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      <title>The Finite Element Model</title>
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      <div class="title_topic3" id="xps10_pagetitle">The Finite Element Model</div>
      <hr noshade="true"><a name="gsfem_11310"></a><p class="para_topic">A single gear tooth is modeled using two CHEXA solid elements with midside grid points as shown in Figure <a class="links" href="javascript:void(0)" onclick="top.openFile('get_start/03topic_9.html#gsfem_11458');return(false);">2-</a>. Midside grid points are useful when the shape of a structure is complex or when bending effects are important.
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         <p align="left"><img align="bottom" src="graphics/gsfem10.gif"></p>
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      <div class="title_figure">Figure. Finite Element Model of a Single Gear Tooth</div>
      <div class="title_division">Applying the Loads</div><a name="gsfem_11463"></a><p class="para_division">Subcase 1 represents aligned gear teeth and uses the distributed load shown in Figure <a class="links" href="javascript:void(0)" onclick="top.openFile('get_start/03topic_9.html#gsfem_11568');return(false);">2-</a>. The total applied load is given by:
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      <p class="para_division">Total Load = Distributed Load · Width of Gear Tooth = 600 N/mm  · 10 mm = 6000 N</p><a name="gsfem_11470"></a><p class="para_division">In order to approximate the &ldquo;contact patch&rdquo; of mating gear teeth, we distribute the total force of 6000 N across the line of contact with 1000 N on each corner grid (grid points 15 and 17) and 4000 N on the center grid (grid point 16). A load set identification number of 41 (arbitrarily chosen) is given to the three FORCE Bulk Data entries of subcase 1.</p><a name="gsfem_11568"></a><div class="figure">
         <p align="left"><img align="bottom" src="graphics/gsfem18.gif"></p>
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      <div class="title_figure">Figure. Gears in Alignment (Distributed Load)</div><a name="gsfem_11569"></a><p class="para_division">Subcase 2 represents misaligned gear teeth and uses a single concentrated force of 6000&nbsp;N as shown in Figure <a class="links" href="javascript:void(0)" onclick="top.openFile('get_start/03topic_9.html#gsfem_11659');return(false);">2-</a>. A load set identification number of 42 is given to the single FORCE entry of subcase 2. Note that the total applied force (i.e., force transmitted from one tooth to the next) is the same in both subcases.
      </p><a name="gsfem_11659"></a><div class="figure">
         <p align="left"><img align="bottom" src="graphics/gsfem22.gif"></p>
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      <div class="title_figure">Figure. Gears Misaligned (Concentrated Load)</div>
      <div class="title_division">Applying the Constraints</div><a name="gsfem_11664"></a><p class="para_division">The base of the tooth is assumed to be fixed as shown in Figure <a class="links" href="javascript:void(0)" onclick="top.openFile('get_start/03topic_9.html#gsfem_11458');return(false);">2-</a>. Consequently, grid points 1 through 8 are constrained to zero displacement in their translational DOFs (1, 2, and 3). Recall that solid elements have only translational DOFs and no rotational DOFs. Since each grid point starts out with all six DOFs, the remaining &ldquo;unattached&rdquo; rotational DOFs must be constrained to prevent numerical singularities. Thus, all grid points in the model (1 through 32) are constrained in DOFs 4, 5, and 6. The constraints are applied using SPC1 Bulk Data entries.
      </p>
      <div class="title_division">Output Requests</div><a name="gsfem_11666"></a><p class="para_division">Stress output is selected with the Case Control command STRESS = ALL. Note that this command appears above the subcase level and therefore applies to both subcases.</p>
      <div class="title_division">The Input File</div><a name="gsfem_11671"></a><p class="para_division">The complete input file is shown in Listing <a class="links" href="javascript:void(0)" onclick="top.openFile('get_start/03topic_9.html#gsfem_11673');return(false);">2-3</a>.
      </p><a name="gsfem_11673"></a><div class="figure"><a name="gsfem_11674"></a><pre class="indent"> ID SOLID, ELEMENT MODEL 
SOL 101 
TIME 100 
CEND 
TITLE = GEAR TOOTH EXAMPLE 
STRESS = ALL 
SPC = 30 
SUBCASE 1 
    LOAD = 41 
    SUBTITLE = GEAR TOOTH UNDER 600 N/mm LINE LOAD 
SUBCASE 2 
    LOAD = 42 
    SUBTITLE = GEAR TOOTH UNDER 6000 N CONCENTRATED LOAD 
BEGIN BULK 
GRID,  1,   ,   86.5,   12.7,   5.0 
GRID,  2,   ,   86.5,   0.0,    5.0 
GRID,  3,   ,   86.5,  -12.7,   5.0 
GRID,  4,   ,   86.5,  -12.7,   0.0 
GRID,  5,   ,   86.5,  -12.7,  -5.0 
GRID,  6,   ,   86.5,   0.0,   -5.0 
GRID,  7,   ,   86.5,   12.7,  -5.0 
GRID,  8,   ,   86.5,   12.7,   0.0 
GRID,  9,   ,   93.0,   8.7,    5.0 
GRID, 10,   ,   93.0,  -8.7,    5.0 
GRID, 11,   ,   93.0,  -8.7,   -5.0 
GRID, 12,   ,   93.0,   8.7,   -5.0 
GRID, 13,   ,   99.6,   7.8,    5.0 
GRID, 14,   ,  100.0,   0.0,    5.0 
GRID, 15,   ,   99.6,  -7.8,    5.0 
GRID, 16,   ,   99.6,  -7.8,    0.0 
GRID, 17,   ,   99.6,  -7.8,   -5.0 
GRID, 18,   ,  100.0,   0.0,   -5.0 
GRID, 19,   ,   99.6,   7.8,   -5.0 
GRID, 20,   ,   99.6,   7.8,    0.0 
GRID, 21,   ,  105.0,   5.7,    5.0 
GRID, 22,   ,  105.0,  -5.7,    5.0 
GRID, 23,   ,  105.0,  -5.7,   -5.0 
GRID, 24,   ,  105.0,   5.7,   -5.0 
GRID, 25,   ,  110.0,   3.5,    5.0 
GRID, 26,   ,  110.0,   0.0,    5.0 
GRID, 27,   ,  110.0,  -3.5,    5.0 
GRID, 28,   ,  110.0,  -3.5,    0.0 
GRID, 29,   ,  110.0,  -3.5,   -5.0 
GRID, 30,   ,  110.0,   0.0,   -5.0 
GRID, 31,   ,  110.0,   3.5,   -5.0 
GRID, 32,   ,  110.0,   3.5,    0.0 
$ 
CHEXA,  1,  10,  3,  5,  7,  1,  15,  17,
     , 19,  13,  4,  6,  8,  2,  10,  11,
     , 12,   9,    16,    18,    20,    14 
$ 
CHEXA, 2,    10,   15,   17,   19,   13,   27,    29,
      ,31,   25,   16,   18,   20,   14,   22,    23,
      ,24,   21,   28,   30,   32,   26 
$
PSOLID, 10,  20 
MAT1,   20,  2.+5,   ,  0.3 
SPC1,   30,   456,      1,   THRU,     32 
SPC1,   30,   123,      1,   THRU,      8 
$    DISTRIBUTED LOAD FOR SUBCASE 1 
FORCE,  41,    15,    ,      1000.,    0.,  1.,  0. 
FORCE,  41,    16,    ,      4000.,    0., 1., 0. 
FORCE,  41,    17,    ,      1000.,    0., 1., 0. 
$    CONCENTRATED LOAD FOR SUBCASE 2 
FORCE,  42,    15,    ,      6000.,   0., 1., 0. 
ENDDATA
  </pre></div>
      <div class="title_figure">Listing 2-3. Gear Tooth Input File</div>
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