Reduced Order Finite Element Modeling of Thermally Induced Bearing Loads in Machine Tool Spindles

1999 ◽  
Author(s):  
Alex O. Gibson ◽  
Jeffrey L. Stein
Keyword(s):  
Finite Element ◽  
Thermal Expansion ◽  
Machine Tool ◽  
Mechanical Load ◽  
Machining Process ◽  
Thermally Induced ◽  
Reduced Order ◽  
Wide Range ◽  
Bearing Load ◽  
Bearing Loads

Abstract Machine tool spindle bearings are subjected to a large range of axial and radial loads due to the machining process. Further the rotating spindle must be extremely stiff to minimize the cutting tool’s deflection. The high spindle stiffness is achieved by applying a mechanical load to the bearings, the preload. In fixed preload spindles the bearing loads tend to increase with increasing spindle speed due to thermal expansion and it is well established that these thermally induced loads can lead to premature bearing failure. A model of thermally induced bearing load in angular contact bearing spindles is developed that includes an axis-symmetric reduced order finite element model of the heat transfer and thermal expansion within the spindle’s housing and shaft and the bearing and shaft dynamics. Nodal reduction is used in the reduced order model to minimize the number of temperature states and the computational load. The reduced order model’s calculated temperature and bearing load values are shown to closely match experimentally measured values over a wide range of spindle speeds. The paper ends with a parameter variation study which predicts a dramatic decrease in the thermally induced bearing load when silicon nitride balls are substituted for steel balls.

Determining track-induced lateral thermal expansion forces on a curved railway track

2021 ◽  
pp. 095440972199531
Author(s):  
Jubair A Musazay ◽  
Allan M Zarembski ◽  
Joseph W Palese
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Thermal Expansion ◽  
Stress Analysis ◽  
Railway Track ◽  
Thin Wall ◽  
Element Analysis ◽  
Thermally Induced ◽  
Wide Range ◽  
Research Studies

This research studies the development of lateral thermal expansion forces on a curved railway track. The geometric alignment of a railway right of way often requires railway tracks to be curved. This curvature which is usually defined by the radius of curvature or degree of curvature represents a higher level of complexity in the track’s analysis and design process. Particularly, presence of curvature on the track introduces multiple sources of force in the lateral (radial) direction, including, but not limited to, lateral thermal expansion, lateral wheel/rail forces due to centrifugal action, lateral components of vertical loads, bogie hunting and nosing effects of locomotives, and vehicle curving dynamics. Some of these forces are well understood such as centrifugal forces while some are not as well understood, such as lateral thermal expansion forces. To bridge this gap, this research studies the development of track-induced lateral thermal expansion forces on a curved railway track. In this research, the curved track is assumed to be an arbitrary arc section of a circular track and is modeled as an equivalent idealized circular ring for analysis. Owing to its importance, three analytical methods are used to include: 1) Timoshenko thermoelastic stress analysis in cylindrical coordinate system, 2) mechanics of thin wall cylinders and 3) adaptation of a variational calculus formulation method from a previous comparable study. A fourth analysis approach is also introduced using a commercially available finite element analysis package. The results of these analyses are compared through a wide range of parametric studies and are then validated by the finite element analysis. The results of this study showed that the several methods presented in this paper, could be used to approximate thermally induced expansion behavior (pre-buckling) on a curved railway track. While all three techniques are effective, the Timoshenko stress analysis method appears to be the most suitable as it is a direct method that examines the stress build up from the element level and takes into account additional material properties, such as the Poisson effect. The research resulted in a methodology for determining load transfer from thermally induced forces in curved railroad track to the fastener and supporting structure.

Research on Thermally Induced Deformation of Reinforcing Plate Based on Finite Element Simulation

2012 ◽  
Vol 197 ◽  
pp. 139-143
Author(s):  
Hua Bai ◽  
Yi Du Zhang
Keyword(s):  
Finite Element ◽  
Ambient Temperature ◽  
Finite Element Simulation ◽  
Temperature Change ◽  
Large Scale ◽  
Machining Process ◽  
Reinforcement Structure ◽  
Thermally Induced ◽  
Finite Element Software ◽  
Element Simulation

The change of ambient temperature will cause deformation during the machining process of large-scale aerospace monolithic component. Based on finite element simulation, thermally induced deformation of reinforcing plate is studied in such aspects as reinforcement structure, clamping method and temperature change, and contact function in finite element software is used to simulate the unilateral constraint between workpiece and worktable. The results indicate that reinforcing plate will produce warping deformation due to the change of ambient temperature. Different reinforcement structures and clamping methods have important influence on the deformation positions and degrees, and the deformation is proportional to the temperature change.

Measurement of Thermally Induced Loads in Back-to-Back Angular Contact Spindle Bearings Using Strain Gauges

2004 ◽  
Author(s):  
John E. Harder ◽  
Jeffrey L. Stein
Keyword(s):  
Metal Cutting ◽  
Strain Gauges ◽  
Future Research ◽  
Axial Loads ◽  
Thermally Induced ◽  
Outer Race ◽  
Repeatability Error ◽  
Bearing Load ◽  
Bearing Loads ◽  
Set Up

Thermally induced bearing loads can potentially create serious problems for metal cutting spindles when used at high speeds. Proper spindle bearing set-up can minimize, but cannot eliminate this problem. Measuring the thermally induced load can alert the user to a potential problem or can be used to control the load directly. The purpose of this paper is to describe the design of a thermally induced bearing load sensor using strain gauges placed around the outer race. A box spindle with strain gauges on a pair of angular contact ball bearings located in the front of the spindle is used in this analysis. In order to calculate the thermally induced bearing load, the outputs of the strain gauges were recorded over a one second interval, sampled at 7500 Hz from each strain gauge and the root mean square of the deviation of this data from its mean is calculated. This value is a measure of the ball load. This calculated output is calibrated by a quadratic regression of these data to applied axial loads over a range of 0 to 2800 N. Values for each bearing were averaged to yield a front and rear value. The repeatability error for the front bearing sensor is 1.36%, and its accuracy is 98.9%. The repeatability error for the rear bearing sensor is 2.17% and its accuracy is 98.3%. These relatively low repeatability errors are attributable in part to filtering that does reduce the sensors’ bandwidth, but not significantly for measuring the relatively slowly changing thermally induced loads. Sensor design improvements and potential avenues of future research are discussed.

Constitutive flow stress formulation for aeronautic aluminum alloy AA7075-T6 at elevated temperature and model validation using finite element simulation

2016 ◽  
Vol 230 (6) ◽  
pp. 994-1004
Author(s):  
Uma Maheshwera Reddy Paturi ◽  
Suresh Kumar Reddy Narala
Keyword(s):  
Finite Element ◽  
Aluminum Alloy ◽  
Flow Stress ◽  
Elevated Temperatures ◽  
Constitutive Models ◽  
Absolute Error ◽  
Machining Process ◽  
Strain Rates ◽  
Average Absolute Error ◽  
Wide Range

A judicious material constitutive model used as input to the numerical codes to denote elastic, plastic, and thermomechanical behavior under elevated temperatures and strain rates is essential to analyze and design a process. This work describes the formulation of different constitutive models, such as Johnson–Cook, Zerilli–Armstrong, Arrhenius, and Norton–Hoff models for high-strength aeronautic aluminum alloy AA7075-T6 under a wide range of deformation temperatures and strain rates. The adeptness of the formulated models is evaluated statistically by comparing the value of the correlation coefficient and average absolute error between experimental and predicted flow stress results, and numerically when simulating AA7075-T6 machining process. Though all the models show a reasonable degree of accuracy of fit, based on the average absolute error of the data and finite element predictions when simulating the AA7075-T6 machining process, Zerilli–Armstrong model can offer an accurate and precise estimate and is very close to the experimental results over the other models.

Controlling Both Thermally Induced Loads in Back-to-Back Angular Contact Spindle Bearings

2004 ◽  
Author(s):  
John E. Harder ◽  
Jeffrey L. Stein
Keyword(s):  
Metal Cutting ◽  
Electric Heating ◽  
Load Control ◽  
Future Research ◽  
Thermally Induced ◽  
Significant Control ◽  
Bearing Load ◽  
Bearing Loads ◽  
Improved Performance ◽  
The Individual

Thermally induced bearing loads may cause serious problems for metal cutting spindles when used at high speeds. While proper spindle bearing setup can help minimize this problem, ultimately the plethora of factors that cause the loads to vary cannot be accounted for by the setup. Previous work has shown that bearing load control is possible, but that improved performance may be realized if the temperature environment of each bearing of a back-to-back pair is considered separately. The purpose of this paper is to provide the results of an experimental evaluation of a bearing load control strategy using two thermal actuators. A box spindle was modified and two electric heating tapes were placed around the front pair of back-to-back angular contact ball bearings, one around each bearing. Significant control over the bearing loads can be achieved for the conditions tested including some level of independent control. Unfortunately, there is cross-talk between the heat actuators and the bearing loads, and this interferes with the level of independent load control that can be achieved over the individual bearings. The significance of this issue is discussed and future research outlined. The authors conclude that it is possible to significantly reduce the transient load variation in both bearings with two rather than one actuator; additionally, the second control loop usually improves the steady-state behavior over that achievable with single heater placed over the rear bearing.

A Thermal-Based Spindle Bearing Load Controller: Preliminary Experimental Evaluation

2002 ◽  
Author(s):  
John E. Harder ◽  
Jeffrey L. Stein
Keyword(s):  
Experimental Evaluation ◽  
High Speed ◽  
Metal Cutting ◽  
Dynamic Performance ◽  
Electric Heating ◽  
Process Conditions ◽  
Thermally Induced ◽  
Significant Control ◽  
Bearing Load ◽  
Bearing Loads

Thermally induced bearing loads are a serious problem for high-speed machining spindles used in metal cutting. Ideally, the bearing loads can be set to provide the necessary spindle stiffness to achieve the desired dynamic performance, while at the same time achieving long bearing life. Unfortunately, this is difficult to do because many process conditions affect these loads, sometimes in difficult to predict ways with significant degradation of spindle performance and life. The purpose of this paper is to describe a preliminary experimental evaluation of controlling bearing loads by controlling the heat generated by a thermal actuator placed around the spindle housing. A box spindle modified with an electric heating tape placed around its front ball bearings is used for this evaluation. The results show that significant control over the bearing load can be achieved for the conditions tested. However, it is discovered that asymmetrical placement of the heater with respect to the pair of back-to-back angular-contact bearings makes it difficult to regulate the loads on each bearing to the set point. Solutions to this problem are discussed and further research outlined. Nevertheless, the feasibility of the control of thermally induced bearing spindle loads with an externally mounted heater appears promising.

scholarly journals Approaches for Reduced-Order Modeling of Electrically Actuated von-Karman Microplates

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Shahid Saghir ◽  
M.I. Younis
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Electrostatic Force ◽  
Element Model ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Linear Eigenvalue Problem ◽  
Von Karman ◽  
Wide Range ◽  
Von Kármán

This article presents and compares different approaches to develop reduced-order models for the nonlinear von-Karman rectangular microplates actuated by nonlinear electrostatic forces. The reduced-order models aim to investigate the static and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First, we investigate the convergence with the number of modes retained in the model. Then for validation purpose, a comparison of the static results is made with the results calculated by a nonlinear finite element model. The linear eigenvalue problem for the plate under the electrostatic force is solved for a wide range of voltages up to pull-in. Results among the various reduced-order modes are compared and are also validated by comparing to results of the finite-element model. Further, the reduced-order models are employed to capture the forced dynamic response of the microplate under small and large vibration amplitudes. Comparison of the different approaches is made for this case.

Tailorable Thermal Expansion of Lightweight and Robust Dual-Constituent Triangular Lattice Material

2017 ◽  
Vol 84 (10) ◽  
Author(s):  
Kai Wei ◽  
Yong Peng ◽  
Weibin Wen ◽  
Yongmao Pei ◽  
Daining Fang
Keyword(s):  
Mechanical Properties ◽  
Thermal Expansion ◽  
Triangular Lattice ◽  
Coefficient Of Thermal Expansion ◽  
Bulk Material ◽  
Structure Design ◽  
Thermally Induced ◽  
Precise Control ◽  
Wide Range ◽  
Lattice Material

Current studies on tailoring the coefficient of thermal expansion (CTE) of materials focused on either exploring the composition of the bulk material or the design of composites which strongly depend on a few negative CTE materials or fibers. In this work, an approach to achieve a wide range of tailorable CTEs through a dual-constituent triangular lattice material is studied. Theoretical analyses explicitly reveal that through rational arrangement of commonly available positive CTE constituents, tailorable CTEs, including negative, zero, and large positive CTEs can be easily achieved. We experimentally demonstrate this approach through CTE measurements of the specimens, which were exclusively fabricated from common alloys. The triangular lattice material fabricated from positive CTE alloys is shown to yield large positive (41.6 ppm/°C), near-zero (1.9 ppm/°C), and negative (−32.9 ppm/°C) CTEs. An analysis of the collapse strength and stiffness ensures the robust mechanical properties. Moreover, hierarchal triangular lattice material is proposed, and with certain constituents, wide range of tailorable CTEs can be easily obtained through the rationally hierarchal structure design. The triangular lattice material presented here integrates tailorable CTEs, lightweight characteristic, and robust mechanical properties, and is very promising for engineering applications where precise control of thermally induced expansion is in urgently needed.

Thermally Induced Fields in Electroelastic Composite Materials: Average Fields and Effective Behavior

1994 ◽  
Vol 116 (2) ◽  
pp. 200-207 ◽  
Author(s):  
M. L. Dunn
Keyword(s):  
Thermal Expansion ◽  
Composite Materials ◽  
Mean Field Theory ◽  
Mean Field ◽  
Matrix Formulation ◽  
Two Phase ◽  
Thermally Induced ◽  
Electroelastic Fields ◽  
Wide Range ◽  
Effective Thermal Expansion

The average thermally induced electroelastic fields and the effective thermal expansion and pyroelectric coefficients of two-phase composite materials are obtained by applying the Mori-Tanaka mean-field theory to the coupled response of electroelastic composites through a field superposition scheme. Results are obtained for composites reinforced by ellipsoidal piezoelectric and pyroelectric inhomogeneities and thus are applicable to a wide range of microstructural geometry including lamina, spherical particle, and continuous fiber reinforcement. The results are shown to obey the recently derived Levin-type equations relating the effective thermal expansion and pyroelectric coefficients of a two-phase composite to those of the constituents and the electroelastic moduli of the constituents and the composite. The analysis is developed in a matrix formulation convenient for numerical computation in which the electroelastic (elastic, piezoelectric, and dielectric) moduli are represented by a 9×9 matrix and the thermal expansion and pyroelectric coefficients by a 9×1 column vector. A limited parametric study is performed to illustrate the interesting behavior exhibited by some typical composite microstructures. Finally, analytical predictions are examined in light of existing experimental observations.

Simulation of Thermal Deformation for Spindle of Machine Tool

2010 ◽  
Vol 97-101 ◽  
pp. 2979-2982
Author(s):  
Chia Lung Chang ◽  
Yung Cheng Wang ◽  
Yi Chieh Wang ◽  
Bean Yin Lee
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Machine Tool ◽  
Machine Tools ◽  
Thermal Deformation ◽  
Experimental Measurements ◽  
Load Rating ◽  
Analysis Model ◽  
Bearing Load ◽  
Speed And Accuracy

In order to increase the efficiency of machine tools, the development of machine tools is toward higher speed and accuracy. The higher speed of spindle causes more thermal deformation, which reduces the accuracy of machine tools. In this study, finite element method is used to simulate the thermal deformation of spindle caused by the friction loads between spindle and bearings. The bearing load is estimated by the basic load rating from the bearing vendor and the required life of bearing. The simulated results are compared with experimental measurements to verify the analysis model. The result shows that the stabilized temperature of spindle increases as the speed increaser, while the stabilized displacement of spindle slightly increases as the speed increases.

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