Thermal Deformation Model Research Articles

Real-time thermal deformation compensation method for active phased array antenna panels

The electromagnetic (EM) performance of active phased array antennas (APAAs) is significantly influenced by thermal deformation of the antenna panels caused by thermal power consumption and ambient temperature change. This paper proposes a method to reduce the influence of thermal deformation on the EM performance of small APAAs via real-time compensation. In the proposed method, a thermal deformation prediction model is first constructed based on analysis of experimental data. The model is then used to accurately predict thermal deformation based on the measured values of several key temperature sensors in real time, and the EM performance is compensated by adjusting the array phase difference controlled by a phased shifter according to the predicted results. The results of experiments conducted indicate that the thermal deformation model has high prediction accuracy, and the decrease in EM performance caused by antenna panel thermal deformation is effectively reduced by the proposed method. Thus, the proposed method has positive implications for improving the overall performance of APAAs.

Mathematical model of coupled thermo-mechanical behavior during plane strain compression of 06Cr19Ni9NbN steel

The process of plane strain compression of 06Cr19Ni9NbN steel was carried out in the temperature range of 1000–1200 °C and the reduction ratio range of 10–50%. Combining the finite element numerical simulation, a new constitutive model of thermal deformation was established, which provides the theoretical basis to optimize the plane strain compression process of the steel. The temperature and grain size at different regions were achieved by experiment and simulation, respectively. According to the results, the mathematical models of stress and temperature during the plane strain compression were established by mathematical analysis method. The new temperature models were established in three regions, respectively, and the stress models took account of the variation of temperature and strain rate. Finally, by comparing the results of calculation, numerical simulation and experiment, the accuracy and validity of these mathematical models were verified.

An accurate thermal performance modeling and simulation method for motorized spindle of machine tool based on thermal contact resistance analysis

Motorized spindle is an inevitable choice of precision machine, but it has a prominent heat problem for its specific configuration of build-in motor. The paper proposed temperature distribution and thermal deformation modeling and a thermal-structural coupling simulation analysis method for a motorized spindle system from a vertical machining center. In order to establish an accurate finite element model, the boundary condition of joint thermal contact resistance (TCR) was taken into account. The paper detailed on how to obtain the TCR value which is related to the machine tool parameters by means of experimental and theoretical methods, and carried out a simulation experiment for the purpose of acquiring a quantitative analysis of the TCR influence on the temperature results. In order to verify the effectiveness of the TCR relevant methods, the experiment was carried out. The agreement between the experimental results and the simulation results showed that the proposed method can more accurately simulate the thermal characteristics of the motorized spindle.

Modelling and compensation of thermal deformation for machine tool based on the real-time data of the CNC system

As one of the main issue affecting the precision and stability of the machine tool, thermal deformation is determined by the environmental temperature as well as the heat generated in the working process of machine tool. Currently, research work on the modelling of thermal deformation mostly rely on the data retrieved from temperature sensors embedded or amount on the machine tool, where the thermal deformation is modelled as function of temperature field in the machine tool. Thermal deformation thus modelled is normally impractical in the thermal compensation process because of the high cost and low stability it may incur when a set of temperature sensors are utilized. In this paper, a novel approach for modelling and predicting the thermal deformation of ball screw is proposed. Instead of relying on the data from temperature sensors, the real-time data of the CNC system, e.g., current and velocity of driving motor, and displacement of axis, is utilized directly to derive the thermal deformation model. With such data, a model is firstly built with considering the heat generated from friction motion as well as the heat dissipation with the machining environment; the parameters of the proposed model were then identified by a multiple linear regression method. Based on the proposed model, the thermal deformation of ball screw can be precisely estimated in both the warming up and cooling down state of the machine tool, as validated by experiments on a ball screw of a small size machine tool.

Research on thermal deformation of large CNC gear profile grinding machine tools

Thermal deformation of large computer numerical control (CNC) gear profile grinding machine tools, which causes the position changes of grinding point between a grinding wheel and workpiece in X and Y directions, affects the machining accuracy significantly. In view of this situation, a theoretical model of thermal deformation based on the theories of thermal expansion of metallic materials, extensional axis of beam, non-uniform temperature distribution of Euler-Bernoulli beam, and Kirchhoff assumption of plane section is proposed according to the complex structure and machining process of the machine tools. To verify the accuracy and the reliability of the model, an experimental system and a platform for thermal deformation are established on a large CNC gear profile grinding machine tool, and the experimental data of temperature and displacement is measured and analyzed. Compared with theoretical value of displacement, the measurement data indicates that the relative errors are no more than 5 %. The proposed theoretical model and the adopted theories, technologies, and methods have great guidance significance and practical value to improve the accuracy of the machine tools effectively.

Influence of thermal deformation of a multilayer dielectric grating on a spectrally combined beam.

In spectral beam combining (SBC) systems, temperature rise inevitably happens to the multilayer dielectric grating (MDG) due to irradiation of the high-power continuous-wave (CW) laser, resulting in thermal deformation of the MDG and degradation of the characteristics of the combined beam due to thermal deformation of the grating. The calculation model of thermal deformation of the MDG has been proposed, and the distributions of temperature field and thermal deformation of the grating have been analyzed. On this basis, a propagation model of a SBC system has further been built up. By utilizing the diffraction integral method and the principle of incoherent superposition, the intensity distribution and the beam quality of the combined beam with different power densities based on the MDG have been numerically calculated and analyzed in detail. The results show that both the maximum temperature rise and the thermal deformation of the MDG increase dramatically with the increasing power density of the incident laser beam. Side lobes appear in the intensity distribution of the combined beam due to thermal deformation of the MDG. Furthermore, the side lobes of the combined beam become increasingly obvious with increasing power density. Additionally, the beam quality of the combined beam degrades significantly with increasing power density of the incident laser beam.

Numerical investigation on screw rotor deformation and influence on volumetric efficiency of the twin-screw multiphase pump

The thermal and force deformation model was established to investigate the rotor deformation and its effect on the volumetric efficiency of the twin-screw multiphase pump with high gas volume fractions (GVFs). Based on the ANSYS software, the deformations under different GVFs were calculated. The influence of the deformations on the clearance, the leakage flow rate and the volumetric efficiency was then analyzed. It was found that the largest clearance variation under the deformation was the radial clearance, followed by the circumferential clearance, and there was little change in the flank clearances. With the GVF increasing from 80% to 94%, the pump volumetric efficiency increased gradually. However, it decreased sharply when the GVF exceeded 94%. Finally, the rotor clearances were analyzed and optimized, and the recommended mounting clearances were proposed, which could decrease the leakage and prevent the rotor from being stuck when large deformations occurred.

Measurement of thermal expansion coefficient of graphene diaphragm using optical fiber Fabry–Perot interference

Application of the Fabry–Perot (FP) interference method for determining the coefficient of thermal expansion (CTE) of a graphene diaphragm is investigated in this paper. A miniature extrinsic FP interferometric (EFPI) sensor was fabricated by using an approximate 8-layer graphene diaphragm. The extremely thin diaphragm was transferred onto the endface of a ferrule with an inner diameter of 125 μm, and van der Waals interactions between the graphene diaphragm and its substrate created a low finesse FP interferometer with a cavity length of 36.13 μm. Double reference FP cavities using two cleaved optical fibers as reflectors were also constructed to differentially cancel the thermal expansion effects of the trapped gas and adhesive material. A temperature test demonstrated an approximate cavity length change of 166.1 nm °C−1 caused by film thermal expansion in the range of 20–60 °C. Then along with the established thermal deformation model of the suspended circular diaphragm, the calculated CTE ranging from −9.98 × 10−6 K−1 to −2.09 × 10−6 K−1 conformed well to the previously measured results. The proposed method would be applicable in other types of elastic materials as the sensitive diaphragm of an EFPI sensor over a wide temperature range.

Dynamic error compensation for industrial robot based on thermal effect model

This paper analyses the kinematic parameters and the positioning accuracy of robot end effectors influenced by temperature factors. Temperature factors include robot self-heating and environmental temperature changes. This paper also builds the thermal distribution model and deformation model using finite element theory. A thermal compensation strategy is presented to validate the significant correlation between the robot kinematics parameters and previous thermal models mentioned above. It is convenient and suitable for industrial field. Thermal compensation is experimentally proved to adjust the position error of the end effectors by less than 0.1mm.

Thermo-mechanical analysis of angular contact ball bearing

The thermal-mechanical character, which is difficult to ensure because of the lack of a corresponding theory and tool, has a significant effect on the dynamics of bearings. It even leads to a sudden failure of bearings in a working situation. In this research, a thermal deformation model was established, based on the analysis of temperature effect on the basic size of angular contact ball bearing. And the transmission from rolling size to bearing axial stiffness was explicit. On the basis of the variation of Hertz contact stiffness and the change of initial contact angle of angular contact ball bearing caused by temperature rise, a “Thermo- mechanical” model of bearing was proposed. According to this model, using the corresponding calculation procedure programmed by MATLAB, the effect of bearing temperature on the axial stiffness has been studied. And the correctness of this model was verified with experiments. Some design suggestions have been made for the decision of bearing preload: to prevent the bearing failure caused by overheating.

Numerical investigation on thermal deformation of friction pair in hydro-viscous drive

Thermal deformation of friction pair has a significant effect on the working performance of hydro-viscous drive. In order to investigate the combined effect of temperature variation and constraints on the thermo-elastic-plastic deformation of friction pair in hydro-viscous drive during the soft-start, transient thermal deformation model is established for numerical simulation. Thermo-elastic-plastic constitutive equations coupled with thermal strain and mechanical strain are described in detail. Using the constitutive equations derived, indirect coupling numerical method based on the finite element program is developed and used to predict distributions of the temperature, displacement and stress of the disks. The research results show that there are three types of saucer-shaped warping deformation and one type of wave-shaped warping deformation with regard to different constraints. The characteristics of various kinds of displacement and stress are concerned with thermal conductivity and constraints. When the disks are under double constraints, the maximum stress that surpasses the yield stress appears in the disk. When the disks are not under any constraints, minimum stress leads to minimum displacement. To a large extent the deformation size is decided by the location and number of constraints.

Thermodynamic properties and X-ray diffraction of Bi4Ti3O12

The temperature dependence of heat capacity of Bi4Ti3O12 has been measured for the first time in the range from 7 to 346 K by precision adiabatic vacuum calorimetry. The experimental data were used to calculate standard thermodynamic functions, namely the heat capacity, enthalpy Ho(T) − Ho(0), entropy So(T) − So(0), and Gibbs function Go(T) − Ho(0), in the range from T → 0 to 346 K. The structure of Bi4Ti3O12 is refined by the Rietveld method (space group Fmmm, Z = 4) at temperatures of 173, 273, 373, 473 K. Thermal deformation model is proposed on the basis of structural data.

Deformation Measurement and Pointing Model Analysis of 25m Antenna

The pointing of an antenna always exists deviation due to track deformation, gravity and thermal influence. Through long time observation, we find that sunlight also has some influence on antenna structure. In order to get the antenna pointing deviation in the effects of the sunlight of 25m antenna in Urumqi, we use the frame-typed level and thermometer to make a week’s measurement about the temperature around the antenna and the antenna tilt. The measured data was analyzed and combined with the track deformation data, and the pointing error fixed model as well as the thermal load deformation model were built. The measured data was fitted by the two models, and the result shows that the model can well reflect the pointing error and thermal load error, thus can give a better understanding of the antenna deformation, and also can give some good reference to antenna pointing calibration and the antenna’s reconstruction.

Thermal Deformation Research on Cutaway Disk of Automatic Brake Adjuster

The thermal deformation model of cutaway disk is proposed for automatic brake adjuster based on its mechanical model. This model can solve the geometrical relationship between cutaway disk and the self-adjust clearance increment, illustrate the thermal deformation law, and calculate the self-adjust clearance increment caused by the thermal deformation of cutaway disk. A self-adjust performance test system of automatic brake adjuster with a multiple incubator is set up to dynamic test the clearance increment in varying temperatures. The experimental result with seven groups of trials shows that the relative error range is [0.01, 0.13]. Comparing with the true values, the grey incidence degree of our suggested model is 0.98 while that of FE model is 0.92. The mean absolute errors are 0.14° for our suggested model and 0.53° for FE model. It indicates that our suggested model is approximate to FE model both for accuracy and veracity. What's more, our suggested model is more suitable for measuring application because it is easy to build comparing twith FE model.

A posture evaluation method for a large component with thermal deformation and its application in aircraft assembly

Purpose – The purpose of this paper is to propose a posture evaluation approach based on temperature compensation and three-dimensional (3-D) tolerance for the key points (KPs). Design/methodology/approach – A large component 3-D compensation model of thermal deformation considering characteristics of the assembly object is developed. Then, the thermal deformation compensation model is used to modify the nominal coordinates for the KPs. By using a combination of relative deviations of KPs as the objective and 3-D tolerance as the constraints, an optimization model for posture evaluation is established. Findings – Deviations of posture and KPs’ coordinates are obtained by solving the non-linear constrained optimization problem. The posture evaluation method is demonstrated in both a simulation case and practical implication of the aircraft components assembly system with the result that a good performance is obtained. Practical implications – The proposed method has been used in several aircraft assembly projects in China, and gained a good effect. Originality/value – This paper proposes a method for eliminating the affection of thermal deformation during posture evaluation process and improving the consistency and stability of posture evaluation results. The results of this research will help to systematically improve the manufacturing process and tolerance allocation efficiency in large aircraft assembly.

Effect of Thermal Deformation on Part Errors in Metal Powder Based Additive Manufacturing Processes

In metal additive manufacturing (AM) processes, parts are manufactured in layers by sintering or melting metal or metal alloy powder under the effect of a powerful laser or an electron beam. As the laser/electron beam scans the powder bed, it melts the powder in successive tracks which overlap each other. This overlap, called the hatch overlap, results in a continuous cycle of rapid melting and resolidification of the metal. The melting of the metal from powder to liquid and subsequent solidification causes anisotropic shrinkage in the layers. The thermal strains caused by the thermal gradients existing between the different layers and between the layers and the substrate leads to considerable thermal stresses in the part. As a result, stress gradients develop in the different directions of the part which lead to distortion and warpage in AM parts. The deformations due to shrinkage and thermal stresses have a significant effect on the dimensional inaccuracies of the final part. A three-dimensional thermomechanical finite element (FE) model has been developed in this paper which calculates the thermal deformation in AM parts based on slice thickness, part orientation, scanning speed, and material properties. The FE model has been validated and benchmarked with results already available in literature. The thermal deformation model is then superimposed with a geometric virtual manufacturing model of the AM process to calculate the form and runout errors in AM parts. Finally, the errors in the critical features of the AM parts calculated using the combined thermal deformation and geometric model are correlated with part orientation and slice thickness.

Research on thermal deformation of large-scale computer numerical control gear hobbing machines

Research on thermal deformation of large-scale computer numerical control (CNC) hobbing machines is on the purpose of obtaining the law of thermal deformation of gear hobbing machines to improve machining precision. According to the structure characteristics of hobbing machines, this paper presents a novel computing model of thermal deformation based on the theory of the thermal expansion deformation of metallic materials, the extensional beam theory, non-uniform temperature distribution of the Euler-Bernoulli beam and Kirchhoff theory of plane-section assumption. Then, the coupling theory of axial and bending deformation of hobbing machines based on the deformation element and equilibrium element method is proposed. The experimental measurement system and platform for thermal deformation of gear hobbing machines is established. The temperature and displacement data of thermal deformation of a certain type gear hobbing machine is analyzed, which has demonstrated the law of thermal deformation of hobbing machines. The locus curves for overall displacement error of cutting points and teeth trace error are obtained. Comparing deformation theory and experimental data, the relative error is lower than 5%, which verifies the computing model proposed by this paper, and shows the research method has great significance for structural optimization, local temperature control, and prediction and compensation for thermal deformation error of gear hobbing machines.

A method for thermal performance modeling and simulation of machine tools

The development of precision machine tools requires an accurate understanding of the thermal be- haviour of the tools. Therefore, by developing highly accurate machine tool thermal behaviour simulations, it can accurately forecast the functional performance of a machine tool at the prototype design stage and provide guidance on its design and performance optimization. To improve the accuracy of the thermal simulation of machine tools, it proposed whole-machine temperature field and thermal deformation modeling and a simula- tion method for vertical machining centers. Based on the studies of thermal-structure coupling finite-element data flow and its critical conditions, it also proposed design and computational methods for obtaining the heat-source power, when various rotational speeds, the forced convection heat transfer coefficient between a rotating surface and the air, the combined heat transfer coef- ficient between a stationary surface and the air/environment, and key contact surface thermal resistances were considered. Furthermore, this paper performed finite-element simulation analysis based on the constructed whole-machine thermal model, and the temperature characteristics and heat deforma- tion mechanism/state were obtained. After comparing the simulation and experimental results, it verified the effective- ness of the finite-element simulation model and the relevant methods and confirmed that the simulation accuracy for both the temperature characteristics and the thermal defor- mation had been improved significantly, with a simulation error less than 10 %.

Mathematical Model of Thermal Deformation in Precision Measurement and its Application

As everyone knows, the temperature changes can cause the changes of mechanical geometric size. The thermal deformation obtained by traditional calculation formulas are approximate and linear, used in low precision requirement, however, if applied in high precision field, it is very limited. In this paper, by using the relations between crystal material line expansion coefficient and volume expansion coefficient, we will establish the thermal deformation mathematical model of cylindrical shaft and hole parts in the steady temperature, the model will consider the effects of the shape factors of parts on thermal deformation.

Thermal Deformation Analysis for the Guideway of Large-Type CNC Lathe Based on Finite Element Method

Friction between the guideway and the bench of large-type CNC lathe will cause thermal deformation of the guideway, which causes processing error of the lathe，thereby reduces machining precision of the workpiece. The authors establish the mathematical model of temperature field and thermal deformation of the guideway in the work process, numerically simulate the guideway thermal characteristics by ANSYS finite element analysis software, and obtain the distribution regularities of temperature field and thermal deformation and their major influencing factors, which provide a theoretical basis for optimizing design and thermal error compensation design of the lathe guideway.