Plantery Gears

Introduction

Gear drives are probably the most widely used mechanical driving devices; ordinary gear trains consist of two or more gears for the purpose of transmitting motion from one axis to another. Ordinary gear trains have axes, relative to the frame, for all gears comprising the train.

Planetary gear trains(as show at figure 1 below) also referred to as epicyclic gear trains, are those in which one or more gears orbit about the central axis of the train. Thus, they differ from an ordinary train by having a moving axis or axes. Planetary gear trains always consist of sun gear, planet gear, arm, or planet carrier, as a planetary gear train has two degree of freedom, so it can add up or branch out the transmitted power that those ordinary gear can't do.

The arm, while not a gear, is an essential part of the planetary because it defines the motion of the moving planet gear axes. The planetary is also unique to a standard gear train in that it requires two inputs to define one output. A good example is your car's differential, which has two inputs: one the drive-shaft, and the second a constraint between the two driven wheels provided by whatever you are driving on

The objective of this project is to study the kinematics fundamentals of epicyclic gear drives, and the project scope is more on finding the velocity ration and the efficiency of the planetary gear trains, the project also need to makes good use of the apparatus inside the lab to prove the theoretical statement and formula.

Comparing with the conventional gear set and planetary gear

Literature Review

The fundamental of the planetary gear trains was applied through out the entire project and the velocity ratio formula VRS→r= ωs/arm/ωr/arm =ωs-ωarm/ωr-ωarm =-Nr / Ns was used as a general formula to calculate the entire velocity ratio in the project. Here the minus sign added on the velocity ration is indicated that the input and output gears are run in opposite direction.

At the first stage, the planetary gear demonstration unit was given and the velocity ratio was tested under different condition as:

1) Carrier (arm gear) fixed 2) ring gear fixed 3) Sun gear fixed

Under the different situation, the velocity ratio can be derived differently, when the carrier was fixed, VRs→r = - Nr / Ns, when the ring gear was fixed, VR = 1- VRs→r, and when the sun gear fixed, VR = 1-1/VR s→r.

The next stage, the teeth condition of planetary gear train was tested out as well, there are 2 conditions for the teeth as: 1) Ns- Nr + 2 Np = 0; 2) Np + 2 < ( Ns + Np ).sin(180о/ np ) To check the rationality of these three conditions, a set of plastic ring gear and spur gears with different diameters was given to assemble, as the teeth number for ring gear was given as Nr =100, for the spur gears, N2 =20, N3 =30 and N4 =40, if assemble the gears according to the requirement condition, there are few possibility, one is that either taken out two kinds of spur gear which N3 =30 as planetary gear, and one spur gear which N2 =40 as sun gear, the condition 2 can also be fulfilled, and the gear train can be assembled up as figure2 show.

Also there was another kind of gear that can meet the requirement condition and was assembled out, this time there were three of N4 =40 and one of N2 =20 to built up the gear train, and it also met the requirement. If the gears chose out that didn't meet the 2 requirement condition then the assembly can't completed.

The Two-speed planetary gear Apparatus was used to check the experiment result and get the data after all the fundamental knowledge on the planetary gear has been mastered.

Methodology

A two-speed planetary gear apparatus is as figure4 has indicated, and the equipment was used to investigate the efficiency of the gear unit., the basic information provided in the handout was made good used of and the procedure of conducting the studying was worked out.

By giving of these gear train, firstly, the design has to been checked whether fulfills the teeth conditions, as np = 3, and Nk = NL = Ns = 24, ND = NG = Nr = 72, Nm = NN = Np = 24, so as stated inside the literature review, Ns - Nr + 2 Np= 24-72 + 2X24 = 0, and Np + 2 = 26, ( Ns + Np ).sin(180о/ np ) = (24 + 24 ) X sin60о = 41.6, Np + 2 < ( Ns + Np ).sin(180о/ np ), so the requirement on teeth conditions is fulfill.

The experiment needed to calculate respectively the speed ratios from the input shaft to the output