Planetary Gear
Aim:
1. To access the gears from the toolbox in SolidWorks present in the ANSI Metric system.
2. Provide the required parameters for defining each and every gear.
3. Designing the carrier, depending upon the shaft diameter of the planet gears.
4. Assembling them in SolidWorks and giving correct constraints to all the parts so that the assembly is perfect for running the motion analysis study.
Theory:
An epicyclic gear train (also known as planetary gear) consists of two gears mounted so that the centre of one gear revolves around the centre of the other. A carrier connects the centres of the two gears and rotates to carry one gear, called the planet gear, around the other, called the sun gear. The planet and sun gears mesh so that their pitch circles roll without slip. A point on the pitch circle of the planet gear traces an epicycloid curve.
The most basic form of planetary gearing involves three sets of gears with different degrees of freedom. Planet gears rotate around axes that revolve around a sun gear, which spins in place. A ring gear binds the planets on the outside and is completely fixed. The concentricity of the planet grouping with the sun and ring gears means that the torque carries through a straight line. Many power trains are "comfortable" lined up straight, and the absence of offset shafts not only decreases space, it eliminates the need to redirect the power or relocate other components.
In a simple planetary setup, input power turns the sun gear at high speed. The planets, spaced around the central axis of rotation, mesh with the sun as well as the fixed ring gear, so they are forced to orbit as they roll. All the planets are mounted to a single rotating member, called a cage, arm, or carrier. As the planet carrier turns, it delivers low-speed, high-torque output.
Problem Statement:
Calculation of Pitch Circle Diameter and No. of Teeth in Planet Gears:
The module is the same for all the gears.
The relation between the pitch circle diameter and no. of teeth is as follows -
D = m * t
D = pitch diameter
m = module and t = no. of teeth
Dia of ring / 2= Dia of planetary gear + Dia of sun gear / 2
115/2 = D.P. + 35 / 2
D.P. (Dia of planetary gear) = 57.5 -17.5 = 40mm
Geometry Creation and assembly:
For creating gear from Toolbox -
go to design library - Toolbox - ANSI metric - Power transmission - gears
for sun and planetary gears choose Spur gear
for Ring gear to choose Internal Spur Gear
Pressure angle = 20 degree
Face Width = 20 mm
1. Ring gear
2. Sun gear
3. Planetary gear
4. Carrier
5. Assembly
The ring gear, planet gears, sun gear, and the carrier are assembled as shown in the below image. The assembly is done using mate option by properly aligning all the components in such a way that no component overlap on each other. Here we are not using mechanical gear mates as we have to analyze the motion for 3 cases.
Motion Analysis and Results:
The motion analysis was carried out for three different cases. Solid contacts were defined between all adjoining contacts and the results were recorded at 600 fps and with precise contacts enabled.
Case 1: Sun gear – Input, Carrier – Output and Ring gear – Fixed
Here, the input rotary motion at a constant speed of 200 rpm is given to the Sun gear and the angular velocity of the carrier was measured, while holding the ring gear stationary.
The material for each contact is Steel (Dry).
The input speed to the motor in each case is 200 RPM. The motion analysis is done for 5 seconds.
Case 1:
Ring gear fixed. Motor - sun gear.
The plot of an angular velocity of the carrier against time.
Case 2:
Sun gear fixed. Motor - Ring gear.
The plot of an angular velocity of the carrier against time.
Case 3 :
Carrier fixed. Motor - Sun gear.
The plot of an angular velocity of the Ring against time.
Observation and conclusion:
- In case 1- when the input is given (200 rpm) to the sun gear and output is obtained at the carrier keeping the ring gear fixed. The planet gear not only rotates about their axis but are also forced to roll on the inside of the ring gear since it is fixed (rolling action is present).
- In case 2- when the input is given to the ring gear (200 rpm) and output is obtained from the carrier keeping the sun gear fixed. The angular velocity achieved is maximum since the internal gear is big and planet gears are small comparatively so when a large gear meshes with a small gear the velocity achieved from the small gear is high because the velocity ratio is high. A this can be seen in the plot of angular velocity.
- In case 3- when a carrier is fixed and output is to be obtained from the ring gear the opposite happens. The planet gears rotate only about their axis and transmit motion from sun to the ring and since the ring gear is big in diameter the angular velocity achieved is less.
- The deviations that are visible in the graphs show that there are points where sliding is occurring between the gears. For making the graph more smoother we can use precise contact.
Animation:
The animation link for the above 3 cases is provided below.