer laser A and laser B in the initial installation position and the second installation position, calculate the angular error ε _ii of the movement direction of the translational axis at each measurement point.

In the step 1, according to the type of the translation axis to be measured, the initial installation position of the laser interferometer is determined, and the relative position of the laser interferometer laser A and laser B is determined, including steps:

Step 1.1, determine the type i of the translational axis to be measured, where i=x, y, z;

Step 1.2, install the laser interferometer so that the straight line where the laser A and laser B of the laser interferometer are located is perpendicular to the motion direction i of the translation axis;

Step 1.3, determine the initial installation position of the laser interferometer, so that the straight line where the laser A and laser B of the laser interferometer are located is parallel to the j direction, j=x, y, z and j≠i;

Step 1.4, measuring the distance M between laser A and laser B of the laser interferometer;

Step 1.5, adjust the position of the reflector in the laser interferometer to ensure the normal operation of the laser interferometer.

In step 3, adjust the laser interferometer to the second installation position, so that the distance between the second installation position and the initial installation position is L, including steps:

Step 3.1, determine the second installation position, so that the distance between the second installation position and the initial installation position is L in the k direction, where k=x, y, z and k≠j≠i;

Step 3.2, keep the distance M between laser A and laser B of the laser interferometer unchanged, and move the laser interferometer to the second installation position along the k direction;

Step 3.3, adjust the position of the reflector in the laser interferometer to ensure the normal operation of the laser interferometer.

The distribution of measuring points on the travel of the translation axis in step 4 is the same as that of the measurement points on the travel of the translation shaft in step 2.

In the step 5, according to the reading of the laser interferometer laser A at the initial installation position, the linear error δ _ii of the motion direction of the translational axis at each measurement point is calculated, and the identification formula is:

δ _ii (p) = A ₁ (p)

Where δ _ii (p) represents the linear error of the motion direction at the measurement point p of the translation axis.

In the step 6, according to the relative position of laser A and laser B at the initial installation position, combined with the reading A ₁ of laser interferometer and the reading B ₁ of laser B, the angle error ε _ik in the direction of translation axis k at each measurement point is calculated and j-direction linear error δ _ij , including steps:

Step 6.1. Combining the reading A _{1 of laser interferometer laser A and the reading B 1 of} laser B, according to the influence of the translation axis angle error on the reading of the laser interferometer, the calculation formula of the angle error _εik in the direction of the translation axis k at each measurement point is obtained for:

Where _εik (p) represents the angular error in k direction at the measurement point p of the translational axis;

Step 6.2, based on the calculation principle of the straightness error of the laser interferometer, calculate the linear error δ _ij of the direction of the translation axis j from the angle error ε _ik of the direction of the translation axis k, and obtain the calculation formula of the linear error δ _ij of the direction of the translation axis j at each measurement point: :

Among them, δ _ij (p) represents the linear error in j direction at the measurement point p of the translation axis, and l _i represents the stroke of the translation axis.

In the step 7, according to the distance between the second installation position and the initial installation position, combined with the reading A ₂ of the laser interferometer laser A at the second installation position and the reading A ₁ of the laser interferometer laser A at the initial installation position, the average value at each measurement point is calculated. Angle error ε _ij in the direction of moving axis j and linear error δ _ik in direction k, including steps:

Step 7.1, according to the distance between the second installation position and the initial installation position, combined with the reading A ₂ of the laser interferometer laser A at the second installation position and the reading A ₁ of the laser interferometer laser A at the initial installation position, adjust the laser according to the translation axis angle error Influenced by the readings of the interferometer, the calculation formula of the angular error ε _ij in the direction of the translation axis j at each measurement point is:

Where ε _ij (p) represents the angular error in the j direction at the measurement point p of the translational axis;

Step 7.2, based on the calculation principle of the straightness error of the laser interferometer, calculate the linear error δ _ik of the translation axis k direction from the angular error ε _ij of the translation axis j direction, and obtain the calculation formula of the linear error δ _ik of the translation axis k direction at each measurement point: :

Where δ _ik (p) represents the linear error in k direction at the measurement point p of the translation axis.

In the step 8, according to the readings A ₁ , B ₁ and A ₂ , B ₂ of the laser interferometer laser A and laser B of the initial installation position and the second installation position, the angle error ε _ii of the movement direction of the translational axis at each measurement point is calculated , containing the steps:

Step 8.1. Combining the reading A ₂ of the laser interferometer at the second installation position and the reading B ₂ of the laser B, according to the influence of the translation axis angle error on the reading of the laser interferometer, the angle in the k direction of the translation axis at the second installation position is obtained The calculation formula of error _εik2 is:

Step 8.2, based on the calculation principle of the straightness error of the laser interferometer, calculate the linear error δ _ij2 of the translation axis j direction at the second installation position from the angular error ε _ik2 of the translation axis k at the second installation position. The calculation formula is:

Step 8.3, according to the influence of the angle error of the motion direction of the translation axis on the linear error δ _ij in different planes in the k direction, the calculation formula of the angle error ε _ii of the motion direction of the translation axis is obtained as:

Where ε _ii (p) represents the angular error of the k-direction motion direction at the measurement point p of the translation axis.

At each measuring point of the translation axis, the geometric error of the translation axis is calculated as a function of the position of the translation axis.

The laser interferometer has two laser emitting devices.

Further, the geometric error of the translation axis is calculated at each measurement point of the translation axis, which changes as the position of the translation axis changes.

Further, the laser interferometer has two laser emitting devices.

Advantage and effect of the present invention compared with prior art:

The specific beneficial effect is: the operation is simple and fast, and the geometric error measurement and identification of each translation axis can be quickly realized by measuring at two installation positions, and at the same time, all the geometric errors of the translation axis can be obtained, and the translation axis can be realized Fast measurement and complete identification of geometric errors.

Description of drawings

Fig. 1 is a flow chart of the present invention;

Fig. 2 is a schematic diagram of the influence of the translation axis angle error on the reading of the laser interferometer in the present invention;

Fig. 3 is a schematic diagram of the calculation principle of the straightness error of the laser interferometer of the present invention;

Fig. 4 is a schematic diagram of the influence of the angular error of the motion direction of the translational axis of the present invention on the linear error δ _ij in different planes in the k direction;

Fig. 5a is the linear error δ _yy of the Y-axis and y-direction of the present invention;

Figure 5b shows the angle error ε _yz in the Y-axis z direction of the present invention;

Fig. 5c is the linear error δ _yx of the Y-axis x direction of the present invention;

Fig. 5d is the angle error ε _yx of the Y-axis x direction of the present invention;

Fig. 5e is the linear error δ _yz of the Y-axis z direction of the present invention;

Fig. 5f is the angle error ε _yy of the Y-axis y direction of the present invention;

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

Accompanying drawing 1 shows the flow chart of the method for rapid measurement and identification of geometric errors of translational axes based on laser interferometer measurement according to the present invention. The method of the present invention is illustrated by taking the Y-axis of a machine tool as an example.

Step 1. Determine the initial installation position of the laser interferometer according to the type of translational axis to be measured, and determine the relative positions of laser A and laser B of the laser interferometer, including steps:

Step 1.1. Determine the Y-axis type of the translational axis to be measured as y;

Step 1.2, install the laser interferometer so that the straight line where the laser interferometer laser A and laser B are located is perpendicular to the y direction of the machine tool;

Step 1.3, determine the initial installation position of the laser interferometer, so that the straight line where the laser A and laser B of the laser interferometer are located is parallel to the x direction of the machine tool;

Step 1.4, measure the distance M=26.87mm between laser A and laser B of the laser interferometer;

Step 1.5, adjust the position of the reflector in the laser interferometer to ensure the normal operation of the laser interferometer.

Step 2, drive the Y-axis, and collect the readings of the laser interferometer on the Y-axis stroke, including steps:

Step 2.1, setting n measuring points equidistantly distributed on the Y stroke, n=16;

Step 2.2, drive the translation axis to each measurement point, and collect the readings of laser A and laser B of the laser interferometer. At measurement point p, laser A reads A ₁ (p), and laser B reads B ₁ (p).

Step 3. Adjust the laser interferometer to the second installation position, so that the distance between the second installation position and the initial installation position is L, including steps:

Step 3.1, determine the second installation position, so that the distance between the second installation position and the initial installation position in the z direction is L, L=150mm;

Step 3.2, keep the distance M between laser A and laser B of the laser interferometer unchanged, and move the laser interferometer to the second installation position along the k direction;

Step 3.3, adjust the position of the reflector in the laser interferometer to ensure the normal operation of the laser interferometer.

Step 4. Drive the translation axis, and read the laser interferometer at the 16 measuring points equidistantly distributed on the Y stroke in step 2. At the measuring point p, the reading of laser A is A ₂ (p), and the reading of laser B is B ₂ (p).

Step 5. According to the laser A reading of the laser interferometer at the initial installation position, calculate the linear error δ _yy of the Y-axis and y-direction at each measurement point. Because the laser direction of the laser interferometer is parallel to the Y-axis movement direction, the reading of the laser interferometer directly measures the positioning error of the Y-axis movement direction. Here, the laser A reading of the laser interferometer at the initial installation position is the corresponding linear error δ _yy , and each measurement point δ _yy is:

δ _yy (p) = A ₁ (p)

Figure 5a shows the calculated linear error δ _yy in the y-direction of the Y-axis.

Step 6. According to the relative position of laser A and laser B at the initial installation position, combined with the reading A ₁ of laser A and the reading B ₁ of laser B of the laser interferometer, calculate the angle error ε _yz in the z direction of the Y axis and the linear error in the x direction at each measurement point δ _yx , including the steps:

Step 6.1, the angle error in the z direction of the Y axis will make the readings of laser A and laser B different. The schematic diagram of the influence of the translation axis angle error on the readings of the laser interferometer is shown in Figure 2. Combining the laser A reading A ₁ and the laser B reading B ₁ of the laser interferometer, according to the influence of the translation axis angle error on the reading of the laser interferometer, the calculation formula of the angle error ε _yz in the Y-axis z direction at each measurement point is obtained as:

Figure 5b shows the calculated angle error ε _yz in the Y-axis z direction.

Step 6.2, the principle of calculating the straightness error of the laser interferometer is to calculate the linearity error of the verticality in a certain direction from the angular error in a certain direction, as shown in Figure 3. Calculate the linear error δ _yx of the Y-axis x direction from the angle error ε _yz of the Y-axis z direction, and the calculation formula of δ _yx at each measurement point is:

Among them, the Y-axis stroke l _y is 315mm. Figure 5c shows the calculated linear error δ _yx in the x-direction of the Y-axis.

Step 7. According to the distance between the second installation position and the initial installation position, combined with the laser A reading A ₂ of the laser interferometer at the second installation position and the laser A reading A ₁ of the laser interferometer at the initial installation position, calculate the x-direction angle of the Y axis at each measurement point Error ε _yx and z-direction linear error δ _yz , including steps:

Step 7.1, the angle error in the x direction of the Y axis will make the readings of the same laser at the initial installation position and the second installation position different, as shown in Figure 2, the translational axis angle error affects the readings of the laser interferometer. According to the distance between the second installation position and the initial installation position, combined with the laser A reading A ₂ of the laser interferometer at the second installation position and the laser A reading A ₁ of the laser interferometer at the initial installation position, according to the influence of the translation axis angle error on the reading of the laser interferometer, The angle error ε _yx in the x direction of the Y axis is obtained as:

Fig. 5c shows the calculated angle error ε _yx in the direction of Y axis x.

Step 7.2, based on the calculation principle of the straightness error of the laser interferometer shown in Figure 3, calculate the linear error δ _yz of the Y-axis z direction from the angle error ε _yx of the Y-axis x direction, and the calculation formula is:

Figure 5e shows the calculated linear error δ _yz in the Y-axis and z-directions.

Step 8. According to the readings A ₁ , B ₁ and A ₂ , B ₂ of the laser interferometer laser A and laser B in the initial installation position and the second installation position, calculate the angle error ε _yy in the y direction of the Y axis at each measurement point, including steps:

Step 8.1. Combining the laser A reading A ₂ and the laser B reading B ₂ of the laser interferometer at the second installation position, according to the influence of the translation axis angle error on the reading of the laser interferometer shown in Figure 2, the Y-axis at the second installation position is obtained The formula for calculating the angular error ε _yz2 in the z direction is:

Step 8.2, based on the calculation principle of the straightness error of the laser interferometer shown in Figure 3, calculate the linear error δ _yx2 of the Y-axis x direction at the second installation position from the angular error ε _yz2 of the Y-axis z direction at the second installation position:

Step 8.3, the angle error of the Y axis in the y direction will make the linear error of the Y axis in the x direction at the initial installation position and the second installation position different. Schematic diagram of the influence of linearity error δ _ij . According to the Y-axis linear error δ _yx at the initial installation position and the Y-axis linear error δ _yx2 at the second installation position, the calculation formula for the Y-axis y-direction angular error ε _yy is:

Figure 5f shows the calculated angle error ε _yy in the y-direction of the Y-axis.

Finally, six geometric errors of the Y axis are obtained. At the same time, the invention can also measure and identify the six geometric errors of the X and Z axes of the machine tool.

The present invention finally obtains six geometric errors of the translation axis. The accompanying drawing is only a preferred embodiment. The above-mentioned embodiment is only for describing the present invention, and is not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall include within the scope of protection of this aspect.

Claims (10)

1. a kind of lathe translation shaft geometric error method for fast measuring based on laser interferometer, it is characterised in that including as follows Step：

Step 1, the type according to lathe translation shaft to be measured, determine laser interferometer initial makeup location, and determine laser interference Instrument laser A and laser B relative position；

Laser interferometer readings on step 2, driving translation shaft, collection translation shaft stroke, including step：

N measurement point being equally spaced in step 2.1, setting translation shaft stroke, wherein n>2；

Step 2.2, driving translation shaft to each measurement point, gather the laser A and laser B of laser interferometer reading, in measurement At point p, laser A reading is A₁(p), laser B reading is B₁(p)；

Step 3, adjustment laser interferometer to the second installation site so that the second installation site is L with initial makeup location distance；

Laser interferometer readings on step 4, driving translation shaft, collection translation shaft stroke, at measurement point p, laser A reading is A₂(p), laser B reading is B₂(p)；

Step 5, the reading according to laser interferometer laser A at initial makeup location, calculate the motion of each measurement point translation shaft Dimension linear error delta_ii, wherein i=x, y, z；

Step 6, the relative position according to laser A and laser B at initial makeup location, with reference to laser interferometer laser A reading A₁ With laser B reading B₁, calculate each measurement point translation shaft k orientation angle error ε_ikWith j dimension linear error deltas_ij, wherein j, K=x, y, z, and i ≠ j ≠ k；

Step 7, according to the second installation site and initial makeup location distance, with reference to the second installation site laser interferometer laser A Reading A₂With initial makeup location laser interferometer laser A reading A₁, calculate each measurement point translation shaft j orientation angle Error ε_ijWith k dimension linear error deltas_ik；

Step 8, according to initial makeup location and the second installation site laser interferometer laser A and laser B reading A₁、B₁And A₂、 B₂, calculate each measurement point translation shaft movement direction angle error ε_ii。

2. a kind of lathe translation shaft geometric error method for fast measuring based on laser interferometer according to claim 1, It is characterized in that：According to translation shaft type to be measured in the step 1, laser interferometer initial makeup location is determined, and determines to swash Optical interferometer laser A and laser B relative position, including step：

Step 1.1, the type i for determining translation shaft to be measured, wherein i=x, y, z；

Step 1.2, installation laser interferometer so that straight line is moved perpendicular to translation shaft where laser interferometer laser A and laser B Direction i；

Step 1.3, determine laser interferometer initial makeup location so that straight line parallel where laser interferometer laser A and laser B In j directions, j=x, y, z and j ≠ i；

Apart from M between step 1.4, measurement laser interferometer laser A and laser B；

Reflector position in step 1.5, adjustment laser interferometer, it is ensured that laser interferometer normal work.

3. a kind of lathe translation shaft geometric error method for fast measuring based on laser interferometer according to claim 1, It is characterized in that：Laser interferometer is adjusted in the step 3 to the second installation site so that the second installation site and initial installation Positional distance is L, including step：

Step 3.1, determine the second installation site so that the second installation site is in k directions distance with initial makeup location distance L, wherein k=x, y, z and k ≠ j ≠ i；

It is constant apart from M between step 3.2, holding laser interferometer laser A and laser B, move laser interferometer extremely along k directions Second installation site；

Reflector position in step 3.3, adjustment laser interferometer, it is ensured that laser interferometer normal work.

4. a kind of lathe translation shaft geometric error method for fast measuring based on laser interferometer according to claim 1, It is characterized in that：Measurement point in the step 4 on translation shaft stroke and the measurement point distribution phase in step 2 on translation shaft stroke Together.

5. a kind of lathe translation shaft geometric error method for fast measuring based on laser interferometer according to claim 1, It is characterized in that：According to the reading of laser interferometer laser A at initial makeup location in the step 5, each measurement point is calculated Locate the linear error delta of the translation shaft direction of motion_ii, recognizing formula is：

δ_ii(p)=A₁(p)

Wherein δ_ii(p) the linear error of the direction of motion at translation shaft measurement point p is represented.

6. a kind of lathe translation shaft geometric error method for fast measuring based on laser interferometer according to claim 1, It is characterized in that：According to laser A at initial makeup location and laser B relative positions in the step 6, swash with reference to laser interferometer Light A reading A₁With laser B reading B₁, calculate each measurement point translation shaft k orientation angle error ε_ikMissed with j dimension linears Poor δ_ij, include step：

Step 6.1, the reading A with reference to laser interferometer laser A₁With laser B reading B₁, according to translation shaft angular error to swashing Optical interferometer reading influences, and obtains each measurement point translation shaft k orientation angle error ε_ikCalculation formula is：

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Wherein ε_ik(p) k orientation angle errors at translation shaft measurement point p are represented；

Step 6.2, based on laser interferometer straightness error Computing Principle by translation shaft k orientation angle error εs_ikCalculate translation shaft J dimension linear error deltas_ij, obtain each measurement point translation shaft j dimension linear error delta_ijCalculation formula is：

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Wherein δ_ij(p) j dimension linear errors, l at translation shaft measurement point p are represented_iRepresent translation shaft stroke.

7. a kind of lathe translation shaft geometric error method for fast measuring based on laser interferometer according to claim 1, It is characterized in that：According to the second installation site and initial makeup location distance in the step 7, with reference to the second installation site laser Interferometer laser A reading A₂With initial makeup location laser interferometer laser A reading A₁, calculate each measurement point translation Axle j orientation angle error εs_ijWith k dimension linear error deltas_ik, include step：

Step 7.1, according to the second installation site and initial makeup location distance, with reference to the second installation site laser interferometer laser A reading A₂With initial makeup location laser interferometer laser A reading A₁, according to translation shaft angular error to laser interferometer Reading influences, and obtains each measurement point translation shaft j orientation angle error ε_ijCalculation formula is：

<mrow> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>arctan</mi> <mfrac> <mrow> <msub> <mi>A</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>A</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> </mrow> <mi>L</mi> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>A</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>A</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> </mrow> <mi>L</mi> </mfrac> </mrow>

Wherein ε_ij(p) j orientation angle errors at translation shaft measurement point p are represented；

Step 7.2, based on laser interferometer straightness error Computing Principle by translation shaft j orientation angle error εs_ijCalculate translation shaft K dimension linear error deltas_ik, obtain each measurement point translation shaft k dimension linear error delta_ikCalculation formula is：

<mrow> <msub> <mi>&amp;delta;</mi> <mrow> <mi>i</mi> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>q</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>p</mi> </munderover> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>&amp;Delta;l</mi> <mi>i</mi> </msub> </mrow> 2

Wherein δ_ik(p) k dimension linear errors at translation shaft measurement point p are represented.

8. a kind of lathe translation shaft geometric error method for fast measuring based on laser interferometer according to claim 1, It is characterized in that：According to initial makeup location and the second installation site laser interferometer laser A and laser B in the step 8 Reading A₁、B₁And A₂、B₂, calculate each measurement point translation shaft movement direction angle error ε_ii, include step：

Step 8.1, the reading A with reference to the second installation site laser interferometer laser A₂With laser B reading B₂, according to translation shaft Angular error influences on laser interferometer readings, obtains the second installed position translation shaft k orientation angle error εs_ik2Calculation formula For：

<mrow> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>i</mi> <mi>k</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>A</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>B</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> </mrow> <mi>M</mi> </mfrac> </mrow>

Step 8.2, missed by the second installed position translation shaft k orientation angles based on laser interferometer straightness error Computing Principle Poor ε_ik2Calculate the second installed position translation shaft j dimension linear error deltas_ij2Calculation formula is：

<mrow> <msub> <mi>&amp;delta;</mi> <mrow> <mi>i</mi> <mi>j</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>q</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>p</mi> </munderover> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>i</mi> <mi>k</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>&amp;Delta;l</mi> <mi>i</mi> </msub> </mrow>

Step 8.3, according to translation shaft movement direction angle error to the linearity error δ in Different Plane on k directions_ijInfluence, Obtain translation shaft movement direction angle error ε_iiCalculation formula is：

<mrow> <msub> <mi>&amp;epsiv;</mi> <mrow> <mi>i</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>arctan</mi> <mfrac> <mrow> <msub> <mi>&amp;delta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mrow> <mi>i</mi> <mi>j</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> </mrow> <mi>L</mi> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;delta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mrow> <mi>i</mi> <mi>j</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> </mrow> <mi>L</mi> </mfrac> </mrow>

Wherein ε_ii(p) k directions movement direction angle error at translation shaft measurement point p is represented.

9. a kind of lathe translation shaft geometric error method for fast measuring based on laser interferometer according to claim 1, It is characterized in that：In each measurement point of translation shaft, translation shaft geometric error is calculated, is become with translation shaft change in location Change.

10. a kind of lathe translation shaft geometric error method for fast measuring based on laser interferometer according to claim 1, It is characterized in that：Laser interferometer has two laser beam emitting devices.