Objectives and Scope of the Study
The evaluation of the machine bed stiffness is part of a broader effort to modernize a prototype of a specialized machine. The goal of this stage is to perform a quantitative and qualitative assessment of the structural stiffness to analyze its impact on machining accuracy.
Based on numerical analysis results and data obtained during prototype operation, key structural elements affecting overall stiffness are identified. The findings will serve as the basis for the customer’s decision on whether design modifications are necessary for future machine models.
Overview of the Object and Input Data
The machine bed is a welded structure consisting of two main components:
Base frame
Platform
The upper surface of the platform serves as the reference surface for installing two feed drives, whose relative positions vary depending on the type of workpieces being processed.
This study evaluates the stiffness of the machine bed for three possible feed drive configurations.
Since the machine bed consists of two welded assemblies connected by bolted joints, the stiffness of these joints must also be considered in the calculations.
The initial data for the numerical analysis were based on solid models of the structure, developed in SolidWorks and presented in Figure 1.
Figure 1. Initial model in SolidWorks format.
The operating loads are represented by axial and lateral forces, acting along and perpendicular to the tool axis, respectively.
Geometry Simplification and Adaptation
The initial model is a welded structure composed of a large number of individual parts. To simplify the computational model, welded joints are treated as monolithic connections.
During model preparation, simplified solid models of the platform and machine bed base were created. Bolted joint elements were replaced with equivalent simplified components (Figure 2).
Figure 2. Model prepared for analysis.
The feed drive housings were replaced with an equivalent remote load applied to the imprints of the housing supports on the platform surface.
A detailed stiffness analysis of the feed drives is not included in this study, as it represents a separate large-scale task within the overall investigation of the machine’s structural stiffness.
Boundary Conditions and Contacts Definition
The following boundary conditions and loads were applied:
Fixed Geometry (Fixed Support) – Constraints were applied to the support components of the machine bed, restricting movement only in the areas of actual contact between the bed and the support.
Gravity Load (Standard Earth Gravity) – Considered in all simulation scenarios.
Preloaded Bolted Joints – Bolts connecting the Base Frame and the machine bed platform were modeled with a preload force (Bolt Pretension) of 31,700 N, applied to the free section of the bolts.
Axial Operational Load – 9,000 N, applied as a Remote Force component.
Lateral Operational Load – 4,000 N, applied as a Remote Force component.
Loading Procedure
The loading sequence was performed in two steps:
Step 1 – Application of the bolt pretension.
Step 2 – Application of the operational load.
For the movable feed drive unit, the load application points varied depending on the installation angle of the drive (0°, 20°, and 60°).
Figure 3. Loads and constraints – Feed drive positioned at 0 degrees.
Figure 4. Loads and constraints – Feed drive positioned at 20 degrees.
Figure 5. Loads and constraints – Feed drive positioned at 60 degrees.
Contact Interactions in the Computational Model
The following contact interactions were defined in the computational model:
Frictional Contact – Between the base of the support frame and the bottom surface of the platform, with a friction coefficient of μ = 0.15.
Frictional Contact – Between the bottom surfaces of bolt heads and their seating areas on the platform.
Bonded Contact – Between the threaded section of the bolts and the threaded holes in the machine bed frame.
Materials
The following materials were used in the computational model:
Welded assembly components – Structural steel S355J2.
Bolts – Carbon steel AISI 1050, water-quenched and tempered at 315°C.
Mesh Generation
A finite element mesh was generated using second-order tetrahedral elements (Tet10).
Based on the minimum feature sizes of the structure, the global element size was set to 15 mm. In contact regions and bolt joint areas, the mesh was refined to 8 mm. The same 8 mm element size was applied to the bolt bodies to ensure accurate stress-strain distribution in these critical zones.
Figure 6. Finite element mesh of the model.
Figure 7. Mesh refinement in bolt joint areas.
To evaluate the quality of the finite element mesh, an analysis was performed using the Jacobian Ratio (Gauss Points) criterion. The distribution graph of this parameter is presented in Figure 8.
Figure 8. Jacobian Ratio (Gauss Points).
Elements with a quality below 0.8 account for less than 12% of the total and are localized in the fillet areas of the machine bed's base channel sections. A refined mesh analysis in these areas demonstrated insignificant impact on the final calculation results while significantly increasing computational costs. Therefore, it was decided to maintain the current discretization in these regions.
Calculation and Results
The distribution patterns of elastic deformations, as well as the deformation behavior along the X, Y, and Z axes and the total deformations, are presented in the following figures.
Three fixed positions of the movable tool mounting unit were analyzed, corresponding to angles of α = 0°, α = 20°, and α = 60°.
This study does not address the factor of safety analysis, and therefore, the corresponding plots are not included.
Figure 9. Elastic deformation plots for the feed drive positioned at 0 degrees.
Figure 10. Elastic deformation plots for the feed drive positioned at 20 degrees.
Figure 11. Elastic deformation plots for the feed drive positioned at 60 degrees.
Figure 12. Elastic deformation plot for the feed drive positioned at 60 degrees.
The strain distribution plots are presented in the figures below.
For better readability and to minimize the influence of localized deformations in the bolted joint areas, the strain plots are displayed in a logarithmic scale.
Figure 13. Strain plot for the feed drive positioned at 0 degrees.
Figure 14. Strain plot for the feed drive positioned at 20 degrees.
Figure 15. Strain plot for the feed drive positioned at 60 degrees.
Results Analysis
It was determined that the highest total displacement, measuring 132.3 µm, occurs when the movable feed drive unit is positioned at α = 60°. For angles 0° and 20°, the maximum elastic displacements are 69 µm and 87 µm, respectively. In all configurations, the largest displacements are observed on the mounting side of the movable feed drive unit.
When the feed drive is positioned at α = 60°, the highest strain levels are observed in the support frame, whereas for other angles, the upper platform plates exhibit the most significant deformations.
The maximum displacement due to joint separation is 5 µm.
Based on the strain distribution patterns and deformation magnitudes, the overall stiffness of the machine is primarily influenced by the stiffness of the support frame and the stiffness of the platform joint beneath the working area. This effect is most pronounced when the movable feed drive unit is positioned above the protruding section of the frame.
Significant deformations were recorded in the welded plate attachment areas for support mounts. In these regions, the lower flange of the channel sections experiences pure bending, which negatively affects the overall structural stiffness. This effect is especially critical when the supports are placed in the central sections of the channels rather than at their corner joints.
Conclusions and Recommendations
Excessive elastic displacements were recorded when the movable feed drive was positioned at α = 60°.
Joint stiffness has a negligible effect on the overall deformation pattern, and bolted connections do not require modifications. However, it is recommended to consider increasing the thickness of the mounting plates for the mating components to improve rigidity.
Structural reinforcement in the working area:
It is necessary to analyze options for modifying the frame under the working area or reinforcing the platform, as significant “bending” deformations of the platform occur in this zone.
Frame modification should be prioritized, as the current arrangement of stiffening elements under the working area is suboptimal.
In areas where significant deformations of the channel sections occur (bending or unbending of the flanges relative to the web), additional stiffening ribs should be incorporated.
The frame structure in the support area under the protruding section should be reinforced to ensure sufficient rigidity when the feed drive is positioned at α = 60°.
The support placement scheme for the protruding section of the frame should be revised. The optimal solution is to replace a single central support with two supports positioned at the corners of the protruding section.
Deformations of the platform’s upper plate:
Due to the orientation of the platform ribs along the areas subjected to feed drive loads, the rigidity of the upper plate significantly affects local deformations.
It is recommended to increase the thickness of the upper plate or install additional transverse ribs under the load-bearing areas.