12ed11 – Advanced Machine Tool Design Ppt

12ED11 – ADVANCED MACHINE TOOL DESIGN

TOPICS: STATIC AND DYNAMIC STIFFNESS

S.BRADEESH MOORTHY, APME

INTRODUCTIONMachine tool design

It deals with the design considerations of the machine components and the machine as a whole.

Machine tool structures Components of machine tools such as beds, bases, columns, box type housings, overarm, carriages, tables etc .

Types of machine tool structures:i. Beds and bases – sub assemblies are mountedii. Housings – individual units are assembled eg speed box,

spindle head iii. Supporting and moving work piece / cutter – table,

carriage, tailstock etc

Requirements & necessary conditions for structures

Requirements• Mating surfaces to be machined with high degree of

accuracy for desired geometrical accuracy.• Geometrical accuracy to be maintained through out the

life of machine.• Provide safe operations and maintenance• Ensure stresses does not exceed safe limit.Conditionsi. Proper material selectionii. High static and dynamic stiffness

STATIC & DYNAMIC STIFFNESS

• Machine tool and its cutting process can be expressed by a closed loop.

• Machine tool interacts with the cutting process.• Both machine tool and cutting process are represented by

their transfer functions.• If input to the machine (dP) is static then the output (dY) is

static in nature.• If the input to the machine (dP) is dynamic in nature then

the output (dY) is also dynamic in nature.• Designer should have good knowledge on the cumulative

static and dynamic characteristics of machine tool as well as elements with which the machine tool is made.

MACHINE TOOL CUTTING PROCESS – BLOCK DIAGRAM REPRESENTATION

Machine tool transfer function

Cutting process transfer function

y

Y(t)

p(t)

p

STATIC STIFFNESS • Behavior of element (stiffness)under

static conditions is examined from its force- displacement diagram.

• Generally the relation is non-linear.• Generally the stiffness is measured along

the direction of the force.• If the stiffness is measured along some

other direction, it is called cross stiffness.• Inverse of stiffness is compliance which is

normally used for analyzing static behavior of machine elements.

• Stiffness behavior of elements affects parameters of machining and quality of machined surface.

ASSESSMENT OF STATIC STIFFNESSi. Static stiffness with respect

to work piece accuracy• Cross stiffness represented by

K’ = P/Y’P – Resultant cutting force between cutting tool and work pieceY’ – relative displacement normal to machined surface

• Higher K’ represents lesser displacement perpendicular to machined surface which results in better accuracy.

Cont….ii. Static stiffness with respect to

dynamic stablity• Cross stiffness represented by K = P/Y

P – Resultant cutting force between cutting tool and work pieceY – relative displacement normal to surface of cut

• Y – significant in chip thickness, major role in machine tool chatter.

REPRESENTATION OF STATIC STIFFNESS

• Every member undergoes deformation under load so it can be considered as a spring.

• Machine tool can be reduced into a combination of springs in series or parallel.

Springs in series

Springs in parallel

321 YYYY

321

321

1111CCC

kkkk

321321 , yyyykkkk

Example for series system• Gear transmission system with four shafts.• The total compliance for the machine tool is the summation of reduced

compliances• Compliance • Major contributor of C is C4, if all are speed reduction.• So compliance can be improved by improving the weak element shaft 4.

42433

243

2322

243

232

2211 ...... CiCiiCiiiCC

Example for series system

• If one spring contributes to 80% of stiffness and other two remaining 20%.

• Increasing stiffness of stronger contributes to increase in stiffness rather than the other.

321321 , yyyykkkk

DYNAMIC STIFFNESS• Dynamic loading causes dynamic displacement.• Sometimes for constant dynamic force response differs with frequency of

input.• The ratio Kdyn =Pdyn/ Ydyn is dynamic stiffness.• Dynamic and static stiffness related by

Where A- magnification factor.• ‘A’ depends on i) damping factor (ii) Frequency ratio• If load is independent of frequency then

• If load is due to unbalanced force then

AYY stdyn .

n

2221

21

1

A

222

2

2

21

A

VARIATION OF ‘A’ WITH RESPECT TO

Cont…..From the graphs• ‘A’ decreases if is increased• ‘A’ is small if exciting frequency is away from natural frequency• If is 0.25 - 2.5 then displacement under dynamic condition is nearly

equal to displacement in static condition.

REPRESENTATION OF VIBRATION BEHAVIOUR AND CONTROL

pkykdt

dyp

dt

ydm iiii

2

2

• By solving n independent equations the displacements are found out.

•Resultant displacement y = y1 +y2+y3+ -----+yn

•Dynamic compliance found out by y/P•In simple modes of vibration contribution of stiffness of elements is same in overall stiffness of machine tool.•By increasing stiffness of elements overall stiffness can be increased.•Highest among the natural frequency should desirably be 2.5 times less than the highest excitation frequency. •Lowest among the natural frequency should desirably be 2.5 times greater than the lowest excitation frequency.