Optimization Design of Large Aperture Curved Prism Bonding Based on Finite Element Analysis
Aiming at the working conditions and performance requirements of large-diameter curved prisms with high face shape precision,an optimized design approach is proposed for bonding such prisms while considering the adhesive curing shrinkage stress.Based on this approach,the bonding process for large-diameter curved prisms is successfully optimized.Firstly,the finite element differential equation for the shrinkage stress during glue curing is derived based on the non-free curing model of the glue.Secondly,by applying the principles of support structure design and flexible structure design theory,a meticulously devised circular flexible bonding structure was created.The topology of the frame structure was optimized with flexibility as the primary objective while adhering to structural weight constraints,resulting in an impressive lightweight rate of 55.79％.Subsequently,a simulation and analysis model was developed to investigate the impact of adhesive curing shrinkage on mirror surface shape using the temperature loading method.The response surface model for the colloid parameters'equivalent gel contraction force was established,achieving a goodness of fit of 97.56％.It was found that the equivalent gel contraction force increased with the increase of colloid contraction rate and thickness.Additionally,the equivalent gel contraction force and the area of colloid spot exhibited different monotonous increasing and decreasing trends under varying gel contraction rates.The degree of influence of colloid contraction rate on the equivalent gel contraction force was found to be the largest,while the area of colloid spot had the least influence on the equivalent gel contraction force.The optimized parameters for the colloid were determined to be 9 mm×23 mm×0.1 mm.The study investigated the influence of adhesive type,gel parameters,and bonding quantity on the surface shape of curved prism components.The results obtained from the surface shape simulation analysis of curved prisms using three kinds of epoxy adhesives(3M-2216,Milbond,and GHJ-01)under the same conditions were compared in terms of relevant properties of adhesive materials.The influence of surface shapes before and after curing was also examined to compare the performance of the adhesives.It was determined that the 3M-2216 adhesive exhibited optimum performance among the three kinds of adhesives.With the increase in the number of bonds,the deformation value of the front and rear mirrors shows a trend of decreasing and then increasing.The maximum stress value shows a fluctuating downward trend,while the average stress value shows a trend of decreasing and then slowly increasing.When bonded with 6 glue dots,the deformation of the upper and lower dome positions can be precisely restrained,so that the maximum deformation is concentrated in the center of the mirror.The deformation value and stress value are smaller.In summary,an optimized solution for high face shape accuracy is obtained by choosing 3m-2216 epoxy adhesive,designing arc-shaped glue spots and their flexible bonding structure.Under these conditions,with 6 glue spots on each side and a homogeneous distribution of gluing,it was found that the PV value for face shape accuracy of the curved prism's front mirror face is 2.78 nm with an RMS value of 0.53 nm;for its back mirror face,it is 1.58 nm with an RMS value of 0.31 nm which is 98％lower than that of the initial structure.Compared to the initial structure,wavefront error caused by adhesive curing has been reduced by 98.89％.Additionally,environmental adaptability was analyzed using the finite element method:Z-direction self-weight significantly impacts curved prism assembly followed by X-direction;Y-direction has the least effect.The maximum deformation observed in the assembly is at its upper surface center(67.6 nm),while the maximum stress value(0.18 MPa)is found on the bonding surface of the bonding ring.For front mirror surface shape accuracy:X-direction self-weight plays a major influence with PV value being 16.3 nm and RMS value of 3.61 nm;whereas for rear mirror surface,Z-direction self-weight plays a dominant role with PV value of 29.3 nm and RMS value of 5.34 nm.The thermal deformation and thermal stress reach their maximum values when subjected to a uniform temperature rise of 4℃ on gel material.As the temperature gradient increases,both thermal deformation and thermal stress initially decrease before increasing again.Among different temperature gradients tested,a rise in temperature gradient by 3℃ shows minimal impact on curved prism assembly,which validates its structural design's rationality.After implementing an optimized gluing scheme,the face shape accuracy for curved prism mirrors is less than 0.059λ in terms of PV value,and less than 0.012λ in terms of RMS value.This proposed gluing optimization scheme considers shrinkage stress during the curing process,meeting high-precision optical system requirements.The findings from this study can serve as a reference for optimizing high-face shape precision gluing schemes and support structure designs for large-diameter curved prisms.
万方数据
维普
