OPTIMO / MOTION - A POWERFUL MOTION ANALYSIS TOOL                         

© Dr. Boaz Eidelberg, April 2005, Optinet Inc.

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Table of Content

Objectives

The purpose of this reference note is to familiarize the reader with the OPTIMO / MOTION tool, as a quick and robust, user friendly analysis tool for optimizing motion profiles in solving positioning application problems.  The note highlights various other motion analysis tools, which are commonly used in the motion control marketplace. It then describes the benefits of OPTIMO / MOTION and concludes with a Walkthrough example a typical sizing application. For further support on using this tool please contact  webmaster@optinetinc.com

General Motion Tools

Almost every  company in the motion control business ( reference list ) provides its customers tools to make the proper selection of their products. Many times tools are quite difficult to use in the sense that they need to be downloaded from a web site into the user controller, they need to be stored and then be recalled for the application. Many times tools are part of the motion controller and use elaborated techniques such as Bode Plots to assist tuning their products. In other cases engineering manuals are provided with lengthy explanations through long hand example problems. Often tools are limited to the manufacturer products.

Example References to Motion Sizing Tools

The following is an example of a tutorial sizing calculations for linear motors provided by Anorad - the world leader in linear motor technology.  Lets review the details and run it as a comparison analysis with         OPTIMO / MOTION.

Motor Sizing Example   Ref: Anorad - http://www.rockwellautomation.com/anorad/products/linearmotors/motor_sizing.html

"Let’s assume we want to move horizontally a mass of 6 kg point to point for a distance of 100 mm (X) in 205 msec including settling time  (Tm) to +/- 1 micron. Total travel is 400 mm, and a dwell time of 200 msec is needed after each move.

Move profile
We will further assume an estimated settling time of 30 msec (Tst).
Now also let also assume a 25 msec smoothing time (Tj) (time for the current to go ramp up linearly from zero to the full peak current).
So the move cycle time (Tc) is 205+200 = 405 msec
Using previous move formula:
T (msec) = Tm – (Tst+Tj)
T (msec) = 205 – (30 + 25) = 150 msec

We will assume an efficient trapezoidal profile (1/3, 1/3, 1/3)
Acceleration needed here (see previous move formula):
A = (4.5)*100*10-3/(0.15)2
      A = 20 m/sec2(about 2 “g”)
V = (1.5)*0.1/0.15
      V = 1.0 m/sec
Jerk = 20/25*10-3
      Jerk = 800 m/sec3

The acceleration and deceleration time becomes (150/3)+25 = 75 msec
Since the smooth time is 25 msec, the time at constant acceleration is 75-(2*25) = 25 msec
The time at constant speed is now (150/3)-25 = 25 msec

Linear Motor Selection
We can estimate the acceleration force of the load only (see previously mentioned formula) at 2g*9.81*6 kg = 117 N.
Based on this we can select coil LC-50-100-D (peak force = 318 N, continuous force = 139 N) assuming a coil mounting plate of 1 kg.
Total moving mass: 6 kg (load) + 1 kg (plate) + 1.63 kg (coil mass) = 8.63 kg
Coil magnetic attraction Force Fa = 690 N, Coil resistance = 3.76 ohm, Coil Force constant 30.3 N/Ap, Thermal Resistance
1.3°C/W, Back Emf 35.8 Vp/m/sec, Inductance p-p 36 mH, Electrical cycle length 50 mm
We assume a good set of linear bearings with µ=0.005 and 20 N of friction.

Friction Force: Ff (N) = 8.63*9.81*[sin(0) + 0.005*cos(0)] + 690*0.005 + 20 = 24 N
  Inertial Force: Fi (N) = 8.63*20 = 173 N
  Lets neglect the damping force Fd = 0
  Total Acceleration Force Fta (N) = 173 + 24 = 197 N
  Total Constant Velocity Force Ftcv (N) = 24 N
  Total Deceleration Force Ftd (N) = 173 – 24 = 149 N
  Total Dwell Force Ftdw (N) = 0 N
  RMS Force Frms (N) = √[{1972*(25*2/3+25)+242*25+1492*(25*2/3+25)+
(1972+1492)*0.25*30}/405]
    Frms (N) = 86.3 N
  RMS Current Ica = 86.3/30.3 = 2.85 Amp 0-p
    Ica = 2.7/√2 = 2.01 Amp rms
  Peak Current Ipa = 197/30.3 = 6.5 Amp (0-p)
    Ipa = 6.5/√2 = 4.6 Amp rms
  Motor Coil Temperature Tc (°C) = 25 + 1/[1/(1.5*3.76*2.012*1.3)-1/259.5]= 58.4°C
  Motor Resistance Hot Rhot = 3.76*[234.5+58.4]/(234.5+25) =4.25 ohm
  Motor Power Losses Pl (W) = 1.5*4.25 *2.012 = 26 W
  Voltage due to Back Emf Vbemf = 1.2*1 m/sec * 35.8 Vp/m/sec = 43 V
  Voltage due to R*I Vri = 1.225*4.25 (ohm) * 6.5 (Amp 0-p) = 33.8 V
  Voltage due to Inductance VL = 7.695*1.2*1 (m/sec)*36*6.5/50 = 43.2 V
  Bus Voltage needed Vbus = 1.15*√[(43+33.8)2 + 43.22] = 101 Vdc

Notes:

  1. Vbus is a worst case since we have assumed no phase advance and no jerk time (max speed at max acceleration).
  2. An Allen Bradley Digital Servo Drives Ultra 3000 Model 2098-DSD-010 with 5 A (0-peak) continuous and 15 A (0-peak) of peak current will do the job here with either AC input "

 

OPTIMO / MOTION Tool

option 1-

other options can be obtained within seconds by changing the input variables in white text box and clicking CALCULATE

Results Comparison

                                                                Anorad         Optinet Option 1

The advantages of OPTIMO / MOTION are as follows:

Note: The motor requirements  are in the lower right corner of the tool and they can be selected from numerous manufacturers.  ( motor manufacturers )

OPTIMO / MOTION Assumptions:

Recommended Method of Operation:

SETUP

  1. Specify the required travel

  2. Select high velocity value ( the tool determines automatically the maximum value you can achieve )

  3. Estimate the value of acceleration ( e.g. 1g or 10,000 mm/s^2. This value will greatly effect the inertial force, motor size and the cost )

  4. Use high jerk ( e.g. 100 times higher than the acceleration  to obtain the shortest move time )

  5. Enter the mass value making sure to  include all moving parts including slides, compounded stages, tools and work

  6. Enter an equivalent resistance force including friction, damping, spring, machining

CALCULATE  ( most application engineering stop here )

            Review the chart results

ADJUST SCALE

            For better reading of the charts, attempt to bring in all graphs to the same height by using proper scale value. If any graph is too high, apply higher scale value to bring it down

FIND A WORKING SOLUTION ( this step is the minimal requirement for proper sizing application )

  1. Read the the S-Filter frequency. This value is the maximum frequency of vibration that the Jerk will introduce. The higher the Jerk the higher the impact and its frequency spectrum content and the longer the settling time.

  2. If high smoothness of motion, or short settling time is needed, reduce the Jerk to result in an S-Filter of about 20 Hz ( This will  filter out the acceleration impact vibrations above 20 Hz. Vibrations above  20  can be filtered by high enough servo bandwidth e.g. 40 Hz.  The lower Jerk value, sometimes referred to as a smooth factor or S curve,  will make the move time a bit longer longer but will reduce settling time.

  3. Adjust the acceleration to be the minimum value which will yield the required move time.

  4. Use the calculated motor forces and power with enough safety margin ( e.g. 30-50% ) to choose a motor / amplifier for the application.

FIND AN OPTIMAL MOTION SOLUTION ( this step is highly recommended for all applications )

  1. Check the sensitivity of motor forces to small perturbations in Velocity, Acceleration, Jerk and Dwell

  2. Optimize the solution to find by trial and error, the best ratio of smallest motor force and shortest move and settle time. You can achieve that by gradually reducing acceleration and increasing velocity, while keeping an eye on the S-Filter

DEVELOP PERFORMANCE CHARTS ( this step is recommended for high volume applications )

  1.  If you are in the process of developing a new positioning stage or any positioning solution for a large volume system project, it is recommended to work with Performance Charts. These charts provide a visual 3D presentation of the effects which various motion parameters have on the desired design criteria.  Performance Charts are  highly effective in providing design road maps to the design engineers. OPTIMO / MOTION can be used effectively to generate these charts.

  2. For more information about Performance Charts and their application, or for assistance in using this tool please contact webmaster@optinetinc.com. Thank you for your interest in Optinet Tools. We are dedicated to excellence in positioning systems sizing tools.