Smith G.T. Cutting Tool Technology: Industrial Handbook

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costs can be calculated, for a simple turning operation:

the method can be modied for machining centres

and for most other machining operations.

As can be seen from Table 12, the cutting s[peed

has a major impact on the value of ‘CT’ , because an

increase in cutting speed normally results in faster

tool wear rates, with the tool charge per component

increasing as a result. Tool costs today, now account

for only a small proportion of the total costs of pro-

duction, owing to the fact that the latest tooling can

operate at higher feeds and speeds than their earlier

counterparts. When the tool costs actually rise – due

to greater wear rates as a result of increased cutting

speeds, it naturally follows that associated tool perfor-

mance will also increase.

For any machining operation there exists an ‘eco-

nomical tool-life’ (T

), which can be calculated from

the following formula:

= (



− )(

+ t

)

Economical tool life

Where:

= Economical tool life (minutes),

α = Slope of the V-T curve (i.e. measured from

graph),

= Cutting tool cost per edge (i.e. obtained as de-

scribed above),

= Machine tool, labour, and related overhead costs

– charged per minute,

= Tool-changing time per minute for operation in

question*.

*is tool-changing time will vary depending upon

whether the chosen cutters are of the ‘conventional‘, or

‘modular quick-change’ tooling varieties.

In Fig. 177a, the tool-life at ‘maximum production rate’

) is shown, which is a variation of the calculation

given above for ‘economical tool life’ (T

), where the

variables are identical, but in the former case a higher

cutting speed is employed, resulting in shorter tool-

life. Even though the lowest possible machining cost

per component can be calculated with the most eco-

nomical cutting speed, it is oen desirable to utilise

a faster machining strategy. is increased speed, will

involve supplementary costs, although it can only be

warranted if higher production output results. If the

number of components per hour (P

) is plotted (Fig.

177d) in relation to the cutting speed (V

), a repre-

sentative curve will result. is curve is redrawn and

shown in Fig. 177e, this now being a ‘composite’ of the

sum of the: machine/labour/overhead costs (Cm); with

tooling cost (CT). e zenith of this curve (Fig. 177e),

represents the highest production rate (P

max). While

the cutting speed (V

) is associated with the peak of

the curve, which is greater than the most economical

rate (V

), with the values between these two points,

representing the ‘high-eciency range’ for a particular

operation.

In Fig. 177e, the additional vertical axis depicted,

represents the production rate (P

) – this being the

number of components machined per hour, it can be

calculated in the following manner:

= 60 (1 – t

T)/tp

Where:

= Tool-changing time per minute for operation,

T = Tool life,

tp = Total time per component (i.e. including: ma-

chining, handling and down-tome).

e relationships mentioned above represent theoreti-

cal associations. So, some caution should be applied

when using these factors and they need to be treated

as a ‘starting-point’ only for both the values and trends

represented here. Moreover, they are subject to vari-

ability, due to the complex relationships and interac-

tions found during machining operations.

7.7.3 Return on the Investment (ROI)

As an alternative approach to the above mentioned

cutting tool costs and production output interactions,

is to relate any productivity improvements to both the

actual machinery cost and the total invested capital

– to achieve this level of manufacturing yield. In the

previously described machinability tests, the work

seldom considers rates of production, or relates the

ndings to actual increases in the total economics of

production.

A signicant scal argument is that any gures

obtained from such testing, should highlight the ‘im-

proved’ ROI, which can be obtained by any manu-

facturing company utilising the latest tooling, in

conjunction with the application of ecient cutting

conditions.

e following simple formula can be utilised to cal-

culate the ROI for a particular: production operation;

machine tool; machining cell; etc.:

342 Chapter 7

ROI = (T

)(M

)/(MT

)

Where:

= Time savings per year (i.e. in hours),

= Machine tool charge (per hour),

= Machine tool investment.

In this section, only a supercial treatment has been

given to the economic argument relating associated

capital equipment costs and their overheads, to out-

put productivity. More intricate and sophisticated eco-

nomic models can be obtained in the literature.

7.8 Cutting Force

Dynamometry

Introduction

During machining operations, plastic deformation,

friction between the tool and workpiece, together with

micro-fractures and -ssures occur. ese mechanical

phenomena produce measurable cutting and forming

forces with very high-frequency acoustic emissions

(AE). e application of AE in association with other

Figure 177. The correlation of typical manufacturing cost factors: machining costs, together with

their resultant productivity. [Courtesy of Sandvik Coromant]

Machinability and Surface Integrity 343

sensors, such as: force transducers, accelerometers can

be coupled to neural networks to give a psuedo-form

of articial intelligence (AI) – more will said relating to

cutting tool monitoring and analysis in a succeeding

chapter. Many of the early attempts at cutting force

monitoring were by using several strategically-placed

resistance-type of strain-gauged mechanical elements.

ese strain-elements were designed so that at a par-

ticlur portion of their geometry they could either

minutely: buckle, bulge, or twist – well within their

elastic limit. At the positions of greatest sensitivity

on these mechanical elements, strain-gauges were se-

curely placed and wired into a ‘Wheatstone bridge re-

stance circuit’

, which as the gauges distorted they

changed their micro-resistance, which could then be

fed through suitable instrumentation. ese strain-

gauged elements could be calibrated against ‘known’

mechanical devices (e.g. ‘proving-rings’

, or similar),

71 ‘Wheatstone bridge resistance circuits’ – invented by Sir

Charles Wheatstone: circa 19

Century, for accurately

measuring resistance in an electrical circuit. Simply, a ‘bridge

circuit’ consists of: four resistances; a galvanometer; with a d.c.

power supply. In essence, in these highly sensitive resistance

‘bridges’ they are used to detect minute changes in strain gauge

resistance. A typical ‘full-bridge’ consists of the four resistors:

‘R

’; ‘R

’; suitably coupled to the galvanometer and

d.c. supply. Typically, the most simple strain-gauged circuit

would consist of: a resistance ‘R

’ which here for argument,

is the gauge used for strain measurement. Resistance ‘R

’ is

a second strain gauge which here, could remain at constant

resistance. e other ‘half of the bridge’ , resistances ‘R

’ and

‘R

’ are variable resistors which by adjustment, are utilised to

‘balance’ and ‘rebalance’ the bridge (i.e employed to reduce

the current across the galvanometer arm to zero). erefore,

when the ‘bridge’ is ‘balanced’ , the ratio of the gauges and the

variable resistances are equal, thus:

= R

∴ R

= R

× R

(Collet and Hope et al., 1974)

72 ‘Proving-rings’ ,

are laboratory calibrated and certicated me-

chanical device, normally consisting of: a steel ring; dial gauge

and loading pads. It is usually employed in the calibration of

force-measuring systems – only within its maximum permis-

sible load. Such ‘proving-rings’ can be manufactured for either

high sensitivity – for strain-gauge applications, or for more

robustness – when calibrating tensile testing machines. In

practice, the steel ring if compressed, allows the diameter to

minutely contract in direct proportion to the applied force,

with its deection accurately measured by a dial gauge located

across the centre of the internal portion of the proving-ring’s

diameter. Changes in the dial gauge readings, can be converted

to force measurement by means of a suitable calibration graph,

or more simply, by multiplying the gradient of the graph – as

the graph produced has a straight-line relationship. (Ramsey

et al., 1981)

allowing the resolved cutting forces during subsequent

machining to be data-logged, for suitable in-depth

analysis by the user. Strain gauge dynamometers based

upon the Shaw and Cook (1954) model, normally re-

quire several design criteria to be addressed, if they are

to perform satisfactorily, these factors are:

. at the dynamometer should have a sensitivity of

1% of its mean designed force,

. Such a dynamometer requires a natural frequency

of at least 4 times the ‘forcing frequency’ ,

3. e strain-gauged circuit elements should produce

the minimum of cross-coupling (i.e. ‘cross-talk’ is

<2%) – when calibrated.

NB 

is latter point, can be assessed by a range

of calibrated ‘proving rings’ , or ‘torque arms’ – if

required to measure torque eects in the circuit,

thegraphical calibration should indicate: both plot-

ted linearity and also be coupled to minimal hys-

teresis

Today, most multi-axes cutting force dynamometers

utilise sensing elements, based upon the piezoelectric

eect

and these ‘active sensors’ , will now be more

fully discussed.

Piezoelectric Dynamometers

ese high-rigidity force transducers provide an elec-

trical output signal under the eect of direct element

deformation. Hence, element deformation can be kept

several degrees of magnitude smaller than that of the

‘passive systems’ – such as those utilising strain-gauged

elements. With most ‘dynamic systems’ such as those

employing quatrz-based elements, their inherent de-

gree of rigidity and a broad measuring frequency

range creates smaller measurement interference and

73 ‘Hysteresis loop’ is an area bound between the loading and

unloading paths (i.e. typically found in a stress-strain curve),

indicating energy dissipation, or damping.

74 ‘Piezoelectric eect’ ,

was discovered by Pierre and Jacques

Curie in 1880. A piezoelectric material (e.g. quartz, or Ro-

chelle salt) is a special kind of insulator which, if compressed

along one of its axis, acquires an electrostatic charge on the

material’s opposite faces. Hence, when such material is ac-

curately and precisely cut to the desired shape, it acts as a

piezoelectric transducer, hence its input is force and its output

is charge. ese piezoelectric elements, can be suitably posi-

tioned and arranged and thus, used in dynamometers for dy-

namic cutting force measurement.

344 Chapter 7

as a result, oer extremely fast process response, in

comparison to those of the of the ‘non-rigid type’

– having long measurement paths (i.e. found in con-

ventional strain-gauged elements). Unlike ‘passive sys-

tems’ utilising strain-gauges, it is virtually impossible

to perform static measurements by using piezoelectric

transducers, even though an electric charge delivered

under static load can be registered, it cannot be stored

for any realistic time period

e design of most of today’s multi-component

dynamometers use piezoelectric elements which are

quintessentially comprised of a stack of quartz discs,

or plates with accompanying electrodes being installed

nto a stainless steel housing (Fig. 178ai and aii). Every

disk, or plate has been precisely cut in a denite crys-

tal axis, with their sensing orientation coinciding with

that of the axes of the force components t

o be measured

(Fig. 178). In practice, the electrodes can collect the

‘charge’ on their respective quartz disk’s surfaces, these

being suitably ‘hard-wired’ to their appropriate and

corresponding plug connectors. As shear forces can

only be transferred by frictional contact, a certain

minimum of friction is essential between the quartz

disks, electrodes and housing. Depending upon the

shear force magnitude (i.e. measured) a more-or-less

high pre-loading of the system must be generated by

a pre-loaded bolt. is act of preloading the system is

absolutely essential and is usually undertaken when

the force transducer is initially installed into the dyna-

momoter by the manufacturer.

A typical three-component dynamometer (Fig.

178ai), consists of sensors with two shear quartz pairs

– namely for ‘F

’ and ‘F

’ , plus one pressure quartz pair

– for ‘F

’ , assembled in a suitable housing. Each quartz

pair has two identical plates stacked with a common

75 ‘Piezoelectric storage’ – for static loading, this cannot be

achieved because an insulating material would have to have

innitely high resistance, together with ampliers that are

perfectly free from any form of leakage and ‘non-operate cur-

rents’ , with an amplication factor of innity! e dri in

today’s charge ampliers is below ±0.03 pC s

–1

. In static mea-

surements performed with ‘load washers’ , this means that in

practice, the zero-shi is limited to within ±10 mN s

–1

. For

example, if a static load of 10 kN is measured for one min-

ute, then aer this time, the result of the measurement can

only be invalidated by a maximum ±0.6 N, that is by ±0.006%.

Hence, it is a simple task to piezoelectrically measure large

forces for minutes, or hours, but small forces can only be mea-

sured ‘statically’ for very short time-periods. us, piezoelec-

tric transducers are normally referred to as being: ‘quasistatic

measurement elements’.

electrode between them, oering twice the sensitivity.

is three-component dynamometer is constructed

with four of these three-component sensors mounted

in parallel between the base and top plate, being as-

sembled with a high preload. Given that the outputs

from the four sensors are in the form of an electrical

charge, they are able to be interconnected within the

dynamometer body. With this particular sensor ar-

rangement, it is possible to obtain up to eight charge

outputs from the dynamometer.

e four-component dynamometer shown in Fig.

178aii, has several shear quartz plates arranged in a cir-

cle (i.e. top circular element), with their sensitive axes

being tangential, allowing an element to be formed

responding to a moment ‘M

’. In this dynamometer,

the four-component sensor is obtained by assembling

this element (i.e. ‘M

’) in a housing, together with two

shear quartz pairs – for ‘F

’ and ‘F

’ , plus one pressure

quartz element pair for ‘F

’. So, by mounting this sen-

sor assembly under a high preload between the base

and the top plate, it results in a four-component dy-

namometer, capable of simultaneous measurement of:

‘F

’ , ‘F

’ and ‘M

’.

For both accurate and precise machinability and

data-gathering assessment, these invaluable piezoelec-

tric dynamometers oer the following advantages and

typical properties:

•

High rigidity (‘c

’ , ‘c

’: >1 kN µm

–1

, ‘c

’: >2 kN µm

–1

hence producing a high natural frequency (‘f

’: ≈3.5

kHz),

•

Wide measuring range (-5 to 10 kN),

•

Extreme linear sensitivity (‘F

’ , ‘F

’: ≈-7.5 pC N

–1

‘F

’: ≈–3.7 pC N

–1

) and virtually free from hyster-

esis (≤0.5%FSO),

•

Minimal cross-talk (≤±2%),

•

Environmentally-protected (IP67), typically sealed

against of both cutting uids and debris ingress.

NB S

uch high-quality apparatus is not cheap to

purchase, therefore it should be carefully main-

tained and looked aer, to ensure an extremely long

life and fail-safe operation.

Piezoelectric dynamometers can have their quartz

sensing elements arranged to t into platforms (Fig.

178b), for tment onto a turning machine tools turret

with the cutting tool suitably arranged for turning op-

erations. ese type of dynamometer platforms can be

located on the machine tool’s bed, with the workpiece

clamped onto the dynamometer for milling, drilling,

or grinding operations to be used for specic types of

machinability investigation. In the former case, it is

Machinability and Surface Integrity 345

Figure 178. Multi-axis non-rotating dynamometers, used for: milling, drilling and turning

experimental data-gathering and analysis. [Courtesy of Kistler Instrumente AG]

346 Chapter 7

not possible to index the turning centre’s turret, due

to the nature of the electrical couplings to the plat-

form, but this problem can be overcome by mounting

a dierent dynamometer conguration, situating the

sensing equipment within the turret – as depicted in

Fig. 179a. Here, the installation of an acoustic emission

sensor (AE)

behind the turret in combination with

a multi-component force sensor mounted in the tur-

ret’s pocket – this force equipment having previously

required the necessary of preloading which was pro-

vided by a suitable ‘preload wedge’.

In Fig. 179b, are exhibited the measuring results

from the sensor installation decribed in Fig. 179a – for

a longitudinal (external) turning operation, with the

cutting force components and the AE signals being

simultaneously recorded. e resulting graphs pro-

duced in both Figs. 179bi and bii, show the AE rms

and force signals in the case of a tool breakage. e

tool breakage can be readily seen in both signal traces.

Figs. 179biii and biv, show the AE and force sensor sig-

76 Acoustic emission sensors (AE), in metal machining applica-

tions usually capture frequencies in the range of 50 kHz to

>1 MHz in range, this being a usual aid for any form of in-

process monitoring operations. By using a combination of AE

and force monitoring, this has been shown to be a means of

condition monitoring of the cutting tool’s state – more will

be said on this topic later. In metal cutting operations AE oc-

curs due to plasto-mechanical processes of crack formation

and chip removal, in combination with surface friction. Any

form of tool wear alters the contact surfaces between the tool

and workpiece, inuencing and increasing the AE signal in-

tensity. Hence, advanced warning of potential tool breakage

sometimes results in the appearance of micro-ssures in the

tool, which cause an escalation of the AE signals – allowing

a basic form of tool and process monitoring to be achieved.

AE generation in metallic machining operations, can extend

over frequencies of several MHz, although the signal intensity

is normally very low and diminishes with increasing distance

from its source. Any form of machine vibrations and inter-

ferences from the local environment introduce signals from

a low frequency range, meaning that any form of signicant

analysis is normally only possible above 50 kHz. Machine tool

interference sources are usually the result of either electrical,

or hydraulic main and feed drives, as well as from bearing

noise, spindles and gears. ese unwanted interferences can

be suppressed by utilising suitable high-pass lters, or alterna-

tively a well-designed AE sensor(s), with inherent high-pass

frequency characteristics.

77 ‘Root mean square’ (rms), is a measure of the eective mean

current of an alternating current. Its actual rms value is de-

rived from the power dissipation by an ac current.

nals respectively, on the ‘over-turning’ of transversal

holes present in the external turning of the workpiece.

Hence, the interrupted cut can clearly be seen peri-

odically in the resultant force traces. In Fig. 179biii,

the AE rms signal shows this interference, albeit not

very well pronounced, unlike that of the force trace

produced in Fig. 179biv, where a denite noise spike

can be seen. is combination of two complementary

sensing elements and their sensor signals, allows the

reliable detection of a process fault, such as tool break-

age detection.

Until approximately the mid-1990’s, commercial

versions of cutting force monitoring equipment for the

measurement of a rotating cutting tool, or an edge was

not readily available for: drilling, reaming, tapping

and milling applications. A major advantage of these

rotating cutting force dynamometers, is that they can

be used for multi-axes contour milling applications,

or simply for an investigation of a discrete tool’s cut-

ting edge geometry and its anticipated machining per-

formance. An early version of such a rotating cutting

force dynamometer, is depicted in Fig. 180a.

In Fig. 180b, graphs have been produced showing

the cutting force and torque results respectively, pro-

duced by the rotating cutting force dynamometer. In-

terest frequently centres on the forces and moments

acting on the rotating tool. A rotating cutting force

dynamometer (Fig. 180a), allows measurement of

three orthogonal forces: ‘F

’ , ‘F

’ , together with

the moment ‘M

’. e data measured by the rotating

dynamometer occurs via miniature charge ampliers,

which are then transferred by telemetry to an appro-

priately positioned stationary antenna. e telemetry

involves a bi-directional transmission, with measured

data being transmitted to the ‘stationary side’ of the

monitoring system and any control commands for the

integral charge ampliers transmitted to the appropri-

ate section of the rotating dynamometer. e power

supply to the electronics in the rotor, occurs by the

same antenna, but having a dierent carrier frequency

to that of the data transfer. Typical resultant signals

produced by the rotating dynamometer are shown in

Fig. 180b and have been ‘zoomed’ for the investigation

of a single drill’s cutting edge.

Cutting force dynamometers of various congu-

rations, are invaluable tools for any form of in-depth

machinability study, as they indicate the precise condi-

tions at the cutting tool’s edge(s), in a truly dynamic

situation. All dynamometers that are purchased from

the manufacturer must come with an appropriate cali-

Machinability and Surface Integrity 347

Figure 179. A Rotating Cutting-force Dynamometer (RCD), utilising piezoelectric sensor systems.

[Courtesy of Kistler Instrumente AG]

348 Chapter 7

Figure 180. A Rotating Cutting-force Dynamometer (RCD), utilising piezoelectric sensor systems.

[Courtesy of Kistler Instrumente AG]

Machinability and Surface Integrity 349

bration certicate, to ensure that the results obtained

are both valid and sound. A cautionary note: if the dy-

namometer has been inadvertently dropped, or it has

possibly collided with an obstruction when in use on

the machine tool, it should be sent back to the manu-

facturer for servicing and recalibration, otherwise,

spurious cutting force data may be the result.

7.9 Machining Modelling

and Simulation

Introduction

Previously, it was been widely accepted that most cut-

ting tool modelling technqiues are somewhat incom-

plete, in both their analysis of the process and their

accompanying derived mathematics. Early, but worthy

attempts at analysing the chip formation mechanics of

the orthogonal cutting process were undertaken ini-

tially by Ernst and Merchant (1941) – shown schemat-

ically depicted in Fig. 181, followed by further work

concerning the analytical graphical interpretation of

the orthogonal cutting action which was presented

by Merchant and Zlatin (1945) and later work by Lee

and Shaer (1951) – not shown. is earlier work

was then followed by Zorev’s (1963) interpretation of

an ‘idealised cutting model’ (Fig. 182). In all of these

above modelling cases and others not mentioned – for

brevity’s sake!, the very complex nature of the cutting

process, is a vast subject ‘straddling’ many engineering

and physical disciplines. Such modelling involves as-

pects of: the tool’s geometry, chip/tool contact lengths

and pressures, chip formation, cutting forces, fric-

tional and thermal factors and so on, making it vir-

tually impossible to obtain close agreement between

with any truly meaningful results between each pro-

posed model. is lack of correlation of these model-

ling processes, is to be expected, as in reality a shear

zone, rather than a shear plane exists, but for mathe-

matical treatment, a shear plane allows some degree of

geometrical association. Due to the complex nature of

the inter-related variables that occur in any dynamic

cutting situation for just simply the orthogonal cutting

process, let alone for oblique machining modelling,

this has meant that the ‘optimum modelling solution’

has as of now, not yet been fully addressed.

Many ‘learned tomes’ have been written in the past,

concerning the ‘mechanics of machining’ and it is not

the intention to fully discuss them here, in this book

which is principally concerned with ‘current practice’

concerning machining applications. However, a brief

resumé of just one of these ‘orthogonal models’ shown

in Fig. 181 will be mentioned below, together with a

concise review of friction in metal cutting operations

(Fig. 182) will be presented, to attempt to show why

the subject of ‘theoretically modelling’ the cutting pro-

cess is so complicated.

Ernst and Merchant’sComposite Cutting Force Circle

If a continuous chip formation is produced when ma-

chining ductile materials in an orthogonal cutting

process, such as that found when cylindrically turn-

ing a component’s periphery with an undeformed chip

thickness (‘t

’), this will cause a chip compression (‘t

’)

– Fig. 181(top). e cutting forces can be obtained by

employing a cutting force dynamometer as discussed

in the previous section, to typically measure the forces

‘F

’ and ‘F

’ and so on. By utilising such cutting tool

dynamometry, Ernst and Merchant (1941) were able

to classify the forces acting in the vicinity of metal cut-

ting which gave rise to both local plastic deformation

and frictional eects. In Ernst and Merchant’s theory

which is oen termed the so-called ‘shear-angle solu-

tion’ ,

it is assumed that the cutting edge is always per-

fectly sharp and that a continuous-type chip without

BUE occurs, this former assumption in practice does

not actually occur. Moreover, another assumption in

their analysis it was that the chip would behave like

‘rigid body’ , which is held in equilibrium by the ac-

tion of the applied forces transmitted across the tool/

chip interface and transversely over the shear plane.

Boothroyd (1975), oered a reasonably ‘elegant solu-

tion’ to Ernst and Merchant’s numerical and geometri-

cal analysis and, this has been somewhat modied and

further simplied below. In order to abridge the ‘shear-

angle solution model’ shown in Fig. 181, the resultant

force ‘R’ is depicted acting at the tool’s cutting edge,

being resolved into components ‘N’ and ‘F’ in direc-

tions along and normal to the tool’s face respectively,

as well as into components ‘F

’ and ‘F

’ – once again,

along and normal to the shear plane correspondingly.

Further, the cutting force ‘F

’ and the thrust ‘F

’ com-

ponents of the resultant force, are also shown. Here, it

can also be assumed that the entire resultant force is

transmitted across the tool/chip interface and that on

both the tool’s ank and edge no force occurs, mean-

ing that a zero ‘ploughing-force’ is present – see Fig.

184 which illustrated this ‘nose-rounding eect’.

350 Chapter 7

e foundation purported by Ernst and Merchant’s

theory, was the proposition that the shear angle ‘φ’

would acquire such a value, thereby reducing the ac-

tual work done to a minimum. In view of the fact that

that for preselected cutting conditions, the work done

during cutting was comparative to that of ‘F

’ in terms

of ‘φ’ ,

hence allowing one to obtain the value of ‘φ’

when ‘F

’ is at a minimum. us, from Fig. 181:

Figure 181. ‘Merchant’s’ composite metal cutting circle for an orthogonal cutting model, where:

• F

= thrust force component,

• F

= cutting force component,

• F

= normal force component on the shear plane,

• F

= shear force component on shear plane,

• R = resultant tool force component,

• N = normal force component on tool face,

• Φ = shear angle,

• α = working normal rake angle,

• τ = mean friction angle on tool face,

• t

= undeformed chip thickness,

• t

= deformed/compressed chip thickness,

• A

= cross-sectional area of uncut chip,

• A

= cross-sectional area of deformed/compressed chip.

NB: Force arrow vector directions have been reversed and some terms have been modied from the original

work. [Source: Ernst & Merchant, 1941]

Machinability and Surface Integrity 351