Circularity fault due to mechanical behavior of the spindle during hard turning operations J.-F. Rigal A. Bourdon M. Remadna Laboratoire CASM., INSA de Lyon Bât. 113 20, av. Albert Einstein 69621 Villeurbanne Cedex France Tél. 33 4 72 43 82 72 - Fax 33 4 72 43 89 13, e-mail:
[email protected]
ABSTRACT The objective of this paper is to propose a method to quantify and to analyze the lathe spindle behavior for hard steel turning. On one hand, circularities of machined surfaces are measured. On an other hand, the variation of the rigidity of the rolling bearing supported spindle are calculated with a specific software. Finally an analyze is proposed to contribute to the design of precision machines for hard turning. KEY WORDS: Spindle, Rigidity, Hard Turning.
Introduction Geometrical quality of the finished surface is one of the goals of the machining operations. The mechanical behavior of the spindle directly control the machine surface quality during turning operation. This fact is highlighted with hard steel turning due to the high quality expected. Saying that the rigidity of the structures must be as higher as possible is not sufficient. The design of the spindle must take into account both static, kinematic and dynamic effects on the machined surface. After a presentation of measures on machined surfaces, mechanical models of the rolling bearing supported spindle are presented. Numerical static and dynamic simulation results are analyzed in relation with the measures. 1. Hard steel turning experiments Hard steel (52HRC) turning operations have been realized with CBN inserts on a classical lathe (GALLIC 20 Muller et Pesant) equipped for laboratory measures of during metal cutting. The circularity faults of several cylindrical parts (length, L=140 mm, diameter, D=75 mm) have been measured on a TALYROND machine. A characteristic periodic surface form, with various frequencies has been observed. Examples are given on the figure 1. In most cases, and heaven if the circularity
value (between 1.0 and 4.5 mm), is not so bad regular waves, with 7 to 10 lobs appear. They are due to periodic event with low frequency (between 120 and 170 Hz). No1: Insert CNGA120408, Cutting speed Vc=200 m/mn Depth of cut a = 0.4 mm Feed rate f = 0.1 mm/rd, Axial position of the measured circle Lm ≈ 90 mm Measures: 8 lobs Circularity : 2.1µm Cutting forces: axial 76 N, Radial 119 N, tangential 148 N No2: Insert CNMA120412 Vc=200m/mn a = 0.5 mm, f = 0.1 mm/rd Lm ≈96 mm Measures: 9 lobs Circularity : 4.5 µm Cutting forces: axial 164 N, Radial 282 N, tangential 190 N Figure 1. Circular waves of the machined surface [REMA-99]
2. Kinematic analysis Design of the analyzed spindle is defined on figures number 2 and 3. Roller bearing geometry is degined on the figure 4.
Figure 2. Spindle design
Y
Chuck
X
Φ 250
B2
28
B1
Z Φ 86
Φ 58 Φ 102
P5 328
66 96
26
Φ 140
Φ 72
P2 P3 Φ 125 P4
P1
B3
Φ 228
72
P6
P7
P8 Φ 164
Φ 85 170
400
3 jaws 52x84x25 84 52
64
P9 85
Cutting Work piece pt. P10 P11 Φ 75 140 20
40
Figure 3. Spindle geometry B1 15 15 17
d roller (mm) L roller Z Nb. rollers
B2,B3 15 30 19
24
40
Φ 125
Φ 140 11°
Φ p 97.5
B1 : Cylindrical roller bearing, NU 214 P6 B2,B3 : Tapered roller bearing GAMET No 140085/140/40
Φ 70
Φ p 112.5 Φ 85
9 30
15
Φ 15
15
1,46°
Figure 4. Roller bearing design After a first static analysis non reported here, the most loaded bearing B3 has been considered. The Kinematic equations and the number of the roller passages (C) on one point of the inner ring are given on the figure 5 Dcr
ωcr A
O
Da ωa
Da D + Dcr VO = ω cr a and VA = 2Vo 2 2 The passage pulsation at a point M fix on the inner ring, VA = ω a
for the Z roller is : M
roller number: Z
Supposing non sliding movement between the rollers and the rings, linear speeds of the inner ring Va and of the roller are equal at the rolling point A. V0 is the speed of the center of the roller.
ω cr = ω a
Da Z. 2(Da + Dcr )
The relation between the rotation frequencies is the same:
N cr =
Da Z * N a or , N cr = C * N a 2(Da + Dcr )
Results : Da (mm) 110 110 110
Dcr(mm) 14 15 16
Z 19 19 19
Figure 5. Kinematic analysis.
C=Ncr/Na 8.42 8.36 8.29
The values obtained for C (8.3) are situated inside numbers of lobs counted during circularity measuring, between 7 and 10. The observed differences are due to the real rolling diameters witch are varying with the cutting force and also due to the sliding between the surfaces in contact. Nevertheless, the relation between the measured frequencies and the frequencies of the spindle rolling bearing elements are in the same range of 120 to 170 Hz. This confirms that the circularity faults observed on the work piece are due to the lathe spindle behavior. More precisely, they are suspected to be due to the rolling bearings. The objective of the next static and dynamic analyses is to confirm this fact. 3. Static analysis of the spindle A model is proposed for the spindle behavior analysis. In this model the axe is a Finite Element model (68 elements and 16 nodes with 6 ddl). Each rolling element of the bearing is finely considered so has the internal geometry and the clearance are introduced [BOUR-98]. So, the real spindle axe support due to the bearing is taken in account for the numerical simulation. Results are given, in the next figures for the static simulation for the first case of loads presented on figure 1. No internal clearance has been supposed for the 3 bearings. 0.5
x 10
-3
Flexion in the plane xz (mm)
-3
Flexion in the plane xy (mm)
x 10 1
0
0
-1
-1 -2
-2
-3
-4
-3
-4
-6
0
200
400
600
800
1000
0
200
400
600
800
1000
Figure 6. Total flexion of the axe 90 70.3 120
90 4.34 60
120
60
49.2 28.1
150
30
150
1.74
30
7.03 180
0
180
210
0
330
210 240
330
300
270 Forces. (N) : Outer ring(o), Inner ring(+)
240 270 forces on the flange
300
Figure 7 a,b. Loading of bearing B2 (Case No1)
90 0.0425 120
60 0.0273
150
0.0121
30
0.0 -0.00309 180
0
210
330
240 300 270 Moments (N.m) : Outer ring(o), Inner ring(+)
Figure 7 c . Loading of bearing B2 (Case No1) Figure 6 shows the total deflection of the spindle (5 µm), due to the shaft and due to the bearings. The most important part is due to the shaft. On figure 7, the roller loading is presented in form of a polar diagram for the bearing B3 . The maximum load on the rings is 70 N. The maximum load on the flange is 4.3 N, and the maximum moment on the ring is 0.04 N.m. Results are summed up in table 1. Case, Fi(N) 1, Fa=76, Fr=119, Ft=148 2, Fa=164, Fr=282, Ft=190 Cutting pt def. (µm) 4.3 6.5 F ring F flange Mt F ring F flange Mt max. (N) max (N) (N.m) max. (N) max (N) (N.m) B1 1 0 8 E-4 1.6 0 12E-4 B2 67 4 46E-3 71 4 43 E-3 B3 90 6 282E-3 103 6 293E-3 Table 1. Static results In conclusion of the static analysis, it can be noticed that the total deflection at the cutting point is important 4.3 and 6.5 µm in regard with the machining precision. The static rigidity at the cutting point is from 44 to 52 N/µm is supposed to be good [TLUS-99]; This fact has be confirmed by experiment. No vibration and no chatter have been observed during cutting. Considering the bearings, B3 is the most loaded. The force acting on the most loaded roller is about 100 N, witch is usually considered has a low value. Practically, no loading is observed on the bearing B1. A simulation non reported has been performed with a clearance for B1. In this case the loading was exactly null. The shaft displacement was 0.1 µm, inferior to the radial clearance of 60 µm.
4. Dynamic behavior. The stiffness of the dynamic model is the same than in the static one, both for the axe and for the bearings. Distributed and punctual masses and inertia have been introduced considering the axe, the jaw-cluck and the work-piece. Results are the free vibrations of the system. The 3 first free modes are presented fig. 8. The vibrations of the spindle have been represented around the static position of the case 2 ( Fa,x 164 N, Fr,z 282 N, Ft,y 190 N). Dynamic results are summed up in table 2: The conclusion of this dynamic analysis, highlight 3 points : - The bearing B3 support the maximum of the potential energy. - The main deformation can be called a flexion of the solid (spindle+chuck+piece) in rotation. That corresponds to the conclusion of the static analysis. - In this case, rigidity of the load bearing B3 is sufficient but, the shaft flexibility control the position of the work-piece during cutting.
mode 2, 332Hz
mode 1, 300Hz Axe z
x 10
Axe z x 10
-3
2
2 0
0
-2
-2
-4
-4
-6
-6
-8 2
-8 5 1000
0 x 10
-3
x 10
-2 -4
-3
-5
Axe x
200
Axe y
1000
0
-3
0
Axe y
-
mode 3, 339 Hz
Axe z x 10
-3
2 0 -2 -4 -6 -8 2 0 x 10
-3
1000 -2 -4
Axe y
-6
200 0
Axe x
Figure.8. The 3 first free modes
0
200 Axe x
Mode Frequency
1 2 3 4
(Hz) 300 332 339 861
Potential energy in bearing B2 (%) 1.7 12 6 59
Potential energy in bearing B3 (%) 92.4 18 23 2
Potential energy Flexion (%) 4 70 71 35
Table 2. Modal analysis
5. Conclusion Numerical results have been compared with the experimental ones to explain manufactured surfaces characteristics. These simulations show how to take in account important parameters during the spindle design stage. The contribution to the design of precision machines for hard turning can be summed up on 3 points : -The spindle shaft deflection is a major problem to be analyze. -The rigidity of classical bearings, designed for machine tool, is sufficient for hard turning -The geometry and the kinematics of the most loaded bearing, close to the chuck, control the circularity quality of the machined surface.
References [REMA-99] M. REMADNA, J.-F. RIGAL, B. ROUMESY, "Testing of CBN Insert Wear in Hard Steel Turning", Intl CIRP Workshop, ENSAM, Paris, pp. 119, 126 [BOUR-98] - A. BOURDON, J.-F. RIGAL, D. PLAY,. "Static rolling bearing models in C.A.D. environment for Studies of complex mechanisms. Part I and Part II". Transactions of ASME, Journal of Tribology, 1999, April. [TLUS-99] J. TLUSTY, J.ZIEGERG, S.RIDGEWAY, "Fundamental Comparison of Use of Serial and Parallel Kinematics for Machines Tools", Annals of the CIRP, Vol 48/1/99
