BND TechSource. Chain & Sprocket Simulation using CATIA V5 DMU Kinematics. (Revised 27SEP09)

Transcription

1 Chain & Sprocket Simulation using CATIA V5 DMU Kinematics (Revised 27SEP09) Website =

2 The following licenses are required to simulate Chain & Sprocket movement with CATIA V5 DMU Kinematics: Digital Mockup + DMU Kinematics Mechanical Design + Part Design Mechanical Design + Assembly Design

3 The end result we are trying to achieve is to simulate the movement of a bicycle chain around the sprockets.

4 There are certain known values when you begin your simulation. 19 T Links Sprocket Center Curve 11 T 40 T Adjustable Sprocket 11 T Drive Sprocket

5 Known values: Sprocket sizes (number of teeth) Sprocket placement (center to center) Sprocket adjustability (lower derailleur) Link size (12.7mm) Total Number of Links (106) These values will help set up the Sprocket Center Curve.

6 To accurately simulate the chain movement around the sprockets, you must first understand the chordal relationship of the Link to the Sprocket. Each Link moves around the Sprocket with a fixed length. This is the Chord of the Angular rotation of the Sprocket.

7 The Chord length is not the same as the Arc length. Ex. Chord Length = 12.7 Ex. Arc Length = This may seem insignificant, but CATIA is very exacting.

8 Time for some trigonometry Ex. 40T Drive Sprocket: 9 O O /40 = 9 O Chord Length = 12.7 Radius = x Sin -1 (6.35/x) = 4.5 O x = (6.35/sin4.5 O ) x = mm 4.5 O Circ = 2πR = mm Arc Length = x /40 = Sprkt Ctr Curve = 106* = mm

9 Now we have the information to proceed. R38.58 R Sprocket Center Curve Length= R R22.539

10 Here are the Joints and Commands to run the Simulation (Laws come later). Sprockets Links Sprockets Links

11 The Gear Joints for the Sprockets will begin with the normal ratio (ex. 40T/19T=2.105). 19T Sprocket 40T Drive Sprocket 11T Sprocket 11T Sprocket

12 The Link Shuttle is created with two Links (Inner & Outer). These two links will run along the Sprocket Center Curve and the Sprocket Tracking Curve. Link Tracking Curve Sprocket Tracking Curve Inner Link Shuttle Point Outer Link Shuttle Point Sprocket Center Curve

13 There will be four Joints in the Link Shuttle. 2) Slide-Curve Joint Inner Link Tracking Curve Sprocket Tracking Curve 1) Point-Curve Joint Point on Inner Link Sprocket Center Curve 4) Revolute Joint Inner Link Outer Link 3) Point-Curve Joint Point on Outer Link Sprocket Center Curve

14 Check Sprocket tooth-to-tooth centerline dimensions. This dimension should be exactly the same as the Link dimension.

15 Check Link roller-to-roller centerline dimensions (for both Links). This dimension should be exactly the same as the Sprocket dimension.

16 Check Drive Sprocket tooth centerline to the Sprocket Center Curve. They should intersect exactly.

17 Check Link roller centerline to the Sprocket Center Curve. They should intersect exactly.

18 Create a Law Sketch 954x954 (106x9 O ). This Law will be applied to the Drive Chain Sprocket for rotation angle.

19 Apply the Law to the Gear Command. a) Double pick the Command. c) Pick the Law Sketch. b) Pick Link. d) Pick OK.

20 Apply a Formula to the Shuttle Command. a) Double pick the Command. c) Hold cursor over Formula. b) Right click inside the Command value box. d) Drop cursor onto Edit.

21 Apply a Formula to the Shuttle Command (cont d) mm+ Chain 2\Commands\Chain Wheel Rotation\Angle1 * mm The start point of the Sprocket Center Curve is from the Link Shuttle Point. a) Type this value with mm followed by + b) Pick the Drive Sprocket Command. c) Double pick this text to place it into the Formula. d) Type the Radius value followed by mm. e) Pick Ok.

22 Apply a Formula to the Shuttle Command (cont d). You will get this Syntax Warning. -Do not be alarmed. -It is telling you that you must be precise when converting angular measurement to length measurement. -This is why it is important to add the mm to your Formula. Else it will assume meters!

23 Run the Kinematic with Laws. Pick Simulation with Laws Icon. When you run the simulation, the Links should end exactly where they began.

24 Return the Kinematic Simulation to the beginning. If you toggle between the start and the end, the Links should appear not to move. Return the Kinematic Simulation to the beginning

25 Check the Links as they travel across the other Sprockets. (19T Sprocket shown) There may be an angular mismatch as the Link meets the Sprocket tooth. This problem is easily corrected by using the compass, while current in the CatProduct, to rotate the Sprocket to the correct position deg

26 A different challenge arises as you rotate the Sprocket further around. This means the Sprocket is rotating faster than the Link is moving. Notice the angle is closing as you rotate deg

27 A different challenge arises as you rotate the Sprocket further around. The reason for this is the smaller radius on this Sprocket results in a larger Arc Length. Notice the angle is closing as you rotate deg

28 Time for some more trigonometry Ex. 19T Drive Sprocket: O O /19 = O Chord Length = 12.7 Radius = x Sin -1 (6.35/x) = O x = (6.35/sin O ) x = 38.58mm O Circ = 2πR = mm Arc Length = x /19 =

29 Adjust the Gear Ratio. To correct the problem of different Arc Lengths, simply divide the Drive Sprocket Arc Length by the 19T Sprocket Arc length, then multiply the current Gear Ratio by that value / = Current Gear Ratio = 40/19 = New Gear Ratio = * = The same technique can be applied to the 11T gears.

30 Adjust the Gear Ratio / = Double pick the Current Gear Ratio = Gear Joint to 40/19 = edit the ratio. New Gear Ratio = * = The same technique can be applied to the 11T gears.

31 Congratulations!! Now the real work begins...

32 Complete the chain with all 106 Links!

33 Complete the chain with all 106 Links! Here is where we left off. Each new Link will have two joints. 1) Point-Curve Joint Point on Link Sprocket Center Curve 2) Revolute Joint Inner Link Outer Link

34 Complete the chain with all 106 Links! Add the remaining 104 Links and Joints And here is where you will get to. Good Luck!

35 Conclusion: This explanation of how we created our bicycle chain simulation put together at the request of our users. If you have a request, please visit our free website at