Estimation of peak deflections

To est1mate the peak deflections, the descnbed above SIMULINK model was run w1th infm1te clearances. Dunng the simulation, the s1ngle environmental shock along w1th long1!Ud1nal g-load was applied to the system. As the VIbration absorber moves harmonically at relatively high amplitudes, 1! was assumed, that the mitial conditions of possible impacts upon the bumper depend on a lime Instance of the shock application. Therefore, in order to make accurate est1mat1on of the spnng's peak deformation, the SIMULINK model was run several times, while the shock was imposed at different t1me instances w1thm one cycle of the V1brat1on absorber motion at the driv1ng frequency An array of spnng's peak deformations was acqu1red versus t1me instance of the shock application. The M-f1le dnv1ng the acquis1t1on was comp1led as shown 1n Appendix C-C1

As seen from the resulting chart of the conducted S1mulat1on, which IS shown m F1gure 56, the max1mal peak deformation of the VIbratiOn absorber spring occurred when the shock began at the time-instance of 0 21 seconds from the start of the simulat1on. However, peak deformation of the decoupler was completely Independent of the shock application time.

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9,---~----~----.---.---~---.~---.---.---,

Instance of shock beginning , s

F1gure 56 Extreme deforma!lons of SPB-compressor spnngs under shock applied at different Instances over mot1on cycle

Through the stress-analysis of suspension spnngs, which is beyond this study, their geometry and matenal were matched to survive the fatigue deformations, as est1mated m (3.4 6) As shown in Figure 57, the peak deformation of the decoupler developed under combmed action of shock, random exc1tation and g-load IS considerably lower than the limit allowed by stress-analys1s. Th1s means that the compressor spnng does not require limitation of 1ts deformation by bumpers. However, deformation of the Vibration absorber spnng, 1f 1! is not lim1ted, reaches sign1f1cantly higher value than the acceptable one. Therefore, llm1tat1on of a redundant deformation 1n that subsystem bemg under environmental shocks becomes an essential task of the SPB-compressor des1gn.

The clearance should be ass1gned beanng in mmd that, on the one hand, the bumper should protect the suspension spring from destructive deformation under shock and g-load action On the other hand, the bumper should be sufficiently distanced from the movmg mass to allow for non-impact operation in

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a lapse between environmental shocks. Satisfactory spnng protectton is achtevable when the clearance of the bumper coinctdes wtth the allowed deformation of the related spnng. Relytng on the stress-analysts of the suspension spnng, the acceptable peak deformation of the vibratton absorber spnng lies below 2.0 mm. Asstgning the same value for the bumper clearance, 1! IS easy to esttmate the restdual gap between the bumper and the vtbra!IOn absorber mass at peak deflectton under g-load and random excita!ton, which amounts to 21% of the enttre clearance.

9,---~==.==========~---~

OAIIowed by stress analysis 8

F1gure 57 Extreme deformations of SPB-compressor spr1ngs under act1on of shock, random v1brat1on and g-load

3.5.2 Objective of optimisation

The bumper ^IS requtred to serve properly during the enttre desired ilfettme, whtch

ts

typtcally a functton of the peak stresses arising m material of the restilent element throughout tmpact, and duty-cycle of tmpacts. The peak tmpact force, whtch IS related to the stress of a bumper matenal, mtght be minimtsed by op!tmtsa!ton of tts dampmg ratto [22]. However, during such an op!tmtsation it is

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also expected to fmd a bumper of a minimal stiffness, maintaimng the allowed deformation in the range of lineanty, as was modelled 1n 3.2.2.

Consequently, the typ1cal problem of optimisat1on of a v1scoelastic bumper with respect to 1ts lifet1me and m1n1mal disturbance of the parent dev1ce IS to minimize the peak impact force keeping the peak elastic deformation of the bumper within predefined tolerances.

3.5.3 Procedure of optimisation

S1nce the compressor does not hit the bumper under the defined environmental shock, only the v1brat1on absorber's bumper needs optimisation. The followmg optim1sation was carried out usmg the mapping techn1que as explained in paragraph 3.4 2. The SIMULINK M-file was compiled to dnve a cyclical run of the model at vanous combinations of bumper parameters, namely st1ffness and damping ratio. The peak deformation (Ll1).,.k of the bumper and the peak force (<fl₁₀(x₁₀

,x

10 )).,.k of Impact were acquired dunng the mapping over the S1mulat1on t1me span The content of the M-f1le comp1led for the conducted opt1m1sa!lon is shown m Appendix C-C2.

3.5.4 Results of optimisation

The chart shown in F1gure 58 portrays the acqu1red data for the optimised v1brat1on absorber bumper. F1gure 58(a) shows the dependence of impact forces at different natural frequencies of the bumper versus 1ts damping ratio.

As seen from the figure, the opt1mal damping ratiO IS 0.2 and IS mdependent of the natural frequency. Th1s is m full agreement w1th [22]. Also, softemng the bumper, as was expected, reduced the peak 1mpact force. As seen from the next chart (Figure 58(b)), the lowest natural frequency, which sat1sf1es the cntenon of the allowed deformation, IS 300 Hz.

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Thus, the v1brat1on absorber of the considered SPB-compressor should be equ1pped w1th opt1mal bumpers w1th a damping rat1o of 0.2 and natural

Damp1ng rat10 of absorber bumper

(a)

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