| As a transmission device for converting rotary motion into linear motion,the planetary roller screw mechanism(PRSM)could transfer power by the contacts between the multiple rollers and screw/nut raceways,which is famous for its many contact points,large carrying capacity and long service life.Thus,the PRSM becomes a critical compoment in the power-by-wire electro-mechanical actuator(EMA)and has been gradually used in industry fields,such as aerospace,shipping and intelligent manufacturing.Compared with other transmission mechanisms,the contact area and load capacity of PRSM is greatly increased,resulting in more serious friction and heat problems.The friction torque,transmission efficiency and temperature rise are important indicators of the PRSM service performance,which directly affect the energy consumption,reliability and durability of EMA systems.Therefore,this research focuses on the friction torque modelling and thermal characteristics analysis,which not only lays a foundation for further analysis of PRSM service life,wear and failure,but also is an important means to promote the engineering application of PRSM.According to the contour equation and spiral surface equation of the PRSM part,a method of solving the principal curvature is proposed,and the Hertzian contact parameters of the contact area are further calculated.Next,a friction torque analysis model is established considering the components caused by the frictional contact between the rollers and raceways,the sliding contact components,the lubricant viscous and the preload.Then,the effects of structural parameters and working conditions on the friction torque,heat flux and convective heat transfer coefficient are studied.Besides,the three-dimensional finite element thermal model and two-dimensional thermal network model of PRSM are proposed,and the transient and steady state temperature characteristics and thermal deformations are also analyzed under different working conditions.The main research work and achievements are listed as follows:1.The generalized contour equation and spiral surface equation of the PRSM part are developed,and the principal curvature of the contact point is derived by the differential geometry principle.Then,the influence of the PRSM structural parameters on the contact behavior is discussed.The calculation model of PRSM friction torque is established,based on the mechanism analysis of the friction torque.The results show that the main curvature values of the screw/nut raceway in a principal plane are not zero,which means the equivalent ball model when calculating the principal curvature would bring a large error.Increasing the pitch of the PRSM part increases the main curvature difference on the two contact interfaces of the roller,but hardly affects the contact ellipse area and the maximum contact stress.Increasing the normal flank angle of thread causes the main curvature difference and contact area of both two contact interfaces to decrease simultaneously,but a big normal flank angle of thread leads to an increased contact stress and thus friction torque.The normal load significantly affects the contact area and the maximum contact stress,and both of them differ greatly between the two contact interfaces due to the difference in the principal curvature.2.The PRSM efficiency and the transmission system efficiency including the bearing are further deduced.The total friction torque,friction torque component and PRSM efficiency under different structural parameters and operating conditions are analyzed.The PRSM friction torque test under no-load conditions and the efficiency experiment of the PRSM transmission system under loading conditions are completed,which indirectly verify the effectiveness of the friction torque model.It is found that the total friction torque increases with the increase of screw speed and lubricant dynamic viscosity,resulting in a decrease of PRSM efficiency.The main factor causing the friction torque is the spin slip of the roller,and the friction torque caused by the differential sliding is very small,which can be neglected.Increasing the preload would significantly increase the total friction torque and reduce the transmission efficiency.The total friction torque not only increases with the increase of sliding friction coefficient,but the friction torque of the screw-roller contact interface is also greater than that of the nut-roller contact interface.The pitch,normal flank angle of thread and number of roller threads have a significant effect on the PRSM friction torque and transmission efficiency.The friction torque test under no-load condition shows that the no-load friction torque of PRSM without pretensioning device has a large fluctuation.3.According to the theory of heat transfer,the relationship between frictional heat and temperature rise of PRSM parts is established.The thermal boundary conditions of heat flow and heat flux are calculated under different working conditions.The convective heat transfer coefficients of different positions are analyzed according to the similarity principle.The thermo-mechanical three-dimensional finite element model of PRSM is established,and thus the transient temperature distributions and thermal deformations of screw and nut are obtained.The analysis shows that the calculation results when considering the moving load are closer to the experimental results.When the axial load or the screw speed is increased,the maximum temperature on the screw and nut will increase significantly with time.The difference of temperature rise level directly determines the maximum thermal deformation of the screw,and the thermal deformation field has a certain lag compared with the temperature field.The long axis structure causes an obvious temperature difference at screw's different positions,while a small temperature difference can be found on the nut due to the relatively compact structure.The cooling medium in the hollow screw and the forced air cooling outside the nut can both effectively reduce the temperature rise and thermal deformation.4.The temperature rise of PRSM temperature nodes are predicted under different working conditions,based on the thermal network method.Different types of contact thermal resistance,conduction resistance and convective resistance are calculated.The transient heat balance equations including the lubricant temperature node are established according to the energy conservation of the node system,and the viscosity-temperature effect of the lubricant is fully considered when study the relationship between node temperatures and time.The calculations show that the temperature difference on the nut and roller becomes obvious when the axial load increases.The temperatures of the nut,ring gear and lubricant rise significantly with the increase of the screw speed,and the temperature difference between the nut and ring gear is also gradually increased.Reducing the convective thermal resistance would greatly decrease the temperature rise of the carrier,but the roller's temperature rise level will not be significantly affected when changing the convective thermal resistance.5.The thermal test system for PRSM is built,and the temperature tests under variable axial load,screw speed,grease type and forced air cooling conditions are carried out,respectively.The validity of the PRSM thermal model is verified by comparing the critical measuring points' temperatures with the calculated temperatures of key points in the finite element model and of nodes in the thermal network model.The Grade 2 and Grade 3 greases are employed according to the consistency classification of the National Lubricating Grease Institute(NLGI).It is found that the NLGI Grade 2 is obviously thinned after a period of operation,flowing out from the gap between the nut and the ring gear and between the roller shaft end and the carrier.The NLGI Grade 3 is relatively viscous to avoid its loss,but the temperature rise of the PRSM parts are higher than the cases using the NLGI Grade 2.Finally,some comments and observations are given and the future research works of the PRSM friction torque and thermal characteristics are proposed. |
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