Analysis for Distortion Control of CNC Machine
Rajan Khakhar
M. T. Rane
R. V. Kulkarni
Larsen & Toubro Limited, Mumbai, India
Abstract
The Machine Shop of Larsen & Toubro Limited has a CNC controlled, vertical spindle machining center
for high accuracy machining. It is a dual spindle machine, which is presently used for deep-hole drilling
operation.
The gantry of this machine was reported to undergo lateral distortions (200-400 microns) at slave end with
respect to time. For a special high precision job, machining with this distortions of the machine was not
meeting the tight tolerance requirements.
The reasons for these distortions were investigated and measurements were carried out. The effects of
variation in environmental conditions on machine distortions were analyzed by finite element method using
ANSYS 6.1 package. The trend of the analysis results closely matched with the actual measurements. This
provided the clues in providing the proper solution. After implementation of the solution experiments were
carried out to check the effectiveness of the solution. The measurements indicated that the distortions were
controlled and requirement of machining accuracy established.
Introduction
The Machine Shop of L&T has a CNC controlled, dual spindle machining center for deep-hole drilling
application.
The structure of the machine is of gantry type. The sketch of the gantry is shown in Figure 1. The gantry is
mounted on guideways through bearings. For transverse motion along the guideways, a drive is provided
on one side of the gantry. This end is called the master end & the other end is called the slave end. The
motion of the gantry in perpendicular direction to guideways is restricted by bearing arrangements at
master end. At the slave end, the gantry is resting on the guide ways and all other motions are free.
Figure 1. Sketch showing overall view of Machine Structure
The gantry of the machine was reported to undergo lateral distortions (200 - 400 microns) at slave end with
respect to time (during different shifts in the shop) even when the machine was in switched off condition.
These distortions of the gantry induced inaccuracies in the finished jobs, which were out of machining
tolerance limits. Hence, it was required to control these distortions. The problem was to find the causes and
suggest a remedial action to control lateral distortions to meet the machining tolerance requirements.
Initial Measurements and Observations
From the initial investigation it was found that the machine was showing lateral distortions at slave end
with respect to time. The ambience of the machine was thoroughly surveyed to check the affecting
parameters like vibrations due to other machines, etc. From the survey it was clear that the most likely
parameter which can affect the machine distortions was the change in ambient temperature. So, it was
decided to carry out measurements to confirm the observations and also to find out the exact magnitude of
distortion of the gantry. Distortions and surface temperatures of the gantry as well as ambient temperature
were measured using high accuracy digital instruments. The measurements were carried out for 24 hours.
The locations of displacement transducers and thermocouples on gantry are shown in Figure 2. Plot of
surface & ambient temperatures v/s time is shown in Figure 3. The surface temperature of gantry was lower
than the ambient temperature, which could be attributed to the condensation of moisture in air and coolant
droplets. The combine plot of distortion at a typical location on slave end v/s time along with ambient
temperature variation v/s time is shown in Figure 4. The ambient temperature variation was 3 deg C for
which the maximum distortion was 370 microns. Also, there was difference in surface temperatures of the
gantry on front and rear side, which varied with time. The combine plot of distortion at a typical location on
slave end v/s time and temperature difference between the front and rear side of gantry v/s time is shown in
Figure 5. The temperature difference between front and rear side of the gantry was 1.7 deg C for the
maximum distortion of 370 microns. The fans directly facing to the exposed surfaces of the machine
increases the convection. It has a predominant effect on the surface temperature. This was observed near
the end of the measurements. The sudden rise in the body temperature (Figure 3) was because the fans
facing the machine were switched on.
Figure 2. Location of Displacement Transducers and Thermocouples on Gantry during
Measurements
Figure 3. Plot of Temperature vs. Time for Initial Measurements
Figure 4. Plot of Ambient Temperature & Distortion at Slave End vs. Time for Initial
Measurements
Figure 5. Plot of Temperature Difference & Distortion at Slave End vs. Time for Initial
Measurements
The other important observation was the provision of bellows on the front side of gantry to protect
guideways for spindle heads from dirt and burs. These bellows enclose stagnant air, which acts as
insulation on the front side of gantry. This slows down the heat transfer from front side as compared to rear
side.
The importance of ambient temperature is also mentioned in the machine manual, which states:
“Absolute machine accuracy depends on four main factors, the accuracy of machine construction, the
accuracy of the measuring system, the stability of the machine foundation and the stability of the machine
temperature and its environment. The temperature of the machine environment will have a significant effect
on the total machine accuracy.”
Hence, it was decided to find the temperature distribution & its effect on lateral distortion of gantry due to
small change in ambient temperature (3 deg C) using finite element analysis.
Finite Element Analysis
The present problem involves thermal-structural analysis. The powerful tool for FEA viz. ANSYS provides
facility for such analysis. The model of thermal analysis can easily be transferred to structural analysis so
modeling time and efforts reduces. Temperature distribution from thermal analysis can be transferred to
structural model to find out structural distortions. So the finite element analysis of the gantry was carried
out using ANSYS 6.1.
Case 1: Analysis for Existing Condition of Gantry
Transient thermal analysis was carried out followed by structural analysis to find out the effect of variation
in ambient temperature on lateral distortions of the gantry.
Finite Element Modeling
The gantry of the machine is a box type structure, which is stiffened with inclined plates. The sectional
view of the gantry is shown in Figure 6. The existing condition of the machine was considered i.e. the
presence of bellows on front side of gantry. The gantry was modeled using 4-noded quadrilateral shell
elements. For thermal analysis, thermal shell elements (SHELL57) & for structural analysis, structural shell
elements (SHELL63) were used. The F.E. Model of the gantry is shown in Figure 7.
Figure 6. Sectional view of Gantry showing Internal Plate Stiffeners
Figure 7. F.E. Model of Gantry showing Structural Boundary Conditions
Thermal Analysis
Transient thermal analysis was carried out to find out temperature distribution in the gantry. Measured
ambient temperature variation was studied and based on the slope of this variation thermal loading was
designed on the conservative side. The initial temperature of gantry was assumed to be uniform and equal
to 30 deg C. Analysis was carried out for a typical ambient temperature variation from 30 deg C to 33 deg
C in 2 hrs and constant at 33 deg C for 3 hrs (Refer Figure 9). The effect of bellows was simulated by
applying equivalent convection heat transfer co-efficient considering the insulating effect of bellows and
stagnant air entrapped between the bellows and gantry structure. Adiabatic condition was assumed for the
inside surfaces of the gantry.
Results of Thermal Analysis
Temperature distribution in the gantry at 18000 sec (5hrs) is shown in Figure 8. The plot of temperature
variation on front and rear side of gantry along with the applied ambient temperature variation is shown in
Figure 9.
Figure 8. Temperature Distribution Plot of Gantry at 18000 seconds for Case 1
Figure 9. Variation of Temperature on Front and Rear Side of Gantry & Applied Ambient
Temperature with Time for Case 1
The temperature variation indicates that the rear side of gantry was approaching ambient temperature faster
than the front side. This is because of
1) More thermal inertia (mass) on the front side of gantry as compared to the rear side.
2) The presence of bellows on the front side encloses stagnant air, which acts as insulation. This reduces
heat transfer between the front side of gantry and atmosphere.
This caused a variation of 0-2 deg C in the temperature difference between front & rear side of the gantry.
This difference could cause lateral distortion of the gantry, which would vary as the temperature difference
changes.
Structural Analysis
The structural analysis was carried out to determine the distortion due to variation in temperature
distribution with respect to time.
Displacement boundary conditions are shown in Figure 7. The master & slave ends of the gantry were
restrained in vertical direction (UY=0). The master end of gantry was also restrained in the direction
parallel to the gantry (UX=0). To avoid rigid body motion the master end was restrained in the lateral
direction (UZ=0) at two nodes. Temperature distribution in the gantry was imported from thermal analysis.
Results of Structural Analysis
Figure 10 shows the plot of total distortion (USUM) of the gantry at 18000 sec (5 hrs). Table-1 gives the
summary of distortions of gantry for present case. The maximum lateral distortions were 103 microns &
190 microns at slave end at 7200 sec & 18000 sec respectively.
Figure 10. Total Distortion Plot at 18000 seconds for Case 1
Table 1. Summary of distortions of gantry for Case 1
Time (Sec)
7200
18000
Location
Distortion (microns)
UZ
UX
USUM
Node 862
2
3
3
Node 887
47
10
48
Max. Value in Model
103
64
106
Node 862
3
7
8
Node 887
88
31
94
Max. Value in Model
190
136
208
(Note: For location of Nodes 862 and 887, see Figure 7.)
This indicates that the distortions were due to uneven temperature distribution. So it was required to reduce
the difference in temperature between front and rear side of the gantry.
Case 2: Analysis without Bellow on the Front Side of Gantry
In Case-1 it was noted that the temperature difference between front & rear side of the gantry varied from
0-2 deg C and one of the reasons for it could be the presence of bellows in the front side. So, in this case
the analysis was carried out assuming absence of bellows.
The model and all other conditions were taken same as in Case 1 (Refer: Finite Element Modeling).
Thermal Analysis
Transient thermal analysis was carried out to find out the temperature distribution in the gantry.
Temperature loading was same as in Case 1 (Refer: Thermal Analysis).
Results of Thermal Analysis
Temperature distribution in the gantry at 18000 sec (5hrs) is shown in Figure 11. The plot of temperature
variation on front and rear side of the gantry along with the applied ambient temperature variation is shown
in Figure 12.
Figure 11. Temperature Distribution Plot of Gantry at 18000 seconds for Case 2
Figure 12. Variation of Temperature on Front and Rear Side of Gantry & Applied Ambient
Temperature with Time for Case 2
The plot shows that the difference of temperature between front and rear side of the gantry was lower than
that in the previous case. It is also clear that the distortion of gantry was proportional to this temperature
difference. So it was desirable to reduce this temperature difference and with the removal of bellows, the
difference reduces considerably. The variation reduced to 0-1 deg C in temperature difference between
front side & rear side of the gantry in this case.
Structural Analysis
To find out the amount of distortion of gantry without bellows, the structural analysis was carried out. The
displacement boundary conditions were same as in Case 1(Refer: Structural Analysis). Temperature
distribution in the gantry was imported from thermal analysis.
Results of Structural Analysis
Figure 13 shows the plot of total distortion (USUM) of the gantry at 18000 sec (5 hrs). Table-2 gives the
summary of distortions of gantry in this case. The maximum lateral distortions were 57 microns & 96
microns at slave end at 7200 sec & 18000 sec respectively. These values of distortions are lower compared
to the values in previous case.
Figure 13. Total Distortion Plot at 18000 seconds for Case 2
Table 2. Summary of Distortions of gantry for Case 2
Time (Sec)
7200
18000
Location
Distortion (microns)
UZ
UX
USUM
Node 862
23
5
24
Node 887
39
32
51
Max. Value in Model
57
61
75
Node 862
56
13
57
Node 887
76
84
113
Max. Value in Model
96
136
155
But it was practically not possible to remove the bellows, because it is used to protect the guideways for
spindle heads from dust and burs. So other alternative was required which is discussed in the following
section.
Case 3: Analysis of Gantry with Insulation on the Exposed Surfaces
Applying insulation on all the exposed surfaces without removing the bellows can help in reducing heat
transfer between the gantry and atmosphere and in turn reduction in distortion. So, in this case analysis was
carried out considering 1-inch thick insulation on all the exposed surfaces of gantry.
The model and all other conditions were taken same as in Case 1 (Refer: Finite Element Modeling).
Thermal Analysis
Transient thermal analysis was carried out to find out the temperature distribution in the gantry assuming
all the exposed surfaces insulated and bellows in its place. Temperature loading was same as in Case 1
(Refer: Thermal Analysis).
Results of Thermal Analysis
Temperature distribution in the gantry at 18000 sec (5hrs) is shown in Figure 14. The plot of temperature
variation on front and rear side of the gantry along with the applied ambient temperature variation is shown
in Figure 15.
Figure 14. Temperature Distribution Plot of Gantry at 18000 seconds for Case 3
Figure 15. Variation of Temperature on Front and Rear Side of Gantry & Applied Ambient
Temperature with Time for Case 3
In this case the difference in temperature between front and rear side of the gantry was 0-0.6 deg C, which
is lower than those in previous cases. Thus providing insulation on exposed surfaces helped in reducing
temperature difference between front & rear side of gantry without removing the bellows.
Structural Analysis
With the reduction in difference of temperatures between front and rear side of the gantry, structural
analysis was carried out to find out the amount of distortion in this condition. The displacement boundary
conditions were same as in Case 1 (Refer: Structural Analysis). The temperature distribution in gantry was
imported from thermal analysis.
Results of Structural Analysis
Figure 16 shows the plot of total distortion (USUM) of the gantry at 18000 sec (5 hrs). Table–3 gives the
summary of distortions of gantry for present case. The maximum lateral distortions were 21 microns & 57
microns at slave end at 7200 sec & 18000 sec respectively. These values are lower than corresponding
values in previous cases.
Figure 16. Total Distortion Plot at 18000 seconds for Case 3
Table 3. Summary of distortions of gantry for Case 3
Time (Sec)
7200
18000
Location
Distortion (microns)
UZ
UX
USUM
Node 862
0
1
1
Node 887
10
2
10
Max. Value in Model
21
13
22
Node 862
1
2
2
Node 887
27
8
28
Max. Value in Model
57
39
61
Thus insulating the exposed surfaces of gantry can considerably reduce the distortions.
Experimental Determination of Distortion after Insulation
Based on the results of the analysis, all the exposed surfaces of the gantry were insulated. Experiments
were carried out to actually determine the improvement in distortion control. The displacement gauges and
temperature sensors were placed at the same locations where placed during initial investigations to compare
the results.
Plot of measured surface temperatures & ambient temperature v/s time is shown in Figure 17. The combine
plot of distortion at a typical location on slave end v/s time along with ambient temperature variation v/s
time is shown in Figure 18. The maximum distortion at this location was 140 microns for the ambient
temperature variation of 8 deg C. The combine plot of distortion at a typical location on slave end v/s time
and the temperature difference between the front and rear side of gantry v/s time is shown in Figure 19. The
temperature difference between front and rear side of the gantry was 0.5 deg C for the maximum lateral
distortion of 140 microns.
Figure 17. Plot of Temperature vs. Time for Measurements after Modification
Figure 18. Plot of Ambient Temperature & Distortion at Slave End vs. Time for
Measurements after Modification
Figure 19. Plot of Temperature Difference & Distortion at Slave End vs. Time for
Measurements after Modification
Thus, with existing conditions for ambient temperature variation of 3 deg C the distortion was 370 microns
(for 8 deg C ambient temperature variation extrapolation gives a value of 987 microns) where as with
provision of insulation, even for actual ambient temperature variation of 8 deg C the distortion was
experimentally found out to be 140 microns. Thus distortion control of the machine was achieved.
Conclusion
The gantry of a CNC machine was reported to undergo cyclic lateral distortions with time at slave end.
These were higher to meet the job tolerance requirements.
The distortions were attributed to change in ambient temperature. Experiments were carried out and
maximum lateral distortion was found to be 370 microns at slave end of the gantry for an ambient
temperature variation of 3 deg C. The surface temperature difference between front & rear side of gantry
was 1.7 deg C and this difference and its variation was the cause of distortions.
Finite element analysis was carried out for a typical ambient temperature variation from 30 deg C to 33 deg
C in 2 hours and constant at 33 deg C for 3 hours. Three different cases were analyzed: i) Analysis without
any modifications, ii) Analysis assuming absence of bellows on front side, and iii) Analysis assuming
insulation on all the exposed surfaces. The maximum lateral distortions were 190 microns, 96 microns and
57 microns respectively for these cases. This indicated provision of insulation as an effective solution.
Based on finding of the analysis, the entire exposed surface of the machine structure was insulated and
measurements were carried out. The measurements showed 140 microns lateral distortion of the slave end
of the gantry for an ambient temperature variation of 8 deg C (for 3 deg C ambient temperature variation,
proportional distortion value works out to be 53 microns which is much less than a distortion value of 370
microns without modification). This is a substantial reduction in distortion value.
But for the state-of-the art FEA tool–ANSYS, proper understanding of the problem and providing a
practical solution in time and with confidence would not have been possible.
Thus, distortion control of the machine was established to achieve required machining tolerances.
Acknowledgement
The authors express their gratitude to the management of Larsen & Toubro Limited for granting permission
to publish this paper.
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