optimal mechanical spindle speeder gearbox design

Presented by : Guided by :Harshal R. Borole D. P. HujareRoll no. ME11804

IntroductionMachining - a form of subtractive manufacturing in which

a collection of material working processes are used with a sharp cutting tool to physically remove material to achieve desired geometry.

All of the current trends in machining, from high-speed machining (HSM) to knowledge-based systems are geared towards maximising production capabilities.

HSM is growing rapidly as it provides several advantages like reduced machining time, reduced mechanical stresses, reduced heating of workpieces, high surface quality etc.

Obvious answers are, either….

Buy a new HSM centers Upgrade an existing lower speed machine tool

Significance of SpindleThe spindle is one of the main mechanical

components in machining centers, since its design directly affects the finished quality of workpieces and machining productivity.

The spindle shaft rotates at different speeds and holds a cutter, which machines a material attached to the machine tool table.

The structural properties of the spindle depend on the dimensions of the shaft, motor, tool holder, bearings, and the design configuration of the overall spindle assembly.

A compact gearbox, low cost option that allows the increase of speed of a conventional machine tool to the speed that of a High Speed Machining

Common range of speed ratios for which mechanical spindle speeders are designed is a multiplication factor from 3.5 to 8 and up to 10.Maximum output: 40,000RPM @ 2KW power input

Spindle Speeder GearboxFunctionality of spindle speeder gearbox depends

directly on its constructional solution (arrangement, volume) and K.E. of transmission.

For optimum functionality, it is desired that volume & K.E. should me minimum which also ensures long working life.

To give a set of optimal designs of mechanical spindle speeders based on different powers and speed ratios which would help manufacturers and engineers involved in marketing and design of mechanical spindle speeders.

Advantages of PGTCompactness.

Ensure high proportion of energy transmitted.

Even Load distribution- greater stability.

Torque capability increased.

In-line transmission.

Figure D is more economic since it offers the advantage of not using a ring gear

Fig A is more advantageous since it is constructed with simple planets with ring gear as fixed member

What advantage……? Rotational Kinetic energy,

Thus, K.E is directly proportional to mass Hence, B,E and F are not appropriate configurations

2

2

Where,

2

1.

rmI

IEK Rot

×=

××= ω

Choose an optimal number of planets for required power and speed ratio

Number of planet members (Np) can vary from two to three, four or even more, depending on application for which it is being designed.

Thus, reduce the weight & kinetic energy of transmission, ensuring good distribution of load on each of planet gears

Planets must be arranged concentrically around the PGTs principal axis to balance mass distribution

Module, mConstraint: For gears to mesh, module for all

gears must be equal

Face Width, b Constraint: 9m ≤ b ≤ 14m

T

Dm =

Gear Tooth Ratio, Znl

Where Znl is the ratio of gear pair formed by linking members n and l

Constraint:

The tooth ratios can take any value, but in practice, they are limited mainly for technical reasons because of assembling gears outside of a certain range of gear ratios.

In this work, the constraint on tooth ratio is as proposed by “Muller” and AGMA norms,

0.2 ≤ Znl ≤ 5 for external gear mesh-7 ≤ Znl ≤ -2.2 for internal gear mesh

l

nnl Z

ZZ =

Ratio of Diameters Constituting Double planet, Constraint:

Where, d’4 is the diameter of the planet gear that meshes with member 2 and d4 is the diameter of the planet gear that meshes with member 1

Minimum Number of Tooth on Pinion, Zmin Constraint: Zmin ≥ 18

3d

d

3

1'4

4 <<

Simple Planet

Where, Z1 is the number of teeth on sun gear and Z2 is the number of teeth on the ring gear (Sign depends on turning direction of the sun & ring gear with arm fixed)For Double Planet

&

Where, Np is the number of planet gears

integeran N

Z

P

12 =± Z

integeran N

PPZ

P

1122 =± Z2

1

4

'4

PZ

PZ =

Hertz Contact Stress (As per ISO norms),

Allowable Hertz contact Stress Hence,

Bending Stress (As per ISO norms)

Allowable Bending Stress Hence,

u

u

db

FZZZZKKKK t

EHHHVAH

1+××

××××××××= βεαβσ

XWVRLNHHP ZZZZZZ ××××××= limσσ

βεαααβσ YYYYmb

FKKKK SF

tFFVAF ××××

×××××=

XrelTNTSTFFP YYYY ××××= δσσ lim

HPH σσ <

FPF σσ <

Volume Function

( )

( ) ( )

( ) ( ) ' D'For ,2max4

' C'For 2,2max4

Planet simpleFor 24

2241'2414

2'4241'2414

24141

dddbbV

ddddbbV

ddbV

D

C

A

+×+×=

++×+×=

+××=

π

π

π

Kinetic Energy Function

( ) ( ) 2

NV

2

N

2

1

Planet DoubleFor

2

1

2

1N

2

1

Planet SimpleFor

24'44

P24

'44

P211

244

244P

211

ωω

ωω

IImmIKE

IVmIKE

CD

A

++++××=

××+××+××=

The design variables are of constructional solution chosen from those of Fig. A,C,D Number of planet gears NpModule of the gear miNumber of teeth on each gear ZiFace width bi Helix angle βi

When these design parameters are determined by minimizing the above objective functions, the PGT is perfectly defined

Conclusions from Table 1 & 2 (For constructional solution of A) Gears designed with different module have greater difference in kinetic energies (i.e. KE2-KE3)

Gears designed with same module have lesser difference in kinetic energies (i.e. KE2-KE3)

Diameter based on minimum K.E design is always smaller than diameter based on minimum volume design

Thus, the inference from above statement is that mechanical spindle speeders must be designed based on minimum KE solution.

Conclusions from Table 3 & 4 (For constructional solution of C & D) and Graph

When compared with constructional solution of A (Table 1&2), C & D have more volume and K.E’s Graph gives comparison between A v/s C/D K.Ec<<K.Ed and Vc<<Vd. Thus, solution D is poorer than C.

Ratio between volume and kinetic energy falls as speed ratio increases.

Adaptable to any machine: Transfer machinesSpecial machinesMachining centers milling machinesDrilling machinesLathe machining centersGrinding machines

The best design of a mechanical spindle speeder is based on the constructional solution of Fig. A which is the most often used by mechanical spindle speeder manufacturers

For Fig. A, each speed ratio, power and maximum output speed, the results given in Table 1 and 2 offer the most appropriate solution i.e. minimum volume and minimum kinetic energy solutions.

The constructional solution of Fig. C can be used for high speed ratios (>1:10)

Salgado DR, Alonso FJ (2009) Optimal mechanical spindle speeder gearbox design for high speed machining. Int. J Adv Manufacturing Technology.

Salgado DR, Alonso FJ (2007) Optimal machine tool spindle drive gearbox design. Int. J Adv Manufacturing Technology

Maeda O, Cao Y, Altintas Y (2005) Expert spindle design system. Int J Mach Tools Manuf

J. Jedrzejewski, W. Kwasny, Z. Kowal, W.Modrzycki Wrocław Operational behavior of high speed spindle unit.