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# Gear vibration project Presentation PowerPoint PPT Presentation

Gear vibration project Presentation. Peter Munz MSc student University of Arizona. Contents. 1. Background 2. Problem statement 3. Modeling the problem 4. Solution 4.1.How the code works 4.2.Results 5. Experiment design 5.1 Equipment data 5.2 Assembly details 5.3 Component design

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Gear vibration project Presentation

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## Gear vibration project Presentation

Peter Munz

MSc student

University of Arizona

### Contents

1. Background

2. Problem statement

3. Modeling the problem

4. Solution

4.1.How the code works

4.2.Results

5. Experiment design

5.1 Equipment data

5.2 Assembly details

5.3 Component design

6. Future work

### 1. Background - 1

• Gearbox failure

### 2. Problem statement - 1

• Find a method to detect cracks present in spur gear teeth from accelerometer data before fracture

### 3. Modeling the problem - 1

• Mechanical arrangment: Motor, Pinion gear, Driven gear, Load

Ti: torques [Nm]qi: angular coordinates [rad]

i = M,1,2,L : Motor, Pinion, Driven gear, Load

### 3. Modeling the problem - 2

• Mechanical model: 4 DoF torsional spring-damper-mass system

ML

MM

Ji: mass moment of inertia [kg m2]Ks1, Ks2 : shaft stiffness [Nm/rad]

Kg(t) : gear mesh stiffness [Nm/rad]

Cs1,Cs2 : shaft damping [Nm s]

Cg(t) : gear mesh damping[Nm s]

MM: motor torque [Nm]ML: load torque [Nm]

### 3. Modeling the problem - 3

• Simplified mechanical model: 2 DoF damped torsional spring-mass system

• Mathematically – 2 damped Hill equations with forcing terms MM and ML:

cG = const.

MM = const.

ML= const.

Rb1: pinion gear base radius

Rb2: driven gear base radius

### 3. Modeling the problem - 4

• kG(t) as a superposition of 2 functions

• k1(t): stiffness function of healthy gears meshing

• k2(t): stiffness function of damaging effect

### 3. Modeling the problem - 5

k1:

Parameters:

k0 – stiffness when two teeth pairs are in contact [Nm/rad]

kr – reduction ratio of stiffness when one pair is in contact to k0 [-]

k2:

kdr – ratio of damage to k0 [-]

z – number of teeth [-]

w - angular frequency of rotation [rad/s]

T – period of revolution T = 2 p / w [s]

k1-k2:

Tm – mesh time Tm=T/z [s]

• Section A

• Section B

• Input shaft

• Ouptut shaft

### 5.3Component design - 3

• Bearing housing

### 5.3Component design - 3

• Bearing housing 2

### 6. Future work

• Simulate: develop analytical model

• Design: make final decision for drive, enclosure, torque coupling, lubrication

• Prepare: assemble rig according to design

• Build: base frame, shafts, bearing housing, sensor adapter

• Buy: motor(?), bearings, coupling, gears

• Experiment: conduct measurements

• Evaluate: compare measurement and simulation results