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Theoretical Friction Assignment - Theoretical Estimation of

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					                             Estimation of Turntable Friction
                              Using Quasi-Static Analysis
                                  Individual Assignment

Overview
Friction slows things down. Since the design objective is to increase turntable table speed,
it is generally desirable to reduce friction in the system. In this assignment the theoretical
friction of the turntable will be calculated. The design benefit includes:
      The sources of highest friction can be identified, and used to prioritize optimization
        efforts.
      Friction calculations can be incorporated into a future dynamic simulation to improve
        the accuracy of the system optimization.
The sources of friction include:
     a. The thrust bearings that support the vertical load on the turntable.
     b. The turntable shaft that supports horizontal loads on the turntable
     c. The internal bearings in the motor
     d. The potentiometer
To find the total friction in the system one cannot simply add the friction on the turntable,
potentiometer, and motor, since they rotate at different speeds. This assignment will guide
you through the various steps in the analysis and will show use of Free Body Diagrams will
properly take into effect the gear ratios in the system. You will see how a relatively simple
1 DOF system requires numerous steps of analysis. The results may surprise you. For
now, circle which of the above friction source you think contributes most to the system
friction.

Parameters
For this assignment, use the provided parameters below, so that all numerical calculations
can be compared to the solutions that will be posted. For actual turntable optimization use
more accurate values measured from your own turntable.
        Turntable mass: mtt = 350 grams
        Spring force on friction drive arm: Fsp = 3.5 Newton
        Coefficients of friction: For this assignment use values below, but for your
           turntable report use more accurate values measured in the lab.
               o Acrylic on Acrylic aa = 0.4
               o Acrylic on Steel as = 0.2
               o Bronze on Steel bs = 0.15

Reference and Tips
      See Guidelines for Drawing Free Body Diagrams (FBDs) at:
       http://www.maelabs.ucsd.edu/mae_guides/analysis_guide/FBD/FBD_guidelines.htm
      Friction torque in the quasi-static sense is defined as the torque that one must apply
       to initiate rotation.
      This assignment can be done with quasi-static planar analysis, which uses
       equations: Fx=0, Fy=0, M=0.
      For this assignment, assume that the motor power is off.


                                         1
Key Dimensions

                              Friction Drive Arm
                                                                           47.625
                                                      127


           Motor                                                   1°
                                                                    1                                            Friction Arm Pivot

                                                             28°



    Motor Shaft                                    Friction Drive Spring




                                                                                                   Turntable Shaft
                                                                                                   ((stationary and press fit into base)
                                                                                    Ø 96
                                                     Ø6




                                                                                                  Turntable       Units are in mm
                                                                                                                  Angles in degrees
                                                                                                                  Drawing Scale
                                                                                                                   0
                                                                                                                  1 mm line
 Thrust Bearing support
                                                                                           Ø159
 (hold weight of turntable)




                                              Top View of Turntable (units in mm)




                          Motor Dimensions (units in inches)
Additional dimensions can be taken from dxf drawing of Turntable and drawing of motor
If the link to the dxf files above do not work, try the direct links below:
http://www.maelabs.ucsd.edu/mae156/A/Assignments/TurnTableFBD.DXF
http://www.maelabs.ucsd.edu/mae156/A/Assignments/high-speed-motor.DXF


                                                                   2
                             Friction due to Turntable Thrust Bearings (Vertical Supports)

The weight of the turntable is supported by four thrust bearings (also referred to as sliders in the
assembly instructions). Draw forces in colored ink on figures below. Calculate a numerical value of
how much torque must be applied onto the turntable to overcome this friction and initiate motion.
                          Figures                                            Equations
       z                                                        Central shaft


               x



                   Thrust Bearing support
                   (hold weight of turntable)
                                                Side View

                                                 f_tt_thrust       Torque necessary to overcome
                                                                    friction of thrust bearings




                                                                  rth
   y


           x



                                                                                    Ø 96




                                                                                      Units are in mm
 Thrust Bearing support                                                               Angles in degrees
 (hold weight of turntable)                                                           Drawing Scale
                                                                                       0
                                                                                      1 mm line



                                                 Top View




List methods by which the friction due to the Thrust Bearings can be reduced:




                                                                                3
              Friction Torque On Turntable Due To Friction In Potentiometer

The friction to rotate the potentiometer is on its spec. sheet. However, the pulley drive that
connects the pot to the turntable has a gear ratio factor due to the different size pulleys.
Use FBD analysis to calculate how much torque must be applied onto the turntable to
overcome the friction in the potentiometer. You can assume that one side of the belt is in
tension and the other is completely slack.

      1. Torque to turn pot from spec sheet: ________
      2. Draw forces on FBDs of Turntable and Pot Pulleys in right column below.
      3. Calculate torque that must be applied onto the turntable to overcome the friction in
         the potentiometer.
      4. Calculate force on turntable shaft due to belt tension for use in following analysis
                                         Torque necessary to
                                         overcome friction of pot
                                                                                                rp1
                                            f_tt_pot


              R17.5                                 Direction of Rotation
                      Turntable Pulley


                      rp1
                                                                                     FBD of Turntable Pulley
                              52°


                                                        Belt




                                                                  Pot Pulley
  y

                                                                                                      rp2
        x                                               rp2



                                                                            R 35.0


                  Top View


                            Reference Drawing                                          FBD of Pot Pulley




                                                              4
Spring Preload Forces
The spring in the friction drive arm is an essential design component of the friction drive. If the
spring force is too low, then excessive slip will occur between the motor shaft and the turntable.
Yet if the spring force is too high it will create excessive friction in the motor and turntable shaft.
Therefore, we need to determine forces due to the spring preload forces before calculating the
friction in the motor or turntable shaft. To simplify the analysis we can assume here that the motor
is not turned on.
     1. Draw the forces on the FBD sketch below
     2. Calculate the horizontal load on turntable shaft and its angle
     3. Calculate the horizontal load on the motor shaft.
                                                49                              75

                                       Friction Drive Arm

                                                                127                      48
                                                                                                     Friction Arm Pivot

                                                                                 1
                                                                                 1°

                        Motor                                                           40°
                                                                         28°

                                                                                              Ø159
                                                                 Ø 96
                                                                Friction Drive Spring
                                               52° 64°
              Motor Shaft
                                                                                                        89

                                64
                   y


                            x




                                     Drawing with Details and Dimensions
                                               y


                                                      x




                                      Complete FBD of Pivot Arm Here




                                                            5
                                  Friction in Turntable Shaft

The spring preload in the friction drive generates a horizontal load on the turntable. The
tension in the belt to the potentiometer also adds to the horizontal load. This load is
resisted by the turntable shaft. The friction of this shaft in its bearings causes a frictional
torque on the turntable.
     Draw forces applied onto the turntable in the horizontal plane on the figure below.
     Calculate the combined vector horizontal force on turntable shaft.
     Calculate torque that must be applied onto the turntable to overcome the friction in
       the turntable shaft (tip; you need to use the turntable shaft radius).

                  Motor
                                                            Turntable


                    Motor Shaft
                                      52°
                     y


                           x
                                                            Ø 96




                                                     Ø6




                                                                        Pot Pulley




                                            6
                         Friction in Motor Bearings –on Motor

Draw the horizontal force on the motor shaft and the reactions on the shaft bearings in the
figure below.
     Draw a top view of the top and bottom bearings showing horizontal forces, including
        bearing reaction forces and friction forces.
     Calculate the torque that must be applied onto the motor shaft to the internal
        friction between the motor shaft and the internal motor bearings (made of bronze).



                          Bronze Bushing




                           Motor Shaft




                                                            33
                           Bronze Bushing




                                                            12
                                               2.9




                                           7
                        Friction in Motor Bearings –on Turntable
The prior section calculated the friction from the motor bearings as applied onto the motor
shaft. Here we calculate the friction from the motor bearings as applied onto the turntable
so that it can be compared to the rest of the friction sources.
                                                                                       Ø159
                                                               Ø 2.9


   
                                               Motor
       Add forces to FBDs below                                                                      Turntable



      Calculate the torque that must be         Motor Shaft
                                                                       52°
                                                  y
       applied onto the turntable to                    x

       overcome the internal motor friction.                                                        Ø 96




                                                                                         Ø6




                                                       Drawing with Details and Dimensions
                                                                             f_tt_m      Torque on turntable necessary to
                                                                                          overcome friction of motor bearings




                f_m
                                                                                              rtt




               FBD of Motor
                                                                       FBD of Turntable




                                         8
Combined Friction Table


Friction Source                 Friction amount in Nm         Percent of total friction
thrust bearings that support
the vertical load on the
turntable
turntable shaft that supports
horizontal loads on the
turntable
internal bearings in the
motor
Potentiometer
Combined Friction on                                                      100%
Turntable




Extra Credit Problems
   1. Some MAE3 friction drives have been observed rotating faster in one direction than
      the other direction indicating that there is more friction in one direction than the
      other. Can you figure out why this may be? Can you propose a design change that
      will create equal performance in both directions? (Tip, consider Free Body
      Diagrams in this assignment and the motor torque when it is turned on).

   2. Calculate the necessary spring preload to avoid slip between the motor shaft the
      and turntable




                                        9

				
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Lingjuan Ma Lingjuan Ma MS
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