WORKSHOP 7 OVER-RUNNING PULLEY

WORKSHOP 7 – OVER-RUNNING PULLEY Problem Statement Model the spring behavior of a one-way clutch in an over-running pulley (ORP). ORPs are used in automotive engine accessory drives to reduce the amplitude of the motion passed to the shafts of a driven pulley, as well as reduce transverse belt vibrations.

WORKSHOP 7 – OVER-RUNNING PULLEY Problem Statement (cont.) The spring loads along one curve and unloads along another. Once a certain angular displacement is reached (max_ang), the spring can no longer provide any more torsional resistance, but the pulley may keep rotating in that direction. Then, once the relative shaft velocity changes direction, the pulley will unload from that point along a new curve.

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) Model Description The model contains two concentric shafts the hub (inner) and sheave (outer). They are attached to ground using revolute joints. The sheave is driven by a sinusoidal motion similar to the input from a belt and combustion engine’s crank pulley. The model also has curve data (in .csv format) for the loading and unloading torque-angle relationships. A FORTRAN VARSUB tracks the angular displacement of the sheave relative to the hub and resets the value to max_ang whenever max_ang has been exceeded and the relative sheave- hub velocity changes direction (that is, from loading regime to unloading regime). Notes: The locking/loading direction is defined as positive rotation about the z-axis of the revolute joint. The time units are milliseconds.

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) Getting Started First, import the model. Then, create and modify the splines. To import the model: Import install_dir/orp/orp.cmd, where install_dir is the directory where the training files are installed. The model looks as follows: Using the data file install_dir/orp/loading_torque.cs v, create a SPLINE for the spring’s torque-angle relationship in the loading direction. Set Independent Column Index to 1. Tip: See Workshop 10: Gatling Gun Fire Mechanism for more information on how to import and SPLINE.

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) To import the model (Cont.): Using the data file install_dir/orp/unloading_tor que.csv, create a SPLINE for the spring’s torque-angle relationship in the unloading direction. Set Independent Column Index to 1. From the Build menu, point to Data Elements, point to Spline, point to Modify, and then select SPLINE_1 (the loading torque). Since the data is short, select Linear extrapolation. Select OK. Modify SPLINE_2 (the loading torque), selecting Linear extrapolation. Select OK.

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) Creating the spring torques Next, create the spring torque variable, and then create the spring torque. To create the spring torque variable: Create a state variable called reset_angle which will count and reset the relative sheave-hub angle according to the logic required by the problem definition. The source code for the VARSUB is already written. You only need to get the proper parameter values into your VARIABLE statement. Symbolically speaking, they are: Tips: Look at parameters passed in par in myvarsub.f Find the solver IDs by getting Info on each marker.

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) To create the spring torque variable (Cont.): (Cont.) From the Build menu, point to Forces, and then select Torque (single component). The Create Forces dialog box appears.

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) To create the spring torque variable (Cont.): Complete the dialog box as shown below. Set the torsion spring to act between the hub and sheave, and use the hub.torque_mar and sheave.torque_mar markers for action/ reaction points. Tip: Right-click to select hub.torque_mar and sheave.torque_mar from a group of markers in the same area.

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) To create the spring torque: The Torque Modify dialog box should appear automatically. If not, right- click the torque, and then select Modify. Complete the dialog box as shown below:

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) To create the spring torque(Cont.): (Cont.) The torque should use the data from the unloading SPLINE when the sheave is falling behind the hub, and from the loading SPLINE when the sheave is racing ahead of the hub (see previous examples for hysteresis). Note: Be careful with signs. We suggest you make the positive z-axis of this torque the same as that of the revolute joints. Tip: step(WZ(MARKER_3,MARKER_5,MARKER_5), 0, -AKISPL (varval(.reset_angle),0,unloading_torque, 0), 0.00001,-AKISPL(varval(reset_angle),0,loading_torque, 0))

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) Creating a damping force: From the Build menu, point to Forces, and choose the torsion spring to represent losses/drags in the pulleys. Create a rotational damper between the hub and sheave. Try a coefficient of 500N-mm-ms/deg. Right-click the torsion spring, and select modify if you need to change the stiffness or damping coefficients.

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) Creating Output requests: From the Build menu, point to Measure, point to Request, and then select New. Create output requests for the following channels: Hub velocity Sheave velocity Relative hub and sheave velocity Spring torque Damping torque Reset angular displacement from the subroutine

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) Creating Output requests (Cont.): Create output requests for the following channels (Cont.): Below are two examples:

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) Creating a custom ADAMS/Solver Library First you create solver library. Then, you run the simulation. To create a custom solver library and run the simulation: Compile the FORTRAN subroutine install_dir/orp/myvarsub.f. Create a custom ADAMS/Solver library. Reference this library in your ADAMS/View session’s simulation settings by performing one of the following: In ADAMS/View: From the Settings menu, point to Solver, point to Solver Executable, and then specify the file in the Solver Library text box. In ADAMS/Solver: From the ADAMS/Solver Command menu, select ru-user, and enter your custom library name. Run a simulation of 500 ms in 5000 steps.

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) To create a custom solver library and run the simulation (Cont.): Examine the results. The plot below shows the spring torque and relative velocity between the hub and sheave. Note: The plot is based on a maximum angle in the VARSUB of 3 degrees.

WORKSHOP 7 – OVER-RUNNING PULLEY (CONT.) Questions Does the ORP spring help reduce the oscillation amplitude that gets passed to the hub? ____________________________________________________________ How could you effectively change the dynamic responsiveness of the spring to changes in relative sheave-hub velocity? If you have time, vary the damping coefficient between the hub and sheave. What effect does this have?