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On the Advanced Efficiency Analysis for Half Toroidal CVT -The Efficiency Analysis Considering Deformation of CVT Components - Masayuki Ochiai Kinji Yukawa Hirotoshi Aramaki 2004/9/23 NSK Ltd.

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Back ground Conventional analysis The CVT components is rigid. Development of the efficiency analysis considering deformation The public demand Influence of deformation ？ Efficiency Durability Size Weight （ Stiffness ） Tradeoff High efficiency, High torque capability, Compactness Deformation More accurate analysis is needed The purpose of our research work A CVT design

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Variator efficiency of CVT ＥＮＤ ＳＴＡＲＴ Running condition of power roller Bearing load Rotational speed Deformation of CVT components ･ Trunnion ･ Disks ･ Yoke etc Deformation of power roller ･ Pivot shaft ･ Inner and outer race etc Deformation Efficiency of Traction surface Torque efficiency Velocity efficiency Traction characteristics Loss of power roller ① ② ③ Traction force Trunnion Pivot shaft Needle bearing Power roller bearing Power roller outer ring Power roller inner ring The flow diagram for calculating CVT efficiency

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The Outline Ⅰ． Traction surface efficiency analysis considering deformation of trunnion Ⅱ． Power roller loss analysis considering deformation of pivot shaft Ⅲ． The calculation results of CVT variator efficiency

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Ⅰ． Traction surface efficiency analysis considering deformation of trunnion

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Output Disk Input Disk Power Roller Trunnion Swing center Deformation θ in =θ out Half contact angle The conventional analysis r in = r out Disk radii r in r out θin θout r in r out

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Power Roller Trunnion Swing center Input Disk The influence of deformation on CVT geometry θ in θ out θ in ≠θ out Half contact angles Geometrical relationship changes. r in ≠r out Disk radii r in r out

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X 1 : Displacement of input disk X 2 ： Displacement of power roller X 1 X 2 δ Output DiskInput Disk Power Roller Trunnion Swing center Out put disk is fixed Calculation model of input disk and power roller displacement δ ： Displacement of swing center

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・ Half contact angles are asymmetric ( in ≠ out ). ・ Consider virtual disk radiuses (r in, r out ) r in r out r1r1 r 2in r 2out r3r3 e in e out o in out F Calculation model for traction surface analysis considering deformation 33 22 11

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Calculation parameter of CVT The load and rotational speed of power roller are calculated by above CVT running parameters. Cavity diameter132 mm Disk radius40 mm Half contact angle62.5 deg. Speed ratio range 0.5 ～ 1.9 Maximum torque350 Nm Oil Temperature 80 ℃ Rotational speed2000 min-1

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Deformation of Trunnion by FEA The swing center is moved by trnnion deformation

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Calculation results of traction surface efficiency (Power transmission efficiency) The influence of trunnion deformation on traction surface efficiency is significant

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Ⅱ． Power roller loss analysis considering deformation of pivot shaft

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Integrated and separate type pivot Shafts Traction force Trunnion Pivot shaft Power roller bearing Power roller inner ring Traction force Trunnion Power roller bearing outer ring Power roller inner ringTraction force Trunnion Pivot shaft Power roller inner ring Power roller bearing Needle bearing Power roller outer ring The Int.type inclination is smaller than sep. type. (a)Separate type (Conventional) (b) Integrated type (Newly developed) Needle bearing

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The conventional analysis can not calculate the difference between above two type efficiencies. Experimental data of the variator efficiency Improved drastically 2% up

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The calculation model of power roller considering the pivot shaft deformation Axial load 1 2 3 4 5 6 7 8 9 10 11 12 ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ x Pivot shaft Power roller inner ring Radial needle bearing Traction force Thrust ball bearing

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Calculation results of load shearing ratio ◎ The Int. type shearing radial load of P/R brg. is lower than Sept. type. The Int. type radial load of power roller bearing is lower. Int. type Sept. type Needle bearing P/R bearing

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Frictional loss of power roller bearing with integrated and separate type ◎ The difference of frictional loss is primarily generated at the cage

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Ⅲ． The calculation results of CVT variator efficiency

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Calculation formula for variator efficiency Power trans mission efficiency (CVT variator efficiency) Cr 1,Cr 2 : Creep of input and output disks Efficiency of traction surface Bearing loss Speed transmission efficiency Variator efficiency of CVT (Power transmission efficiency) Tanaka ， JSME53 （ C ） -149 ， (1987) η p = η s ・ η T Torque transmission efficiency T brg ： Torque loss of power roller

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Calculation results of variator efficiency compared with experimental results i =1.0 ・ The theoretical results show good agreement with experimental one. ・ The Int.type efficiency is better than the sep. type. 2% up

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Conclusion The efficiency analysis for half toroidal CVT considering deformation is described. ・ The influence of trunnion deformation is significant. ・ The loss difference between the int. and sep. types can be calculate by new calculation method. ・ The influence of the deformation of the trunnion on the total variator efficiency is relatively small. It is important to analyze the influence of the deformation on traction surface and power roller individually, in order to develop high performance CVT.

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The thrust load changes by trunnion deformation Thrust load act on power roller is decreased Loss of power roller is decreased

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Calculation results of variator efficiency compared with experimental results i =0.5

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Calculation results of variator efficiency compared with experimental results i =1.9

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The half contact angle （ Input side ）

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The half contact angle （ Output side ）

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Displacement of Input disk

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Displacement of power roller

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Calculation results of variator efficiency compared with experimental results i =1.9 i =1.0 i =0.5

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・ Rotating radius of contact point ・ Speed ratio ・ Creep ・ Spin angular velocity ・ Half contact angles are asymmetric ( in ≠ out ). ・ Consider virtual disk radiuses (r in, r out ) r in r out r1r1 r 2in r 2out r3r3 e in e out o in out F Calculation model for traction surface analysis considering deformation 33 22 11

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Power Roller Trunnion Input Disk Input disk and power roller are move. The influence of deformation on CVT geometry

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Misalignment between the power roller inner and outer rings Cage Fast Slow r 1 r 2 Traction force Heat generation Rolling element 2 Rolling element 1 Outer ring Inner ring

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Ball excursion and Cage gap Fast Slow The Running of ball Cage gap Heat generation

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Calculation formula for variator efficiency Traction surface loss Power roller bearing loss Main losses of CVT variator Variator efficiency

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