Model and Detect Drivetrain Faults

This example shows how to detect and respond to a fault in a drivetrain using a Rotational Damper block. The Rotational Damper block allows you to specify the damping coefficient as a function of temporal or behavioral triggers. You can program the damping coefficient to change at a particular time in the simulation or when the number of shocks for a given acceleration exceeds a limit to model fault behavior. Fault modeling allows you to predict how your actual physical system responds when it experiences real faults. It also allows you to test the robustness and responsiveness of your control system.

In the example, the fault is detected by a damper that is attached to a flexible shaft. Although you can perform most of the steps in this example using the tools that tshhe Simulink^® and Simscape™ Driveline™ user interfaces provide, scripts are supplied. You can combine the scripts into a larger script for parameter sweeps.

1. Open the model. At the MATLAB^® command prompt, enter:

   openExample('sdl/ShaftWithTorsionalFlexibilityExample')
   model = 'ShaftWithTorsionalFlexibility';

   

   This model contains two flexible aluminum shafts modeled using a lumped parameter approach. A motor drives the motor shaft. A viscous damper is connected to the load shaft. The viscous damper is represented by a Rotational Damper block from the Simscape > Foundation Library > Mechanical > Rotational Elements library. The Foundation Library Rotational Damper block is not able to detect or respond to faults.

2. Simulate the model and plot the results.

    Script for Generating and Plotting Simulation Results

   %% Simulate Model
   sim(model)
   
   %% Get simulation results
   simlog01 = simlog_ShaftWithTorsionalFlexibility;
   simlog_t = simlog01.Clutch.P.series.time;
   simlog_pClutch = simlog01.Clutch.P.series.values('Pa');
   simlog_wMotor = simlog01.Shaft_Motor.F.w.series.values('rad/s');
   simlog_wLoad = simlog01.Shaft_Load.F.w.series.values('rad/s');
   
   %% Plot results
   X1 = simlog_t;
   YMatrix1 = [simlog_wMotor simlog_wLoad];
   Y1 = simlog_pClutch;
   
   % Create figure
   figure1 = figure('Name','ShaftWithTorsionalFlexibility',...
       'OuterPosition',[107 336 733 822]);
   
   % Create axes
   axes1 = axes('Parent',figure1,...
       'Position',[0.13 0.709 0.775 0.216]);
   hold(axes1,'on');
   
   % Activate the left side of the axes
   yyaxis(axes1,'left');
   
   % Create multiple lines using matrix input to plot
   plot1 = plot(X1,YMatrix1,'LineWidth',2);
   set(plot1(1),'DisplayName','Motor Shaft', 'Color', 'k');
   set(plot1(2),'DisplayName','Load Shaft', 'Color', 'b');
   
   % Create ylabel
   ylabel('Speed (rad/s)');
   
   % Comment/uncomment the following line to remove/
   %  preserve the Y-limits of the axes
   ylim(axes1,[-100 250]);
   
   % Set the remaining axes properties
   set(axes1,'YColor',[0 0.447 0.741]);
   
   % Activate the right side of the axes
   yyaxis(axes1,'right');
   
   % Create plot
   plot(X1,Y1,'DisplayName','Clutch Pressure','LineWidth',2, 'Color', 'r');
   
   % Create ylabel
   ylabel('Pressure (Pa)');
   
   % Comment/uncomment the following line to remove/
   %  preserve the Y-limits of the axes
   ylim(axes1,[0 2000000]);
   
   % Set the remaining axes properties
   set(axes1,'YColor',[0.85 0.325 0.098]);
   % Create xlabel
   xlabel('Time (s)');
   
   % Create title
   title('Shaft Speeds and Clutch Pressure');
   
   % Uncomment the following line to preserve the X-limits of the axes
   % xlim(axes1,[0 0.2);
   
   % Set the remaining axes properties
   set(axes1,'LineStyleOrderIndex',2);
   box(axes1,'on');
   grid(axes1,'on');
   
   % Create legend
   legend1 = legend(axes1,'show');
   % set(legend1,'Location','best');
   set(legend1,...
       'Position',[0.6944 0.9125 0.1982 0.07270]);
   

   

   At the start of the simulation, the clutch is unlocked and the driven shaft is free. The initial velocity of the motor shaft is the specified 200 rad/s and the system starts at steady state. The oscillations triggered by the engaging and disengaging of the clutch are due to the flexibility in the shafts.

3. Replace the Simscape damper with the Simscape Driveline Rotational Damper, which is in the Simscape > Driveline > Couplings & Drives > Springs & Dampers library. Label the new block Faultable Damper.

    Script for Replacing the Rotational Damper Block

   %% Replace Rotational Damper from Foundation Library with
   %  Faultable Rotational Damper from the Simscape Driveline Library
   
   % Define Unfaultable Damper Block 
   foundationDamper = [model,'/Damping Bearing'];
   
   % Get Unfaultable Damper Block Damping Coefficient
   dampingCoefficient = get_param(foundationDamper,'D');
   
   % Get Unfaultable Damper Block Position
   damperPosition = get_param(foundationDamper, 'Position');
   
   % Delete Unfaultable Damper Block
   delete_block(foundationDamper)
   
   % Add Faultable Damper Block
   faultableDamperLib = ...
       'sdl_lib/Couplings & Drives/Springs & Dampers/Rotational Damper';
   faultableDamperPath = [model,'/Faultable Damper'];
   add_block(faultableDamperLib,faultableDamperPath,...
       'Position',damperPosition,...
       'NamePlacement', 'alternate',...
       'D',dampingCoefficient)
   

   

4. Enable a time-based fault and specify a response that includes a change in the damping coefficient and the generation of a MATLAB warning. Use these values for the damper Fault parameters:

   • Enable faults — Enabled

   • Faulted damping coefficient — 10

   • Enable temporal fault trigger — Enabled

   • Simulation time for fault event — 0.06

   • Reporting when fault occurs — Warning

    Script for Configuring the Rotational Damper Block Using a Timed Fault

   %% Define Faultable Damper Block Parameters
   underDamp = '10';
   overDamp = '150';
   
   faultTime = '.06';
   
   aMaxDef = '100';
   aMaxHigh = '400';
   aMaxLow = '50';
   
   shockNMaxDef = '1';
   shockNMaxHigh = '5';
   shockNMaxLow = '2';
   
   disabled = '0';
   enabled = '1';
   
   none = '1';
   warning = '2';
   error = '3';
   
   %% Parameterize a Timed Fault
   set_param(faultableDamperPath,...
        'enable_faults', enabled,...       % Enable faults
        'b_fault', underDamp,...           % Faulted damping coefficient 
        'temporal_fault', enabled,...      % Enable temporal fault trigger
        'fault_time', faultTime,....       % Simulation time for fault event
        'shock_fault', disabled,...        % Disable behavioral fault trigger
        'acceleration_limit', aMaxDef,...  % Maximum permissible acceleration
        'shock_limit', shockNMaxDef ,...   % Maximum number of shocks
        'report_fault', warning)           % Reporting when fault occurs
   

5. Simulate the model and plot the results.

    Script for Generating and Plotting Simulation Results

   %% Simulate
   sim(model)
   
   %% Get Simulation Results
   simlog02 = simlog_ShaftWithTorsionalFlexibility;
   simlog_t02 = simlog02.Clutch.P.series.time;
   simlog_pClutch02 = simlog02.Clutch.P.series.values('Pa');
   simlog_wMotor02 = simlog02.Shaft_Motor.F.w.series.values('rad/s');
   simlog_wLoad02 = simlog02.Shaft_Load.F.w.series.values('rad/s');
   
   %% Plot Results
   X2 = simlog_t02;
   YMatrix2 = [simlog_wMotor02 simlog_wLoad02];
   Y2 = simlog_pClutch02;
   
   % Create axes
   axes2 = axes('Parent',figure1,...
       'Position',[0.125 0.4 0.775 0.216]);
   hold(axes2,'on');
   
   % Activate the left side of the axes
   yyaxis(axes2,'left');
   
   % Create multiple lines using matrix input to plot
   plot1 = plot(X2,YMatrix2,'LineWidth',2);
   set(plot1(1),'DisplayName','Motor Shaft', 'Color', 'k');
   set(plot1(2),'DisplayName','Load Shaft', 'Color', 'b');
   
   % Create ylabel
   ylabel('Speed (rad/s)');
   
   % Comment/uncomment the following line to remove/
   %  preserve the Y-limits of the axes
   ylim(axes2,[-100 250]);
   
   % Set the remaining axes properties
   set(axes2,'YColor',[0 0.447 0.741]);
   
   % Activate the right side of the axes
   yyaxis(axes2,'right');
   % Create plot
   plot(X2,Y2,'DisplayName','Clutch Pressure','LineWidth',2, 'Color', 'r');
   
   % Create ylabel
   ylabel('Pressure (Pa)');
   
   % Comment/uncomment the following line to remove/
   %  preserve the Y-limits of the axes
   ylim(axes2,[0 2000000]);
   
   % Set the remaining axes properties
   set(axes2,'YColor',[0.85 0.325 0.098]);
   
   % Create title
   title('Time-Faulted Speeds and Clutch Pressure');
   
   % Create xlabel
   xlabel('Time (s)');
   
   % Uncomment the following line to 
   % preserve the X-limits of the axes
   % xlim(axes1,[0 0.2]);
   
   % Set the remaining axes properties
   box(axes2,'on');
   grid(axes2,'on');
   set(axes2,'LineStyleOrderIndex',2);
   

   Warning: At time 0.060000, one or more assertions are triggered.
   A fault event has occurred The assertion comes from:
   Block path: ShaftWithTorsionalFlexibility/Faultable Damper
   Assert location: (location information is protected)
   

   

   At simulation time t = 0.06 s, the time specified for the fault, a warning is reported. The damping coefficient drops and slows the speed of both shafts.

6. Enable a shock-based fault and specify a response that includes a change in the damping coefficient and the generation of a MATLAB warning. Then, simulate the model and plot the new results. Use these values for the damper Fault parameters:

   • Enable faults — Yes

   • Faulted damping coefficient — 150

   • Enable temporal fault trigger — Disabled

   • Enable behavioral fault trigger — Enabled

   • Maximum permissible acceleration — 50

   • Maximum number of shocks — 2

   • Reporting when fault occurs — Warning

    Script for Configuring the Rotational Damper Block Using a Timed Fault

   %% Paramaterize a Shock Fault
   set_param(faultableDamperPath,...
        'enable_faults', enabled,...       % Enable faults
        'b_fault', overDamp,...           % Faulted damping coefficient 
        'temporal_fault', disabled,...     % Disable temporal fault trigger
        'fault_time', faultTime,....       % Simulation time for fault event
        'shock_fault', enabled,...         % Enable behavioral fault trigger
        'acceleration_limit', aMaxHigh,...  % Maximum permissible acceleration
        'shock_limit', shockNMaxLow ,...   % Maximum number of shocks
        'report_fault', warning)           % Reporting when fault occurs
   

7. Simulate the model and plot the results.

    Script for Generating and Plotting Simulation Results

   %% Simulate
   sim(model)
   
   %% Get Simulation Results
   simlog03 = simlog_ShaftWithTorsionalFlexibility;
   simlog_t03 = simlog03.Clutch.P.series.time;
   simlog_pClutch03 = simlog03.Clutch.P.series.values('Pa');
   simlog_wMotor03 = simlog03.Shaft_Motor.F.w.series.values('rad/s');
   simlog_wLoad03 = simlog03.Shaft_Load.F.w.series.values('rad/s');
    
   %% Plot Results
   X3 = simlog_t03;
   YMatrix3 = [simlog_wMotor03 simlog_wLoad03];
   Y3 = simlog_pClutch03;
   
   % Create axes
   axes3 = axes('Parent',figure1,...
       'Position',[0.125 0.08 0.775 0.216]);
   hold(axes3,'on');
   
   % Activate the left side of the axes
   yyaxis(axes3,'left');
   
   % Create multiple lines using matrix input to plot
   plot1 = plot(X3,YMatrix3,'LineWidth',2);
   set(plot1(1),'DisplayName','Motor Shaft', 'Color', 'k');
   set(plot1(2),'DisplayName','Load Shaft', 'Color', 'b');
   
   % Create ylabel
   ylabel('Speed (rad/s)');
   
   % Comment/uncomment the following line to 
   % remove/preserve the Y-limits of the axes
   ylim(axes3,[-100 250]);
   
   % Set the remaining axes properties
   set(axes3,'YColor',[0 0.447 0.741]);
   
   % Activate the right side of the axes
   yyaxis(axes3,'right');
   
   % Create plot
   plot(X3,Y3,'DisplayName','Clutch Pressure','LineWidth',2, 'Color', 'r');
   
   % Create ylabel
   ylabel('Pressure (Pa)');
   
   % Comment/uncomment the following line to 
   % remove/preserve the Y-limits of the axes
   ylim(axes3,[0 2000000]);
   
   % Set the remaining axes properties
   set(axes3,'YColor',[0.85 0.325 0.098]);
   
   % Create title
   title('Shock-Faulted Shaft Speeds and Clutch Pressure');
   
   % Create xlabel
   xlabel('Time (s)');
   
   % Uncomment the following line to 
   % preserve the X-limits of the axes
   % xlim(axes1,[0 0.2);
   
   % Set the remaining axes properties
   box(axes3,'on');
   grid(axes3,'on');
   set(axes3,'LineStyleOrderIndex',2);
   

   Warning: At time 0.026048, one or more assertions are triggered.
   A fault event has occurred The assertion comes from:
   Block path: ShaftWithTorsionalFlexibility/Faultable Damper
   Assert location: (location information is protected)
   

   

   At simulation time t = 0.026 s, the maximum number of shocks for the specified acceleration is reached. A warning is reported and the damping coefficient increases and slows the speed of both shafts.