Static analysis of multi-support spindle shafts with nonlinear elastic bearings

In this paper a mathematical model and computational tool are developed for the static analysis of multi-bearing spindle shafts with nonlinear elastic supports. Based on the Timoshenko beam theory a resolving system of equations is obtained that takes into account the nonlinear dependence of the bearing stiffness on the reaction forces acting upon them. A solution method is proposed and appropriate software is developed that implements the static analysis of multi-support spindle shafts with non-linearly elastic bearings in MATLAB environment. Key words: spindle, shaft, nonlinear elastic support, multi-bearing, nonlinear elastic stiffness, Timoshenko beam.

Optimization of two support spindle shaft on nonlinear elastic supports by rigidity characteristics

One of the main structural elements of metalworking machines is the spindle assembly (spindle), which is used to hold cutting tools or workpieces. The rigidity of the spindle assembly plays a decisive role in ensuring the accuracy and efficiency of the machine as a whole. The assessment of the spindle shaft stiffness is carried out on the basis of the analysis of the static bending of the spindle shaft, which made it possible to formulate and solve the problems of optimizing the spindle shaft according to the stiffness characteristics for two supporting structures on nonlinear elastic supports. To determine the stiffness of roller bearings, the work uses the dependence obtained on the basis of solving the problem of contact interaction of an elastic steel cylinder with curvilinear elastic steel half-spaces. For the considered design scheme, the optimization goals were chosen for the conditions of the smallest displacement of the end section of the spindle shaft console, the achievement of the minimum angle of rotation in this section or the minimum of their normalized superposition, which ensures maximum rigidity in the processing zone. Consideration has also been given to minimizing the swing angle at the front support to maximize bearing life. Mathematically, the problem is presented in the form of minimizing one of the 4 proposed objective functions by changing the variable parameters - the length of the cantilever and the value of the inter-support distance, represented as dimensionless quantities - the cantilever coefficient and the inter-support distance coefficient. Minimum and maximum values ​​of the cantilever length and shaft span were considered as constraints on the variable parameters. Varying the console coefficients and the inter-support distance was carried out by the method of sequential enumeration within the specified constraints, the solution of optimization problems is presented in a graphical form. The solution to the problem of shaft bending was carried out on the basis of the equation of the bent axis of the beam in the framework of the Euler - Bernoulli hypotheses and presented in an analytical form together with analytical dependencies for calculating the radial stiffness of a roller bearing as a function of the supporting force acting on it. The algorithm for solving optimization problems is implemented in the MatLAB package. Optimal solutions have shown that the minimum of the combined functions, consisting of the sum of the relative deflection values ​​at the end of the console and the angles of rotation at the end of the console and on the front support, is achieved at the same variable parameters as the minima of the angles of rotation at the end of the console and on the front support. The proposed approach to the design of the shafts of spindle units of metal-cutting machines, which are optimal in terms of rigidity characteristics, forms a tool for a reasonable choice of bearings and design parameters of spindle shafts.

Parameter Sensitivity Analysis on Dynamic Coefficients of Partial Arc Annular-Thrust Aerostatic Porous Journal Bearings

Aerostatic bearings are widely used in high-precision devices. Partial arc annular-thrust aerostatic porous journal bearings are a prominent type of aerostatic bearings, which carry both radial and axial loads and provide high load-carrying capacity, low air consumption, and relatively low cost. Spindle shaft tilting is a resource-demanding challenge in numerical modeling because it involves a 3D air flow. In this study, the air flow problem was solved using a COMSOL software, and the dynamic coefficients for tilting degrees of freedom were obtained using finite differences. The obtained results exhibit significant coupling between the tilting motion in the x-and y-directions: cross-coupled coefficients can achieve 20% of the direct coefficient for stiffness and 50% for damping. In addition, a nonlinear behavior can be expected, because the tilting motion within 3°, tilting velocities within 0.0012°/s, and relative eccentricity of 0.2 have effects as large as 20% for direct stiffness and 100% for cross-coupled stiffness and damping. All dynamic coefficients were fitted with a polynomial of eccentricity, tilting, and tilting velocities in two directions, with a total of six parameters. The resulting fitting coefficient tables can be employed for the fast dynamic simulation of the rotor shaft carried on the proposed bearing type.

METHOD OF SELECTING THE OPERATION PARAMETERS OF ELECTRIC SPINDLE WITH AEROSTATIC SUPPORTS FOR SEPARATION OF SEMICONDUCTOR PLATES TO CRYSTALS. PARTS 2–3

The article presents the results of studies of the shaft oscillation processes of a precision horizontal highspeed electric spindle with aerostatic radial and axial supports, used at Planar OJSC in equipment for separation of semiconductor plates into crystals. The studies were carried out using the developed mathematical models that take into account the design features of these electric spindles, including the cantilever mounting of the cutting tool, the imbalance of the diamond disc with the mandrel and the mass ratio of the main components of the electric spindle, as well as the results of their full-scale tests. Based on the analysis of the data obtained, regularities are shown that connect the amplitude values of the oscillations of the electric spindle shaft with the imbalance of the diamond disc with the mandrel and the rotational speed of the electric spindle, which made it possible to propose engineering dependences for choosing the permissible values of the imbalance and rational, from the standpoint of resonance conditions and permissible shaft oscillations, rotational speed of the electric spindle. Recommendations have been developed for the creation of a system for monitoring and active control of the parameters and functioning of the electric spindle in the process of separating semiconductor plates into crystals, which make it possible to use the resonant mode of radial oscillations to improve cutting conditions, excluding direct contact of the working surfaces of aerostatic supports, their seizure and loss of performance of the electric spindle. The article presents a method of selecting the operation parameters of a high-speed precision horizontal electric spindle with aerostatic radial and axial supports and a cantilever mounting of a diamond cutting disc. It is based on the analysis of the simulation results of shaft forced oscillations and data on the shaft oscillations during the operation of the electric spindle with different rotation frequencies and imbalances. The results obtained can be used to monitor shaft oscillations during the operation of the electric spindle, while the high operation efficiency of which is achieved by adaptive control of rotation frequencies taking into account the amplitudes of these oscillations.

Development of Hydraulic Turbodrills for Deep Well Drilling

The article discusses the possibility of improving the design of the turbine of a hydraulic drilling machine for drilling wells in very hard rocks and at considerable depths (5000–12,000 m). The analysis of the results of studies on the technical and technological characteristics of downhole drilling motors showed that it is impossible to ensure stable operation due to the limitation on the operating temperature, while with an increase in the flow rate of the drilling fluid, they do not provide the required power on the spindle shaft, and cannot reach high-speed drilling. In such conditions, turbodrills with a significant change in the profile of the stator and rotor blades and a reinforced support unit are most suitable. The paper presents an invariant mathematical model, which made it possible to determine the optimal geometric parameters based on preselected boundary conditions and the main performance characteristics of the turbine being developed. The results obtained were tested by the finite element method, which showed a convergence of 12.5%. At the same time, zones with the lowest and highest flow rates were identified. Additionally, this paper presents a comparative analysis of the obtained hydraulic turbine with turbodrills of the TSSH-178T and Neyrfor TTT 2 7/8 brands. In comparison with the domestic turbodrill, the developed turbine design shows a 13-fold reduction in its length and a 3-fold reduction in torque, provided that the maximum power is increased by 1.5 times. In comparison with the foreign analog, there is a decrease in length by 8.5 times, an increase in torque by 5 times, and in maximum power by 6.5 times.

Flow-Heat-Solid Coupling Thermal Deformation Analysis of Hydrostatic Spindle under Viscosity Temperature Effect

The hydrostatic bearing oil film plays a key role in supporting and lubricating. As the speed increases, the temperature of the lubricating oil increases and the viscosity decreases. As a result, the bearing capacity of the oil film is reduced, which affects the motion accuracy of the hydrostatic bearing. In this paper, the simulation and analysis of the temperature rise of the hydrostatic bearing oil film under the constant viscosity and the viscosity-temperature effect are performed respectively. Then, based on the fluid-heat-solid coupling analysis theory, the temperature field of the hydrostatic bearing and the thermal deformation of the spindle shaft with and without the viscosity-temperature effect are analyzed separately. The temperature field of the shaft and the thermal deformation of the spindle shaft are analyzed separately. Finally, the bearing temperature and shaft deformation are compared with the experimental values for error analysis. It is found that the error rate is smaller when the viscosity-temperature effect is considered. Considering the viscosity-temperature effect, the maximum error rates of the temperature of the radial and thrust bearing bushes are 11.05% and 7.82%, and the maximum error rates of the thermal deformation of the spindle shaft in the axial and radial directions are 12.03% and 18.57%.

Multi-Field Coupling Dynamics Modeling of Aerostatic Spindle

The aerostatic spindle in the ultra-precision machine tool shows the complex multi-field coupling dynamics behavior under working condition. The numerical investigation helps to better understand the dynamic characteristics of the aerostatic spindle and improve its structure and performance with low cost. A multi-field coupling 5-DOF dynamics model for the aerostatic spindle is proposed in this paper, which considers the interaction between the air film, spindle shaft and the motor. The restoring force method is employed to deal with the times varying air film force, the transient Reynolds equation of the aerostatic journal bearing and the aerostatic thrust bearing is solved using ADI method and Thomas method. The transient air film pressure of aerostatic bearings is obtained which clearly presents the influence induced by the tilt motion of the spindle shaft. The motion trajectory of the spindle shaft is obtained which shows different stability of the shaft under different external forces. The dynamics model shows good performance on simulating the multi-field coupling behavior of the aerostatic spindle under external force. which is quite meaningful and useful for the further research on the dynamic characteristics of the aerostatic spindle.

Perbandingan Eksperimental dan Simulasi Frekuensi Pribadi pada Struktur Spindel CNC

The Research was about the comparison between experiment and simulation of natural frequency in CNC spindle. CNC spindle vibration will reduce machine tool performance. It could lead to the damage of the machine tool. The spindle structure unbalances of machine tools will cause vibration when it is operated. In the CNC machine, the spindle shaft vibration should be minimum. Based on this point, the natural frequency testing on the spindle shaft structure was carried out. The experiments were conducted by employing oscilloscope which could provide the vibration data in the time domain. The data was converted into the frequency domain using FFT. Measurements were carried out on 7 times of testing. Every one time of testing, 10 data were taken at each testing points. The tests were conducted at 10 testing points. Therefore, the total data obtained were 700 test data. The test results were then compared with the results of simulation modeling in 10 vibrate modes using Solidwork software. After testing and simulations were compared, 4 personal frequency values were obtained in the test that uses a measuring instrument and 6 personal frequency values could not be read. These were because the accelerometer used could not read up to 0 Hz frequency. Natural frequency obtained from simulations and tests were expressed in the percentage of errors. The largest error value in the 9th vibration mode measurement with a natural frequency was 2117.96 Hz with an error of 0.32%. The smallest error value was 0.11% with a natural frequency of 2995.79 Hz.

Experimental and numerical investigation of difference in diameter enlargement and circularity of micro-holes drilled by flexural spindle head

The flexural bearing or the flexural cartridge allows very nano-meter axial displacement movement, which is frictionless and noiseless. The repeatability of the mechanism obtained is achieved by bending of the load element. The bearing can operate under stringent conditions such as vacuum, elevated temperatures (0–40 °C), and moist conditions. Hence, due to these indigenous properties, these bearings are observed in applications such as linear bearing of linear compressor, flexural bearing electromagnetic linear actuator, and parasitic error-free mechanism. The endorsed capability of obtaining high-level positional accuracy along with repeatability leads to design and development of low-cost flexural cartridge for micro-drilling spindle head. This flexural cartridge provides a linear guideway while feeding inside the test specimen (in micro-drilling operation). The designed head dampens and nullifies the force, acting on the shaft carrying the micro-tool. The designed spindle head carrying the three-leg spiral flexural stack is assembled on the designed machine tool. The run out measured on the spindle shaft is 50 µm. Four test specimens, namely aluminum, brass, acrylic and mild steel, are drilled by three drills of diameter 1 mm, 0.8 mm, and 0.5 mm each. The main objective of the article is to understand the differential analysis of diameter enlargement and circularity between the experimental method and the numerical method. The answers predicted by the experimental method may have second possible value as it depends upon judgment of inscribing the circle/points in the computer-aided design (CAD) environment. This ambiguity is excluded by the MATLAB code, which gives one specific answer. The maximum difference in diameter enlargement for aluminum, brass, acrylic, and mild steel specimens are 3.8 µm, 11 µm, 24.6 µm, and 16.1 µm, respectively, whereas the maximum difference in circularity for the same specimens is 11.8 µm, 1.3 µm, 8.2 µm, and 16.8 µm, respectively. This difference is termed as the |error|.