Stress analysis of a rolling slideway.
Rusu-Casandra, Aurelia ; Iliescu, Nicolae ; Baciu, Florin 等
1. INTRODUCTION
The qualitative leap registered lately in machine-tool building
industry can be estimated mainly by the increasing of the processing
accuracy, of the kinematic precision and of the dynamic performance of
the machine-tools in terms of reducing energy consumption. In order to
achieve these performances, new machine parts have been developed,
examples being the driving screws, the guides and the transmissions with
intermediate elements (Ito, 2008; Nicolescu, 2009). All these machine
structures are subjected to complex loads that occur during service. In
order to properly design them and to increase their reliability in
operation it is necessary to know the state of stress in the component
elements. This analysis, based on the classical methods of mechanics of
materials, the theory of elasticity (Rusu-Casandra, 2008) or the finite
element method, requires several simplifying assumptions regarding the
geometry of the structure, the way of applying the loads, the mechanical
behavior etc. As a result, the behavior of structures resulting from
calculation differs from reality sometimes. Therefore, more accurate
knowledge of the state of stress in the machine components is necessary.
Correspondingly, this paper presents a comparative study of the
stress state in the guiding elements of a rolling slideway (Fig.1). The
analysis was performed using two methods, a computational and an
experimental one respectively. On evaluating various alternative methods
of experimental analysis, the photoelastic technique (Iliescu &
Atanasiu, 2006). has been chosen in order to validate the mathematical
model of calculation obtained with the finite element method.
2. NUMERICAL CALCULUS
A finite element analysis was performed using SOLIDWORKS software
(***2010). The model representing a cross section through a rolling
slideway, with a Poisson's ratio value applicable to photoelastic
materials, was loaded through a system of levers in two separate ways:
a) with the weight [P.sub.H]=640N applied in the horizontal plane, in
five different sections corresponding to common working operating
conditions; b) with the weight [P.sub.V]=800N applied in the vertical
plane. Both the boundary conditions and applied loads used for the
finite element model were chosen to be similar to those of the
photoelastic model. The contour plots of the principal stress
[[sigma].sub.1] for the model subjected to the force [P.sub.H] applied
in one of the five investigated sections are shown in Fig.2, and for the
model loaded with [P.sub.V] in Fig.3 respectively.
[FIGURE 1 OMITTED]
3. PHOTOELASTIC INVESTIGATION
The two elements of the photoelastic model of the rolling slideway
(the sled and the guide prism) were cut from a DINOX-010 plate of 0.5mm
thickness, at a scale 1:2, while the balls were modeled by cylindrical
rollers made of plexiglass. The processing of these components was made
with high precision, so the interference to be minimal. The loaded
photoelastic model was examined in the polarized light from a circular
polariscope. Figure 4 shows the isochromatic patterns photographed for
the model subjected to force [P.sub.H] applied in the same section as
for the case presented in Fig.2. Fringe-patterns obtained in the model
loaded with the force [P.sub.V] are shown in Fig.5.
In all six investigated cases it was noticed that the values of
stresses in the guide prism is much smaller in comparison with the ones
in the sled, the latter taking over the load transmitted by the
machine-tool. Therefore the principal stress distribution
[[sigma].sub.1] on the unloaded boundaries was determined only for the
sled. In Fig.6 and Fig.7 are plotted the curves of the principal stress
[[sigma].sub.1] on the interior contours of the sled for the cases of
loading shown in Fig.4 and Fig.5 respectively.
4. CONCLUSION
The stress analysis of a model of a rolling slideway, performed
numerically (Fig.2 and Fig.3) and experimentally (Fig.6 and Fig.7) for
five cases of loading in the horizontal plane and one case of loading in
the vertical plane led to the conclusions:
a) In all cases it has been found that the load is mostly taken
over by the sled, the values of stresses in the guide prism being much
smaller.
b) The maximum stressed area for loading in horizontal plane is in
the interior of the sled, on the force side. Studying all five cases, it
was remarked that the values of the principal
stress [[sigma].sub.1] in this area increase as load moves
downwards, the highest stress occurring when force [P.sub.H] is applied
on the lower end of the sled (Fig.8).
c) The loading in vertical plane shows a tendency of deformation of
the sled, that makes the contact between the sled and the guide prism
take place at the top, in the central area. As a result, in this region
will appear sliding friction forces that will affect the normal movement
of the sled. At the same time, due to the deformation the sled will
open, the interference between the sled and rollers will increase and
the rollers will no longer be involved in rolling motion. Therefore, in
such situations, it is necessary to make an appropriate adjustment of
these interferences.
d) No noticeable discrepancies occur between theoretical and
experimental results.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
As further work, with the more accurate information regarding the
stress state offered by this study, it is possible to correct the shape
and dimensions of the elements of rolling slideways and finally obtain a
reduction of the material consumption in terms of high reliability.
5. REFERENCES
Iliescu, N.& Atanasiu, C. (2006). Metode tensometrice in
inginerie (Stress Analysis Techniques in Engineering), Editura AGIR,
ISBN 973-720-078-0, Bucuresti
Ito, Y.(2008). Modular Design for Machine Tools, McGraw-Hill
Companies, ISBN 978-007-149-660-5, New York
Nicolescu, A. (2005). Roboti industriali (Industrial Robots), EDP Publishing House, Bucharest, Romania
Rusu-Casandra, A. (2008). Elasticity in Engineering, Editura AGIR,
ISBN 978-973-720-188-1, Bucuresti
*** (2010) Solidworks User Manual, Dassault Systems SolidWorks
Corp, Concord, MA, USA
