Simulate Early, Simulate Often... In Rhino
An important feature of the new Scan-and-Solve work in progress (WIP) software is the ability to simulate on wood, both straight and curved. This is a very useful addition for woodworkers, especially those working independently. Simulation and strain analysis is a very important preceding step to building to ensure both safety and longevity of a product. The SnS WIP wood feature allows for the accurate simulation of wood by accounting for the effect of grain direction and its role in material deformation. To demonstrate the process of simulating curved wood, I have designed a chair for testing.
This chair is composed of two different wood types, Black Walnut and African Mahogany. African Mahogany makes up the body of the chair (light brown), while the heavier and more stable black walnut makes up the legs.
After choosing the wood material, the orientation of grain must be determined. There are 4 options to design the desired grain.
1) Rift Sawn - Cutting wood radially so that the grain is aligned at a 90 degree angle to the board face. The direction of radial growth will be in the geometrically longer direction. Rift sawn tends to be a more expensive market option.
2) Flat Sawn - Cutting the wood so that the rings are around 30 degrees or less to the board face. The direction of radial growth will be in the geometrically shorter direction. It is the most common type of cut and typically cheaper.
3) Specify - This allows the user to specify the desired long and radial grain directions manually. This is ideal for symmetrical parts such as a cube, since there is no long or short side for the software to read.
4) Guide - The software will generate a grain that is always longitudinally tangent to the curve specified. For curved wood, this will organize the grain such that the stiffness is maximized, which will minimize deformation upon external loads. For this grain option, a guide curve and a guide surface must be specified for the software to read from.
The specified guide curve and guide surface (left) have been separated from the leg for displaying purposes. For actual use, they would overlap the surface and edge of the leg they were extracted from. An example of the resulting coordinate system created from the guide option is displayed (right). The red arrow indicates the longitudinal grain direction, which is continuously tangent to the curve.
For more information on how to set up the desired grain, view http://www.youtube.com/watch?v=j-t3_11RuVw
To better understand the expected displacement the chair would experience while in use, a downward (-z) force of 250 lbs. was applied to the seat, and a backwards (-x) force of 50 lbs. was applied to the backrest. The chair contains a rubber stopper at the bottom of each leg, and thus was restrained from that location.
To demonstrate the effect grain direction has on the deformation of the chair, 3 simulations were performed utilizing the same external conditions, but different grain orientations. In the first simulation the legs were rift sawn, in the second they were flat sawn, and in the third they were guided.
For each of the following images, the displacement color scale was set to a maximum of 0.4 inches (the maximum displacement experienced throughout the 3 simulations). This allows the color schematic of the 3 simulations to be on the same scale, and thus readily comparable. Additionally, the chair displacement in each simulation is magnified by a factor of 10 to better display the differences in behavior. While the chair displacement is emphasized from the magnifications, the ratios will remain accurately depicted.
Simulation 1 (rift sawn legs) displacement results
Simulation 2 (flat sawn) displacement results
Simulation 3 (guided) displacement results
The 3 analysis tools available in the above images all suggest the same outcome. The color schematic shows the most red and yellow in the chair containing flat sawn legs, green in the chair containing rift sawn legs, and blue in the chair containing guided legs. This indicates that the flat sawn chair legs yield greater deformation than the other two options, guided legs yield the least deformation. This theory is backed by the visual representation of the chair deformation, which clearly depicts maximum deformation in the flat sawn option, and minimum in the guided. additionally, the numerical representation of maximum displacement is in accordance with these findings.
By analyzing the different grain orientation coordinate systems, it becomes clear why the guided option is the best.
Rift sawn coordinate system
Flat sawn coordinate system
Guided coordinate system
Wood tends to be the most stiff in the longitudinal direction. The guided coordinate system shows that the longitudinal grain direction (red arrow) is always tangent to the curve, optimizing the chairs resistance to displacement yielding from the applied forces. This grain orientation is substantially the best building option, and can be applied through the use of steam bending.
As for determining the difference between rift and flat sawn, the difficult curved geometry makes it almost impossible to manually determine which option will better resist displacement. This is a common problem when building curved and complex geometries with wood, and emphasizes the importance of simulating. The flat sawn legs show a 60% increase in deformation from the rift sawn, making for a poor chair, and more likely to fracture.
Simulating before building could be the difference between a nice evening dinner, and ending up laying over a broken chair on your back.
Simulate early, simulate often!