Bentley MicroStation Workshop 2017 FLUG Fall Training Event

Transcription

1 Bentley MicroStation Workshop 2017 FLUG Fall Training Event F-2E - Modeling Designing 2D/3D Curves in MicroStation CONNECT Edition Bentley Systems, Incorporated 685 Stockton Drive Exton, PA

2 Practice Workbook This workbook is designed for use in Live instructor-led training and for OnDemand self-study. The explanations and demonstrations are provided by the instructor in the classroom, or in the OnDemand electures of this course available on the Bentley LEARNserver (learn.bentley.com). This practice workbook is formatted for on-screen viewing using a PDF reader. It is also available as a PDF document in the dataset for this course. Modeling and Designing 2D/3D Curves in MicroStation CONNECT Edition This workbook contains exercises to help you learn how to create, evaluate, and modify B-spline curves and their special cases like parabola to meet specific engineering design goals. TRNC /0001 Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 1

3 Modeling and Designing 2D/3D Curves This course covers - Helices Conical and Cylindrical Hands on Exercise Spirals Hands on Exercise Logarithmic Spiral Approximation with Lines Hands on Exercise Archimedes Spirals Approximation with Arcs Hands on Exercise Creation of a Curve from its Equation/ Formula Hands on Exercise Related Math concepts (offer more powerful and flexible usage of the tools, but could be skipped) How to use this course? This course can be undertaken to accomplish two goals. 1. Learn the Workflow A procedural track, where tools and steps are learned using hands on exercises. With intermediate MicroStation skills, this track can be completed in about 2 hours. 2. Understand the Formulation Mathematical concepts and calculations needed when the data or goal does not directly relate to MicroStation tool settings. E.g. slope of a helical ramp of a parking structure is an important design aspect, but it cannot be directly specified. So knowing the formulae to convert it into pitch and radius (available in the Tool Setting), helps plot desired helix. Concepts are presented in an intuitive form rather than abstract rigor and based on familiarity, this part would take an additional hour. How to navigate? A purely procedural track can be followed by skipping the mathematical formulations marked [Optional] or by clicking the skip links. Following the entire course sequentially would cover the procedural track along with the theoretical background. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 2

4 Helix Back to Index The curve: Helix is a three dimensional curve which coils around an axis and with each turn, rises through a specific distance called the pitch. Based on whether the helix rises up or descends down, on a clockwise rotation, it is termed as left handed or right handed respectively. Further, the diameter of a helix may remain constant or taper as if wound over a cylinder or a cone. Application: Helices are seen in springs, threads of nuts and bolts and screw jacks used for raising heavy loads. At a larger scale, they are used in helical screw conveyors used in chemical and processing plants. At a still larger scale they are used in so called spiral staircases and the ramps in multi-level parking structures. Exercise: Here helices will be used to plot the air paths inside an Industrial air cleaning system often called Cyclone due to the air flow patterns. Air with particulate matter (soot, dust, liquid droplets etc.) enters sideways at the top, is guided into a helical flow by a baffle and as it descends down a cone along a helical path, it is stripped of the pollutants by centrifugal action. Finally, the constriction at the bottom, reverses the flow of (now cleaned) air. It finds an upward, helical path closer to the axis and exits from the top. Since the air rotates the same way on both downward and upward journey, the two helices are of the opposite hand. 1. Open the file 03 Advanced Curves Exercise.dgn 2. Open the Model A Cyclone Dust Separator. It shows a Target Model of a cyclone depicting the incoming and clean air currents. These paths are to be constructed in the Work Area and then placed in the empty shell of the cyclone in the Assembly Area. The air flowing in from point A to point B shown in the work area, is redirected by the helical baffle plate at the top, into a right handed helical path winding downward. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 3

5 3. From Drawing Workflow, Home Tab, Placement Section, start Place SmartLine Tool. In the Work Area - Click point B to start a SmartLine With Snap Mode = Perpendicular, click on the Axis CD This gives the center E at the top of the helix Reset to terminate the SmartLine 4. From Drawing Workflow, Home Tab, Placement Section, start Helix Curve Tool Set: Thread = Right Axis = Points (AccuDraw) Orthogonal = ON Top Radius = 475 Base Radius = 475 = Top Radius to match the cylindrical top Height = 475 Pitch = 250 matched to the baffle plate Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 4

6 Click point E as the Center to locate the Helix Click a point snapping to line CD to define axis [Optional] In case the start point of the helix does not coincide with point B, rotate the helix about its own axis.. From the right click menu start the Rotate Tool and set Method = 3 Points. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 5

7 Select the Helix Select point E as the center of rotation. Set AccuDraw compass in Top Orientation Select the top end of the helix to define the start of rotation Click at point B to define the end of rotation. This makes B the starting point of the helix. [Optional] Following theory and calculations can be skipped. Useful Helix Parameters: The number of turns, the sweep angle and change in direction, slope etc. can be found as follows Number of Turns: N = Height Pitch = = 1.9 Sweep angle: θ = 360 N = = 684 Change in Direction of flow: Angle between the entry and exit directions = Rounded off N x = = 36 Length of a Turn: is given by Hypotenuse. p 2 + (2πR) 2 of the right triangle unrolled from the helix, with height (p), base (2R) Slope: Defined as Rise = Pitch Run 2πR, For example, in helical ramps of parking structures, where the floor height or the pitch and permissible value of slope are given and an appropriate radius is to be found. slope % = Floor Height 2πR 100 Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 6

8 From the end of the above helix the downward, tapering helical path will be placed specifying the radii and height with data points. 5. From the lower end (F) of the helix, drop a perpendicular on the axis to meet it at point (G) 6. Start the Helix Curve Tool Set: Thread Axis Orthogonal Pitch = Right = Points (AccuDraw) = ON = 250 same as before All other Checkboxes OFF. In the Work Area - Click point G as the Center. Rotate AccuDraw Compass to Top rotation. Click point F to define Radius. Rotate AccuDraw Compass to Front rotation Click point D to define the Height and Axis. Rotate AccuDraw Compass to Top rotation and set Mode to Polar. Enter distance = 125 in the AccuDraw Coordinate window and accept with a data point. This places a conical helix in continuation with the previous helical path. Next, the clean air path will be plotted, defining all parameters interactively, without specifying any numerical values. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 7

9 7. Continuing with Helix Curve Tool, Set Thread = Left Note this has changed due to reversal of the flow Axis = Points (AccuDraw) Orthogonal = ON All other Checkboxes OFF. In the Work Area - Click point D (bottom end of axis) as the Center. Rotate AccuDraw Compass to Top rotation and Polar Mode. Click a point at Distance = 125 and Angle = 54. This is how the start point of the helix can be controlled, eliminating the need to rotate it later about the axis. Rotate AccuDraw Compass to Front rotation Click a point at Distance = 250 along the axis as shown to define the Pitch. Click point C (top end of axis) to define the height. Rotate AccuDraw Compass to Top rotation. air Click a point at Distance = 125. This completes the path upward. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 8

10 Now that all the helical paths are created in the Work Area, they can be moved to their precise location within the Cyclone Shell in the Assembly Area. 8. Select all the three helices along with the short straight line path AB in the Work Area. 9. Start the Move/Copy Tool from the Right Click Menu. Click point D on the axis to define the start of the Move/Copy. 10. Click the point corresponding to D (bottom end of the axis) in the Assembly Area. This precisely locates the air paths within the Cyclone Shell, completing the modeling process. Suggested Exercise: The air paths created are more for visualization than for actual engineering design. So for further visualization, these paths can be used in Path Animation. An Actor (particle of air) can be defined and assigned this path to follow along. Though not part of this course, it is a visually rewarding exercise! Extreme & Special Cases Flatter, conical helices of low pitch & overall height, but with a sizable change in radius from top to bottom are found in places like open cast mine ramps and solid - liquid separation equipment used in ore/mineral beneficiation or water & waste water treatment plants. The solid liquid mixture (slurry) is fed into a large tank and the solids settling down on the sloping bottom, are racked towards a central pit by rotating arms fitted with a series of blades. The solid particles raked follow a conical helix with low pitch, but with a large reduction in the radius from the periphery to the central pit as shown. The top view of such a helix or its extreme case with zero pitch is the Spiral. Spiral The curve: Spiral is a two dimensional curve which coils around a center further from it with each turn. The change in radius in one turn is called the pitch. Back to Index Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 9

11 Types: MicroStation can plot three types of spirals commonly used in engineering design. Archimedes: Has a constant pitch. Radius increases by a constant addition with each turn. Logarithmic: Pitch varies. Radius scales up by a constant multiple with each turn. Clothoid has two mirrored halves curving in opposite directions, connected with a point of zero curvature (called the point of inflection) where the transition from positive to negative curvature takes place. This makes it useful in road and rail design for connecting curved and straight sections, without causing a jerk (sudden change in acceleration) to the vehicle. Besides these, approximate spirals using circular arcs and line segments can also be created with MicroStation s basic geometry tools. Application: Road and rail profiles, feeders in pharmaceutical and packaging machinery, pump casings and impeller vanes, spiral springs, cams, architectural design and product design etc. Exercise: The raking arms of a thickener collect the solids from a radius of 3340 to the central pit of diameter 1400 in 11 rotations, as they descend downward by 440. Plot the projection of this path in the top view. [Optional] Following theory and calculations can be skipped. Pitch Calculation: Here the actual path (conical helix) and its projection (spiral) define the pitch differently. For helix, Pitch (P H ) = the axial distance moved in one complete turn. For spiral, Pitch (P S ) = the radial distance moved (or the change in radius) in one turn. P H = Axial Distance = 440 = 40 ; P Change in Radius Number of turns 11 S = = = 240 Number of turns 11 Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 10

12 1. Open the file 03 Advanced Curves Exercise.dgn 2. Open the Model B Archimedes Spiral. Target Model shows helical path in a thickener, whose top view is to be plotted in the Working Area. 3. From Drawing Workflow, Home Tab, Placement Section, start Spiral Curve Tool. Set Method = Archimedes Initial Radius = 3340 Final Radius = 700 Angle = (= 11 x 360 ) In the Work Area - With AcciDraw ShortCut O, place AccuDraw Compass at the given origin O. Click a point at Distance = 3340, angle = 0 as the start of the spiral. Click a point below this point to define the tangent. This is the direction in spiral takes off from the start point. Blades in the target model suggest the wind inward when traversed clockwise in the top view. Click a point on the left to define the direction in which the end point lies. This desired spiral. which the spiral should places the Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 11

13 Approximate Logarithmic Spirals Back to Index The Curve: Spirals are sometimes approximated by circular arcs and even straight line segments - either by design or for ease of fabrication. For example circular air-conditioning ducts made sheet metal approximate a spiral with straight lines (chords) as shown. Exercise: Here two turns of a logarithmic spiral will be created with straight line segments using Basic Geometry Tools. With each turn the radius will be halved from 60 to 30 to 15 as shown. 1. Open the file 03 Advanced Curves Exercise.dgn 2. Open the Model C Spiral by Chords. Target Model shows two turns of spiral, each formed by 12 line segments. This will be reconstructed in the Working Area. [Optional] Following theory and calculations can be skipped. Given: R 1 = Initial Radius = 60, R 2 = Final Radius = 30, N = Number of segments = 12, To Find: S = Scale Factor or Ratio of successive segments The line segments forming the spiral are successively scaled by S. Since N such scalings reduce the radius from R 1 to R 2, R 1 x S x S x... N times = R 2, Here, R 1 = radial distance of first point of the spiral S = R 2 = 30 N = R 2 R1 12 = 30 = Hence the radial distance of the second point of spiral r 2 = R 1 x S = 60 x = R 1 x S N = R 2 Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 12

14 3. Start Drawing > Home > Placement > SmartLine Tool, Click start point at A given at a radial distance of 60 from center C. Place AccuDraw Compass at center C in polar mode. Click end point at Distance = and Angle = 0 and reset. This is the first segment of the spiral. 4. From right click menu, start Rotate Tool, Set Method = Active Angle Angle = 30 Copies = 11 Select the segment just placed Select C as the center of rotation Accept This creates 11 rotated copies of the segment. Next they ll be scaled about the center C, so that beginning of one segment coincides with the end of the previous one. 5. From right click menu, start Scale Tool, Set Method = 3 Points, Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 13

15 Proportional = ON All other CheckBoxes OFF Select the second segment Click C as the center for scaling Select the start of segment to scale Click the end of previous segment 6. Repeat the scaling process for the remaining ten segments in the order shown. This lines up all segments in continuation. 7. From Drawing Workflow, Home Tab, Groups Section, start the Create Complex Chain Tool. Set Method = Automatic because there are just too many elements to chain one by one. For all other settings accept default Turn off the level Support Geometry to hide the radial lines. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 14

16 Select the first segment and accept a preview of complex chain is displayed. Accept. This connects all the segments in one continuous turn of the spiral. The second turn can be quickly added, as a scaled replica of the previous one! 8. From the right click menu, start the Scale Tool. Set Method = 3 Points Copies = 1 Select turn of the spiral just crated Click C as the origin for scaling Select the start (outer tip) of the spiral Click the end (inner tip) of the spiral The desired spiral as such is complete, but a check can be made if the correct dimensions are achieved. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 15

17 9. From Drawing Workflow, Analyze Tab, Measure Section, start the Measure Distance Tool. Set: Method = Between Points Flatten Direction = Global Z Click at center C as the first point Select the inner end of the spiral, this should show Distance = 15 Continue in the same radial direction to click a point representing one complete turn. This too should show Total = 30 The dimensions match the expected values, indicating the accuracy used for calculations was adequate! Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 16

18 Approximate Archimedes Spirals Back to Index The Curve: Archimedes spirals have a constant pitch causing a steady increment in the radius. It can be readily approximated using circular arcs. Based on the accuracy needed, a turn of a spiral can be divided into appropriate number of segments (arcs). Exercise: Plot three turns of an Archimedes spiral approximated by six circular arcs segments for each turn. Each turn reduces the radius by 20 from 75 to 55 to 35 as shown. 1. Open the file 03 Advanced Curves Exercise.dgn 2. Open the Model C Spiral by Arcs. Target Model shows three turns of spiral each formed by six circular arcs as shown. This will be reconstructed in the Working Area. [Optional] Following theory and calculations can be skipped. skip Smoothness and Continuity: A curve pieced together from different segments is better formed, if the segments join smoothly. Mathematically, the idea of smoothness is described by Continuity. At the basic level, continuity ensures an unbroken curve (no gaps between the pieces). Continuity can be refined further, by matching the Tangents and then even the Curvatures of the pieces at their meeting point. Continuity can also be applied beyond the visual aspect, giving smooth motion of a particle along the curve, without sudden change in velocity and acceleration. For this, a time value (called as a parameter) is associated with every point on the curve. The Curve by Formula Tool (covered later) uses such a parametric definition of curves. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 17

19 Approximation with Arcs: When two circular arcs connect smoothly, to share a common tangent at the junction, they also have a common normal (perpendicular to the tangent) at that point. Since normal to a circular arc is the radius, their radii at the common point get aligned. Hence for two arcs to connect with tangent continuity, their common point P must lie on the line joining their centers C 1 and C 2 as shown. This is a useful idea for building a smooth spiral from circular arcs. Circular arcs can never be connected with curvature continuity, because curvature is the reciprocal of the radius, which is different for the two meeting arcs. Calculations: Each turn of the spiral is built using six arcs. So by symmetry, each sweeps one sixth of the full angle i.e., 360 /6 = 60. This also gives, six common radii containing centers C 1 -C 2, C 2 -C 3, C 3 -C 4,.. etc. forming a regular hexagon. Change in radius from one arc to next = Distance between their centers =. Side of the hexagon Since change in radius in one turn = Pitch = 20; occurs in six steps, the change in radius in one step or the side of the central hexagon must be 20/6 = 10/3 3. Zoom in the Target Model for a closer look at the central hexagon. The six centers C 1, C 2,, C 6 are seen color matched (green and blue) to the corresponding arcs. This will be reconstructed in the Working Area from the center C 6 given there. 4. From Drawing Workflow, Home Tab, Placement Section, start the Place Regular Polygon Tool. Set Method = By Edge Edges = 6 Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 18

20 Click at center C 6 in Working Area as the First edge point. This places the AccuDraw Compass origin there and shows a preview hexagon following the cursor. Move the cursor in X direction and in AccuDraw Coordinate Window, enter X = 20 With focus still in AccuDraw Coordinate Window, press the forward slash (/) key for division. This brings up a text box where the divisor can be entered. Enter 6 as the divisor this shows the result Press enter to get this numerical value as the X coordinate. The hexagon in preview adopts the edge length Accept the hexagon 5. Start Drawing > Home > Placement > SmartLine Tool and from center C 1 draw a horizontal line of length 80 or more. This is the first common normal (or radius) Five copies of this common normal rotated about the center of the hexagon will be made next. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 19

21 6. Right click to start Rotation Tool. Set Method = 3 Points the angle is known to be 60 but this approach is more general Copies = 5 All other CheckBoxes OFF Select the common normal With Center Snap, click the center of the hexagon as the center of rotation Click on C 1 to define the start of rotation Click on C 2 to define the amount of rotation five rotated copies are placed Reset 7. [Optional, but greatly adds to speed] With AccuDraw shortcut GS open AccuDraw Settings. In the Coordinates Tab, type Angle = 360/6 and press Enter. Now angle 60 and all its multiples will be readily available! If instead of 6, each turn of the spiral is to be made from N arcs, Angle should be set to 360/N Further efficiency can be gained by using SmartLIne instead of the Arc tool. This saves the step of connecting all the arcs in a single Complex Chain. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 20

22 8. Start SmartLine Tool, Set Segments = Arcs Vertex = Sharp Join Elements = ON Snap to point C 1 and place the AccuDraw Compass there with AccuDraw shortcut (O). Move the cursor in the X direction and enter Distance = 75 (the outer radius of the spiral) Click to place the first vertex Click C1 as the arc center. Moving the cursor around shows arcs with center C 1 and sweep angles 60, 120, 180 etc. Click to accept a counter clock wise arc of 60 sweep. This places the first arc segment, whose end point automatically lands on the common normal through C 2. Continuing without reset with SmartLine, snap to C2 and move the cursor to get the next CCW arc segment of 60 sweep. Click to accept the second arc segment. This process of placing 60 arc segments is continued using centers C 3, C 4, C 5, C 6, and back from C 1, C 2,... again to add 18 arc segments in all (3 turns made of 6 arcs each). Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 21

23 Curve by Formula Back to Index MicroStation s Curve by Formula Tool can plot virtually any curve (2D or 3D), given in a Parametric form, which expresses the coordinates (x, y, z) of a point on the curve in terms of a parameter (t). The curve is then plotted as a Bspline. [Optional] Following theory and calculations can be skipped. What is Parametric Form of a Curve?: If each of the coordinates x, y, z of any point on a curve are given in terms of an independent variable (called the parameter) such a definition of the curve is called its Parametric Form. E. g. any point P (x, y) on the circle of radius R, can be written using a parameter as: x = R.cos y = R.sin... a full circle is traced as goes from 0 to 360 Inbuilt Parameter in MicroStation: The Curve by Formula Tool, uses a Predefined Parameter (t) which automatically varies from 0 to 1. Coordinates (x, y, z) are then directly correlated to (t) or via intermediate variables like above. E.g. = 180 * t in the parametric form of the circle above, places a semicircle. Exercise: Place 3 turns of an Elliptical helix with pitch = 25, semi-major axis = 50 and semi-minor axis = 30. Formulate this as: N = 3; number of turns. Note each statement is terminated with a semicolon ; theta = t * N * 360; as the internal parameter t varies from 0 to 1, theta goes from 0 to 3 x 360 = 1080 a = 50; semi-major axis b = 30; semi-minor axis p = 25; pitch x = a * cos (theta); Coordinates (x, y, z) are expressed indirectly in terms of parameter t via the parameter y = b * sin (theta); z = p * theta / 360; Note for each complete turn, increases by 360 and z goes up by one pitch p. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 22

24 Note a semicolon (;) at end of each line. Operators (*) & (/) stand for multiplication and division. Trigonometric Functions like Sin and Cos can be directly used. 1. Open the file 03 Advanced Curves Exercise.dgn 2. Open the Model E Curve by Formula. Target Model shows three turns of an elliptical spiral. This is to be reconstructed in the Working Area. 3. From Drawing Workflow, Home Tab, Placement Section, start the Curve by Formula Tool. From its File Menu, select New Curve. Set Name = Elliptical Helix Tolerance = 0.10 Mode Angle = Defined = Degree CreatedAs = Bspline 4. Type in the list of expressions for theta, a, b, p, x, y, z given above, in the blank space as shown. In MicroStation, variables x, y, z, and t have a specific meaning. Other variables can be named suitably for readability. 5. Set View Rotation = Top. because the tool attaches top view of the curve to the cursor. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 23

25 6. Click the Place Button and snap to click the origin provided in the Work Area. This places the desired helix. 7. Set View Rotation back to Isometric. This shows the desired helix. [Optional] The curve definition could be saved for future use from File > Save To in a new file or using File > Save in an existing Resource File. A rich library of additional curve formulations can be found in the resource files provided in installation, like Curve.rsc, Curve3d.rsc, Cycloid.rsc, Spiral.rsc. They can be accessed using File. MicroStation File > Open What Next? Curves are closely related to surfaces. Operations like extrusion, revolve, sweep, loft etc. can generate a surface using one or more curves. Conversely, curves can be extracted from surfaces as their edges, intersections, cross sections or the iso-parametric lines. Learning the two together provides better understanding and insights. Understanding of the geometric ideas (slope, tangency, curvature, continuity etc.) and specific curve parameters, help achieve the right visual and physical properties in a curve. 3D Curves and surfaces are increasingly used in the freeform designs in modern architecture. A course in Generative Components could be the next step in that direction. Alternatively, curves are also generated as a result of constrained motion, which is covered in the course on 3D Constraints. Copyright Bentley Systems, Incorporated DO NOT DISTRIBUTE Printing for student use is permitted 24