DE102010021829B4 - Method for in-process measurement of a radius error of a workpiece and machine tool - Google Patents

Abstract

Method for in-process measurement of a radius error of a workpiece, in particular during a machining process, comprising the steps of: (a) machining the workpiece while rotating the workpiece about an axis of rotation, (b) applying a measuring device to the workpiece so that the measuring device in (c) bringing a sensing device of the measuring device into contact with the workpiece, and (d) measuring and storing a deflection of the sensing device at different rotational angles of the rotational axis, (e) detecting the rotational angle (φ) at equidistant angular steps (φn), wherein the angular steps (φn) as a product (n · φ0) from an integer count index (n) and a circular pitch (φ0) are described, the product (N · φ0) from a and the circle pitch (φ0) gives 360 °, and (f) calculating the radius error (Rw (φ)) from the displacement of the Tasting device for a number of angular steps corresponding to the circular line number (N), characterized in that (g) the radius error for each angle of rotation is determined by a minimum phase transfer function, the minimum phase transfer function obtained by breaking a transfer function into the minimum phase transfer function and an allpass and wherein the transfer function assigns the associated angle-dependent radius to each angle of rotation for a given contour of the workpiece.

Description

The invention relates to a method for in-process measurement of a radius error of a workpiece according to the preamble of claim 1. According to a second aspect, the invention relates to a machine tool according to the preamble of the independent claim.

In machining, in particular in the hard fine machining of crankshafts, pendulum lift grinding machines have been increasingly used since the end of the 1990s. In this type of machine, the connecting rod bearings are ground by crankshafts by the grinding wheel is tracked to the eccentric rotating bearing. For in-process evaluation of the diameter and the oversize in pendulum lifting is from the WO 2005/119383 A2 known to use a prismatic measuring body, which is held in contact with the bearing. The disadvantage of this is that a roundness of the crankshaft at the ground point can be controlled only after processing. Due to the process, the eccentricity can not be detected during the process. For evaluating and improving the machine kinematics, therefore, the described method can not be used.

From the DE 600 15 654 T2 a generic device is known in which recorded by means of a V-prism measurement data to be ground crankshaft seat and processed by a Fourier analysis. The use of a minimal phase transfer function is not described.

The invention is based on the object to better capture purely local radius errors.

The invention solves the problem by a method according to claim 1 and a machine tool according to the independent claim

An advantage of the invention is that it is possible to evaluate fluctuations of the allowance during processing in the correct phase. Thus, geometry errors that manifest during machining may be due to dynamic machine errors, such as tracking errors and technological errors, for example due to compliance or workpiece errors. Accordingly, it is possible over methods according to the prior art, better distinguish error sources from each other.

It is a further advantage that the method according to the invention can be used to shorten the processing time. The knowledge of the distribution of allowances over the component radius creates the prerequisite for adaptive feed control of the grinding process. This regulation has the goal to quickly reduce the cost fluctuations and to reach the final contour of the warehouse in a time-optimized manner.

It is a further advantage that the ripple of the workpiece can be assessed in the process. In particular, from the angle-dependent radius error, for example by means of a prior analysis, a possible dominant vibration is detected. Such a dominant vibration may be due to process vibrations or vibrations of the tool, such as a grinding wheel. The invention therefore makes it possible to regulate the machining process so that the radius error is minimized.

Preferably, the monitored machining process is a grinding process, in particular a pendulum stroke grinding process. But it is also possible that the method for in-process measurement of the radius error during winding, for example of sheets or strips, is used.

In the context of the present description, the measurement of the radius error is understood in particular to mean a deviation of the actual radius from a nominal radius. Since this nominal radius can basically also be defined as zero, the invention also includes a method for in-process measurement of a radius of a workpiece.

The machining of the workpiece is understood in particular to mean machining, for example grinding or turning. In addition, the rotation of the workpiece about the axis of rotation, but not the cutting machining process to be understood.

The deflection of the sensing device is understood in particular to mean a change in position of at least part of the sensing device relative to the remainder of the measuring device. For example, the sensing device may be configured such that a change in curvature of the workpiece results in the sensing device shifting linearly in a housing of the measuring device.

The detection of the angle of rotation is understood to mean, in particular, that at least one point in time when carrying out the method, the deflection at the corresponding angle steps is known. It is possible, but not necessary, for the deflection to be measured precisely at the angular steps; in particular, it is also possible for the deflection to be measured at angles other than the specified angular steps, after which an interpolation to the equidistant angular steps is performed. Such a process is known as resampling.

It is particularly favorable if the measuring device rests on the workpiece on the one hand with the sensing device and on the other hand with two other points which do not belong to the sensing device. It can thus achieve a very high accuracy.

Preferably, the machining is a machining of acentrically clamped workpieces, in particular a pendulum stroke grinding of crankshafts. For crankshafts, the shape deviation is an important quality criterion, since high accuracy requirements are made. The invention can therefore be used particularly advantageously in this field.

In the following the invention will be explained in more detail with reference to the attached figures. It shows

1 a sketch of the kinematics of pendulum lift grinding to explain the formula sizes used in the calculations,

2 a sketch for calculating the deflection of a sensing device of a machine tool according to the invention, with an inventive process can be performed

3 the course in the deflection measured by the probe device (probe length LT) as a function of the angle of rotation φ in the case of a pulse-shaped excitation,

4 the coefficients for the angles of rotation in the equidistant angular steps in the event that the circular line number M = 64,

5 the resampling of continuously measured data for the deflection of the sensing device and

6 an illustration of the calculation of the radius error from the deflection of the locking device from a convolution sum.

1 shows a tool 10 in the form of a grinding wheel which is part of a machine tool, in particular a pendulum stroke grinding machine. The machine tool comprises a rotating device having a drive and a receptacle for rotating the tool 10 around an axis of rotation protruding from the plane of the drawing, around which the tool 10 in a storage 12 is stored. The tool 10 is engaged with a workpiece 14 , in the present case a crankshaft, which grinds it on a bearing seat. The machine tool also comprises a measuring device which is used to measure a radius error R _w (φ) on the workpiece 14 is applied.

The measuring device 16 lies in a first contact point 18 and a second contact point 20 on the workpiece 14 and has a tactile device 22 on that in a touch point 24 to the workpiece 14 touches. If the workpiece 14 If the cylinder is ideally cylindrical and tensioned in the center of the cylinder, the position of the sensing device changes 22 relative to the remainder of the measuring device 16 also when turning the workpiece 14 Not. In all other cases leads a rotating workpiece 14 to that the feeler device 22 relative to the rest of the measuring device 16 emotional. It also changes a probe length LT, which is specified relative to an arbitrarily selected zero point.

About a line not shown, the measurement results for the probe length LT to a control device 26 the machine tool forwarded to a digital memory 28 having. A program is stored in the digital memory which, as explained below, calculates the workpiece radius R _w (φ) as a function of the angle of rotation from the measured probe lengths LT (φ).

1 Transformation of the pressure angle

1.1 Calculation of the pressure angles via trigonometric functions

The basis here are the geometric constants (e _w , r _w , r _s , L ₁ , L ₂ , M _x , M _y ) in 1 are shown. 1 schematically shows the kinematics of the eccentric conrod bearing grinding with tactile diameter detection in machine coordinates with auxiliary variables:

1.2 Grinding wheel engagement angle β

The grinding wheel engagement angle β of the grinding wheel 10 is calculated according to the theorems on the right-angled triangle, which is formed from a freely selectable zero point 30 , the center of storage 12 and a tool center 32 of the workpiece

1.3 palpation angle κ

Center position of the warehouse:

Length between connection and center

Angle between L and y-axis from vector product

Calculation of the triangle angle from Cossinussatz:

Pressure angle of the probe κ

• κ = -σ + δ + π / 2 Eq. 1.3-e

2 Calculation of the probe length LT

The goal is to know the probe length LT as a function of the prism geometry (α ₁ , α ₂ , r _G ).

2.1 Calculation of the probe length on the prism with in basic position

2 shows the workpiece 14 , In the following, vectors between points are marked with an overline, z. B. FROM , The amount of the vectors is indicated by sums, for example as | FROM | ,

Due to the sum of angles in the triangle, the following applies: β ₂ = 180 ° - 90 ° - α ₁ Eq. 2.1-a β ₁ = 180 ° - 90 ° - α ₂ Eq. 2.1-b

In the contact points 18 (additionally referred to as B) and 20 (also referred to as C) is the measuring device 16 tangential to the workpiece 14 at. With an intersection C of the two flanks of the prism-shaped inner contour of the measuring device 16 follows

The distance of the center M of the workpiece 14 to a tip A of the touch device 22 follows from solution of the equation system

Accordingly, the probe length LT can be determined to: LT = | s'a ' | = | S'M | - r _G Eq. 2.1 g

3 Calculation of the radius-dependent probe length for non-circular bearings

The goal is to know the probe length LT (φ) as a function of a radius error Rw (φ). As an alternative to the procedure described below, the probe length can also be solved numerically. Importantly, the in 2 illustrated relationship is known.

In the following it is assumed that the eccentricity of the bearing e _w = 0. This causes β and κ to be constant and simplifies the viewing.

As a reference, a radius error is assumed as a function of the angle φ. The shape of the reference signal is irrelevant to the calculation, as long as the deviation is significantly smaller than a radius r _{g of} the workpiece 14 and the highest occurring frequencies in the signal do not exceed the period length of 2 * Δφ. By way of illustration, the in 3 selected signal selected. The radius R _B (φ) at point B (first contact point 18 ) in dependence on the rotation angle φ is given. This can be described to:

Boundary function of the radius at point B:

With
r _w = 23.5 mm radius of the workpiece
h _B = 2 μm height of the bump
b _B = 10 ° width of the bump
w _B = 78 ° angular position of the bump
Δφ = 360 ° / 128 = 2.8125 ° Resolution of the angle

3.1 Calculation of the tangent at point B

For further calculations, the radius is converted into Cartesian coordinates:

The tangent at point B results in:

The derivative is calculated from the approach function

3.2 Calculation of the angle Δφ _C

The prism lies tangentially in points B and C at a given prism angle (α ₁ + α ₂ ). The angle between the distances MB and MC is now no longer Δφ _C , but β _Σ . β _Σ is the result of an iterative calculation. The starting values are the angles from 2.1-a and 2.1-b. β _{Σ, 1} (Φ) = β ₁ + β ₂ Eq. 3.2-a

Thus, the radius at point C, ie the distance MC can be calculated to:

The tangent at point C is thus:

From this tangent, an angle error Δα _n at the point S can be determined. The angle error Δα _n should actually be zero and it is usually not only because the assumption according to Equation 3.2-b is only an approximation.

From equation 3.1-b and equation 3.2-e the angle Δα _n (Φ) is obtained.

The new iteration value for Equation 3.2-a is now β _{Σ, n + 1} (Φ) = β _{Σ, n} (Φ) - Δα _n (Φ) Eq. 3.2 g used. Through the iteration, Δα _n (Φ) tends to zero, so that the iteration can be aborted when it falls below a threshold value. The iteration over n (3.2-b to 3.2-g) is usually sufficiently accurate after five iteration steps.

3.3 Calculation of the intersection point S

The point S (φ) can be calculated via the vector equation by solving for θ and λ MS (φ) = MC (φ) + λ · T _c (φ) = MB (φ) + θ · T _b (φ). Eq. 3.3-a

3.4 Calculation of the shifted intersection point S '

3.5 Calculation of the radius R _A (φ)

Analogous to 3.2-b

By assuming the constant angle β ₂ in Equation 3.5-a, a numerical error arises, since this angle is also dependent on Φ. At the in 3 selected parameters, this error is negligible.

3.6 Calculation of the probe length LT (φ)

The geometry can be calculated using the vector sum A'S ' (φ) = R _{A '} (φ) - MS ' (φ) Eq. 3.6-a LT (φ) = | A'S ' (Φ) | Eq. 3.6-b

Thus, the probe length LT (φ) is known in non-circular bearing as a function of the angle of rotation.

4 Calculation of the transfer function

The goal is to know the probe length LT (φ) as a function of any radius error R _w (φ).

4.1 Basics

It is known from discrete-time digital signal processing that the behavior of systems can be completely described by the impulse response (h [n]) of the LTI (Linear Time Invariant) system. One can calculate the system response (y [n]) for a given input (x [n]) via a convolution:

The derivation of this formula can be taken, for example, from A. Oppenheim, R. Schafer, J. Buck: Discrete-Time Signal Processing, Person Study, which is referred to below as [1].

Analogously, this relationship can be described by the corresponding (linear time invariant) (compare [1] chapter 5). Y (e ^jω ) = H (e ^jω ) X (e ^jω ) Eq. 4.1 b

The frequency response can be calculated from the power density spectra (see [1] Chapters 8 and 9 for H1-Estimation):

4.2 Calculation of the transfer function

From the in Ch. 4 calculated curves, the spectra can be calculated by means of Fourier transformation: RB ( ^ejω ) = F (Rb (φ)) Eq. 4.2-a LT (e ^jω ) = F (LT (φ)) Eq. 4.2-b

From this the car power density spectrum can be calculated: S _RB (e ^jω ) = R B (e ^jω ) · conj (R B (e ^jω )) Eq. 4.2-c

And the cross power density spectrum: S _RBLT (e ^jω) = LT (e ^jω) · conj (RB (e ^jω)) Eq. 4.2-d

From this, according to Eq. 4.1-c which calculates the leadership frequency response:

With the inverse Fourier transformation, the impulse response can be calculated as follows: F (Φ) = F ^-1 (F (e ^jω )) Eq. 4.2-f

4.3 Adjusting the resolution

The impulse response is in 4 shown. According to Eq. 4.1-a calculate the probe length as a function of the angle Φ.

5 Calculation of the invertible impulse response

5.1 Basics

A direct recalculation of a transfer function is not possible. Only if it is a minimum phase system (poles and zeros in the unit circle) can the inverse function be calculated (see [1] chapter 5.2.2). Therefore, an allpass decomposition is performed on the filter. The system is described by the allpass and the minimum phase system (with the same amplitude response) (see [1] chapter 5.6.1). F = F _AP · F _MIN Eq. 5.1-a LT (Φ) = (F _AP * R _w ) [Φ] + (F _MIN * R _w ) [Φ] Eq. 5.1-b

5.2 Calculation (decomposition into minimal phase system)

For the allpass decomposition, the transfer function, which is represented as an impulse response, must first be converted to pole / zero notation. This is done by means of partial fraction decomposition.

When connecting, all zeros are divided into zeros outside and zeros inside the unit circle

Zeros outside the unit circle are replaced by the following term:

Thus, the minimal-phase transfer function can be calculated by polynomial winding: F _MIN (Φ) = K · Π (Φ - N ₁ ) · Π (Φ - N '/ A) Eq. 5.2-d

The resulting impulse response of the minimal phase transfer function is in 4 shown.

6 calculations during the measurement

All previous calculations were carried out in advance. The transfer function F _MIN determined in this way is subsequently used during operation to determine the actual radius during the rotation.

The aim is to calculate the actual radius R (Φ) from the measured probe length LT (Φ)

6.1 Resampling of the signals

The time discrete signals probe length LT (t) and the angle of rotation φ (t) are measured. The angular steps (φn) result as a product (n · φ ₀ ) from an integer count index (n) and a circular pitch (φ ₀ ) (see 5 ). The subsequent calculation is performed only at changing angles.

6.2 Calculation of the radius

The calculation of the convolution (equation 4.3-b) is done by 6 illustrated in the left part of the picture. The probe length LT is calculated as the sum of the current radius (R _w (Φ)) and the previous n - 1 values (R _w (Φ - Θ)). Thanks to the conversion to the minimum phase system, this equation can be changed to: R _w (Φ) = (F -1 / MIN x LT) [Φ] = LT (Φ) - Σ N-1 / Θ = 1F _MIN (Θ) * R _w (Φ - Θ) Eq. 6.2-a

This is illustrated in 6 right. The calculated radius (R _w (Φ)) thus depends on the current probe length (LT (Φ)) and the previous n - 1 values of the radius (R _w (Φ - Θ)).

LIST OF REFERENCE NUMBERS

φ

Angle of rotation of the workpiece 14

β

Pressure angle of the tool 10

κ

Pressure angle of the measuring device 16

e _w

Eccentric of the workpiece 14

r _w

Radius of the workpiece 14

L ₁

Length 1 of the movable measuring arm

r _s

Radius of the tool 10

L ₂

Length 2 of the movable measuring arm

M _x

Fixed point of the measuring arm relative to the storage 12 (Horizontal)

M _y

Fixed point of the measuring arm relative to the bearing (vertical)

α ₁

Opening angle 1 measuring device 16

α ₂

Opening angle 2 measuring device 16

r _G

Basic radius of the measuring device 16

R _w (φ)

Radius of the workpiece 14 depending on the workpiece rotation angle

LT (φ)

Probe length depending on the workpiece rotation angle φ

R _w (Φ)

Radius of the workpiece 14 in dependence of the workpiece discretized angle of rotation Φ

LT (Φ)

Probe length as a function of the workpiece discretized angle of rotation Φ

F (Φ)

Transfer function of the measuring prism (f (Φ, α ₁ , α ₂ , r _G ))

Φ

Discretized angle of rotation of the workpiece

Θ

Auxiliary operator in the folding

F _AP

Allpass component of the discredited transfer function F (Φ)

F _MIN

Minimal phase component of the discredited transfer function F (Φ)

x _m

X-coordinate Center of the workpiece 14

y _m

Y coordinate Center of the workpiece 14

L '

Length between connection of the measuring arm and center point

M

Center of the workpiece 14

S '

Center of the measuring device 16

B

First contact point 18

C

Second contact point 20

A '

Contact point of the button

β ₁

First opening angle on the workpiece 14

β ₂

Second opening angle on the workpiece 14

β _Σ

Sum opening angle on the workpiece 14

R _R

Radius at point B, corresponds to | MB |

R _C

Radius at point C, corresponds to | MC |

R '/ A

Radius at point A ', corresponds to | MA ' |

r _w , h _B , w _B , b _B

Parameters of the excitation function used here

10

Tool

12

storage

14

workpiece

16

measuring device

18

first contact point

20

second contact point

22

sensing device

24

touch point

26

control device

28

Digital storage

30

zero

32

Workpiece center

LT

probe length

Claims (7)

Method for in-process measurement of a radius error of a workpiece, in particular during a machining process, comprising the steps of: (a) machining the workpiece while rotating the workpiece about an axis of rotation, (b) applying a measuring device to the workpiece so that the measuring device in (c) bringing a sensing device of the measuring device into contact with the workpiece, and (d) measuring and storing a deflection of the sensing device at different rotational angles of the rotational axis, (e) detecting the rotational angle (φ) at equidistant angular steps (φ _n ), wherein the angular steps (φ _n ) as a product (n · φ ₀ ) from an integer count index (n) and a circular pitch (φ ₀ ) are writable, the product (N × φ ₀ ) from an integer circular line number (N) and the circular pitch (φ ₀ ) gives 360 °, and (f) calculating the radius error (R _w (φ)) from the A deflection of the scanning device for a number of angular steps corresponding to the circular line number (N), characterized in that (g) the radius error for each angle of rotation is determined by a minimum phase transfer function, the minimum phase transfer function being broken down by splitting a transfer function into the minimum phase transfer function and a Allpass is obtained and wherein the transfer function assigns each angle of rotation for a given contour of the workpiece the associated angle-dependent radius. A method according to claim 1, characterized in that - as a measuring device, a V-shaped prism is used and - the radius error is calculated from the radius, wherein the radius according to the formula

where Φ is the rotation angle, LT is the deflection of the probe for this rotation angle, N is the circular pitch, F _{MIN is} the minimum phase transfer function of the transfer function, and Θ is an auxiliary variable. Method according to one of the preceding claims, characterized in that the machining comprises a machining of acentrically tensioned workpieces, in particular a pendulum stroke grinding of crankshafts. Method according to one of the preceding claims, characterized in that the rotation angle (φ) and the associated deflection of the feeler device is interpolated from continuously recorded measurement data. Method according to one of the preceding claims, characterized in that the sensing device is brought into contact with the workpiece in such a way that a possibly changing radius error is detected by the machining and the machining is effected by means of a tool and a predetermined position predetermined for a predetermined rotation angle of the tool is changed based on the radius error (R _w (φ)) so that the radius error is reduced one full revolution of the workpiece later. Machine tool, in particular pendulum stroke grinding machine, with (i) a tool, in particular a grinding wheel, and a rotating device for rotating a workpiece about a rotation axis, (ii) a measuring device for application to a workpiece received in the rotating device, the measuring device being designed in that it can be brought into contact with the workpiece in a first contact point and at least one second contact point, and - has a feeler device which can be brought into contact with the workpiece so that a deflection of the feeler device at different angles of rotation of the axis of rotation can be measured, such that (Iii) a memory connected to the measuring device for storing displacement measurement data, and (iv) an electric control device arranged to automatically perform a method comprising the steps of: detecting the angle of rotation (FIG. φ) at equidistant Winkelschri tten (φ _n), wherein the angular increments (φ _n) as a product (n · φ ₀₎ of an integer counting index (n) and an angular pitch (φ ₀₎ are writable, said product (N · φ ₀₎ from a integer circular pitch (N) and circular pitch (φ ₀ ) gives 360 °, and - calculating the radius error (R _w (φ)) from the deflection of the keying device for a number of angular steps corresponding to the circular pitch number (N). characterized in that (v) the control device is arranged to determine the radius error for each rotation angle based on a minimum phase transfer function, the minimum phase transfer function being obtained by decomposing a transfer function into the minimum phase transfer function and an all pass and wherein the transfer function is each rotation angle for a given contour of the workpiece assigns the associated angle-dependent radius. Machine tool according to claim 6, characterized in that the control device is adapted to automatically perform a method with the step: - Changing a machining program, by means of which a movement of the grinding wheel is controlled or regulated relative to the workpiece, so that the radius error is reduced.

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