Effect of Temperature on Mechanical Properties and Dynamic Characteristics of the Rotor in High Acceleration Mei-Hui JIA a,*, Cheng-Lin WANG b

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1 2016 International Conference on Mechanics Design, Manufacturing and Automation (MDM 2016) ISBN: Effect of Temperature on Mechanical Properties and Dynamic Characteristics of the Rotor in High Acceleration Mei-Hui JIA a,*, Cheng-Lin WANG b School of Logistics, Beijing Wuzi University, Beijing , China a jiameihui2008@163.com, b wangchenglin6688@126.com *Corresponding author Keywords: High acceleration, Rotor, Temperature, Stress and strain, The natural frequency. Abstract. To deeply grasp the operating characteristics and influence factors of the rotor in high acceleration, based on ideal rotor model, the Finite Element Model of rotor including manufacturing errors is established, respectively, taking parallelism error and symmetry error for example, using sequential coupling method for heat-structure analysis of the rotor, then the influences of temperature on mechanical properties and dynamic characteristics of the rotor are obtained. The results show that: in range of 20 C-70 C, temperature, stress and strain of the rotor are positively correlated, when the temperature is coupled with parallelism error, stress and strain of the rotor change little, when the temperature is coupled with symmetrical error, all of the stress and strain of the rotor increase, and temperature changes have no significant effect on natural frequencies and mode shapes of the rotor. Introduction With the rapid development of the aerospace, military and other fields, mechanical devices frequently operate in high acceleration bearing conditions, parts of the device subjected acceleration value has reached g(g, Acceleration of gravity). Therefore, carrying capacity test in high acceleration is very important. Rotor is the core of the experimental system, the mechanical properties and dynamic characteristics directly affect the stability of the system and test capabilities. As we all know, it will produce a lot of heat in the high acceleration rotation of the rotor, so the temperature of the rotor rises, the uneven distribution of temperature can cause thermal stress in internal parts, in structural analysis, the effects of temperature field on structural stress and strain should be considered, in addition, the material properties and temperature are closely related, generally the material properties are different with the different temperature, it can also cause changes in stress distribution. So, in order to deeply understand the characteristics and influence factors of the rotor, it is very important to analysis the influences of temperature on the rotor characteristics. There are many studies on the structure of the thermal stress at home and abroad, in paper[1], the casting thermal stress have been studied using numerical simulation technology, lastly, thermal stress of plate and the waveguide is predicted. Paper[2] studied the temperature distribution on the dynamic characteristics of rod rotor, the influence of axial temperature on the mechanical properties is analyzed, and the influence of circumferential temperature on the vibration characteristics is studied. But the studies on influence of temperatures on the rotor characteristics in high accelerate is little, on the basis of the preceding studies [3-], using ANSYS and sequential coupling method, the influences of temperature on the mechanical properties of the rotor are analyzed, including the FEM of rotor including manufacturing error

2 is established, respectively, parallelism error and symmetry error coupled with temperature, the stress and strain of the rotor were analyzed, finally, the dynamic characteristics of the rotor are comparative analyzed, considering temperature and without considering temperature. Analysis on Mechanical Properties of The Standard Rotor Based on The Temperature Influence Analysis step of thermal stress In this paper, we will study the mechanical properties changes of the rotor in temperature change conditions, so the problem belongs to heat-structure coupling analysis, the resolve methods for thermal-stress analysis in ANSYS include, the sequential coupling and the direct coupling, here, sequential coupling method will be selected for the thermal stress analysis. Thermal stress analysis steps of rotor are: (1) Firstly, steady-state thermal analysis of the rotor is preformed, then thermal unit model is selected as SOLID70, loading the heat load, solving and view the results; (2) Secondly, the static structural analysis is started, the unit type can be converted into the structural unit SOLID18, the material properties including thermal coefficient of expansion are defined, then, the structural loads, the temperature obtained from the previous heat analysis, are all applied on the rotor, finally, the solve results are obtained. Establishment of standard FEM of the rotor To study the effect of temperature on the mechanical properties of the rotor part, based on FEM of the rotor in ideal state, not including manufacturing errors, the room temperature 20 C is taken as a reference, and based on the actual measured temperature of the rotor in high acceleration, the temperature range field is set C, in 10 C intervals, distribution and variation of the rotor stress and strain are analyzed. In this study, titanium is selected for rotor material, the Elastic Modulus E=110GPa, the density ρ=4.g/cm3, the Poisson's ratio ϑ=0.34, the rotor diameter D =200mm, the rotor thickness H =100mm, the rotation axis diameter d0=4mm, the fillet radius of rotation axis r =1.mm, the rotational acceleration of the rotor a=1. 10 g, the hole diameter d1 =10mm, the distance of two holes e =140mm, the thermal expansion coefficient α= / C, thermal conductivity = W/(mm K), parameters marked as Fig.1below. d D e d H Figure 1. Schematic diagram of the rotor geometry. To improve accuracy, the elements at the intersection of the rotation axis, and the elements around the hole, should be meshed subdivision, others can be meshed by automatic intelligent meshing. According to the rotation characteristics of the rotor, Z direction DOF of one end of the rotary axis is constraint, the other end is free, the radial displacement of the rotor is limited, the angular velocity that normal to the rotation axis is applied.

3 Effect of temperature on the mechanical properties of the standard rotor Under the above conditions, finite element analysis is carried out, then the solution results are extracted, changes of mechanical properties of the rotor are compared in temperature and without temperature, as shown in Fig.2, Fig. (a) shows that with the rise of temperature, the maximum equivalent stress of the rotor showed a linear growth trend, and when the temperature is close to the reference temperature, the maximum equivalent stress of the rotor is almost equal to that of no temperature. From Fig.(b) it can be seen, with the rise of temperature, the rotor of the maximum equivalent strain also close to linear growth trend, when the temperature is close to the reference temperature, the strain value slightly less than of no temperature. (a) Von Mises stress (b) Von Mises strain Figure 2. Effect of temperature on the mechanical properties of the rotor. Influences of temperature changes on the mechanical properties of the rotor while considering manufacturing error On the basis of considering the temperature changes, the parallelism error and symmetry error are also considered, the coupling influences of manufacture error and temperature on the mechanical properties of the rotor are researched, referencing the actually manufacturing precision of the rotor, the fourth tolerances is selected, the rotor FEM including the manufacturing errors is established. Influence of parallelism error on the mechanical properties of the rotor when consider temperature Description of parallelism error. According to the definition of parallelism, parallelism of line to line in any direction is the region of cylindrical plane, it is orientation error. In this paper, the parallelism error of single hole centerline relative to the rotation axis of the rotor is studied, as shown in Fig.3, in order to effectively describe the parallelism error, the centerline of the hole should be deviated from the ideal centerline while modeling, the deviation amount is corresponding to the maximum parallelism error. Actual centerline Rotary axis Ideal center Figure 3. Schematic diagram of parallelism error.

4 Coupling the parallelism error and temperature changes. The depth of the hole is the measured feature, according to the national standard GB/T , when parallelism tolerance is selected four precision, parallelism error is 0.008mm, then the parallelism error value is converted into angle, and through the coordinate transformation, the rotor FEM including the parallelism error is established, the loading and the solution process are as described in 2.2, the analysis of stress and strain changes at different temperatures are as shown in Fig.4. Fig.(a) shows whether consider parallelism error, as the temperature rises, the rotor maximum equivalent stress showed a significant linear growth trend, when the temperature increase 10 C, the maximum stress value increased 0MPa, such parallelism error stress occurs slight increase, the largest growth rate is about 0.49%. Fig.(b) shows whether consider parallelism error, as the temperature rises, the rotor maximum equivalent strain showed significant linear growth trend, when temperature increase 10 C, the maximum equivalent strain grew 0.004, parallelism error caused the equivalent strain increases, the maximum growth rate is 1.3%. (a) Von Mises stress (b) Von Mises strain Figure 4. Effect of parallelism error on the mechanical properties of the rotor when considering temperature. Influence of symmetry error on the mechanical properties of the rotor when considering temperature Description of symmetry error. Symmetry is the minimum distance of two planes including the symmetry plane of the measured surface (or axis), the standard is the symmetry center, so it belongs to position error. Symmetry error of rotor refers to the distance of the two symmetry holes, the symmetry center is the rotation centerline of the rotor, as shown in Figure. Similarly, when establishing the rotor FEM including symmetric error, one hole maintains its ideal position, offset is set in the other hole, and the offset should be corresponding with the maximum symmetry error. Actual distance Theoretical distance Symmetry error Rotation axis Figure. Schematic diagram of symmetry error.

5 Coupling the symmetry error and temperature changes. The centerline distance between the rotation axis and two holes is the measured factor, according to the national standard GB/T , symmetry tolerance accuracy is four, the symmetry error is 0.008mm, the rotor FEM including the symmetry error is established, the loading and solution process are as described in 2.2, changes of rotor stress and strain at different temperatures are analyzed, as shown in Fig.6. Fig.(a) shows whether consider the symmetry error, as the temperature rises, the maximum equivalent stress of the rotor shows a significant linear growth trend, whenever temperature increase 10 C, maximum stress value increased 0MPa, the symmetry error makes the stress value increase, the largest growth rate is 4.6%. Fig.(b) shows that whether consider symmetry error, as the temperature rises, the maximum equivalent strain of the rotor shows significant linear growth trend, whenever the temperature increase 10 C, the maximum equivalent strain grows 0.004, the symmetry error also causes strain to increase, the maximum growth rate is 4.2%. (a) Von Mises stress (b) Von Mises strain Figure 6. Influence of symmetry error on the mechanical properties of the rotor considering temperature. Effect of temperature on dynamic characteristic of the rotor To study the effect of temperature on rotor dynamics, based on the FEM of the rotor as 2.2, the heat-structure coupling stress analysis and the structural stress analysis are carried out respectively, the analysis are all pre-stressed analysis, then the first ten natural frequencies are extracted, such as Tab.1 shown. When considering the temperature, the natural frequency of the rotor is larger, and without consideration of the temperature, the natural frequency of the rotor is smaller, the maximum growth rate appears in the second-order natural frequency, the increase is 9%. Through vibration shape diagram, it can be determined that the temperature has no influence on vibration shape of the rotor in high acceleration, because of space limitations, the vibration shape of the rotor is not repeated in this paper. natural frequenc yf/hz Table 1. First 10 natural frequencies of the rotor in both states. Order i Consider temperatu re Without temperatu re

6 Conclusion (1) In the range of 20 C-70 C, temperature has some influences on the mechanical properties of the rotor, as the temperature increases, the maximum equivalent stress and equivalent strain of the rotor are linear growth. (2) Based on the consideration of temperature, the influences of parallelism and symmetry error on the mechanical properties of the rotor are gotten, parallelism error did not bring significant impact on the mechanical properties of the rotor, and the symmetry error make the maximum equivalent stress and equivalent strain increase, the maximum growth rates are 4.6% and 4.2%. (3) In high acceleration conditions, the natural frequency of the rotor considering temperature is significantly larger than that without considering temperature, the maximum growth rate of 9%, which appears on the second order natural frequency, but there is no significant effect of temperature on the rotor vibration mode. Acknowledgement This research was financially Supported by National Natural Science Foundation of China (Grant No ), University Youth Fund of Beijing Wuzi University(Grant No ). References [1] Wang Yueping. Numerical simulation of thermal stress in casting process based on finite difference method [D]. Harbin Institute of Technology, [2] He Peng. Research on the influences of elastic-plastic contact and temperature distribution on tie-bolted fastened rotor dynamics. [D]. Harbin Institute of Technology, [3] Wang Chenglin. The characteristic analysis on typical fit coordination under the condition of continued high acceleration load-bearing. Manufacturing Automation. 2012, 32(4): [4] Wang Chenglin, Li Xiaojie. Topology optimization of rotor in high-acceleration rotation experiment based on ANSYS. Manufacturing Automation. 2014, 36(9): [] Li Xiaojie, Wang Chenglin, Jia Meihui. The research of structure reliability of rotor based on ultra-high steady acceleration. Manufacturing Automation. 201, 37(1):