Rolling Contact Bearings (pg 599)

Transcription

1 Bering V9.xmcd [Pg / 6] Title [234] The Units used s stndrd: m, kg, N, P, sec, wtts N, kg, m, P, sec/min, wtts/kw Rolling Contct Berings (pg 599) This note is only guideline for using the text book. Detiled explintion nd tbles re found in Shigley Mechnicl Engineering Design text book. ) double row deep groove bll bering b) roller bering c) ngulr contct bering Bering types ) single row deep groove b) double row deep groove c) ngulr contct d) roller or needle e) self-ligning f) tpered roller bering (for thrust lod)

2 Bering V9.xmcd [Pg 2 / 6] Bering Lod Most bll berings re designed to support high rdil lod nd limited xil lod. Roller bering, however, support very high rdil lod nd very little xil lod. All thrust bering support only xil lod. Bering Life The objective of this nlysis is to determine the life of bering before the first tngible evidence of ftigue. Common life mesures re. Number of revolutions of the inner ring (outer ring sttionry) or 2. Number of hours of use t stndrd ngulr speed AFBMA stndrd sttes tht the first evidence of ftigue is the splling or pitting of n re of 0.0 in 2 (by Timken Compny lbortories). The AFBMA (nd most other mnufctures) term rting life s the life spn of 90% of btch of berings. Bering Lod-life trde-off t constnt relibility For 0.90 relibility, the regression eqution form is FL constnt this is the bsic lod-rting eqn for bering where F is stedy rdil lod, nd L is the desired life nd 3 0/3 for bll bering for roller berings L d L r F r F d where Lr, Fr refer to specs provided by mnufcturers nd Ld, Fd re the design vlues.

3 Bering V9.xmcd [Pg 3 / 6] From the eqution bove, ctlog lod rting known s C0 is use to represent the 0th percentile rting life where the relibility R Hence the ctlog rting (unit: kn) is given by L D n D 60 C 0 F r 60 L R n R F r L D n D L R n R - rdil lod (in kn) pplied to the bering - designed life (in hours) --> the expected life of the bering - designed rottionl speed of the bering in RPM - rted life (in hours) provided by mnufcturer of the bering - rted rottionl speed of the bering (RPM) The vlue (L R x n R ) provide the rted life in revolutions for minute. Most bering mnufcturer chooses rted cycles vlue of,000,000 revolutions in hr period to correspond to bsic lod rting in the ctlog. Hence for most clss of bering where R 0.90, the ctlog rting is given by: L D n D 60 C 0 F r 0 6 N.B: If relibility is not mentioned, then the defult vlue of R 0.90 is ssumed. Smple A A bll bering is to be selected to crry rdil lod of 6.5 kn. The designed life is 5000 hr with rottion rte of 900 rpm. For bering relibility of 0.90, find the suitble bering. Designed (desired) lod is rdil lod, F r 6.5kN Designed life, L D 5000 Inner ring rottes, n D 900rpm Bll bering, 3 L D n D 60 C 0 F r kn Refer to Tble -2 pg 57, column for Deep Groove Lod Rtings. The next higher C rting C kn corresponding to Bore 55mm. The selected bering is 55mm 02-series deep groove bll bering!

4 Bering V9.xmcd [Pg 4 / 6] Relibility of the Berings The Relibility-Life Trde-Off [bering survivl nd lod-life] : Relibility R > 0.9 (For higher ccurcy of Life of bering bsed on relibility nlysis, empiricl formules re used for bering) X d C 0 F r x 0 ( θ x o )log b + R > The designed life expressed in multiples of rting life. L D n D 60 X d 0 6 The eqution bove is most ccurte for bering nlysis. But for cdemic purposes, it cn be simplified s below: X d C 0 F r x 0 + ( θ x o )( R) b Bsed on experimentl dt, the finl eqution for lod rting :- X d L C 0 A f F r D n D 60 X d ( R) If Appliction fctor (sfety fctor ) if not mentioned, A f.0

5 Bering V9.xmcd [Pg 5 / 6] Smple B If relibility, R 0.95 in Smple A, nd (given A f.5), find the new lod rting? Find the suitble bering if it is to be mounted on 65mm round shft. X d C 0.5 F r ( 0.95) Answer: C kn The next higher C lod rting is ( C kn) for 70mm deep groove bll bering. However the shft dimeter is only 65mm. A 70mm bering will be dncing on the shft becuse of the generous tolernce (i.e. the bering is too big for the shft) Comments: 70mm bll-bering - Not recommended Solution: Use the lterntive Angulr Contct bering. The next higher Angulr Contct C rting ( C kn) corresponding to 65mm bering. This bering will slip perfectly on the 65mm shft. Recommended: 65mm Angulr Contct bll bering Overll Relibility (or combined relibility) for multi-berings system Most shft re supported by t lest 2 berings. If the overll relibility of the berings supporting the shft is given s R, then Individul bering relibility, R n R where n is the number of berings supporting the shft (used t lest 2 more deciml points) Overll relibility, R 0.99 for 3 berings system supporting shft, R

6 Bering V9.xmcd [Pg 6 / 6] Combined rdil nd thrust loding A bll bering is cpble of resisting rdil loding, F r nd thrust (xil) loding, F. To consider both lods, n equivlent rdil lod, F e is obtined tht does the sme dmge s combined rdil nd thrust lod. The eqution is given s below: F e X 2 VF r + Y 2 F To correct for vrious rotting-ring conditions, rottion fctor, V is used. V inner ring rottes V.2 outer ring rottes The X nd Y fctors depends on severl conditions including number of blls nd its dimeter. The Equivlent Rdil lod fctors for bll-bering is shown in Tble -. The Y 0 for stright nd cylindricl roller berings becuse it does not tke ny xil lod. If F VF r e then use X nd Y in Tble - If F VF r > e then use X 2 nd Y 2 in Tble - Use the eqution: N.B. :- tbultion my be needed to get the exct dimensions indirectly 60 L D n D F e X 2 VF r + Y 2 F C 0 F e 0 6 Smple 2 An bll bering is to be selected to crry rdil lod of 8 kn nd thrust lod of 4 kn. The desired life L D is to be 5000 h with n inner-ring rottion rte of 900 rpm Wht is the bsic lod rting tht should be used in selecting bering for relibility of 0.95? Smple 3 A bering is to be selected to crry rdil lod of 5.0 kn. The designed life is 2500 hrs with rottion rte of 500 rpm. For bering relibility of 0.99, find the suitble bering if it is to be mounted on 35mm round shft. Appliction fctor.5