11
Int. J. Math. ToolsManufact. Vol. 30, No. 4. pp. 549-559. 1990. (1890--6955/9053.00 ÷ .00 Printed in Great Britain Pergamon Press pie HIGH-CAPACITY COMPACT THREE-COMPONENT CUTTING FORCE DYNAMOMETER S. E. OeABY* and D. R. HAYNURSTt (Received 14 November 1989; in final form 16 February 1990) Abstract--The design is reported of a compact three-component tool-shank dynamometer. It is based on a design in which the load bearing section has its stiffness reduced by two holes symmetrically positioned about the centre-line, and connected by a narrow slit. The holes are positioned to enable strain gauges to record the highest local strains; and, hence to maximize sensitivity and to minimize cross-sensitivity. Experimental analysis has identified the critical location, relative to the hole, at which the maximum surface strain is attained. Improvement of the dynamometer accuracy has been achieved by accurate location of the point of force application to eliminate the cross-sensitivity between the different components. Further improvement of the dynamometer sensitivity has been achieved by appropriate design of the electrical circuits. Force signals have been captured and processed using a micro-computer through specially designed strain-gauge amplifiers and analogue-to-digital converter ADC. A series of tests have been carried out to determine the dynamometer static and dynamic characteristics. Mathematical models have been developed to characterize and formulate the dynamometer performance. INTRODUCTION THE NEED is expressed for new types of transducers to measure cutting force during machining operations. The dynamometer should be compact and simple enough to be safely accommodated close to the cutter tip without interruption of the production flow, and with a minimal modifications of the structure of the machine tool and its relevant elements. The need for measurement of all cutting force components arises from many factors, but probably the most important is the need for correlation with the progress of tool wear [1]. If this can be achieved then it is possible to achieve in-process tool wear monitoring based on force variation measured during machining. In turning operations it is convenient to consider the force system as shown in Fig. 1. These force components are often measured using either an octagonal-ring dynamometer type [2,3], or a tool shank type [4-8]. In addition to its large size the conventional octagonal-ring prototype is, in most cases, capable of measuring up two force components. The tool-shank type is always characterized by its inaccuracy and insensitivity in measuring either one or two components. In this study, a new type of dynamometer is investigated to overcome the aforemen- tioned drawbacks. MECHANICAL DESIGN CONSIDERATIONS As shown in Fig. 2, the basic elements of the dynamometer are the base and the body. The dynamometer base utilizes a block of cast iron to replace the original tool- post of a Colechester Mascot 1600 centre-lathe. Its configuration could be changed to suit the possibility of using the dynamometer for different lathes~ shapers or planners. While its lower part is clamped to the lathe cross-slide, the upper part is ground to ensure firm and accurate clamping with the dynamometer body. The dynamometer body, Fig. 3(a), consists of three zones: the front zone (A) which is the tool-insert holder; the middle zone (B) which is the transducer house; and, the *Department of Production Engineering, Suez-Canal University, Port-Said, Egypt. tDepartment of Mechanical and Process Engineering, University of Sheffield, Mappin Street, Sheffield $1 3JD, England. ~M .~o:4-E 549

High-capacity compact three-component cutting force dynamometer

Embed Size (px)

Citation preview

Int. J. Math. Tools Manufact. Vol. 30, No. 4. pp. 549-559. 1990. (1890--6955/9053.00 ÷ .00 Printed in Great Britain Pergamon Press pie

H I G H - C A P A C I T Y C O M P A C T T H R E E - C O M P O N E N T C U T T I N G

F O R C E D Y N A M O M E T E R

S. E. OeABY* and D. R. HAYNURSTt

(Received 14 November 1989; in final form 16 February 1990)

Abstract--The design is reported of a compact three-component tool-shank dynamometer. It is based on a design in which the load bearing section has its stiffness reduced by two holes symmetrically positioned about the centre-line, and connected by a narrow slit. The holes are positioned to enable strain gauges to record the highest local strains; and, hence to maximize sensitivity and to minimize cross-sensitivity. Experimental analysis has identified the critical location, relative to the hole, at which the maximum surface strain is attained. Improvement of the dynamometer accuracy has been achieved by accurate location of the point of force application to eliminate the cross-sensitivity between the different components. Further improvement of the dynamometer sensitivity has been achieved by appropriate design of the electrical circuits. Force signals have been captured and processed using a micro-computer through specially designed strain-gauge amplifiers and analogue-to-digital converter ADC. A series of tests have been carried out to determine the dynamometer static and dynamic characteristics. Mathematical models have been developed to characterize and formulate the dynamometer performance.

INTRODUCTION

THE NEED is expressed for new types of transducers to measure cutting force during machining operations. The dynamometer should be compact and simple enough to be safely accommodated close to the cutter tip without interruption of the production flow, and with a minimal modifications of the structure of the machine tool and its relevant elements.

The need for measurement of all cutting force components arises from many factors, but probably the most important is the need for correlation with the progress of tool wear [1]. If this can be achieved then it is possible to achieve in-process tool wear monitoring based on force variation measured during machining.

In turning operations it is convenient to consider the force system as shown in Fig. 1. These force components are often measured using either an octagonal-ring dynamometer type [2,3], or a tool shank type [4-8]. In addition to its large size the conventional octagonal-ring prototype is, in most cases, capable of measuring up two force components. The tool-shank type is always characterized by its inaccuracy and insensitivity in measuring either one or two components.

In this study, a new type of dynamometer is investigated to overcome the aforemen- tioned drawbacks.

MECHANICAL DESIGN CONSIDERATIONS

As shown in Fig. 2, the basic elements of the dynamometer are the base and the body. The dynamometer base utilizes a block of cast iron to replace the original tool- post of a Colechester Mascot 1600 centre-lathe. Its configuration could be changed to suit the possibility of using the dynamometer for different lathes~ shapers or planners. While its lower part is clamped to the lathe cross-slide, the upper part is ground to ensure firm and accurate clamping with the dynamometer body.

The dynamometer body, Fig. 3(a), consists of three zones: the front zone (A) which is the tool-insert holder; the middle zone (B) which is the transducer house; and, the

*Department of Production Engineering, Suez-Canal University, Port-Said, Egypt. tDepartment of Mechanical and Process Engineering, University of Sheffield, Mappin Street, Sheffield $1 3JD, England.

~M .~o:4-E 549

550 S . E . ORASY and D. R. HAYHURST

HACHINE TOOL CO-ORDiNATE 5FSTE~

N

z / / I_// l '°°' L /

FEED FIG. 1. Cutting force components in turning operations.

C l n ~ - ~ r - ~ e

Z - c i r cu i t

~lon - Cent ral. c l re~ar-ho~e

FtG. 2. A view of the basic elements of the dynamometer.

back area (C) which is used to clamp the dynamometer body to the base. The front part, tool-insert holder, is designed to accommodate the standard SPUN 12 03 12 indexable cutting tool insert to take the geometry as of the Sandvik standard toolholder CSTPR 20 20 K12 (Fig. 3b). As indicated in Fig. 4, the geometry of the tool-insert holder has been adjusted so that the true point of application (O) of the cutting force passes through the centroid of the section of the dynamometer body. The tool-tip is

Cutting Force Dynamometer 551

(a)

Ik~i.t Thtokn~e For Fy

I..

I- ~ i : l ~ L Hol.e

ltlil.L lhl©lmiill FIN'. Fx

(b)

i l i l , ITl

I III

'!I', . _I_ I L

, , , i l ] I I I I I I I I I I I I I I i 1 !

C

0

0

0

0

0

FIG. 3. (a) The dynamometer body and the sensing elements. (b) Tool angles for CSTPTR T-MAX Sandvik standard toolholder.

h

Tool "rip

T P u e ~ X ,~1

i

I

I

Y -

!4, I .J

~ ,~=~e ram. B=42.8 mm.

FIG. 4. Determination of the true application point.

552 S . E . ORABY and D. R. HAYHURST

not the true point of application of the force since the cutting process is executed along the cutting edge rather than only on the tool-tip. Similarly, the height of the point of application of the force is set so that when the insert is assembled with its shim, chip- breaker, and the mechanical clamp, the line of action of the force will pass through the centroid of the section of the dynamometer body. This eliminates the cross-sensitivity between the various force components through elimination of the sources of the moment components.

DYNAMOMETER SENSING ELEMENTS

The transducer house of the dynamometer contains the sensing elements, as shown in part (B) of Fig. 3(a). This consists of two zones: the first acts as sensing elements for each of X and Y force components (T1 and T2), and the second, which is shoulder shaped and situated at the back of the dynamometer body, acts as sensing elements for the Z force component (73). The circular holes shown at T1, /2 and 73 are fitted with electrical resistance strain gauges to provide an electrical output proportional to the excitation force.

The use of a circular-hole provides a fresh approach to the construction of the sensing elements since it was found to be the best way to achieve a reduction in the dynamometer size while maintaining the other requirements of sensitivity and rigidity. Tani et al. [9] have developed a low capacity (100 N) small sized square-hole, parallel-beam dynamometer; they used the finite element method FEM to obtain information about its characteristics and performance. The problems with their prototype are: its very small size; its limited capacity; and difficult to manufacture. However, during the investigation of the effect of the corner radius of the square hole on the output level, they found that by further increasing the radius so that a square-hole became a circular one, the dynamometer rigidity and accuracy were significantly increased. However, for the dynamometer to be sensitive enough, the diameter of the hole should be as large as possible and/or the wall thickness should be as low as possible. These affect the dynamometer stiffness in terms of increasing its overhang and/or decreasing its load bearing cross-sectional area. The problem becomes even worse if more than one circular- hole is required in other co-ordinate directions. Therefore, an alternative technique of using non-central circular-holes connected by a narrow slit has been introduced in this study. Figure 5 shows the difference between the circular-hole (dl) and the non-central circular holes designs proposed in this study. The conventional way to improve the transducer sensitivity is by increasing the hole diameter from (dl) to (d2) and conse- quently, reducing the wall thickness from (tl) to (t). As shown in the figure, the same thickness (t), is achieved for the circular holes system (d2) and for the non-central hole system. If the overall length of the beam element remains constant, then the stiffnesses of the two systems are comparable [9]. The stiffness reduction due to the presence of

L7

T - B O

1

/ /

/

1 /

t

FIG. 5. Central and non-central circular-hole structure.

Cutting Force Dynamometer 553

the holes may be judged with reference to the standard toolholder cross-section. The dynamometer stiffness in the X direction for both the central hole (d2) and the non- central hole design is 10068 N/mm; this compares with a value of 34505 N/mm deter- mined for the standard toolholder cross-section without holes, and having the same overhang. However, the advantage of the non-central circular hole technique is that the overall length of the beam element can be significantly decreased, and by reducing the wall thickness t the same sensitivity can be achieved. The principal advantage being the achievement of a better dynamical characteristic. However, while this aspect of non-central circular-hole technique is suitable for each of the X and the Y directions, a central circular-hole type is found to be most appropriate for component in the Z direction. The preliminary dynamometer design has been based on the detailed finite element analysis performed by Tani et al. [9] for similar geometries; and, the detailed design has been carried out by prototype development.

A prototype dynamometer was designed and manufactured in aluminium to investi- gate the best values of the hole diameter d and the wall thickness t, or the ratio [d/(d+2t)], and to determine the gauge locations where the highest output is obtained. This resulted in choosing the best configuration as shown in Fig. 6.

DYNAMIC CALIBRATION OF DYNAMOMETER

This study was carried out to determine the fundamental natural frequencies and the dynamic characteristics of the dynamometer so as to enable the determination of the range of its working frequencies. The natural frequency Of the dynamometer usually determines its general dynamic stiffness. In order that the recorded force is not influ- enced by the dynamic response of the dynamometer, its natural frequency must be large compared to the frequency of the exciting vibration.

/

Y-D i rec t i o ~ d~ C2t+d) =0.65

~ {2t+d~ =0.65 Z-DiPect i ~ ~

FIG. 6. The relative gauge-hole positions.

554 S.E. ORABY and D. R. HAYHURST

The natural frequencies of the dynamometer were determined by setting the dyna- mometer into vibration using appropriate hammer blows, and by measuring its response using accelerometers and oscilloscope. For each direction, the number of oscillations per unit time was counted to represent the damped natural frequency ~,a, or the time taken until the structure reached a stand-still state. For the X, Y and Z directions, the values of such damped natural frequencies were found to be 1648, 850 and 3046 Hz, respectively.

The dynamometer damping may be estimated by observing the rate of decay of oscillations of the vibration signature. For viscously damped harmonic motion, the successive amplitudes of motion have a logarithmic relationship with one-another expressed by the term "logarithmic decrement", which is defined as the natural logar- ithm of the ratio of any two successive amplitudes. For more accurate estimation, however, decrement 8 may be computed over N cycles from the relationship:

1 I In L (1)

where c is the damping ratio. According to equation (1), the damping ratio c, for X, Y and Z directions were found to be 0.00737, 0.00996, and 0.00668, respectively.

The damping is characteristically low, as would be expected for this structure; and, the lowest natural frequency, for the Y direction, is significantly in excess of the maximum operating frequencies. Hence the design requirements are met by this design.

ELECTRICAL DESIGN OF DYNAMOMETER

Two requirements were specified for the design of the electrical circuits of the dynamometer; namely the accurate location of gauges to receive the true maximum output; and, the proper selection of sensitive measuring instruments. The latter require- ment is essential since the output from strain-gauge is very low due to the high stiffness requirement of the dynamometer.

As shown by Fig. 7(a), the hole wall is deformed in such a way .that a maximum positive strain exists at one end of the hole boundary (point A) while a maximum negative one exists at the other end (point B). This operation is reversed at the opposite hole so that, if gauges arrangement is set as shown in Fig. 7(b), a full four active arms bridge arrangement can be achieved, Fig. 7(c); and, the bridge output becomes eight times greater than that achieved using a single arm bridge. Alongside the significant improvement in the sensitivity achieved by this arrangement, the bridge is fully compen- sated for any change in resistance due to temperature rise. Moreover, the use of two gauges per arm allows the duplication of exciting voltage without overheating the gauges as is explained shortly.

While this circuit design is suitable for the sensing elements for each of X and Y directions, the case is slightly different for Z direction. As shown in Fig. 8, the sensing elements of the Z component are affected by two force components, Fx and Fz. While the Fz produces a direct effect of simple bending sb, the Fx produces an indirect effect of double bending db. The total effect of both phenomena on the sensing elements of Z direction are shown in Fig. 8(c). Gauges positions are chosen, Fig. 8(c) and (d), so that the effect of the tension double bending tension tdb in gauge no. 2 will cancel the effect of the compression double bending cdb in gauge no. 3, and the same will occur for gauges nos 1 and 4. This results in a four active arms bridge by which the only effect is detected is the direct force Fz, Fig. 8(d).

The strain-gauges selected were self-temperature-compensation STC type [EA-06- 045 AL-350] recommended for steel specimens, the gauges has the following character- istics: gauge factor (K) of 2.01---1.0%; effective gauge length of 1.14 mm; gauge resistance of 350-0.15%1"1; and, transverse sensitivity of +0.6%.

Cutting Force Dynamometer 555

Cb)

B

FIG. 7. Circuit design for each of X and Y directions.

The limit of maximum excitation voltage was carefully selected to achieve low energy dissipation and hence a stable zero setting over a long time. The voltage applied to a bridge creates a power loss in each arm, all of which must be dissipated in a form of heat. This causes the sensing grid to operate at a higher temperature than the substrate to which it is bonded. When the temperature is excessive, gauge performance is affected in terms of loss temperature-compensation, hysteresis, and creep effects. According to [10], the range of the excitation voltage may be obtained from the relation:

Vi. = 2 VR P' g Ag (volts), (2)

in which R is the gauge resistance, P' g is the power density in the gauge grid, and Ag is the active grid area (active gauge length x grid width). When each arm consists of two gauges in series, this relation becomes:

Vi. = 8\/R P' g A , (volts). (3)

According to [10], for a thick steel mounting surface working under dynamic conditions, a grid power density P' g is achieved between 7.8 and 31 kW/m 2. Substitution of these values, along with the gauge area and its resistance value R, into equation (3), the recommended excitation voltage is found to be between 5.47 and 10.62 volts. For convenience, an excitation voltage of 10 volts was employed.

The output from the strain gauge was amplified by means of a specially designed strain-gauge amplifier. A BBC microcomputer was used to capture and process the force signals through a specially designed analogue-to-digital ADC converter. The requirements for the ADC were to include three separate circuits to receive voltage range of ±5 volts with sampling rate of 1666 samples/s.

DYNAMOMETER STATIC CALIBRATION

The static calibration of the dynamometer usually determines the relation between the input, in terms of applied load, and the output, in terms of bridge output. To ensure similar conditions to those that would be found in a real machining situation,

556 S . E . ORABY and D. R. HAYHURST

F× IFz / ~"/-J~sb \ ~ - " T' ~"

I

I

\

) . = I A i

(b)

I

I I I I T

I

I I

!

SECTION AT A A

/ • b'o A o~,

x~y x,~ x

FIG. 8. Mechanical and electrical circuit design for Z direction.

the calibration procedures were carried out while the dynamometer was mounted on the lathe. A hydraulic jack was used to induce the load, in forms of a uni-directional displacement from the jack piston. This load was transferred to the dynamometer body through a pre-calibrated load cell and a carrier bar. The load cell was calibrated to read the output in newtons. The corresponding strain levels were recorded by parallel connection of the output to a Vishay strain-indicator. To ensure that the load was accurately applied to the true application point, a flat dummy tool-insert was machined and used in the calibration procedures. This ensured an accurate location where the applied load is perpendicular to the intended surface. It also avoids any slipping which may occur due to the geometry of the true insert. A hardened steel bali was inserted between the load carrier bar and the dummy insert to ensure an accurate location. The

Cutting Force Dynamometer 557

calibration procedures were carried out for each of the three co-ordinate directions in turn. For each direction, the load was gradually increased in 100 N steps, and the reading from the corresponding channel, along with the readings from the other two inactive channels, were simultaneously recorded. On reaching the full load of 4000 N, the load was gradually released in 200 N steps, and the equivalent readings were recorded. The calibration curves for each direction together with cross-sensitivity curves with the other two components are shown in Fig. 9. Excellent linearity, sensitivity, and accuracy is noticed in all directions, and no hysteresis was detected.

MATHEMATICAL MODELLING OF DYNAMOMETER OUTPUT

The goal in any multi-channel transducer is that the output of each channel should be affected only by the corresponding excitation, and the cross-sensitivity between the three directions should be nil. In dynamometry and cutting force transducers this goal has never been achieved even when the most sophisticated techniques have been used. In this work efforts have been directed towards the minimization of the undesired effect of so-called interaction, or cross-sensitivity.

4 • Vxx ~_mv ~v'O0

1200 v Vyx _ , , ~ r " 3 a Vzx ~ . C ~ ~ 1000

2 _ ~ / " 800 . . ~ - L ' " 600

' 11 i J i l l 0 L

0 500 1000 1500 2000 2500 3000 3500 4000

0

> 4

^ 3 II II II II , 2 il II ;J

II

~ 0 Q

O

• Vxy _,~~00

, Vyy ,,,...wv ','~'~._..._ 1000 m Vzy ~ 800 m Vzy

" " 600 . ~ (b) Y-Ot~o~Ion 400

L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2oo

500 1000 1500 2000 2500 3000 3500 4000

4 ~ o Vxz _ j 0 0

3 f • v×= ~ . e00

; _ , ~ ' ~ J ? - a , ~ o , , o ~ 4o0

o . . . . . . :: . . . .

[ . . . . T . . . . i . . . . i . . . . i . . . . i . . . . i . . . . i " ' ~ i

0 500 I000 1500 2000 2500 3000 3500 4000

Losd = => [ N ] FIG. 9. Calibration curves and cross-sensitivity of the dynamometer.

io e-

M L

o 1. u

/% tl g tl H I] H tl U I I I I

n

558 S . E . OeAeV and D. R. HAYHURST

In this section, the possible elimination of the effect of the cross-sensitivity among the different component is examined through mathematical modelling of the dynamometer performance. Mathematical modelling of the dynamometer output allows on-line assess- ment of the whole operation. For accurate measurement to be obtained, the degree of interaction between each of the three channels has to be modelled. While interaction is easily detectable in the static situation when only one channel is active, it is impossible to know what is happening in the real application where all channels are loaded. The only way to distinguish the real output, of a certain channel, from the measured signal is through the analytical pre-determination of the whole system performance, or mathematical modelling of the system characteristics.

The idea is to relate a certain force component not only to its channel but to the simultaneous output of all three channels. This takes the general form:

F = bl Vx + b2 Vy + b3 Vz (4)

where F is the force component (N); Vx, Vy and V~ are the output voltage for X, Y and Z channels, respectively; and bs are the output contribution from each channel. Generally, the entire system can be expressed by the arrangement:

= [a] [v] (5)

where F = Fi, B = bi/, V = V,., and i and j take values x, y and z. A non-linear regression procedure was used to determine the coefficients of each direction in turn using the experimental data of the static calibration procedures. Data were fed to a computer program in a form suitable for the SPSSX statistical package available on the IBM 3083 main-frame computer. This resulted in the best predicted parameters as follows:

1008.2 20.100- 45.400

B = 12.570 987.46 -6.4800 (N/volt). (6)

-48.00 16.690 1059.80

Table 1 summarizes the confidence intervals of the parameters, along with the other statistical characteristics. As shown, the models are statistically perfect. The percentage of interaction among the different directions can be computed from arrangement (6) as follows:

The lowest level of interaction is between Y component and each of X and Z ones, while the highest values are between X and Z components, and with negative effects. However, the cross-sensitivity shown in Table 2 is sufficiently low to justify being neglected; but, since the results are processed on-line using a microcomputer, the corrections have been systematically included in the processing of results using equation (5).

TABLE 1. STATISTICAL CHARACTERISTICS FOR FORCE MODELS

Fi aix Lower

Coefficients asymptotic 95% confidence interval aiy aiz

Upper Lower Upper Lower Upper Corrected

correlation factor

R 2

F, 1007 E,. 10.93 F. -51.4

1009 19.28 20.95 -46.3 -44.5 0.999 14.2 985.8 989 -8.20 -4.75 0.999

-44.6 13.3 20.0 1056 1063 0.999

Cutting Force Dynamometer

TABLE 2. DYNAMOMETER CROSS-SENSITIVITY BETWEEN DIFFERENT COMPONENTS

X Y Z

X - - 1.99 4.5 Y 1.27 - - 0.66 Z 4.5 1.6 - -

559

CONCLUSIONS

An efficient, high capacity, wide frequency response, three-component cutting force dynamometer has been designed and manufactured to be accommodated on the original lathe tool-post block. A new technique of using a non-central circular-hole to form the sensing elements has been shown to increase the device sensitivity, accuracy and stability. Gauge locations have been determined to achieve maximum output of the structure under deformation. Cross-sensitivity between the components has been reduced to its lowest level by accurate location of the point of cutting force application, and by the proper design of the electrical circuits. The dynamometer static calibration test has indicated a very high standard of system linearity. Mathematical models have been developed to characterize and formulate the dynamometer performance; and to deal with the cross-sensitivity so as to give the true output of cutting force values.

REFERENCES

[1] S. E. OP~BY, Mathematical modelling and in-process monitoring techniques for cutting tools, Ph.D. Thesis, The University of Sheffield (1989).

[2] T. C. Hs0 and C. Y. C. Y. CHAOI, Measurement and representation of cutting force due to oblique machining, Int. J. Mach. Tool Des. Res. 10, 40 (1970).

[3] Y. ZHE-JUN, C. LI-JUN and Z. PAN, A ne,w type of three-component dynamometer with high stiffness and high natural frequency, Proc. 26th Int. M.T.D.R. Conf., p. 313 (1986).

[4] W. R. BECKER and E. J. KRABACHER, New techniques in metal cutting research, Trans. ASME, p. 1479 (1958).

[5] R. LEVI, Multicomponent calibration of machine tool dynamometer, J. Engng Ind., p. 1067 (1972). [6] R. A. HALLAld and R. S. ALLSOPF, The design, development and testing of a prototype boring

dynamometer, Int. J. Mach. Tool Des. Res. 2, 241 (1962). [7] P. Y. SUN, Y. K. CMANG, T. C. WANe and P. T. LIU, A simple and practical piezo-eleetric shank type

three-component dynamometer, Int. J. Mach. Tool Des. Res. 22, 111 (1982). [8] G. F. MICHELErn, V. TURKOVlCH and S. RossL~rro, Int. J. Mach. Tool Des. Res. 10, 305 (1970). [9] Y. TANi, Y. HATAMURA and T. NAOOA, Development of small three-component dynamometer for cutting

force measurement, Bull. Jap. Soc. Mech. Engrs 26, 650 (1983). [10] Selection and optimizing strain-gauge excitation voltage, WSM Technical Note TN 502 (June 1882).