FR2468876A1 - METHOD AND APPARATUS FOR MEASURING THE THICKNESS OF A SURFACE LAYER IN A METAL PIECE - Google Patents

Abstract

A method and apparatus for measuring the thickness of a surface layer of a metal part is disclosed. A constant current is passed through part 1 and a potential distribution is established on its surface which depends on the thickness of the surface layer. The measurement of the potential difference between two points, then the comparison with a series of reference values obtained under identical conditions for known thicknesses make it possible to obtain the desired thickness. The measuring device comprises a direct current generator 3 supplying two electrodes 2, and a micro-voltmeter 5 connected to two measuring electrodes 4. Application to the verification of parts produced in large series.

Description

The present invention relates to a method and an apparatus for

  measure the thickness of a surface layer

  in a metal part, this layer having characteristics

  physical ticks different from those of the rest of the room.

  It is a common practice to subject the surfaces of metal parts to be exposed to wear during their use in thermal, chemical, or chemical-physical surface treatments (such as quenching and carbonitriding), or

  a combination of these treatments to improve the characteris-

wear of surfaces.

  During the long-run production of parts subject to surface treatment there is a problem of having to carry out non-destructive type measurements rapidly to check whether the surface treatment has been satisfactorily performed and, in particular, whether the thickness of the treated layer is within certain pre-established limits. Such a problem does not have

  has so far been satisfactorily resolved.

  In order to solve this problem, the invention

  provides a method of measuring the surface layers which comprises the following operations: - passing a constant electric current of known value through the workpiece between two regions of its surface so as to establish a current distribution within the

  piece and, consequently, a superficial distribution of

  electric wire which decays from the thickness of the superficial layer; measuring the electrical potential difference between at least a couple of points of the surface of the part; - make a comparison between the measured value for the potential difference and a series of reference values

  each corresponding to a known thickness of the superficial layer

sky, and

  - deduce from the comparison the indication of the thickness

  the surface layer of the room.

  According to another aspect of the invention, there is provided a surface layer measuring apparatus which comprises: a DC generator; two electrodes connected to the generator and intended to be placed, in use, in contact with two regions of the

  the surface of the test piece so as to pass a

  constant electrical current of known value across the workpiece and thereby establishing a current distribution within the workpiece resulting in a superficial electrical potential distribution which depends on the thickness of the surface layer; - a voltage measuring instrument; and two measurement electrodes connected to the measuring instrument and intended to be placed, in use, in contact with two points on the surface of the part under test in order to measure the difference in electrical potential between said two points of contact.

the surface of the room.

  The following description, designed as an illustration of

  the invention aims to give a better understanding of its characteristics.

  features and benefits; it is based on the appended drawings, among which: - Figure 1 shows a first form of the measuring apparatus, this form being adapted to the implementation of the measuring method on a flat surface of a metal part ; - Figure 2 shows a second form of the apparatus, this form being adapted to the implementation of the measuring method on a cylindrical metal part; FIG. 3 is a perspective view of a part

  cylindrical metal identified in a cylindrical coordinate system

driques;

  FIG. 4 is an illustrated Cartesian representation

  trant a current density distribution, theoretically imagined,

  on the surface of the piece in Figure 3, this distribution cor-

  responding to currents flowing perpendicularly to the surface of the workpiece and for calculating the theoretical distribution of the voltage on the workpiece surface when currents are applied thereto according to said measuring method; FIG. 5 is a graph showing the theoretical values

  and measured values of the voltage V at the surface of cylindrical pieces

  driques chosen as samples for several thicknesses S of the surface layer (the corresponding values of the ratio S / R being also indicated and R being the radius of the part); and

  FIG. 6 is a graph showing theo-

  values and measured values of the potential difference ratio.

  existing between a first pair of points and the potential difference existing between a second pair of points on the surface of cylindrical pieces chosen as samples in the case of a

  variation of the thickness S (and of the ratio S / R) of the superficial layer

  cial. In FIG. 1, there can be seen a metal part 1 provided with a surface layer having characteristics

  different from those of the remainder lb of part 1.

  The layer has for example been formed by application to the surface 1c of the part (which is a flat surface on the

  Figure 1) a quenching or carbonitriding treatment.

  The method for measuring the surface layers which will now be described comprises a first operation of passing a constant electric current of a known value through the part 1 between two regions of the surface 1 of the part so as to establish a distribution current inside the room and, consequently, a superficial distribution of potential

  which depends on the thickness of the outer layer

  the sky. For this purpose, the apparatus of FIG. 1 comprises two electrodes 2 placed in contact with two distinct regions of the

  the surface of the room 1. The electrodes 2 are connected to a gen-

  direct current generator 3 designed to deliver a current

  substantially constant about 10 amps.

  Due to the difference in physical characteristics between the surface layer 1a and the part 1b of the part, the layer 1a has different electrical characteristics from those of the remaining part 1b. In particular, the layer la has an electrical conductivity different from that of the part lb. Therefore, the current passing through the room 1 through the electrodes 2 is distributed in the room 1 in a manner that depends on the depth of the layer 1a. Therefore, the electrical potential existing at a general point of the surface 1c of the part 1 takes a value which, in addition to being dependent on the arrangement of the electrodes 2 and the position of the point considered relative

  to the electrodes, also depends on the thickness of the super-

  -ficial. The measurement method of the surface layers therefore involves a second operation-which-consists in measuring the difference-of electrical potential existing between at least a pair of points of the surface 1c of the part 1. For this purpose, the measurement apparatus comprises two measuring electrodes 4 which are connected to a micro-voltmeter 5 and are placed in contact with respective points of the surface 1c of the part 1. The two pairs of electrodes 2 and 4 are carried by

  an insulating support structure 6.

  Once the measurement of the potential difference between the selected points on the surface has been made, a third

  operation of the measurement method is then implemented. This operation

  tion is to compare the measured value of the potential difference

  with a series of reference values each corresponding to

  at a determined value of thickness of the layer la.

  These reference values can be determined empirically

  by measuring-values of said potential difference

  for a series of pieces with superficial layers of

  thicknesses (the other parameters which affect the value of this potential difference being kept at the same value and being those used for carrying out a test measurement, these parameters including the dimensions and the material composition of the parts, the configuration electrodes of the meter, and the value of the circulated current). The thicknesses of the surface layers 1a of the parts used to determine the reference values are obtained for example by means of measurements

  effected by destructive methods.

  In this way, it is possible to prepare a table or diagram relating to the values of the difference of potential

  measured according to the various thicknesses of the layer la.

  Therefore, by comparing the reference values and the value of the potential difference that is measured for a part having a surface layer of unknown thickness, it is

  possible to deduce a value of the thickness of the superficial layer

  the room of the room under test.

  The shape of the apparatus illustrated in FIG. 2 is adapted to the use making it possible to measure the thickness of the superficial layer of a cylindrical part 11. The elements of

  the apparatus of Figure 2 which correspond to elements of the

  same in Figure 1 are shown in Figure 2 by means of the

  same reference numbers. In the apparatus of Figure 2, the structure

  insulating support of electrodes 2 and 4 is a structure

ring 6 surrounding the piece 11.

  The apparatus of FIG. 2 is used in the same manner as that of FIG. 1 for implementing the method of measuring the surface layers, the measured value of the difference in

  potential between the electrodes 4 being compared with reference values

  this difference in potential. These reference values can be determined either empirically in the manner indicated above, or from a mathematical relationship expressing the value of the theoretically measurable difference in potential between

  two points of the surface 11c of the part 11, depending on the thickness

  of the superficial layer 11a. Obtaining this mathematical relation for a cylindrical part will be given below in relation with FIGS. 3 and 4, this relationship expressing how the potential difference depends on the thickness of the surface layer as a function of the geometrical characteristics of the piece and the geometric arrangement of the feed electrodes 2

  current and measuring electrodes 4.

  FIG. 3 schematically shows, in perspective, a cylindrical metal piece P of radius R2 which

  has an outer surface Pc of length 1 and a superimposed

  Pa has a thickness of 1 to 2. The layer Pa has a conductivity

  The different points of the inside and the surface of the part are identified in a cylindrical coordinate system Z, (, z, the origin of the axis. z located at a point O in the center of room P.

  The two regions M and N lying on the cylindrical surface

  of the room P are the supposed areas of contact

  trodes 2 power supply of the apparatus of Figure 2.

  Conveniently, the centers of the regions M and N are in the plane z = 0, while the rays connecting the point 0 to said centers form between them an angle e. The dimensions of the circle segments and line segments that delimit each of the M and N regions are respectively designated a and b. In the following discussion, the electrical conductivities of the inner untreated cylindrical portion Pb and the surface layer Pa of the part will be respectively designated r and -2. In addition, it will be assumed that a current of intensity I passes into the room between the regions M and N. The density J of this current is substantially constant over the entire surface of the regions M and N. As shown in FIG. 4. The parameters I and J are connected

by the expression I = J (a.b).

  As is known, the electric potential V at a general internal point, separated from the discontinuity surfaces, must satisfy the Laplace equation: 2V o (1), which is written in cylindrical coordinates: 2v + 1. For all the points of the inner region Pb of the part P, therefore being at a distance r from the axis z which is smaller than R1i, the solution of the Laplace equation is of the type:

V- A (p). cos pz I (pr) ein (2).

  pn n to n For the points of the superficial layer Pa, which are therefore at a distance r from the axis z between R1 and R2> the solution of the Laplace equation takes the form:

  V2 = p [B n (phn (pr) + On (p) Kn (pr)] ei cospz (2 ').

  The symbols appearing in the expressions (2) and (2 ') giving the potentials V and V have the indicated meanings

1 2

  below: p., n: integers; An (p), Bn (p), Cn (p) coefficients that can be determined by the setting of the boundary conditions; I: modified Bessel function of the first type, of order n; K: modified Bessel function of the second n type, of order n; e: base of natural logarithms;

i: imaginary unit \ (-1).

  The coefficients An, Bn, Cn can be determined by setting the boundary conditions. The first condition relates to the

  continuity of potential V for r = R1. The second condition relates to

  carries the continuity of the current density vector for r = R1, that is:

J E = -grad V (3).

  The third condition relates to the distribution

  currents on the cylindrical surface of the part P, for r = R2.

  More precisely, the radial component of the current density for r = R2 must be zero everywhere, except in correspondence with the

  regions M and N, as illustrated by the graph of FIG.

  By setting the boundary conditions above, it is possible to get the following expression for the potential at a general point

  lying on the circle that is the intersection of the over-

  the cylindrical face of the workpiece P and the plane z-O: 2J 1 n V 2 1. sin (a) [cos n1-cos n-) v i2 'u: l n2R lim 1 Kn Kn (pR2) In (pR2) kn (PR2)

Y

  p4O 0K'pR + hnP [i pR) K (pR P 'n (PR2 n 2) n (PR2) 2Jlir 1 V n (R2

  -j - Summer -; z- sin (-ob sin (2Ra) [Cos n, - cos n (-9)].

  n 2 R 2 z) K '() hY 2mir (n (m In (m92) Kn (2 M tOS t) n (m nh I n (m * 2) K' (m) 5 (4) 'K n (2) Il (m% 2) K '2) o: = 1 + (. N (mp2) K' (My,)., N = i (my2) 2I nR (m X 1 K (mi ') - l -1 No. 1

Y2 = 2, X = - to

  In the case of small-diameter cylindrical pieces, the modified Bessel functions that appear in the expression given above can be approximated as follows: n-i 1 K (r) Z__. 2n. (n-) rn I (r) 'r 2 nn 2 n: which satisfy: limi K <pR2 I (pR) K (PR) p IK'n (PR2) n () [I2n (pR2) K (pR2) 2

2R 2 2 2

n.çî 2n

1 + + -)

  It is therefore finally possible to simplify the expression

sion of V given above.

  Since the potential is set to a close constant,

  we can impose that it is zero for À = 0.

  In this way, if one poses in addition: 2a a _ = 2rb, = 2Y'z, and knowing that J: I / ab, one obtains

V = (F1 + F2)

  (4), or F1 = 2 1 na [os2ng ni -2in2) [cos nt-cos n ('- O) -2sin t] 2 a_ 1

  (continuation of the formula, following page).

2-1 1 -1 1) 2n 4% 1 + s 1 (p a

2 aj 21 = 1sin (>) sin (-2).

ml1 n1 m n

cos m [Icos n + cos n (q-9)] - 2 sin-9.

  (Kn (M_2) + h (m_2) n (m? 2) {K '& mf2) + mn _I n (m2) KI (m1'2) Once the expression of the one-point potential of the circle formed by the intersection between the cylindrical surface of the part 1 and the plane z = 0 is known, it is possible to calculate, for various values of the ratio R1 / R2 (that is to say for various values of the thickness of the surface layer la), the potential difference existing between two points of the circle when a current of known current density passes through the two regions M and N of known dimensions which are angularly separated from each other

by a known angle.

  As can be seen in Figures 5 and 6, the comparison

  its theoretical curves obtained by evaluating the potential difference between two points by means of mathematical expression with various experimental expressions obtained by measurements

  on pieces chosen as samples confirms the trustworthiness

  the data that can be derived from the mathematical expressions

matic.

  In FIG. 5, the curve A represents the variation of the potential V in microvolts which is theoretically measurable between two points of the cylindrical surface of a cylindrical piece of steel of the C43 type when the thickness S of a surface layer P varies.

  between 0 and 4.5 mm; the values of the thickness are also expri-

  in relative values S / R (where R is the radius of the part) included

  between 0.9% and 25%. Curve A was produced using the expressions

  previously obtained mathematical assumptions, assuming that the current passing through the room is 10 amps. The difference

  potential "V (150 '- 2700) which is carried along the ordinate.

  of Figure 5 was calculated by determining the calculated potential difference for two points whose angular coordinates * are 150 and 270, respectively. The small crosses in the immediate vicinity of curve A of FIG. 5 indicate the values corresponding to "V (150'-270 ')" measured experimentally on cylinders taken as samples of steel C43 in which a current flows 10 amps. The close agreement between values

  theoretical and experimental values can be clearly seen.

  A second curve B is shown in FIG. 5, and this curve represents the theoretical values of the voltage "V (270'-330 ')" calculated for two points of angular coordinates Rode 270 and of 330 respectively, the same values of S. and S / R and the same samples being used as for curve A. The small crosses that are near curve B indicate

  the values of "V (270 '- 330) are measured experimentally.

  calf, the agreement between theory and measurement is remarkably good.

  In fact, a careful examination of the curves shown in Figure 5 shows that the correlation between the theoretical values and the actual values of the potential difference deviates for the parts of the curves A and B o S / R> 20%. However, it has been verified that, if the expressions given above are used to evaluate the ratio of V (150-2700) / V (2700-330) as a function of S (or S / R), then

  the agreement between theoretical and experimental results is excellent

  slow for S / R) 20%; the accuracy of this agreement can be seen in FIG. 6. On this basis, the described process for measuring the surface layers for cylindrical parts can be modified so that the method comprises the following operations: a) measuring the electrical potential between three distinct points X, Y, Z (instead of two) on the cylindrical surface of the part or, rather, measure the potential difference for example between X and Y and between Y and Z; b) calculating the ratio between said potential differences (for example Vx / VZ ratio; and c) comparing this ratio with a series of reference values or a continuous set of values (tables, graphs, etc.) obtained by means of theoretical mathematical expressions given above. The mathematical expression of the V / V ratio can x-Y Y-Z

  be easily deduced from the expressions already given.

  The determination of the reference values quoted

  operation c) above can of course be carried out empirically

  rather than theoretically, operations (a) and (b) remaining the same. The empirical determination of a series of reference values is carried out by measurements on a series of pieces chosen as samples which each have the same dimensions and the same composition as those of the part under test and which each have a superficial layer of a thickness

  different from those of other rooms.

  What has just been indicated above shows that the method and the measuring apparatus of the invention make it possible to solve in a simple and economical way the problem posed by rapid measurement.

  the thickness of the surface layer of metal parts

picks in large quantities.

  Of course, those skilled in the art will be able to imagine

  from the processes and devices whose description comes

  given merely illustrative and not illustrative,

  various variants and modifications that are not outside the scope of the

vention.

X E V E N-D I C AT IO N S

  1. Method for measuring the thickness of a superficial layer

  of a metal part, this layer having physical characteristics different from those of the rest of the part, the method being characterized in that it comprises the following operations - passing a constant electric current of value

  known across the room between two regions of the surface of that

  in order to establish a current distribution within

  the room and, consequently, a superficial distribution of the

  electrical density dependent on the thickness of said superimposed layer

  10. ficial; measuring the electric potential difference between at least a couple of points of the surface of the part; - Comparing the measured value of said potential difference with a series of reference values

  each corresponding to a known thickness for said superimposed layer

ficial; and

  - deduce from this comparison the indication of thick-.

  the surface layer of the room.

  2. Method according to claim 1, characterized in that the comparison operation is carried out by comparing the measured value of the potential difference with a set of potential difference values measured in the same manner over a series of times. test samples each having the same dimensions and the same material composition as said part, said blanks

  having surface layers of different known thicknesses.

  3. Method according to claim 1, wherein the metal part has a cylindrical shape, the method being characterized in that the measuring operation is carried out by measuring the value of the potential difference between at least one pair of points. located on the cylindrical surface of the workpiece at a circumference defined by the intersection of a plane perpendicular to the longitudinal axis

  of the workpiece with said cylindrical surface, the operation of comparison

  reason involving the comparison of the difference value of potential

  measured with a series of reference values deduced from a mathematical expression expressing the potential difference

2'45.8876

  measurable between two points of said circumference of the workpiece.

  function of the thickness of the surface layer.

  4. Method according to claim 3, characterized in that said series of reference values form a continuum of values represented by a curve linking the value of the potential difference.

  measured at the thickness of the surface layer.

  5. Method according to claim 3, characterized in that

  the measuring operation involves measuring the difference in potential

  between two pairs of points, the two measured potential difference values being then divided by one another to form a characteristic ratio which is compared, in said comparison operation, with reference ratios obtained by

  the division of reference values of potential difference cor-

respondantes.

  6. Apparatus for measuring the thickness of a superficial layer

  metal layer, this layer having physical characteristics different from those of the rest of the room, the apparatus being characterized in that it comprises: - a generator (3) of direct current;

  two electrodes (2) connected to the generator

  in use, in contact with two regions of the surface (1c, 11c) of the part (1, 11) under test so as to pass a constant electric current of known value through the piece and, thus, establish a distribution

  current inside the room and, consequently, a distribution

  superficial solution of electrical potential which will take

  the superficial layer (la, la); an instrument (5) for measuring potential; and a pair of measuring electrodes (4) connected to the measuring instrument and intended to be placed, in use, in contact with two points of the surface (lc, llc) of the piece

  tested to measure the difference in electrical potential between

  between said two points on the surface of the workpiece.

  7. Apparatus according to claim 6, characterized in that it further comprises a support means (6) made of an electrically insulating material, the feed electrodes (2) and the

  measuring electrodes (4) being carried by this support means.

  Apparatus according to claim 6 or 7, characterized in -

  what the voltage measuring instrument is a micro-voltmeter.