ES3C2 Design Report - The Geneva Mechanism

Transcription

1 ES3C2 Design Report - The Geneva Mechanism Philip Fulcher January 7, Design Problem and Objectives There is a need to produce a small mechanical assembly which demonstrates an engineering principle or mechanism, which is suitable to be manufactured using the 3D printing facilities within the School of Engineering. For this purpose, the Geneva Mechanism has been chosen as a subject of study and development. The conventional Geneva Mechanism is typically used as an indexing mechanism, where intermittent motion is required, [3] for example, the mechanisms were used extensively in motion picture film projectors to advance film, giving the film a quick advance whilst the shutter is closed, and a stationary period whilst the shutter is open. [4] The name of the mechanism can be traced back to Geneva, Switzerland, where it is said the device was originally invented; for use in watches to prevent them from being over-wound, hence it s alternative name, the Geneva Stop. [2] 1.1 Introduction to Mechanism Functionality Figure 1 shows a generic format of a Geneva Mechanism. Driver, A carries a pin, P in a constant circular motion, so that it engages with one of the four (although it could be any number, usually between 3 and 18) slots in output follower B. Surfaces C and S are important: surface S engages with the concave profile in between the follower slots, preventing the follower, B rotating when the pin is not engaged. Surface C, therefore, allows the follower to rotate as the pin, P engages with the follower, rotating it, in this case, a quarter of a turn. Figure 1: Diagram of simple Geneva mechanism. The Geneva Mechanism produces a complex motion from a simple set of mechanical parts, making it an excellent subject of study for this design project. 1

2 1.2 Design Specification To create a Geneva mechanism that can be manufactured through 3D printing methods, using the University of Warwick s Objet24 3D printer. (Printer specification Appendix item A, section 6.1). The mechanism must be suitable to be produced in the material VeroWhitePlus (Material specification Appendix item B, section 6.2). The mechanism must be powered by the hand, and feature an ergonomic and anthropometrically considered manner by which to power the driver and follower. The mechanism should be durable enough to be dropped and mistreated. The mechanism must be smooth in operation and free from mechanical binding. The mechanism s design should allow for a printing tolerance of 100 microns. The mechanism should be both able to stand on a surface and be comfortable to hold. The mechanism should be simple enough to be manufactured and built in a reasonable time frame The mechanism should be easy to construct and will use no fixing adhesives. The mechanism should be safe. It will not be constructed from harmful materials and will be designed to feature no sharp edges. 2 Design Documentation The following section gives an overview of the design, features, and decisions made during the development process. 2.1 Design Renders Figure 2: Diametric view of the mechanism. 2

3 Figure 3: Back view. Figure 4: The mechanism can be detached from the base, making it easier to hold and operate in the hands. 3

4 2.2 Mechanism Operation Figure 5: Exploded view of the assembly. The design is intended to be used both whilst placed on a flat surface, and whilst held in the hand, therefore the mechanism detaches from its base to achieve this. The operator may rotate the driver wheel using his or her finger, made easier by the inclusion of the ridged outer surface, facilitating purchase. The operator can observe the indexing output of the driver as they rotate the driver wheel, demonstrating the Geneva Mechanism principle. 2.3 Design Decisions As mentioned in section 1.1, the follower wheel can functionally contain between 3 and 18 indexing slots. The follower for this design includes 5 indexing slots, because a five slotted follower is a similar size to the driver, leading to a more symmetrical design. For additional durability, the decision to use a non-printed pin was taken. Instead, the driver wheel features a cavity for an M5 nut, and the pin is to be machined from brass, as shown in figure 6. (a) Pin Nut (b) Brass Pin Figure 6: Brass pin attachment to the driver wheel. The stand for the mechanism holds the mechanism in place via axle pins, which feature a hexagonal boss, which inserts through the stand and slots snugly into the mechanism wheels, which feature a hexagonal slot, as shown in figure 7. 4

5 (a) Axle pins inserting into the stand. (b) Section view through the stand Figure 7: Geneva wheels connected The stand for the mechanism features two parts. The upper portion supporting the mechanism components, and the lower portion acting as a stand, so the mechanism can be placed onto a desk. This detachable base conforms to the requirement for the mechanism to be pleasant to use in the hands: the base would otherwise get in the way and make the device difficult to hold. The bosses and holes that locate the bottom part of the stand to the top have clearance factored in, and also include chamfers for user forgiveness. 2.4 Material Saving Methods To conform to the specification, material saving methods have been used in the design to keep costs as minimal as possible, due to the costly nature of the VeroWhitePlus material. Figure 8 shows the stand geometry which has been employed to reduce material whilst maximising stiffness and durability, as well as the hollowed-out base of the stand. In addition to this, as seen in figure 2, the driver and follower wheels include slots which keep material usage to a minimum, whilst retaining functionality. Figure 7 shows how the axle pins are partially hollowed-out, again to keep material usage down. (a) Material saving stand pattern (b) Section view of the stand Figure 8: Material saving techniques employed in the design. 5

6 3 Photo-Realistic Renders Photo-realistic rendering tools available in Solidworks PhotoView 360 have been used to produce impressions of how the mechanism might look once printed in VeroWhitePlus 3D printing material. Figure 9: Render of the complete assembly. Figure 10: Render of the mechanism detached from the base. 6

7 Figure 11: Artist s impression of the device held in the hands, after being detached from the base. 4 Theoretical Design and Analysis This section describes the geometric calculations used to design the Geneva mechanism and the motion and stress analysis tools used to improve and verify the validity of the design s function and durability. 4.1 Geometric Properties of the Geneva Gear The geometric proportions for the Geneva mechanism can be deduced from the following set of equations, once the radius of the follower, b has been decided upon. a = Drive crank radius n = Driven slot quantity p = drive pin diameter t = allowed clearance c = centre distance = sina180 n b = Geneva wheel radius = c2 a2 s = slot centre length = (a + b) c w = slot width = p + t y = slot arc radius = a 1.5p z = stop disc radius = y t v = clearance arc = bz/a 7

8 Figure 12: Adapted from McGraw-Hill, Machining and Metalworking Handbook, D. Cornier. [1] Allowed clearance, t, is important to consider, given that the dimensional tolerance of the machine is around 100µm. The design includes a value t of 500µm to reduce the risk of interference, either from manufacturing or slight user-induced deformation preventing the mechanism from operating correctly. Chamfers added to the receiving end of the follower slots will correct a misalignment. 4.2 Motion Study Analysis The motion of the Geneva gear must be precise in order for it to operate correctly. A Solidworks Motion Analysis model was created to predict the rotational dynamics, force, and stress on the components. The animation of said model can be viewed by following the URL: The following plot shows the angular displacement, speed and acceleration (in blue, red and green respectively) of the follower wheel as the driver experiences a slow input of 10RPM. The slow input produced the most stable motion study results, as complex contact relationships began to fail at higher speeds. The results are scalable for different driver speeds. Figure 13: Solidworks Motion Study Plot of angular displacement, velocity and acceleration at the follower wheel with 10RPM input to driver wheel. 8

9 4.3 Stress Simulation The following set of equations were used to describe the force acting on the follower wheel by the driver, via the brass pin. Torque, T can be expressed as a function of follower Inertia, I and angular acceleration, α and as a function of viscous friction and angular velocity, to factor in the friction between components. T = Iα + bω (1) Torque produces a given force at a given distance, by the relationship: T = F r (2) Where F is force and r is perpendicular distance from the centre of rotation. Rearrangement of equations (1) and (2) outputs a value of force applied to the follower: Iα + bω F = (3) r The inertia, I of the follower gear is 1.14x10-5 Kgm 2, assuming the most likely maximum input to the driver is 150RPM (15.71 Rads -2 ), Solidworks Motion analysis produces a peak value of angular acceleration at the follower, α max of 115 Rads -2. Since the effects of viscous friction, b are negligible with such light components, torque required to overcome the friction between follower and stand can be estimated to be a constant 0.1Nm. α max coincides with the point at which the brass pin is 30.08mm from the centre of rotation (the mimimus radius being 26.3mm.) Inputting the above into equation (3) gives a force of 3.37N applied to the follower gear by the brass pin. Figure 14: Max follower deformation of mm with applied 3.37N force. Note: visual deformation scaled by factor of 550. Figure 15: Max follower stress of Von Mises (Nm 1 ). Figure 16: Max driver deformation of mm with applied 3.37N force. Note: visual deformation scaled by factor of 900. Figure 17: Max driver wheel stress of Von Mises (Nm 1 ). 9

10 For stability, a static stress FEA simulation was run using Solidworks. The material chosen was selected to match as closely as possible that of VeroWhitePlus, and the pin was modelled as brass. The simulation shows that the follower experiences a maximum deformation of mm and a peak stress of Von Mises (although this appears to be an irregularity of the FEA tools used, the biggest regions of stress experience closer to Von Mises). Likewise, the reaction force of 3.37N experienced by the driver wheel leads to a maximum deformation of mm and a peak stress of Von Mises. This analysis, therefore, verifies that the follower and driver wheels will experience stress and deformation well within their tensile strength and elongation parameters (see appendix item B, section 6.2). Changes were made to several iterations of designs to find optimum balance between material saving, durability and strength. Figures displaying the meshing and force application to the models can be found in appendices items C and D. 5 Bill of Materials and Cost Analysis References [1] D. Cormier. Machining and Metalworking Handbook. McGraw-Hill Handbooks ISBN: [2] Encyclopaedia Britannica Inc. Geneva mechanism Accessed [3] C. Johnson. How to Design Geneva Mechanisms. Eastman Kodak Co., Rochester, N. Y., [4] D. Kirkpatrick and A. Kurtz. Geneva mechanism and motion picture projector using same. Google Patents, February US Patent 6,183,087. [5] J. Lee and B. Jan. Design of geneva mechanisms with curved slots for non-undercutting manufacturing. Mechanism and Machine Theory, 44(6): , [6] Stratsys Ltd. PolyJet R Materials Data/Specification Sheet Retrieved from

11 6 Appendices 6.1 Item A Figure 18: Objet24 Product Specifications available from Stratasys website. 11

12 6.2 Item B Figure 19: Data Sheet for VeroGray RGD850, VeroBlackPlus RGD875, VeroWhitePlus RGD835, VeroYellow RGD836, VeroCyan RGD841, VeroMagenta RGD851 [6] 6.3 Item C Figure 20: Fine meshing was used to generate the most accurate FEA results for the follower. Figure 21: 3.9N force and fixed geometry shown. The internal hexagonal hole was treated as fixed. 12

13 6.4 Item D Figure 22: Fine meshing was used to generate the most accurate FEA results for the driver Figure 23: 3.9N Force applied shown. As with follower, hexagonal hole treated as fixed geometry for FEA. 6.5 Item E - General Arrangement 13

14 A B C D A B SECTION B-B SCALE 1 : 2 SECTION A DETAIL D SCALE 1 : 1 DETAIL C SCALE 1 : 1 UNLESS OTHERWISE SPECIFIED: DIMENSIONS ARE IN MILLIMETERS SURFACE FINISH: TOLERANCES: LINEAR: ANGULAR: FINISH: DEBUR AND BREAK SHARP EDGES DO NOT SCALE DRAWING REVISION DRAWN NAME SIGNATURE DATE TITLE: The Geneva Mechanism CHK'D APPV'D MFG Q.A MATERIAL: VeroWhitePlus DWG NO. ActualFinal A4 WEIGHT: SCALE:1:5 SHEET 1 OF 1