Discontinuous

Backlash Block

Models mechanical backlash (play). Output only changes when input moves beyond the deadband width from the current output position.

Open Backlash in BlockWerk →

# Backlash Block

Description

Models mechanical backlash (play/speling). The output stays constant until the input moves more than half the deadband width away from the current output position. Used for modeling gears, linkages, and other mechanical systems with play.

Mathematical Model

if u > y_prev + D/2:  y = u - D/2
if u < y_prev - D/2:  y = u + D/2
otherwise:            y = y_prev

where u is the input, y the output, y_prev the previous output, and D the deadband width.

Parameters

deadbandWidth

Total width of the deadband (play). The output remains unchanged while the input is within ±(deadbandWidth/2) of the current output.

initialOutput

Initial output value at simulation start.

Remarks

Direction-dependent: Backlash output trajectory depends on whether the input is increasing or decreasing
Initial condition: The initialOutput parameter should match the physical system's rest position
Deadband symmetry: The deadband is centred around the current output; total play equals deadbandWidth
Cascading: Multiple backlash blocks in series model complex mechanical drivetrains
Numerical stability: Small deadband widths relative to signal amplitude may cause chattering