Double-sided, spring-loaded translational detent
The Translational Detent block represents a double-sided, spring-loaded translational detent with a ball and conical notch.
The detent slider slides horizontally over the detent case. These two parts develop a horizontal shear force between them. The inside of the slider is the conical notch. The detent case contains a vertical spring. The detent ball lies between the spring and the conical notch. With the block, you can model ball and angled notch detents with geometric and spring characteristics, peak force and notch width, or a lookup table. The model also includes viscous damping and kinetic friction between the slider and case. You can set the friction to zero.
R and C are translational conserving ports associated with the slider and case, respectively.
The dialog box has one active area, Parameters, with two tabs.
Select how to specify the detent characteristics. The default is By peak force and notch width.
By peak force and notch width — Specify detent characteristics by the peak shear force and the notch width.
By lookup table — Define the detent characteristics by one-dimensional table lookup based on the relative displacement between the slider and case. If you select this option, the panel changes from its default option.
By geometry — Define the detent characteristics by ball-notch geometry and dynamics. If you select this option, the panel changes from its default option.
The relative displacement of the slider and case when simulation starts. The default is 0.
From the drop-down list, choose units. The default is millimeters (mm).
Specify the viscous friction coefficient for the ball-notch contact. Must be greater than or equal to 0. The default is 0.1.
From the drop-down list, choose units. The default is newtons/(meters/second) (N/(m/s)).
Specify the kinetic friction coefficient for the ball-notch contact. Must be greater than or equal to 0. The default is 0.01.
The kinetic friction is this ratio multiplied by the peak shear force.
Specify the relative velocity required for peak kinetic friction in the detent. Must be greater than 0. The default is 0.05.
From the drop-down list, choose units. The default is meters/second (m/s).
The geometry of the ball-notch detent is shown in the following figure. As the conical slider slides horizontally over the case, the relative displacement x = xR – xC causes a horizontal shear force F to develop.
|α||Notch half angle|
Depending on your choice of parameterization, the shear force model is defined by geometric and spring parameters, by the peak force and notch width, or by a lookup table specifying relative displacement versus force.
The geometric and spring parameterization uses four regions to define the shear force. The following figure displays these regions.
Because the ball is spherical and the notch is symmetric, the horizontal force versus displacement function is symmetric about the origin. (See Peak Force and Notch Width.)
|Region||Ball Position and Contact Angle||Shear Force|
|1||Ball is outside conical notch. Contact angle is vertical.||Viscous damping and kinetic friction only. No spring contribution.|
|2||Ball is entering notch, in contact with notch corner. Contact angle rotates from vertical.||Spring, viscous damping, and kinetic friction contributions. Peaks at transition from region 2 to region 3.|
|3||Ball slides along face of notch. Contact angle is constant.||Force decreases as spring extends, but does not go to zero (spring preload force).|
|4||Ball moves from one face to the other. Contact angle switches direction.||Force switches direction. Shear reversal region width controls how smooth this switch is.|
If you choose the peak force and notch width parameterization, the block ensures that the force-relative displacement curve provides a continuous force and force derivative over the detent region. The peak forces are halfway between the detent center and detent edge, as shown in the following figure.
With the lookup table parameterization, you can create an arbitrary function relating shear force to relative displacement. If you create such a function, consider the following best practices.
If you want to ensure that the detent conserves energy, the total integral of the force-relative displacement curve (area under the curve) must be zero.
To stabilize simulation of the detent, avoid discontinuities in the force-relative displacement function. The most important requirement is to have a shear reversal region of nonzero width, analogous to region 4 in the geometric parameterization.
The model does not account for inertia. Add mass terms externally to the R and C ports as required.
If you use the peak force-notch width or the lookup table parameterization, the kinetic friction is independent of the detent normal force.