CLOSED GEAR SYSTEMS From Charlie Chaplin to 3

CLOSED GEAR SYSTEMS From Charlie Chaplin to 3 D Printing Something That Moves Something, created by Ohad Meyuhas, architect

IN THIS LESSON • • • Definition of a gear system How a gear system works Types of gear systems 3 D printing of gear systems Gear system design – concept and calculations

WHAT IS A GEAR SYSTEM? SEVERAL GEARS (COG-WHEELS), USUALLY WITH TEETH OF IDENTICAL SHAPE, MESHED TOGETHER IN ORDER TO TRANSMIT TORQUE AND PRODUCE A MECHANICAL ADVANTAGE THROUGH A GEAR RATIO

WHAT ARE GEARS USED FOR? Transmitting rotational motion between parallel shafts Transmitting rotational motion between perpendicular shafts Separation processes and mass transfer

WHERE CAN WE FIND GEAR SYSTEMS? c

GEAR SYSTEM CHARACTERISTICS Teeth of the gears prevent slippage. Few elements can create great force. Decreased power creates more force. Movement direction is controlled.

GEAR SYSTEM CHARACTERISTICS Complex design Complex production (modeling > casting > sanding > assembly)

GEAR SYSTEM ASSEMBLY LINE Imagebank Israel / Getty Images

GEAR SYSTEM IN THE 21 ST CENTURY IS IT STILL RELEVANT?

HOW DOES A GEAR SYSTEM WORK?

IN THIS LESSON • • • Definition of a gear system How a gear system works Types of gear systems 3 D printing of gear systems Gear system design – concept and calculations

TYPES OF GEAR SYSTEMS Spur gears Helical gears Worm gear sets Bevel gears Rack and pinion sets

TYPES OF GEAR SYSTEMS – SPUR GEARS • Tooth profile is parallel to the axis of rotation • Transmits motion between parallel shafts Gear (large gear) Internal gears Pinion (small gear)

TYPES OF GEAR SYSTEMS – HELICAL GEARS • Teeth are inclined to the axis of rotation. The angle provides more gradual engagement of the teeth during meshing. • Transmits motion between parallel shafts.

TYPES OF GEAR SYSTEMS – BEVEL GEARS • Teeth are formed on a conical surface. • Transmits motion between non-parallel and intersecting shafts. Straight Bevel Gears

TYPES OF GEAR SYSTEMS – WORM GEAR SETS • Consists of a helical gear and a power screw (worm). • Transmits motion between non-parallel and nonintersecting shafts.

TYPES OF GEAR SYSTEMS – RACK AND PINION SETS • A special case of spur gears with the gear having an infinitely large diameter. The teeth are laid flat.

IN THIS LESSON • • • Definition of a gear system How a gear system works Types of gear systems 3 D printing of gear systems Gear system design – concept and calculations

3 D PRINTING OF GEAR SYSTEMS – ADVANTAGES One print production Less room for errors Shortened production time Decreased human labor

3 D PRINTING OF GEAR SYSTEMS – CONSIDER Printer technology and surface quality Material characteristics and properties Printing positioning and scale Support material Cost

3 D PRINTING OF GEAR SYSTEMS – DESIGN TIPS Always test your print and consider: • An element’s size • Orientation and print direction

3 D PRINTING OF GEAR SYSTEMS – DESIGN TIPS Poly. Jet FDM

3 D PRINTING OF GEAR SYSTEMS – DESIGN TIPS* Poly. Jet FDM • 0. 2 mm minimal space between elements in high quality printing mode for XY axis and 0. 06 mm for Z axis • 0. 5 mm minimal** element thickness recommended • Consider how to remove the support material. * The information on these slides serve as a guide. Do not substitute this guidance for testing print jobs. • **For gears we recommend a minimal thickness of ~2. 5 mm.

3 D PRINTING OF GEAR SYSTEMS – DESIGN TIPS* Poly. Jet FDM • Space between the elements: (Gap in Z = one slice thickness) – Most materials: 0. 2 mm minimal space – ABS high quality mode: 0. 15 mm minimal space • 0. 5 mm minimal element thickness recommended. • Consider how to remove the support material. * The information on these slides serve as a guide. Do not substitute this guidance for testing print jobs.

DESIGNING A GEAR CUBE WITH POLYJET TECHNOLOGY

IN THIS LESSON • • • Definition of a gear system How a gear system works Types of gear systems 3 D printing of gear systems Gear system design – concept and calculations

GEAR SYSTEM DESIGN – CONCEPT AND CALCULATIONS • • • How does a gear system work? Operation principle Main physical terms Linear velocity and radial velocity Calculations – – Basic parameters Basic parameter equations Worm gear set calculations Conventional gear train calculations

HOW DOES A GEAR SYSTEM WORK?

HOW DOES A GEAR SYSTEM WORK? Gears and shafts interact:

OPERATION PRINCIPLE Weight Speed Scalar Vector Expressed by dimension magnitude and direction

MAIN PHYSICAL TERMS • • R – Radius α – Angular Acceleration [radian/sec^2] at – Tangential Acceleration [m/sec^2] ar – Radial Acceleration [radian/sec^2] V – Tangential Velocity [m/sec] ω – Radial Velocity [radian/sec] θ – Radial Displacement [radians]

VECTOR y • x

LINEAR VELOCITY The distance to time taken to cross it ratio It has not only magnitude but also direction. It’s a differential of distance to time.

LINEAR VELOCITY – EXAMPLE •

LINEAR ACCELERATION The rate of change in speed Direction will determine acceleration or “deacceleration. ”

RADIAL VELOCITY – SIMPLE RADIAL VELOCITY Velocity vector is constant and is tangential to the trajectory.

RADIAL VELOCITY – VELOCITY AND ACCELERATION • θ ω ar at atotal

RADIAL VELOCITY – EXAMPLE: TWO WHEELS WITH AN IDENTICAL CENTER POINT 1 • 2 ω

RADIAL VELOCITY – EXAMPLE: TWO WHEELS WITH TWO DIFFERENT CENTER POINTS 1 • 2

RADIAL VELOCITY – LOTS OF MOVEMENTS • 3 4 2 1

HOW DOES GEAR SYSTEM WORK?

GEAR SYSTEM DESIGN – CONCEPT AND CALCULATIONS • • • How does a gear system work? Operation principle Main physical terms Linear velocity and radial velocity Calculations – – Basic parameters Basic parameter equations Worm gear set calculations Conventional gear train calculations

BASIC PARAMETERS • • N – Number of Teeth D – Pitch Diameter P – Diametral Pitch, “Density of Teeth” p – Circular Pitch Do – Outer Diameter CD – Center Distance Pressure Angle – Measured between the line of action to the tangential line of the pitch circle

BASIC PARAMETERS – PRESSURE ANGLE Measured between the line of action to the tangential line of the pitch circle:

BASIC PARAMETERS – EQUESTIONS •

WORM GEAR SETS KINEMATICS • Ng = number of teeth on the helical gear • Nw = number of threads on the worm, usually between 2 -6 • Speed ratio = Ng / Nw • Large reduction in one step, but lower efficiency due to heat generation Helical gear Worm

CONVENTIONAL GEAR TRAINS KINEMATICS Ω 3 N 2 ω2 = N 3 ω3 = ω4 Speed ratio: N 2 N 4 mv = N 5 N 3 ( mv = ω5 N 4 ω4 = N 5 )( )= ω5 ω2 = output input Product of number of teeth on driver gears Product of number of teeth on driven gears mv = e = Train value

CONVENTIONAL GEAR TRAINS KINEMATICS Reverted gear train • Output shaft is concentric with the input shaft. • Center distances of the stages must be equal.

GEAR SYSTEM DESIGN – CONCEPT AND CALCULATIONS • • • How does a gear system work? Operation principle Main physical terms Linear velocity and radial velocity Calculation – – Basic parameters Basic parameter equations Worm gear set calculations Conventional gear train calculations

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Thank you. Something That Moves Something, created by Ohad Meyuhas, architect