Harmonic Drive AG

Harmonic Drive

Simulation of HD gearboxes

Andreas Kayser

Simulation of dynamical systems

"Employment of modern simulation tools saves time and money."

This statement sounds like a vacuous headline at first. But in fact it defines entirely why computer based simulation tools spread an unexpected magnitude within only a couple of years. This trend is considered to be state of the art in electronic industry but becomes more and more important in mechanical engineering as well.

People at Harmonic Drive AG realized soon that computer based simulation provides enormous opportunities as well for developing new products as for supporting customer's projects. Looking for the best suited solution finaly the software package MATLAB/SIMULINK was choosen due to its open design. MATLAB itself is a powerful programming language for technical calculation. The SIMULINK add-in is an interactive toolbox for simulating nonlinear dynamic systems. The software family was developed by The MathWorks, Inc. Today there is an increasing MATLAB user group all over the world.

Modeling and simulation of systems containing HD gear boxes

Drive trains can be considered to be the one-dimensional special case of 3D multi body systems. In Figure 1 the kinematic structur of such a system (open chain) and a possible approach for component oriented modeling this kind of systems is shown. Calculation is done performing three successive steps:

Calculation of kinematic values (angle, angular velocity) starting at root (s.a. motor) towards the end of the chain (s.a. load)
Calculation of force values (torque, moment of inertia) in reverse direction
Calculation of the acceleration (angular acceleration)

Figure 1: Kinematic structure of a drive train

The most relevant term in modeling a technical system is its behaviour. The convergence of the mathematically modeled behaviour and the behaviour of the real world component rises increasing the model's level of detail. But modeling effort and time demand for computation will increase as well. Depending on the concrete task modeling one real world part, s.a. Harmonic Drive gear box, can lead to multiple model representation (ideal gear, gear with compliance, etc.).

Figure 2: The Harmonic Drive model library (Gear box sub-library "Getriebe")

Because real drive systems are built from components it seems reasonable to do the modeling a modular and object-oriented way. Typical elements of drive trains are shafts, motors, gears or clutches. Additionally components like controllers, numerical value schedulers or sensors are used. Another important need is to analyse the driven subsystem being a simple load or a very complex maschine system. Models of standard components can be collected in libraries. Figure 2 displays the component "elastisches Getriebe" (gear box with compliance) being part of "HDLibrary" and the underlying model representation. Figure 3 shows the SIMULINK model of a typical drive train consisting of components from "HDLibrary" model library.

Figure 3: Model of a typical drive train

Example: Force Feedback Device

Figure 4 shows the SIMULINK model of the manipulator (mechanical structure) used for a 6 degree of freedom Force Feedback Device. This device is particularly dedicated to act as a haptic interface in the field of computer-aided surgery but is also suitable for general use in "Virtual Reality" systems.

Figure 4: SIMULINK model of the Force Feedback Device

Simulation is always performed for the purpose of getting information about the modeled system. A suitable preparation of this information from a machine-oriented description to a man-readable representation is a decisive factor for working effectively with simulation software. One exceptionally proper way to illustrate complicated motion processes is 3D visualization. Therefore a data link was established to connect SIMULINK and RealiMation, a capable computer animation tool. Figure 5 explains the principle of program coupling via a TCP/IP socket.

Figure 5: Connecting the computer animation tool

Beside online animation this tool allows to create scheduled motion sequences which can be saved as video files.

Video sequence of the FFD manipulator's motion cycle (AVI)

Harmonic Drive AG will focus on modeling and simulation in future with more intensity. In addition to internal employment of this modern technology within our company we will concentrate on close collaboration with our customers and partners.