A System for Automated Fixture Planning with Modular Fixtures

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Vise jaws should be pked against the part. face to k e. Once both jaws are placed against the part, the contactareabe~eachjswandthepertcanbeidentifiedarabolwiingconvexpolygon. Each vertexof a polygon can be represented by a m h . Since both polygons lie on parallel planes, all wrenches describing each polygon are perpendicular to the planes. Screw theory can be used to detect any part mouon dunng clamping. Geomemc reasoning can be used to determine if the pan would rotate due to the locarion of a movable jaw. The part will move during contact by a movable jaw if two polygons are not overlapped at all when they are projected onto a plane paIlel to both. 3.4. Computation of clamping force This section desuibes a method to estimate necessary clamping force wben a fixture plan is generated with overhead clamps 01 a vise. Estimation of clamping force is the most critical process because it affects the quality of a fatme plan. ‘Ihe inadequate clamping force will scrap the part by not holding the pan rigidly during machining. Applying a larger clamping force thau necessary may deflect or deform the part. nus, it is necessray to estimate the minimum clamping force, In order to estimate necessary clamping force, cutfing force should first be. estimated accurately. However. the accurate estimation of cutting force is difficult becaw. it depends on cutting pammtm such as the depth of cut aod feed rate, etc, as well as tool weas which is hard to quanm. Experienced tool designers can make a reasonable estimation of the magnitude. of cutting force. As discussed earlier, in fixture plans with ovemead clamps 01 a vise, planar motions such as translation on a plane and mtation a ht a0 axis peqendicular to the plane need to be restraiOed by friction force. Since the friction d cimt between the pft and fwure mmponents is typically small, a large damping force is required to mainrain a pan’s W e and moment equilibrium during machining, when the. motion due to the cutting force must be mixed mainly by friction force. When a cutting force is directed out of the plane, the. necessafy clamping force is much smaller since the part’s equilibrium does not depend on fricth force. Once the magnitude and direction of the cutting force are e s t i d the clamping force’s magnitude can be estimated with formulas found in a machining hdbmk. 3.4.1. Estimation of Cutting Force Since the magnitude of the clamping force is directly affected by the magnitude and direction of cutting force. it is impatant to estimate the magoin& and direction of every cutting force applied to the pat as precisely as possible. Here, only the esrimatiCm of the magnitude and the direction of drilling and milling operations are considered In a drilling operation. the direction of thrust is equal to the direction of drill feed. Reasonable estimates of torque and thrust of sharp twist drills of various sizes and &signs uio be made from the following formulas [Handbook 881:
For toque: For thrust M Kp]8d1.8A T=Xpadl.aB i Kd2E Where M = toque, in-lbf T = tluust force. lb K = Work-& ~Mlstam f = drill feed ioch per rev~lution(ipr) d = drill diameter, in. A, B, E = mill design coll~tants 23 Variom constants can be found in the same machining handbDok according to the part material and drill cutters. For example, K is 24,000 for steel with 200 Bhn (Brirmell Hardness) and 7000 for most aluminum alloys. Drill design comts, A, B, and E are based up00 he ratio dd, where c is the chisel edge length. For drills of standard design, dW.18 and A, B, and E are found m be 1.085, 1.355, and 0.03 from the table in amachm handbook Wbook 881. If the diameter of thedrill is 1 inchand the drill feed is O.OO3 ipr, when chilling a hole in steel, he torque and thmst fuce woold be 260 in-lbf and 1370 Ib, respectively. Wih the same diameter and feed on aluminum alloy materid, the torqw and thrust force would be 76 in-lbf and 400 lb, mpwfively. In practice, exm 30-5009b should be added to the fme estimate m allow for dulliog. In a miiling operarion, a cutting force can have three components: a tangential. radial, and axial cutting force (see Figure 3-7). The magnitude and direction of the overall cutling h e should be obtained by the vector summation of the tangential aod radial cutting forces at every cum tooth. The dimtion of a tangential and radial force changes conMucusly at each tooth as the cutter revolves. Thus, it is not possible to estimate the magnin~de. of cutling force accurately and tbe krion cannot be expressed as a single direction. The magnitude of tangential cutting force can be estimated from the following formula [Handbook 881: Fl = taogential force, lb HP = approximate horsepow required at the cum D = culm diameter, in. rpm = rotatid sped of the cutter Several methods have bee0 developed for calculating the power required at the machine spindle for milling. A widely used formula is as follows mdbook 881 [Sakurai 901:
Page 1: A System for Automated Fixture Plan
Page 5: Abstract This thesir desribes a sys
Page 9: Acknowledgements First of all, I wo
Page 12 and 13: 4.7.1. Position and Orientation of
Page 15 and 16: List of Figures Figure 1-1: A modul
Page 17: Figure 6-26: A force model to estim
Page 20 and 21: describes how the pan is held on .t
Page 22 and 23: 1.3. Effect of Fixture Plans on Cos
Page 24 and 25: 6 New and existiog analytical mls a
Page 27 and 28: Chapter 2 Literature review Two maj
Page 29 and 30: 11 Inim 2-2: A fixnae plan by C~OU
Page 31 and 32: 13 Thaoreridy, grasp planning and f
Page 33 and 34: 3.1. Introduction 15 Chapter 3 Nece
Page 35 and 36: Y A A x . X mul max 17 - x P i e 3-
Page 37 and 38: 19 are projected onto the same plan
Page 39: Z X 21 Wrenches from bodom referenc
Page 43 and 44: 2s The equation (3.5) conservativel
Page 45 and 46: n @ friction force _.. .- normal I
Page 47 and 48: Minimize N1 -p - N
Page 49 and 50: 31 area is 1 square inch. the stres
Page 51 and 52: 4.1. Introduction 33 Chapter 4 A Sy
Page 53 and 54: 35 checking part deflection and sel
Page 55 and 56: 4.4. Assumptions 37 The future plan
Page 57 and 58: 39 A touch probe should be used to
Page 59 and 60: 4.6.2. Cutting plan 41 1 major refe
Page 61 and 62: Cutting force and direction 43 Chap
Page 63 and 64: Clamp bar 45 , .....-, . strap clam
Page 65 and 66: aata base for supports> Type No. R
Page 67 and 68: 49 thickness. If the part is suppor
Page 69 and 70: 51 While the z coordinate of the pa
Page 71 and 72: 5.1. Introduction 53 Chapter 5 Fixt
Page 73 and 74: 55 Because the goal is to generate
Page 75 and 76: Accessible edge 57 Inaccessible edg
Page 77 and 78: clamps are oriented so that they am
Page 79 and 80: 61 unacceptable part deflection due
Page 81 and 82: Enlarged f I ! 63 Y 4 Figure 5-9: E
Page 83 and 84: clamp location I 65 Pipre 5-11: par
Page 85 and 86: 67 desirable contact area Y Zt X
Page 87 and 88: 69 When every candidate plan genera
Page 89 and 90: 71 5.9.1. Generation of Candidate L
Page 91 and 92:
73 Egure 5-20 shows the actual loca
Page 93 and 94:
5.10. Rating Fixture Plans 75 Typic
Page 95:
n not be possible to install a clam
Page 98 and 99:
L jaw geometry in the local c odite
Page 100 and 101:
m = no. of contact planes for a mov
Page 102 and 103:
84 The following rearming is used m
Page 104 and 105:
86 F i €4 shows obstacles mapped
Page 106 and 107:
88 In our reasoning. each pan face
Page 108 and 109:
i obstacles Figure 6-11: Globally f
Page 110 and 111:
7 obstacles I case 3: If xiax < 92
Page 112 and 113:
6.7. Determining the loeation of vi
Page 114 and 115:
xo Case 1 96 X common contact area
Page 116 and 117:
98 Obr Option 1: adjust the jaw loc
Page 118 and 119:
100 Parallel bars should be placed
Page 120 and 121:
When LCfc Lbor+ 2 d Case 1: When %=
Page 122 and 123:
movable jaw 1W . . . . . . There is
Page 124 and 125:
X m Pigore 6-28 Invalid fume plans
Page 126 and 127:
planner getg cutting plans for a se
Page 128 and 129:
0.150 110 ; IMW Teat Part 2 -- boon
Page 130 and 131:
112 For a clamp libmy, we have cons
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114 *** Plan with clamp type with 5
Page 134 and 135:
116 II II Fipre 7-6: F m plans with
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118 77 1 Y II’ .- Figure 7-7: Fut
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120 I i Figum 7-9 Fuhue plans with
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The system has generated multiple f
Page 142 and 143:
,170 Chamfered hole 124 Chamfer 1 C
Page 144 and 145:
I1 i Figure 7-14: Fixture plans for
Page 146 and 147:
I 0.150 - 2582 - 7.7.1. Speed of Fi
Page 148 and 149:
130 Figure 7-18: F’art geometry o
Page 150 and 151:
134 8.1.1. Fixfure Planning with Ov
Page 152 and 153:
for holding rectangular parts due t
Page 154 and 155:
138 series of fixture plans fm each
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the fixture plan viokea any fixture
Page 158 and 159:
142
Page 160 and 161:
144 Ohwovoride [Ohwovoriole 801 app
Page 162 and 163:
[Ahmad 871 t m 851 [Goldman 561 Ref
Page 164 and 165:
Menassa, R. J. and Devries, W. R. O
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A System for Automated Fixture Planning with Modular Fixtures

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