The Complete Part Design Handbook

Transcription

1 The Complete Prt Design Hndbook For Injection Molding of Thermoplstics Berbeitet von E. Alfredo Cmpo 1. Auflge 006. Buch. XXI, 870 S. Hrdcover ISBN Formt (B x L): 1,5 x 7,7 cm Geicht: 3050 g Weitere Fchgebiete > Technik > Technik Allgemein > Konstruktionslehre und -technik Zu Inhltsverzeichnis schnell und portofrei erhältlich bei Die Online-Fchbuchhndlung beck-shop.de ist spezilisiert uf Fchbücher, insbesondere Recht, Steuern und Wirtschft. Im Sortiment finden Sie lle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) ller Verlge. Ergänzt ird ds Progrmm durch Services ie Neuerscheinungsdienst oder Zusmmenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr ls 8 Millionen Produkte.

2 The Complete Prt Design Hndbook E. Alfredo Cmpo For Injection Molding of Thermoplstics ISBN Weitere Informtionen oder Bestellungen unter soie im Buchhndel

3 .16 Flt Circulr Pltes 01 Tble -5 Flt Circulr Plte Equtions, Prt I W Concentrted lod (lb); Unit lod (psi); M Moment (in-lb/in); Deflection (in); θ Chnge in slope (rdins); E Modulus of elsticity (psi); H Deflection fctor (in.); υ Poisson s rtio; Stress (psi); t Wll thickness (in); Outer rdius (in); b Inner rdius (in); d Shft rdius; r 0 Rdius of lod (in); K Plte constnt Cse Type Stress nd Deflection Equtions (Constnt Thickness) Concentrte Center Lod Edge Simply Supported W y 3 W (1 + υ ) 1 1 υ r 0 + log + πt υ 1 r υ 3 W (1 υ)(3 + υ) π Et Mx. 3 0 Uniform Distribute Lod Edge Simply Supported edge simply supported 3 (3 + υ ) y Mx. 8 t 3 (1 υ)(5 + υ) 16 Et Mx. 3 For > r 0 Concentrted Center Lod Outer Edge Fixed W y 3 W (1 + υ ) r 0 log + π t r Mx. 0 3 W (1 υ ) π Et Mx. 3 Uniformly Distributed Lod Outer Edge Fixed y 3 t Mx. 3 (1 υ ) 16 Et Mx. 3 3 (1 υ ) H 16 Et Mx. 3 For thicker flt circulr pltes hving (t / 0.1), multiply the defl ection eqution by the constnt (H ), here *H (t / ). Centrl Couple Outer Edge Simply Supported M 0.9 K ( d ) d 3M ( d ) 1 + ( υ + 1) log π dt K Mx. Centrl Couple Outer Edge Fixed M d 0.10 K ( d ) 3M (0.5 d ) 1 + ( υ + 1) log π dt 0.5 K Mx. Rdil Center Lod Edge Simply Supported W b y W υ υ 1 log + 1 π t ( + b ) b μ Mx W υ 1 ( b ) + 1 b + 1 υ υ υ + log π Et 1 1 b + 1 ( b ) υ υ 1 Mx. 3

4 0 Engineering Product Design Tble -5 Flt Circulr Plte Equtions, Prt II W Concentrted lod (lb); Unit lod (psi); M Moment (in-lb); Deflection (in); θ Angulr chnge (rd.); Q sher (lb/in); E Modulus (psi); υ Poisson s rtio; 6M / t (psi); t Wll thickness (in); Outer rdius (in); r 0 Rdius of lod (in); D Et 3 / 1 (1 ν ); N Equivlent rdius (in); K, C, L, G Constnts (rtio-dependent) Cse Type Boundry Vlues Specil Cses Outer nd Inner Edge Simply Supported; Centrl Rdil Lod W Outer & Inner Edges Fixed; Chnge in Slope O Uniform Distributed Lod; Edge Simply Supported 0, M 0, 0, M 0 b rb r Kθ W b θ b D Q K W b Qb θ θ W b C + Qb C6 L6 D D b Wro Q Qb 0, θ 0, 0, θ 0 b b KMrb θ o D b Mrb ; Q Q b KQb θ o D Qb ; Mx. K o θ D Mr Mrb C8 + Qb C9 + θ o L 7 0, Mr 0; MC G 17 θ W G 17 C G 11 D 1+ υ ( ) 8 D(1 + υ ) ro b / r o / K Mx K θ K θ b K Mrb K Mro K Qb b / r o / K o K Mrb K Mr K Qb r o / K C K θ K MC (3 + υ ) Q ( ro); If ro 0, G , G1 0.06, G (5 + υ ) (3 + υ ) LT G11; LTθ G1 ; C ; M C ; θ D D 6 D(1 + υ) 16 8 D(1 + υ) Liner Increse Lod; Edge Simply Supported 0, Mr 0; MC G 18 G 18 C G 1 D 1+ υ Q ( ro r o ) 6 θ r o / G 18 G15 ; If ro 0, G1 0.00, G15 0.0, G 18 K C K θ K MC ( + υ ) D 1+ υ o (6 υ) ( υ) 1; C ; C ; θ o υ r + + LT G M D r 15 D(1 + ) 5 15 D (1 + υ) Centrl Circulr Lod; Edge Simply Supported W r W (3 + υ ) Wr 1 For r > ro ; ( r ) r ln ; θ ln 16 πd + (1 + υ) r πd (1 + υ) r W ( ) r (1 )ln (1 ) r N M + υ + υ ; N 1.6r o + t 0.67 t; If ro < 0.5 t 16 π r r W N or N r, If r > 0.5 t; M (1 + υ)ln + (1 υ) 16 π r r o o t W (3 + υ ) W W t r ; Mx. ; θmx. ; M Mx. (1 + υ )ln πd(1 + υ) πd(1 + υ) π N

5 .16 Flt Circulr Pltes 03 Besides the usul lodings, Tble.5 Prt II lso includes severl loding cses tht my be described best s externlly pplied conditions tht force lck of fltness into the flt circulr pltes. The first time e look t Tble.5, Prt II it ppers to be formidble tsk to clculte the strength of these structures. Hoever, hen e consider the number of cses it is possible to present in limited spce, the reson for this method of presenttion becomes cler.with creful inspection, e find tht the constnts nd functions ith subscripts re the sme except for the chnge in vribles. In Tble.5, Prt II, the tbulted vlues in the Specil Cses re listed for the preceding functions for the most frequently used denomintor vlues of the vrible rtios, such s b / nd r 0 /. Exmple -1 A flt circulr plte is mde of nylon 6/6 ith 33% fiber glss reinforcement t 73 F nd 50% reltive humidity. The rdius is 3.00 in ith ll thickness of 0.5 in. The plte is simply supported round its edge nd it is loded ith lb t the center. The lod is distributed through round re of 0.15 in rdius. Determine the mximum bending stress t the surfce of the plte nd the mximum deflection t the center of the plte. Solution This flt circulr plte nd loding re covered in Tble.5, Prt I, cse lod t center ith the outer edge simply supported. The digrm nd equtions in Figure -96 ere obtined from this tble: t 0.50 in, 500 lb, 3.00 in, r in, E 900,00 psi, υ 0.39, 18,000 psi 3 W (1 + υ ) 1 1 υ r 0 Mx. log πt + υ + 1 r 0 1+ υ 10,79 psi ( ) log W Figure -96 Flt circulr plte, concentrted center lod, nd simply supported edge 3 W (1 υ)(3 + υ) (1 0.39) ( ) π Et , Mx in Exmple - A thick flt circulr plte is mde of nylon 6/6 ith 33% fiber glss reinforcement t 73 F nd 50% reltive humidity ith rdius of.00 in nd uniform ll thickness of 0.50 in. The plte s outer edge is fixed nd it is uniformly loded long the round re of plte ith lb/in. Determine the mximum bending stress t the surfce of the plte nd the mximum deflection t the center of the plte.

6 0 Engineering Product Design Figure -97 Flt circulr plte, uniformly distributed lod, nd fixed edge Solution This thick flt circulr plte nd type of loding is presented in Tble.5, Prt I, cse Uniformly Distributed Lod ith the Outer Edge Fixed. The digrm nd equtions in Figure -97 ere obtined from the tble. Becuse this exmple cse dels ith thick plte, e need to investigte if the thickness / rdius rtio is greter thn 0.1 to modify the mximum deflection by multiplying the vlue by the constnt (H ). t in, 00 psi,.00 in, E 900,00 psi, υ 0.39, 18,000 psi For thicker flt circulr pltes ith rtio t / > 0.1, multiply the deflection eqution by the constnt (H ), here H (t / ). t > H ( t/ ) (0.50/.00) ,3.00 psi π t Mx. 3 (1 υ ) ( ) 0.07 in Et , Hxy in Mx. Exmple -3 A flt circulr plte, mde of cetl homopolymer, hs ll thickness of in nd 5.00 in outside dimeter, nd is simply supported ith uniformly distributed lod of 6.0 psi. Clculte the mximum deflection in the center, the mximum stress, nd the deflection eqution for Figure -98. This flt circulr plte nd type of loding is presented in Tble.5, Prt II, cse Uniformly Distributed Lod Edge Simply Supported. First, e need to determine the mximum moment, the bending stress, the plte constnt, nd the deflection cused by the lod. Second, e need to clculte the totl deflection of the plte cused by the lod, the moment, nd the loding constnt. Finlly, e need to check the deflection t the outer edge. t in, 6.0 psi,.50 in, r 0 0, E 10,000 psi, υ 0.35, 10,000 psi Figure -98 Flt circulr plte, uniformly distributed lod ith simply supported edge M Mx. (3 + υ ) ( ) MCenter 7.85 lb-in M , psi t Mx.

7 .16 Flt Circulr Pltes Et 10, D (1 υ ) 1( ) C (5 + υ ) ( ) in 6 D (1 + υ ) ( ) The totl deflection eqution for the flt circulr plte is: MC y C + + LTy, here for this cse D (1 + υ ) LT y D G 11 Where the constnt G , hen r Checking the deflection t the outer edge, hen.50 in Exmple - A flt circulr plte is mde of cetl homopolymer ith ll thickness of 0.15 in nd.00 in outside dimeter. It is mounted in fi xture to produce sudden chnge in slope in the rdil direction of 0.05 rdint t rdius of 0.75 in. It is then clmped beteen to fl t fixtures s shon in Figure -99. Clculte the mximum bending stress. This is n exmple of forcing knon chnge in slope into fl t circulr plte, clmped (fixed) t both inner nd outer edges. This flt circulr plte nd type of loding is presented in Tble.5, Prt II, cse Outer nd Inner Edge Fixed nd Chnge in Slope, here: θ , b / 0.10, r 0 / 0.50 nd Poisson s rtio of υ t 0.15 in, 1.50 in, b 0.15 in, r in, θ rd., θ b 0.0 rd., b 0.0 in, E 10,000 psi, υ 0.35, 10,000 psi 3 3 Et 10, D (1 υ ) 1( ) θ O.00 di M Q b rb KMrb θ D lb-in KQb θ D lb/in r r rd r. Figure -99 Flt circulr plte hving chnge in slope ith both outer nd inner edges fixed

8 06 Engineering Product Design D Mr Mrb C8 + Qb C9 + θ 0 L C + ( 0.15) C + L M rb Mx , psi t 0.15 Mx. Ky0 θr in Exmple -5 A flt circulr plte, mde of cetl homopolymer, hs ll thickness of 0.50 in nd 5.00 in outside dimeter, it is simply supported t the outer edge nd subjected to to types of lods. One center lod provides uniform pressure over dimeter of in. The other is xis-symmetriclly loded ith distributed lod tht increses linerly from the center to the outside rdius 1.00 in;, this lod hs vlue of psi t the outer edge. Clculte the mximum bending stress. This exmple requires nlyzing to different cses nd to superposition the results. The first cse is the liner increse of the distributed lod ith simply outer edge supported (Figure -100), the second cse is the centrl circulr uniform lod ith simply supported outer edge (Figure -101). Both cses re presented in Tble.5, Prt II. t 0.50 in,.50 in, r in, r in, E 10,000 psi, υ 0.35, 10,000 psi From the specil cse dt, the folloing vrible rtios re obtined: 1 r 01 / 1 /.5 0.0, K y C 0.016, K θ 0.078, K MC 0.09 Figure -100 First cse: Liner decresing distributed lod nd edge simply supported 3 3 Et 10, D (1 υ ) 1( ) KyC in D P r M K lb-in. Mx. MC P (3 + υ ) P.50 ( ) in 16 π D (1 + υ) 16 π ( ) P 0.76 lb. Figure -101 Second cse: Center uniformly circulr lod nd edge simply supported The second moment component is clculted by using the equtions provided in Tble.5, Prt II, cse Centrl Circulr Loding nd Simply Outer Edge Supported.

9 .17 Torsion Structurl Anlysis 07 0 N 1.6r + t t in M Mx. P (1 + υ )ln + 1 ( )ln + 1 π N π lb-in. 6 M 6( ) 613. psi t 0.50 Mx..17 Torsion Structurl Anlysis A br is rigidly clmped t one end nd tisted t the other end by torque T F d, pplied in plne perpendiculr to the xis. Plne sections remin plne nd rdii remin stright. There is t ny point sher stress ( τ ) on the plne of the section; the mgnitude of this stress is proportionl to the distnce from the center of the section nd its direction is perpendiculr to the rdius drn through the point. The deformtion nd stresses re shon in Figure -10. In ddition to these deformtions nd sher stresses, there re the longitudinl strin nd stress. The longitudinl strin is reduced hile the stress is in tension on the outside nd blncing compression stress is exerted on the inside. F d Figure -10 Deformtion nd stress under torque L TFxd Assumptions The torsion equtions re bsed on the folloing ssumptions: The br is stright, of uniform circulr cross section (solid or tubing), nd of homogeneous isotropic mteril. The br is loded only by equl nd opposite tisting couples, hich re pplied t its ends in norml direction to its xis. The br is not stressed beyond the elstic limit of the mteril. Angle of Tist ( θ ) If shft of length ( L ) is subjected to constnt tisting moment ( T ) long its length, then θ is the ngle through hich only one end of the br ill be tisted. Tisting Moment (T ) The tisting moment T for ny section long the br is defined to be the lgebric sum of the moments of the pplied couples tht lie to one side of the section in question. Shering Strin If br is mrked on the surfce (unloded), then fter the tisting moment ( T ) hs been pplied, this line moves s shon in Figure -10. The ngle ( θ ) is

10 08 Engineering Product Design mesured in rdins; the finl nd originl position of the genertor is defined s the shering strin t the surfce of the br. Shering Stress ( τ ) For solid circulr cross section br, let T Tisting moment; L Length of the br; r 0 Rdius; J Polr moment of inerti; τ Sher stress; θ Angle of tist (rdins); G Modulus of rigidity. Then: θ ( TL)/( GJ) ; τ Mx. ( Tr0)/ J By substituting for J ( π r0 )/ in the eqution bove for solid circulr cross section ith rdius r 0, the folloing equtions re obtined: 0 θ ( TL)/( πr G) ; τ 3 Mx. T πr0 ( )/( ) For circulr tube cross section ith outer rdius r 0 nd inner rdius r i : 0 i θ ( TL)/ π( r r ) G ] ; τ Mx. Tr0 π r0 ri ( )/[ ( )] The torsionl stiffness of the br cn be expressed by the generl eqution: θ (T L) / (G K), here K is fctor dependent on the br cross section. For cross section brs, the fctor K is equivlent to the polr moment of inerti J. In Tble -6, the equtions for the fctor K nd for the mximum sher stress ( τ Mx. ) for vriety of cross section brs re given. Exmple -6 Compre the strength nd stiffness of circulr injection molded tube mde of plstic mteril, 1.00 in outside dimeter nd in ll thickness, versus n extruded solid circulr br of the sme mteril ith the sme dimeter. The strengths of both cross sections ill be compred by using the tisting moments ( T ) required to produce the sme sher stress. The stiffness ill be compred by using the vlues of fctor (K ) for both cross sections. For the circulr tube br: 0 i K π ( r r )/ ( )/ in 0 i 0 τ T τπ( r r )/( r ) ( )/( 0.50) τ lb-in. For the solid circulr br: K T π r / / in 3 3 ( τπr )/ τ / τ lb-in. The solid circulr cross section br is therefore 1.18 times s stiff s the circulr tube cross section br nd 1.18 times s strong.

11 .17 Torsion Structurl Anlysis 09 Tble -6 Torsion Equtions Cross section Constnt K in TL θ KG Sher stress mx. Solid circle K π τ Mx. 3 π T Circulr tube K O ri π ( r ) τ Tr O Mx. π ro ri ( ) r i Solid ellipse r S K 3 3 π rl rs rl + rs τ T Mx. π rl rs r L Solid squre K τ Mx. 3 T 0.08 Solid rectngle b K b b 1 b τ T (3 b ) b Mx. θ Angle of tist (rdins); T Tisting moment (lb-in); τ Sher stress (psi); G Modulus of rigidity (psi); J Polr moment of inerti (in ); K Constnt equivlent to J (in ); r o Outer rdius (in); r i Inner rdius (in); r S Ellipticl short rdius (in); r L Ellipticl lrge rdius (in); Height (in); b Width (in).

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13 11 3 Structurl Designs for Thermoplstics Poor design 3.1 Uniform nd Symmetricl Wll Thickness The ultimte design rule for injection molding thermoplstic products is to ensure tht the ll thickness is uniform nd symmetricl. Non-uniform nd/or hevy ll thicknesses cn cuse serious rpge nd dimensionl control problems in the injection molded products. Hevy ll sections cuse not only internl shrinkge, voids, nd surfce sink mrks, but lso nonuniform shrinkge resulting in poor dimensionl control nd rpge problems. Figure 3-1 shos poor cross section design of perpendiculr corner lls tht cuses molding problems, such s differentil shrinkge, rpge (concve) of both lls, nd internl voids in the corner of the thicker ll. The lst to designs re recommended to void these molding problems. Figure 3- shos hevy ll cross section design tht could cuse molding problems nd the recommended design using thin ll nd proportionl ribs. Figure 3-3 shos nonuniform ll section tht should be replced ith thin uniform ll hving the sme strength of the originl hevy ll section. Figure 3- shos nother poor nd the recommended uniform ll design. Figures 3-5 nd 3-6 sho cross sections of to nonuniform ll designs nd the recommended designs ith uniform ll thickness to void rpge, internl voids, long molding cycles, nd surfce sink mrks. Wrpge Molding problems Good design R. r. Shrp corner Voids Figure 3-1 Perpendiculr lls, end corner designs Good design r. Set Poor design Good desig n Figure 3- Hevy ll vs. thin uniform ribbed ll designs Poor design Good design Figure 3-5 Nonuniform ll vs. thin uniform ll designs Poor design Good design Figure 3-3 Nonuniform ll vs. thin uniform ll designs Poor design Good design Poor design Good design Figure 3- Nonuniform ll vs. thin uniform ll designs Figure 3-6 Nonuniform ll vs. thin uniform ll designs