Lopez de Lacalle L.N., Lamikiz A. Machine Tools for High Performance Machining

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112 G. Quintana, J. de Ciurana and F. J. Campa

users. If spindle and machine manufacturers integrate the dynamics of each of

their products in a software utility, the final user can introduce the specific ge-

ometry of his/her tools to obtain the frequency response. This FRF is an input for

the stability lobes calculation which leads to the selection of highly productive

conditions.

Otherwise, if a model is not provided or it is not accurate enough, the FRF can

be obtained with an experimental approach based on the excitation and response

measurement. At 0

rpm, it is easily made by tap testing the tool tip with an impact

hammer and an accelerometer. However, at higher speeds the tap test may be

dangerous and less accurate; therefore, alternative procedures as the use of active

magnetic bearings for both non-contact excitation and response measurement are

currently being investigated [1,

14].

3.5.3.2 The Estimation of the Stability Lobes

For the evaluation of a spindle in working conditions it is necessary to have

a model of the process where the cutting parameters, the workpiece material prop-

erties and the tool geometry are involved.

The real milling model is the simulation in the time-domain that integrates the

equation of motion [17]. This model reproduces the evolution in time of forces,

displacements and chip thickness, making it possible to determine if machining is

stable or unstable, and in the stable case if the amplitude of forced vibration is

acceptable. The main drawback of time-domain modelling is the high computation

time for the stability lobes calculation.

The alternative solution is to calculate the stability lobes directly in the fre-

quency domain or to resolve the periodic delay-differential equation. A schematic

description of these models is outlined in Fig. 3.29 and Table 3.2. Models follow

the following steps: a) the relation between the chip thickness and the vibration of

the system must be formulated, b) a cutting forces model is proposed, c) the sys-

tem dynamics is introduced, and finally d) the eigenvalue problem that defines the

stability of the process is solved.

For spindle behaviour verification purposes in terms of cutting force, a simple

semi-mechanistic force model with a linear relation between the force and the chip

thickness is accurate enough. Cutting tools for high speed roughing of aluminium

alloys have a typical helix angle lower than 30º so, at the usual depths of cut, the

effect of this angle on the shape of lobes is minimal and can be neglected [27]. If

the purpose is to calculate stability lobes for tools with complex geometries or

helical end mills, a more complex model is needed.

Furthermore, it is essential to modify the algorithms to include the dependency

of the system dynamics on the spindle speed. In Fig. 3.29 there is a comparison of

the stability lobes considering the FRF at 0

rpm and the speed dependent FRF for

the tool with an O-D ratio of 7:1 in Fig. 3.30.

3 Machine Tool Spindles 113

waviness left by the

previous cutting edge

waviness left by

the jth cutting edge

jth cutting edge

solid body path

previous cutting

edge solid body path

sin

Feed

κ=90º

h(t)

h(t T)

−

Fig. 3.29 Schematic diagram of a 2D model of milling

0.5 1 1.5 2

x 10

Spindle Speed (rpm)

Depth of Cut(mm)

FRF at 0 rpm

variable FRF

Tool:

Diameter 16 mm

2 cutting edges

Helix angle: 25º

Cutting conditions:

25% of radial

immersion

Down-milling

Material:

Aluminium 7075-T6

= 870 N/mm

’

=0.1

Fig. 3.30 Stability lobes obtained with the FRF measured at 0 rpm and with the effect of spin-

dle speed on the FRF

114 G. Quintana, J. de Ciurana and F. J. Campa

Table 3.2 Fundamentals of methods for directly obtaining the stability lobes diagram

Approach

Resolution of the chatter loop Resolution of the periodic delay-differential

equation

Examples

Single-frequency

[1]

Multi-frequency

[7]

Semi

discretisation

[9]

Pseudo

spectral

Chebyshev

Temporal

finite element

[5]

a) Chip thickness model

()( )

sin cos

jjj

hx y

φφ

=Δ⋅ +Δ⋅ ;

=() ( )

xt xt TΔ−−

;

=() ( )yyt ytTΔ−−

b) Cutting forces model

()

tp jj

Ka h

⎧⎫

⎪⎪ ⎪⎪

=⋅⋅ ⋅

⎨⎬ ⎨⎬

⎪⎪

⎩⎭

()

cos sin

=()

sin cos

xj tj

yj rj

φφ

⎧

⎫⎧⎫

−−

⎡⎤

⎪

⎪⎪⎪

⎢⎥

⎨

⎬⎨⎬

−

⎢⎥

⎪

⎪⎪⎪

⎣⎦

⎩⎭ ⎩⎭

∑

()

aK At

⎧⎫

⎧

⎫Δ

⎪

⎪⎪⎪

=⋅⋅⎡⎤⋅

⎨

⎬⎨⎬

⎣⎦

⎪

⎪⎪

⎩⎭

c) System dynamics

()

−

⎧

⎫

⎧⎫

⎪

⎡⎤

=− Ω⋅

⎨⎬ ⎨⎬

⎣⎦

⎪

⎩⎭

Operates with the FRF at the tool tip

[

]

{

}

[

]

{

}

[

]

{

}

()

{

}

() () ()

;;

xCxKx Ft

MCK

++ =

⎡ Ω ⎤⎡ Ω ⎤⎡ Ω ⎤

⎣⎦⎣⎦⎣⎦

 

Modal parameters at the tool tip

d) Stability analysis procedure

Sweep the FRF

searching the

stability limit at

each frequency

Sweep the spindle

speed and the

frequency of the

FRF searching the

stability limit at each

spindle speed

For a grid of cutting conditions, test if

the eigenvalues of the matrix that defines

the stability of the process have a modulus

lower than 1

Nomenclature

: Dynamic chip thickness of the jth cutting edge

: Angular position of the jth cutting edge with respect to the Y axis

z: Number of tooth of the tool

T: Tooth passing period, calculated as

260/Tz

=Ω

t,r,x,y

: Cutting force in tangential, radial, X and Y direction

: Tangential shearing cutting coefficient

’

: Radial shearing cutting coefficient normalised with respect to K

: Axial depth of cut

): Window function equal to 1 when the jth cutting edge is cutting

[A(t)]: Directional coefficients T-periodic matrix

: Frequency of chatter in rad/s

: Spindle speed in rad/s

;

3 Machine Tool Spindles 115

3.5.3.3 Methods for the Reduction and Avoidance of the Chatter Vibration

The estimation of lobes explained above is the off-line approach to prevent the

unstable machining. If the lobes are finely calculated, the user can select cutting

conditions for stable machining with, at the same time, a very high axial depth of

cut, in other words with a high removal rate. However this approach implies

a complete analysis of machine dynamics, difficult to be carried out by industrial

users, and an in-depth knowledge of the machining process and material. For this

reason, several on-line approaches are being developed, monitoring the vibration

or noise level and rapidly modifying the process parameters:

• Spindle speed variation: The CNC monitors the vibration or noise level and

rapidly modifies the spindle speed. For example, the software Harmonizer™ by

Metalmax

searches a stable speed [26]. A variation of the previous one is the

continuous spindle speed variation (SSV) that continuously changes the spindle

speed during the cutting process [6].

• Increasing damping: There are several methods for this, for example, using an

active magnetic bearing to absorb dynamic forces [1], taking advantage of the

damping properties of the electro-rheological fluids, or supporting the rolling

bearing with a non-rotating hydrostatic bearing and regulating the pressure [20].

Regarding the tool and toolholder, there are several options to increase the dy-

namic behaviour of the spindle system:

• Using tools with integrated dampening like the Sandvik

Coromant CoroMill

390 or special boring bars.

• Reducing the tool O/D ratio. This is an advantage of five axis machining.

• Using monoblock tools, where the shank and toolholder are in the same body.

• Breaking the periodicity of the tooth impacts using variable pitch and variable

helix tools.

3.5.4 The Thermal Behaviour

In machine tools and spindles, the three kinds of heat transference, conduction,

convection and radiation, can be present and, furthermore, they may appear sim-

ultaneously. Conduction occurs, for example, in the contact area between the

cutting tool and the workpiece. Convection occurs when the cooling emulsions,

the minimum quantity of lubricant (MQL) or air, make contact with the rotating

cutting tool, exchange heat and are then expulsed. And finally, radiation, which is

the least important as far as machine tools are concerned, occurs when, for exam-

ple, the temperature of an element rises because of the exposure to the sun or

other nearby machines that behave as heat sources. All three forms of heat trans-

ference must be taken into account in order to improve machine tool behaviour in

response to internal temperature changes from the machine tool elements and

machining process, and external temperature changes.

116 G. Quintana, J. de Ciurana and F. J. Campa

The increase in spindle temperature increases the length of the spindle shaft.

The thermal expansion can be represented as follows:

()

LL TT

=×+×− (3.11)

where α is the thermal expansion coefficient which varies according to the mate-

rial and is determined experimentally, T

and T

are the final and initial tempera-

tures, respectively, and L

and L

are the corresponding lengths at each tempera-

ture. Equation 3.13 is of limited use since it assumes that the heat distribution is

constant throughout the whole body and that it is homogenous and uniform, but it

gives a good idea of the main factors involved. The thermal expansion depends on

the material, the initial length of the element and the variation in temperature.

Table 6.2 in Chap. 6 shows the thermal expansion coefficient for materials com-

monly found in the design and manufacture of machine tools. Therefore, to mini-

mise the effects of heat, it is necessary to intervene in three areas: the material

used should have a low thermal expansion coefficient, the shaft length should be

minimised and the increase of temperature should be reduced by a cooling system.

Thermal growth affects the precision of the process. The shaft expansion

“pushes” the tool axially toward the workpiece, so the machined surface location

differs from the desired. This effect is clearly shown in Fig. 3.31, where a high

speed spindle has been heated during 3.5 hours. Infrared pictures were taken in

minute increments. Over this time, the spindle temperature was increased from

approximately 20ºC to 41ºC. The error between the initial image and the last for

a simple slot machining resulted in a depth variation of 0.1

mm. One solution for

reducing this problem is to compensate for the deviation in the spindle, which

requires the measurement of the thermal induced deformation. Mazak

has devel-

oped and commercialised this solution in the heat displacement control function of

their Mazatrol Matrix™ CNC control.

§20ºC

§41º

0 min 30 min

60 90

120 150 180 210

Fig. 3.31 Main spindle temperature during 3.5 working hours. Each image has been taken in

minute increments

3 Machine Tool Spindles 117

The bearings are also affected by the thermal growth, changing their mechanical

characteristics. The inner and outer rings and the rolling elements suffer a different

thermal growth, so the initial bearing preload changes. Also, the shaft thermal expan-

sion adds more preload in such a way that the inner race is forced into the bearing. As

a consequence of the excessive preload, friction forces rise, the temperature is higher

and the bearing life is reduced. There are several solutions to reduce this effect. For ex-

ample, one technique used in high speed milling and grinding spindles is to mount the

rear bearings on a floating housing preloaded with springs that allow axial movement.

Another technique is to use a hydraulic device to compensate the preload on the bear-

ings at high rotational speeds, so it is possible to maintain low friction forces [20].

3.5.4.1 Heat Sources

In order to avoid heat problems and increase the spindle service life, it is necessary to

know about the heat sources to reduce their contribution. The main sources of heat

that affect the spindle are the motors, the friction in bearings and the cutting process.

The heat generated by electric motors in stator and rotor is a function of torque and

speed and it is defined by the motor efficiency. The electrical power that enters the

motor is transformed into mechanical power, but also into heat, due to the primary

copper losses, iron and stray losses and secondary copper losses. In built-in spindles

the heat source is very close to the spindle shaft so the heat has to be properly evacu-

ated. Belt-driven and gear-driven spindles also have heat sources in their transmis-

sion elements, pulleys and gearbox, respectively, due to friction. Another heat source

is due to the viscous friction between the rotating elements and the air.

The heat generated in the bearings is due to the friction between the rolling ele-

ments and the inner and outer raceways and it depends on the speed, the preload

and the lubrication. Faster speeds mean higher contact forces due to the centrifugal

force and, hence, higher friction. In addition, the larger the diameter of the ball

bearings, the faster the linear speed is and, again, friction rises. Although a heavy

preload may be desirable to increase the spindle stiffness, it also implies higher

contact and friction forces, thus the bearing life is reduced. Finally, poor lubrica-

tion drastically reduces the spindle bearings life at high speeds.

The heat produced in the cutting zone due to the chip removal mechanism can

be transferred from the tool to the toolholder and the spindle. The magnitude of

the problem depends strongly on the workpiece material, the tool and toolholder

material, and the cutting fluid. Weck reported a case of thermal growth reduction

of up to 50% in finish milling using a toolholder made of low expansion Invar

material instead of tool steel [22].

3.5.4.2 The Refrigeration

Cooling the spindle is necessary in order to stabilise temperatures and avoid the

negative effects of excessive heat and the temperature variations during spindle

118 G. Quintana, J. de Ciurana and F. J. Campa

operation. That is the reason why coolant fluids are forced to circulate through

various zones of the headstock and spindle structure to absorb the heat generated.

The objective is to create a cooling “jacket” around the spindle and this is achieved

surrounding it with coolant by means of cavities or channels; see Fig. 3.32. There

is a variety of coolant fluids, the most typical of which are air, oil and water with

additives to prevent oxidation of the conduits.

The most common spindle cooling for a good control of the temperature is

based on a closed loop cooling system where the coolant that comes from the spin-

dle is fed into an external refrigeration unit to cool it, and then is pumped back into

the spindle. The refrigeration units have heat exchangers where the refrigerant

circuit cools the coolant circuit. Closed loop cooling systems have a greater capac-

ity for removing heat and need less time to do so than other heat exchange systems.

They are controlled with a thermostat that controls the temperature of the coolant

that circulates around the spindle, keeping it stable in such a way that the tempera-

ture of the coolant is not affected by room temperature.

Another solution consists on the continuous circulation of cool dry air around

the spindle. More economic although more inefficient systems use the cutting

fluid to cool the spindle. The cutting fluid is fed into the cavities of the spindle and

then is sprayed onto the tool. This solution is a bit outdated as the circulating fluid

is heated by the cutting process, so its cooling capability is limited.

3.5.4.3 Spindle Warm-up Cycles and Warm-up Systems

Keeping a stable spindle temperature is more important than simply reducing the

temperature. The idea of a warm-up is to achieve a stable operation temperature

during the entire machining process in order to reduce the effects of thermal ex-

pansion caused by temperature variations. The warm-up cycle should be carried

out in conditions similar to the operating conditions, with the same cutting tools,

if possible. This is because warming-up at feed rates and rotational speeds that

are much higher or lower than subsequent operating conditions means that the

warm-up temperature will be much higher or lower than the operating tempera-

ture, thus leading to thermal expansion errors. It is advisable to start up the ma-

chine in a dry run mode, for example. Nowadays, many machine tools have

automatic spindle start-up and warm-up systems that bring the machine to the

correct temperature ready for the operator to begin work as required.

There is also another method employed in special machines based on a system

of warm-up circuits that carry fluid at a specific temperature to the different ele-

ments in the spindle. These systems are permanently engaged and controlled by

a thermostat which is responsible for conducting the heated liquid to the spindle

jacket and other elements. The fluid recirculates and is reheated to a set tempera-

ture considered to be optimum for the spindle operation.

3 Machine Tool Spindles 119

3.5.5 Spindles in Use: Other Problems

Other problems related to the performance of the spindle that the machinist has to

face are the runout of both the spindle and tool, which can lead to poor accuracy

and collisions with the workpiece or with the elements of the machine, which may

damage the spindle.

3.5.5.1 Runout

The term “runout” in machining describes the state of a spindle and tool when

they have a rotational axis that differs from their geometrical axis. The total indi-

cated runout, TIR, is the total distance measured from the maximum position in

radial direction to the minimum position in the same direction; see Fig. 3.32. This

factor limits productivity, as it negatively affects the dynamic balance, the chip

load distribution, the part finish and the tool life. The runout can refer to the spin-

dle or to the tool.

Eccentricities in the nose of the spindle can arise for various reasons, such as

defective elements of the spindle, inaccuracies in the assembly, slack or simply

the ageing of the spindle, among other possibilities. Although radial and axial run-

outs are measured at the nose of spindles, it is the radial runout that is the most

significant.

Cutting tool runout is usually measured as a composition of radial and angular

runout, and is produced by inaccuracies in the mounting operation. The result is

that one tooth supports larger chip loads than the others. This error is due to defi-

ciencies in the tool-collet adjustment, the degree of collet wear, or small impurities

Fig. 3.32 a Tool runout schematic. b Effect of the tool runout on the real cutting edge path and

TIR. c Laser control of tool runout

120 G. Quintana, J. de Ciurana and F. J. Campa

of chips or coolant that may have been left on the collet that render the grip of the

cutting tool imprecise or less rigid.

Runout can be measured while the spindle is in operation (dynamic measure-

ment) or at rest, using static tests. Dynamic measurement provides more reliable

and precise results, although the instruments required are more expensive.

3.5.5.2 Collisions

Accidental collisions produced during material removing operations are one of the

biggest worries for machine tool operators. They can have extremely negative,

even irreversible, effects on the machine tool structure and especially on the spin-

dle, the cutting tool or the workpiece. Generally, when a significant collision oc-

curs, the machine undergoes an emergency shutdown to reduce damage and allow

the operator to fix the problem if possible. The operator can also press an emer-

gency shutdown button to stop the machine when necessary.

Nevertheless, accident prevention and safety involving machine tools has im-

proved in recent years. One way to prevent collisions is to predict them using

simulations of the machining process. Computer-aided manufacturing (CAM)

programmes provide this kind of evaluation and analysis of the possible problems

that may arise, so that they can be resolved before the actual work with the ma-

chine begins. Also, there are CNCs that can detect machine interferences online. It

is the case of Mazak Mazatrol Matrix™ that uses a synchronised 3D model for

checking collisions when an operator manually moves the machine axes.

3.6 Spindle Selection

As mentioned in the introduction, the spindle industry provides a large range of

spindle options and configurations to satisfy the particular requirements of each

sector. Figure 3.33 shows an example of three added options to the standard spin-

dle, offered by EDEL

Selecting the most suitable spindle is an iterative process that must take into

account the final characteristics of the end product and the requirements of the

production system. Maximum spindle speed, effective power, torque, drive

method, type of bearings, stiffness and dynamic behaviour, tool holder technology

and thermal properties are all spindle characteristics that should be taken into

consideration and evaluated to get the best final product specifications in terms of

tolerances, surface finish, etc. and meet the production system requirements in

terms of productivity, flexibility, etc.

Hence, choosing the right spindle is an important but far-from-easy task, as the

wrong decision can negatively affect the production system and the performance

of a company. The decision-maker has to be familiarised with spindle technol-

ogies in order to select the most suitable spindle bearing in mind all the factors

3 Machine Tool Spindles 121

involved; see Fig. 3.33 where the basic steps for the selection of a spindle for

a milling process are shown.

3.6.1 Conventional Machining or HSM

Conventional machining processes combine low spindle speeds and feed rates and

high depths of cut and tool immersions. These processes require a spindle with high

effective power and torque. In comparison, high speed machining means higher

spindle speeds and increased feed rates to achieve high material removal rates.

Conventional spindles usually run at speeds lower than 10,000

rpm and their ef-

fective power does not exceed 25

KW. There is a relationship, or a compromise,

between the effective power of the machine and its maximum rotational speed. As

Fig. 3.34 shows, it is unusual to find machines on the market that can offer high

spindle speeds coupled with high power. Generally, they are very expensive spin-

dles and are oriented to the aluminium machining for the aeronautical sector,

which demands this kind of spindles as the workpiece material and the tooling

allow machining at very high speeds.

Production System Capabilities

ÆConventional/High Speed Machining

Æ Productivity (MRR)

Æ Flexibility

Æ Rough/Semifinish/Finish/Superfinish

Æ Tools and coatings

Final Product Requirements

Æ Geometric complexities

Æ Material

Æ Flexibility

Æ Tolerances

Æ Surface finish

Spindle Characteristics

Æ Spindle speed

Æ Power and torque

Æ Drive method

Æ Bearings

Æ Stiffness

Æ Runout and vibration

Æ Tool holder

Æ Thermal properties

Fig. 3.33 Production system and final product requirements are decisive factors in selecting

spindle characteristics