06 International Conference on Materials, Information, Mechanical, Electronic and Computer Engineering (MIMECE 06) ISBN: 978--60595-40- The ynamic Characteristics of the Torque Sensor by Bearing Interference Fit Bei Li, Zhongtao Tian and Haitong Liang ABSTRACT Taking high-speed dynamic torque sensor shaft with an interference fit bearing whose effect is on the dynamic characteristics of the sensor shaft as the research content. It introduces a analysis of the bearing fit interference quantity model of the impact of the bearing contact angle. It is focused on dealing with the fit tolerance between inner ring of bearing and shaft as well as outer ring of bearing and bearing seat taking 7004C as an example. Bearing interference fit of the equivalent model is established based on the theory of thick wall cylinder, and then it is verified by the Ansys Workbench simulation results. INTROUCTION ynamic torque measurement is widely used in electric motors, engines, water pumps and other rotating equipment. High speed dynamic torque sensor would be the best choice for torque measurement. Key parameters of the rotating shaft equipment in its operating state can be obtained directly by high speed dynamic torque sensor. With torque detection, it is efficiency to prevent shaft fatigue breaking and plastic deformming [-4]. However, restricted by its structure, bearings are necessary for dynamic torque sensor and generally interference fitted. ynamic behavior of torque sensor is seriously affected by the amount of interference. In this paper, the relationship between assembly interference quantity and dynamic characteristic of the sensor is studied, which is meaningful for the production practice and improving the dynamic characteristics of the product. Bei Li, Zhongtao Tian, Haitong Liang, China Academy of Aerospace Aerodynamics, ivision of Measurement and Control, No.7 the West Road of Yungang Beijing, China, 00074 6
SUMMARY Angular contact ball bearings are usually interference press fit installed on the shaft and bearing seat in dynamic torque sensor. This installation can prevent fretting wear between bearing inside ring and shaft, and fretting wear between bearing outside ring and bearing seat. In this paper, a type dynamic torque sensor is taken as the research object, and its installation model is shown in chart. Assembling Mathematical Model Bearings whose Poisson s ratio is ξ, modulus of elasticity is E are pressed into the bearing seat whose poison s ratio and modulus of elasticity are ξ and E. Inside ring of shaft is and it is not marked in chart because it is zero here. The pressure between the two torus is P. magnitude of interference is I. Based on elastic-plastic mechanics, increment of bearing inside ring caused by press fit is s. Chart. ynamic torque sensor shaft. Chart. Shaft mathematical model identification. + E + / = + s - E - - For bearing inner ring and bearing seat, expansion of bearing inner ring is: () = I s In a similar way, for bearing outer ring and bearing seat, expansion of bearing outer ring is: - h I - The Influence of Interference Fit to Ball bearing Contact stiffness Geometric meaning of ball bearing parameters is shown in chart 3, is the diameter of the ball in bearing. istance of rolling groove of inner ring and outer ring is: () (3) A r r (f f ) B o i o i (4) 63
The angle between bearing radial plane which is perpendicular to the axis of the bearing rotation and the plane which contains attachment points of bearing balls and inner and outer ring grooves is called initial contact angle and it is: 0 cos pd p d A (5) Chart 3. Bearing internal parameters schematically. Pd is initial clearance of the bearing. pd is reducement amount of radial internal clearance caused by changing the diameter of bearing ring when bearing is interference fitted. (6) P b In this paper, dynamic torque sensor is 7004C. The specific bearing parameters are shown in table below. Bearing inner ring diameter is 4.5 mm. Bearing outer ring diameter is 36.5 mm. Bearing seat outside diameter is 86 mm. With numerical calculation, the bearing clearance in dynamic torque sensor can be P b 0.8630.807 s h. I is the shaft and bearing inner ring assembly tolerance caused by the change of bearing interference in this calculation method. I* is the bearing and the bearing outer ring assembly tolerance caused by the change of bearing interference. Table. Specifications of Bearing7004C. s Parameter Value Parameter Value i/mm 0 α o / 5 o/mm 4 ρ /g cm3 7.8 /mm 5.5 E /MPa.e5 dm/mm 3 ξ 0.3 h Table. Relationship of bearing assembly interference and initial contact angle (μm). I 6 0 40 Δ S.636 4.8978 9.7956 6.36 3.65 Δ h.644 4.843 9.6864 6.44 3.88 ΔP b 3.47 9.74 9.48 3.47 64.94 α o 5. 5.6 6.4 7.365 9.63 The bearing interference quantity takes, 6,, 0 and 40μm on the scope of research. The assembly interference quantity affects bearing initial contact angle. Take I=I * and enumerate then several groups of data were compared and shown in table. According to the theory of bearing channel control and Hertz s contact mechanics, the initial contact angle of angular contact ball bearing affect the stiffness of the bearing directly [6]. Bearing stiffness varied with different initial contact angle under different interference fit shown in table 3. 64
Table 3. Bearing assembly and stiffness interference relationship (I:μm,K:N/μm). I 6 0 40 K 0.53.3 4.33 5.60 3.343 YNAMIC SIMULATIONS Contact characteristics of the bearing affect the dynamic performance of the dynamic torque sensor directly. Contact characteristics of bearing rolling elements mainly perform stiffness characteristics. Theoretical calculation and analysis of the rolling element contact are composed of several spring mechanics model for equivalent. At present, In dynamic characteristics analysis of dynamic torque sensor shafting with ANASYS, most researchers usually adopt simplified model when they analyze the contact between the rolling element and ring grooves. The difference between theoretical analysis results and the actual results is bigger without a mature method of dealing with bearings rolling body contact, and the results of the analysis cannot serve as the basis of a detailed design. So we need to take in-depth analysis of the bearing contact features ANSYS Workbench Model Equivalent Contact angle of angular contact ball bearing varied and will affect bearing stiffness, when angular contact ball bearing is interference fitted. Springs are taken to simulate bearing stiffness in the simulation model in this paper. The stiffness of the bearing are defined for the deformation coefficient of spring, shown in chart 4. Angle spring is taken into shaft model, shown in chart 5. Chart 4. bearing equivalent spring. Chart 5. Shaft equivalent model. Results and Analysis of Simulation STEP : PRE-PROCESS In accordance with the principle of the simplified model, shaft system of highspeed dynamic torque sensor entity model was established, finite element model is shown in chart 5. STEP : SOLVING Set order number for the simulation modal, and solve numerical. STEP 3: VIEWING RESULTS According to the purpose of this study, Each order modal vibration model and modal frequency should be abstain. Each order modal shape should be exported. 65
Equivalent stiffness of eight springs was set according to different bearing stiffness. First-order mode frequency with different magnitude of interference was concluded in table 4 below. Table 4. Assembly of bearing and shaft interference Modality. I(μm) 6 0 40 First-order mode(hz) 95. 40 7 9 30 It had been shown in table 4 that he assembly interference quantity of bearing had influence to first-order mode frequency of shaft which affect rotation speed of high speed dynamic torque sensor directly. In order to ensure stable and reliable in the operation of the sensor, the rotation speed must be smaller than the first order modal corresponding vibration characteristics under the limit speed. Speed calculation formula is shown: =60 model. Rotation speed of this kind of dynamic torque sensor was set as 0000r/min. with the formula above, angular contact ball bearing assembly interference quantity should be set at least as 0.0mm in order to ensure the speed of the dynamic torque sensor design requirements, and some design margin (Generally as.5 times) should be reserve. Tolerance of fit between shaft and bearing can be set between 0.0mm and 0.0mm.Too much interference fit increased difficulty of the assembly, and affect little on improving critical speed of rotation. CONCLUSION In this paper, bearing interference fit model of dynamic torque sensor was established based on the elastic-plastic mechanics theory. ynamic simulation models of bearings were established in Ansys Workbench, and stiffness of the bearing was equivalent to spring. The stiffness of the bearing is equivalent to the spring. The following conclusions can be getting based on above date..the mathematical models of angular contact ball bearing and shaft interference fit was established based on the elastic-plastic theory hypothesis and was correct within the scope of the hypothesis of small deformation.. With the increment of the assembly interference, positively related angular contact ball bearing contact angle increased, the contact Angle change and indirectly affect the contact stiffness of the bearing. 3. In this paper, bearing was equivalent to angler spring and simulation analysis was carried out on the shafting modal, the model research more accurate and reliable than before. 4. Bearing stiffness depending on bearing interference fit influenced the modal of the axis, which limit the sensor rotate speed, thus the bearing assembly tolerance can be chosen based on sensor designing. This paper provided the basis for selection of interference magnitude of dynamic torque sensor shaft and bearing, and then the speed requirements of torque design was the guaranteed, which makes sure that the torque sensor has good dynamic characteristics during operation. REFERENCES. Zhu Qiong, Yang Guobiao. esign of torque measurement system based on resistance strain gauge [J]. Experimental and Management, 009, 6(3): 58-59. 66
. Fan Haojie, Chen Kunming, Cui Lei. iscussion on the calibration method of large torque sensor testing system [J]. Metrology and Testing Technology, 009, 36(3): 6-9. 3. Jin Yuanqiang, Hu Liguo. Principle and dynamic characteristic analysis of torque measurement of ultra high speed rotating shaft [J]. Missile and Space Vehicle Technology, 007, (): 39-4, 6. 4. Zhang eying, Huang agui, Chen Ming. A new intelligent torque speed sensor and its experimental study [J]. Sensor Technology, 004, 3(3): 54-56. 5. Pu Guangyi. Basic tutorial and example explanation of Ansys Workbench [M]. Beijing: China Water Conservancy and Hydropower Press, 00: -8. 6. Li Bei, Zhang Jianbin. A Research of Shaft Modal Simulation Method Based on the Preloaded Angular Contact Ball [C]//ICMSMA 03, Guangzhou, China: Mechatronic Systems and Materials Application, 03: 389, 364-370. 67