Adjustment method of verticality of adjustable table surface and measuring axis

1 Overview

When making precision comparative measurements on a terminal measuring instrument, the adjustable table of the instrument must be adjusted so that the perpendicularity of the surface of the table and the measuring axis is within the allowable accuracy range. However, some metrological verification personnel may not be able to adjust the perpendicularity of the surface of the table and the measurement axis to the required accuracy because the structure, adjustment principle and adjustment method of the work are not very clear and often take more time.
In this paper, the three-point support table and the cone support table commonly used in vertical optical meters are taken as examples to discuss the structure, adjustment principle and adjustment method of the adjustable table. Practice has proved that the adjustment method is simple, rapid adjustment, high precision, generally in 1 ~ 2min can be perpendicular to the surface of the table and the measurement axis to adjust the allowable accuracy (0.3μm) range.

2 Structure of adjustable table

The structure of the adjustable worktable is shown in Figure 1. Fig. 1(a) is a three-point support table with an upper layer supported by three support points A, B, and C, wherein C is a fixed support point, and A and B are movable support points composed of two fine-adjusting screws. Two perpendicular tilt axes are formed by AC and BC. Note that when installing the table in the taper hole in the base of the instrument, be sure to align the tilt axis AC and BC with the operator's left and right and front and rear azimuths, and adjust the screws A and B to make the table surface and the instrument. The measuring axes are perpendicular to each other to achieve the adjustment of the table.
Figure 1(b) is a conical support table, which is a movable table supported by a circular conical surface. By adjusting two pairs of mutually perpendicular left and right and four front and rear adjustment screws A, B, C, D to change the position of the table with respect to the support of the cone, so as to achieve the purpose of adjusting the surface of the table and the measurement axis perpendicular to each other.

Figure 1 Structure of an adjustable workbench

3 adjustable table adjustment principle

The adjustment principle of the adjustable table is based on the geometric principle of “two intersecting straight lines on one plane are parallel to two intersecting straight lines on the other plane, and the two planes are parallel”, and the end face of the flat measuring cap is mounted on the measuring axis. The upper surface of the gauge block placed on the table top is parallel to each other for adjustment purposes. The principle of workbench adjustment is shown in Figure 2.

Figure 2 Adjustable principle of adjustable table

As can be seen from Figure 2 (a) and Figure 2 (b), whether the three-point support table, or the cone support table, the actual surface of the table EE 'and the ideal surface CC' intersect at P (for the convenience of the narrative In this paper, the surface of the workbench surface parallel to the end of the cap is called the "ideal surface", and the actual surface and the ideal surface of the workbench refer to the upper surface of the gauge block placed on the workbench). In the process of coincidence between EE' and CC', point P also moves along CC'. When EE' and CC' coincide, the surface of the table is an ideal surface. From the position of the point P, that is, the distance of the OP, the distance t at which the end face of the measuring cap is moved when the surface of the inclined table is adjusted to be an ideal surface can be obtained from both of FIGS. 2(a) and 2(b). get:

Tgα=2δ/d=2(N1-N2)/d (1)

Where N1—the gauge block is placed on the left (front) half instrument reading of the cap;
N2—The gauge block is placed on the right (rear) half of the cap to read the instrument;
d - flat cap diameter;
α - the angle between the actual surface of the table and the ideal surface.
From equation (1), it can be seen that when the difference between two instrument readings is zero, ie, δ=N1-N2=0, the surface of the table is an ideal surface.

4 Workbench adjustment method

4.1 t value solution
4.1.1 The t-value of the three-point support table.
Because of ΔABD∽ΔPOD in Figure 3,

OD=BD.OP/AB (1')

OD = t, BD = δ, OP = l ± Δl (OP = l - Δl in Figure 3 (a), OP = l + Δl in Figure 3 (b)), AB = d/2, (1')

t=2δ(l±Δl)/d (2)

Also obtained from ΔCKP

Δl=H.tg(α/2) (2')

Fig. 3 t-value calculation of three-point support table

In fact, due to the small inclination angle of the table surface, α≈0, it can be considered that tg(α/2)≈1/2tgα=δ/d.

Δl=Hδ/d (3)

Substituting equation (3) into equation (2), simplifying it:

t=2lδ/d±2H.(δ/d)2 (4)

When the fixed support center C is on the high side of the table surface (Fig. 3(a)), the value of t is calculated by the negative sign in equation (4); on the low position side (Fig. 3(b)), the value of t is Calculate by the positive sign in equation (4).
Since α≈0, and d δ, when (δ/d)2 approaches zero, the height H from the fixed support center C to the ideal surface CC′ has negligible effect on the t value. Equation (4) can be rewritten as

t=2lδ/d (5)

Where t is the distance from the end face of the cap to the ideal surface;
l - the distance between the projection of the measuring axis and the tilt axis on the ideal surface;
δ—The instrument readings at the high and low points of the table are poor;
d - The diameter of the plane cap.
According to the vertical optical meter three-point support table design parameters: the two tilting axes of the table is vertical, ie ∠ACB=90° in Figure 1(a), l=12.5mm, when using d=8mm flat cap When using a 10mm block (with no effect on the adjustment of the block size), the equation (5) can be used to calculate

t=3.13δ≈3δ

Where t and δ are in μm.

4.1.2 The t-value of the cone-supported table is shown in Figure 2(b) as BD∥AC, B'D'∥A'C', and BD=AC, B'D'=A'C', respectively. Connect DD' and CC'. At this time, DD' and CC' intersect at P'.
Since ΔCDP'≌ΔABQ
To succeed DCP'=∠BAQ=
∠CDP'=180°-( +α)
Available from sine theorem

DP'=CP'sin /sin( +α) (6)

Same reasoning

ΔC'D'P'≌ΔA'B'Q

Dee C'D'P'=∠A'B'Q= -α
∠D'C'P'=180°-

Available from sine theorem

P'D'=C'P'sin?/sin( -α) (7)

also

DP'+P'D'=CP'+P'C'=D (8)

It can be obtained from equations (6), (7) and (8)

It can be seen from Figure 2(b)

OP'=CP'-OC=CP'-D/2

So

In ΔPP'Q

∠PQP'=α/2,P'Q=AC=H'

PP'=Htg(α/2)
Thus getting

(9)

t=OPtgα (10)

Under normal circumstances, the tilt angle of the table surface is small, α ≈ 0, which can be considered cosα = 1, tgα = sinα = 2tg (α/2), substituting equation (9) into equation (10), and taking Α≈0 is the condition of finishing, you can get

t=2(Dctg +H).tg2(α/2) (11)

Also by formula (1)

Tg(α/2)=δ/d

Substituting the above equation into equation (11),

t=2(Dctg +H) (12)

Due to the bevel of the annular bearing cone Small (about 5°), the height H from the bearing surface to the ideal surface has negligible effect on the t value, then equation (12) can be rewritten as

t=2Dctg (δ/d)2 (13)

The design parameters of the cone-surface support table of the vertical optical meter D=76mm, =5°, if a planar cap with d=8mm is selected, it can be obtained from (13)

t=0.027δ2≈0.03δ2

Where t and δ are in μm.
In order to facilitate the adjustment and avoid mistakes, the t values ​​of several commonly used planar measurement caps are listed in the following table.

Table t

Three-point support table δ=N1-N2
Μm Cone Support Table t=2lδ/d/μm t=2Dctg (δ/d)2/μm/d=10mm d=8mm d=5mm d=3mm d=3mm d=5mm d=8mm d=10mm 1.25 1.56 2.50 4.17 0.5 0.05 0.02 0.01 0.01 2.50 3.13 5.00 8,33 1 0.20 0.07 0.03 0.02 5.00 6.25 10.00 16.67 2 0.80 0.30 0.11 0.07 7.50 9.38 15.00 25.00 3 1.70 0.60 0.24 0.16 10.00 12.50 20.00 33.33 4 3.10 1.10 0.40 0.30 12.50 15.63 25.00 41.67 5 4.80 1.70 0.70 0.40 15.00 18.75 30.00 50.00 6 6.90 2.50 1.00 0.60 17.50 21.88 35.00 58.33 7 9.50 3.40 1.30 0.90 20.00 25.00 40.00 66.67 8 12.30 4.40 1.70 1.10 22.50 28.13 45.00 75.00 9 15.60 5.60 2.20 1.40 25.00 31.25 50.00 83.33 10 19.30 6.90 2.70 1.70

4.2 Adjustment Methods and Procedures <br> Both the three-point support table and the taper support table are adjusted in the left, right, front, and back positions under the end face of the cap as shown in FIG. 4 . Gauge block, and determine the adjustment amount based on the reading difference δ between the high and low points of the instrument

Figure 4 Placement of Gauge Blocks with Adjustable Workbench Adjustment

* Three-point support table adjustment method Place the gauge block between the table and the end face of the cap so that the gauge blocks are in the left, right, front, and rear positions. See Figure 5. Adjust the screw A, then the upper table with BC as the axis for tilting movement, can adjust the table surface AC tilt; adjustment screw B, the upper table with AC axis for tilting movement, adjustable table surface BC The direction of the tilt. In this way, by repeatedly adjusting the screws A and B, the surface of the table can be perpendicular to the measurement axis.

Figure 5 Adjustment method of three-point support table

For example, choose to adjust the AC (left, right) direction. According to Figure 5(a), place the gauge block to the left, read the instrument reading N1, then move the gauge block to the right, and read the instrument reading N2. At this time, the difference between the left and right instrument readings is

δ=N1-N2

When δ exceeds the specification, the workbench needs to be adjusted. According to the magnitudes of d and δ, t value is found in the t-value table, and the worktable is adjusted based on the low point. When δ is positive, the right position is low, N2 is the low point instrument reading; when δ is negative, the left position is low, and N1 is the low point instrument reading. When the tilt axis (fixed support center C) is on the high side (see Figure 3(a)), raise the low point by a t value; when the tilt axis is on the low side (see Figure 3(b) )), lower the low point by a value of t. That is, through the lifting and lowering A, the instrument reading N when the surface of the worktable is an ideal surface can be obtained.

N=N2+t
N=N1-t

Similarly, according to Fig. 5 (b), the gauge block is placed at the front and rear positions, and the BC (front and rear) direction tilt adjustment is performed by the lift B. After the tilt of the front and rear directions is adjusted, the left and right directions are calibrated until the left, right, front and rear directions are within the specified range, and the verticality of the surface of the work table and the measurement axis is considered to be acceptable.
* Adjustment Method of Cone Support Table The adjustment of the conical support table can be performed in the following three ways.
1 Coarse adjustment - t value correction method.
According to the values ​​of d and δ, the t value is determined from the t-value table, and the table adjustment is performed based on the low point. By rotating the screws A, B (see Fig. 1(b)), the adjusted instrument reads N=N2-t, then the surface of the table is at an ideal surface, as shown in FIG.

Figure 6 Adjustment Method of Cone Support Workbench

2 fine tuning - high point lower method.
From the t-value table, it can be seen that when δ is not large, the value of t is small, and the influence of t value may not be considered. Place the gauge block directly at the high point (Figure 6(a)), read the instrument reading N1, and then move the gauge block to the low position (Figure 6(b)), read the instrument reading N2, and then place the gauge block Put back into the high position and adjust the reading N1 to N2 by turning the screws A and B, even if N1=N2. This is repeated 1 or 2 times to adjust δ to zero, then the surface of the table is on the ideal surface.
3 Empirical Method - turning point method.
For skilled instrument operators, adjustments can also be made directly to changes in instrument readings at high and low points. The method is to find the reading of the instrument at the instant that the point P coincides with the point O in Fig. 2(b), that is, the indication of the turning point. From Figure 6

N=N2-t=N1-(t+δ)

Where N2 - low instrument readings;
N1 - high point instrument readings;
Adjust the A and B screws to lower the high point 1, and then the low point 2 also decreases. When the reading N2 decreases by t and N1 decreases by t+δ, it indicates that the surface of the table is an ideal surface. Continue to adjust the A, B screws, N1 continues to decrease, while N2 increases instead, N2 from turning down to rise is the turning point. The reading of the instrument at this time is the indication of the turning point, that is, the reading N of the instrument on the surface of the table that is ideal. Similarly, the directions of C and D are also adjusted according to the above method until A, B and C, D direction are qualified.
It should be pointed out here that whether the three-point support table or the conical support table, when the left, right, front, and rear four positions shown in FIG. 4 are placed for retesting (proofreading), if the instrument is reading The difference δ does not exceed the specified range (0.3μm), indicating that the surface of the table is already on the ideal surface, that is, the adjustment of the perpendicularity of the surface of the table and the measurement axis is completed.

5 Some explanations

1 When the high and low point of the instrument reading is determined and δ is determined, the low point reading is adjusted to zero (without changing the tilt of the table surface) through the micro-motion lifting device of the work table. Then, according to the size of δ, The value of t is determined from the t-value table and the instrument reads t or (-t) by adjusting the screw. In this way, the workbench can be adjusted more easily, faster, and less prone to error.
2 When the three-point supporting table's movable support A, B (Micro-motion screw) and Fixed support C (steel ball) are inconsistent with the radius of curvature when the contact with the bottom of the upper table (vertical optical meter is an example), when the adjustment work When tilting in the other direction of the desk, it affects the direction that has been adjusted and thus affects the adjustment speed. If the radius of the ball end of the two fine-tuning screws is the same as the radius of the fixed support ball, the adjustment speed of the table can be made faster.
3 If the same as the stand of a vertical contact interferometer, the fixed support center C is designed in the center of the three-point support table (strictly speaking, the point at which the axis of the measurement axis is projected on the table). In this way, there must be a point on the tilt axis when adjusting, when the value of t is equal to zero, you can directly adjust the reading difference δ between the high and low points: if the high point falls on the tilt axis, raise the low point. High δ; if the low point falls on the tilt axis, lower the high point by δ. Only a slight improvement in the structure of the workbench will make the adjustment of the workbench easier and will greatly increase the adjustment speed of the workbench.
4 There are many ways to adjust the adjustable table. This article describes a method that quickly achieves adjustment by using quantitative values. However, it should be pointed out here that if you only understand the adjustment principle and adjustment method of the adjustable worktable, you are not familiar with the performance and operation of the equipped instrument. The method, as well as some details and techniques of the workbench adjustment, will also cause mistakes in the adjustment process, and even lead to adjustment failure. This is even more of a concern for metrology operators who are initially operating with adjustable table equipment.