Consider the assembly of two steel plates, each plate having a hole. drilled in

Question

Consider the assembly of two steel plates, each plate having a hole. drilled in its center. The plates are to be joined by a pin. The plates are aligned for assembly relative to the bottom left corner (0,0). The hole placement is centered at (3, 2) on each plate. The standard deviation in each direction is 0.0045. The hole diameter is normally distributed, with a mean of 0.3 and a standard deviation of 0.005. The pin diameter is also distributed normally, with a mean of 0.29 and a standard deviation of 0.004. What fraction of pins will go through the assembled plates? Base your answer on a simulation of 50 observations.

Hint Clearance = Min(h1 , h2) - [(x1 - x2 )2 + (y1 -y 2 )2]5 -p, where

h.= hole diameter, i = plate 1, 2

p = pin diameter

xi = distance to center of plate hole, horizontal direction, i = 1, 2

yi = distance to center of plate hole, vertical direction, i = 1, 2

Explanation / Answer

h1 and h2 follow normal distribution with a mean of 0.3 and a standard deviation of 0.005 and p follows normal distribution with a mean of 0.29 and a standard deviation of 0.004. We draw two sets of 50 random nos from N(0.3, 0.005) and 50 random nos from N(0.29,0.004) and (x1-x2)2=(y1-y2)2=0.00452, the necessary calculations are shown below:

h1 h2   Min(h1,h2) p (x1-x2)2 (y1-y2)2 Clearance

[1,] 0.3030984 0.3082251 0.3030984 0.2909332 2.025e-05 2.025e-05 1.196269e-02
[2,] 0.3012888 0.2852559 0.2852559 0.2898391 2.025e-05 2.025e-05 -4.785756e-03
[3,] 0.3058602 0.2893584 0.2893584 0.2869254 2.025e-05 2.025e-05 2.230513e-03
[4,] 0.2964481 0.3084647 0.2964481 0.2916645 2.025e-05 2.025e-05 4.581119e-03
[5,] 0.2963421 0.2939395 0.2939395 0.2893629 2.025e-05 2.025e-05 4.374064e-03
[6,] 0.2945776 0.2941872 0.2941872 0.2878547 2.025e-05 2.025e-05 6.130053e-03
[7,] 0.2947913 0.3023280 0.2947913 0.2816629 2.025e-05 2.025e-05 1.292582e-02
[8,] 0.2999815 0.3006955 0.2999815 0.2890296 2.025e-05 2.025e-05 1.074937e-02
[9,] 0.2935473 0.2976652 0.2935473 0.2885858 2.025e-05 2.025e-05 4.758956e-03
[10,] 0.2995258 0.2913658 0.2913658 0.2900293 2.025e-05 2.025e-05 1.133930e-03
[11,] 0.3042207 0.3088651 0.3042207 0.2862899 2.025e-05 2.025e-05 1.772823e-02
[12,] 0.3005494 0.2929859 0.2929859 0.2922947 2.025e-05 2.025e-05 4.886776e-04
[13,] 0.3061877 0.3008320 0.3008320 0.2943390 2.025e-05 2.025e-05 6.290442e-03
[14,] 0.3014957 0.3008704 0.3008704 0.2849534 2.025e-05 2.025e-05 1.571458e-02
[15,] 0.3036952 0.2889127 0.2889127 0.2901382 2.025e-05 2.025e-05 -1.427990e-03
[16,] 0.3005219 0.2972541 0.2972541 0.2922641 2.025e-05 2.025e-05 4.787500e-03
[17,] 0.3028029 0.2998723 0.2998723 0.2835654 2.025e-05 2.025e-05 1.610439e-02
[18,] 0.3002357 0.3020949 0.3002357 0.2963298 2.025e-05 2.025e-05 3.703372e-03
[19,] 0.3005181 0.3074532 0.3005181 0.2876925 2.025e-05 2.025e-05 1.262312e-02
[20,] 0.3058506 0.2995265 0.2995265 0.2939069 2.025e-05 2.025e-05 5.417073e-03
[21,] 0.3028092 0.2894808 0.2894808 0.2904288 2.025e-05 2.025e-05 -1.150529e-03
[22,] 0.2839501 0.3016324 0.2839501 0.2897394 2.025e-05 2.025e-05 -5.991869e-03
[23,] 0.3073758 0.2990948 0.2990948 0.2858113 2.025e-05 2.025e-05 1.308097e-02
[24,] 0.3077725 0.2918677 0.2918677 0.2836467 2.025e-05 2.025e-05 8.018578e-03
[25,] 0.3007258 0.2946318 0.2946318 0.2891886 2.025e-05 2.025e-05 5.240739e-03
[26,] 0.3071475 0.2898438 0.2898438 0.2868850 2.025e-05 2.025e-05 2.756385e-03
[27,] 0.2931388 0.2986264 0.2931388 0.2908690 2.025e-05 2.025e-05 2.067249e-03
[28,] 0.3014650 0.2960197 0.2960197 0.2877438 2.025e-05 2.025e-05 8.073380e-03
[29,] 0.2939941 0.2955167 0.2939941 0.2878942 2.025e-05 2.025e-05 5.897345e-03
[30,] 0.3143272 0.3049606 0.3049606 0.2877073 2.025e-05 2.025e-05 1.705075e-02
[31,] 0.2960489 0.3087901 0.2960489 0.2935374 2.025e-05 2.025e-05 2.309096e-03
[32,] 0.2987717 0.2995974 0.2987717 0.2902528 2.025e-05 2.025e-05 8.316371e-03
[33,] 0.2952967 0.3017763 0.2952967 0.2899042 2.025e-05 2.025e-05 5.190024e-03
[34,] 0.2955569 0.3030614 0.2955569 0.2901561 2.025e-05 2.025e-05 5.198331e-03
[35,] 0.2933643 0.3011612 0.2933643 0.2931884 2.025e-05 2.025e-05 -2.659317e-05
[36,] 0.3026480 0.3087046 0.3026480 0.2985333 2.025e-05 2.025e-05 3.912253e-03
[37,] 0.3066533 0.3097768 0.3066533 0.2880587 2.025e-05 2.025e-05 1.839218e-02
[38,] 0.2968149 0.3067808 0.2968149 0.2858628 2.025e-05 2.025e-05 1.074964e-02
[39,] 0.3063493 0.2975349 0.2975349 0.2925542 2.025e-05 2.025e-05 4.778115e-03
[40,] 0.3024176 0.2985959 0.2985959 0.2854044 2.025e-05 2.025e-05 1.298899e-02
[41,] 0.3029142 0.3036677 0.3029142 0.2867909 2.025e-05 2.025e-05 1.592080e-02
[42,] 0.2993976 0.2990579 0.2990579 0.2924685 2.025e-05 2.025e-05 6.386925e-03
[43,] 0.2961229 0.2983601 0.2961229 0.2869504 2.025e-05 2.025e-05 8.970000e-03
[44,] 0.2977183 0.2951714 0.2951714 0.2879309 2.025e-05 2.025e-05 7.037962e-03
[45,] 0.2930522 0.3063442 0.2930522 0.2942171 2.025e-05 2.025e-05 -1.367371e-03
[46,] 0.3018177 0.2924574 0.2924574 0.2925612 2.025e-05 2.025e-05 -3.063685e-04
[47,] 0.3037537 0.2943929 0.2943929 0.2847855 2.025e-05 2.025e-05 9.404871e-03
[48,] 0.3078637 0.2913187 0.2913187 0.2892994 2.025e-05 2.025e-05 1.816812e-03
[49,] 0.2968681 0.3028920 0.2968681 0.2879547 2.025e-05 2.025e-05 8.710858e-03
[50,] 0.2987604 0.2988145 0.2987604 0.2889355 2.025e-05 2.025e-05 9.622373e-03

Average Clearance=Total 50 clearance/50=0.00657

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.