Objectives Upon successful completion of this lesson, you will be able to:
I Understand the definition as well as the description of contacts.
I Use expressions to prescribe the magnitude of forces and motors.
I Analyze some causes of the incorrect solution or a contact solution failure.
I Use alternative numerical integrators.
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Contact Forces The objective of this lesson is to get familiar with the definition of solid body contacts, as well as understanding their limitations and use in SolidWorks Motion. The expressions utilizing various mathematical functions prescribing displacements and other study features will be introduced. Contact force as the latch closes and the force needed to close the latch will be extracted; accuracy of the contact force will be discussed as well.
Case Study:
Latching Assembly
In this assembly, an over-center latch is used to hold the Carriage part against a spring.
Problem Description
For the latching mechanism, determine:
I The contact force generated on the Spring Lever and Keeper as the latch closes.
I The forced needed to close the latch.
1 Open an assembly file.
Open Full Latch Mechanism. from Lesson04\Case Studies folder.
2 Examine the assembly.
The assembly has several mates however not all components have enough mates to allow the parts to move based on the mechanical motion of the final assembly.
The Carriage part is concentric to the center spindle, but can rotate through the side spindles.
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Three components of the latch, knurled_pin, spring and Series Lever are not restrained laterally.
3 Verify the units.
Verify that the document units are set to MMGS. 4 Create a new Motion study.
Name the study Tessellated geometry and set Type of Study to Motion Analysis.
5 Center the latch.
Add a Coincident mate between the Front planes of the Base and Series Lever.
This is a local mate. If you select the Model tab in the MotionManager, the Series Lever can still move.
We could add another mate to restrict the motion of the J_Spring. In the next few steps we will practice an alternative approach to constrain the motion of free parts.
Fixing Motion with Motors
An alternative approach to additional mates is the addition of a motor.
The advantage of such an approach may not be immediately apparent, but we will use it in this motion model.
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One reason for using a motor instead of a mate is that it does not introduce additional constraints to the motion model and helps to reduce the number of the redundant constraints. Redundant constraints will be discussed in Lesson 8: Redundancies.
6 Restrict the linear translation of the latch.
Create a Linear Motor.
Attach the motor to the face shown.
For Motion, select Distance and set it to 0mm. Set the Start Time to 0s and the Duration to 3.5s.
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7 Restrict rotation of the Carriage. Create a Rotary Motor.
Attach the motor to the edge shown.
For Motion, select Distance and set it to 0deg.
Set the Start Time to 0s and the Duration to 3.5s. The simulation will run for 3.5 seconds, so this motor will stop the Carriage from rotating during the entire simulation.
Motor Input and Force Input Types
SolidWorks Motion allows you to set the motor input to a number of different types. We have used Constant Speed, Distance and Data Points in most of our lessons thus far, but Expression, Oscillating and Segments are also available.
Expression lets us to define a profile that dictates the motion of the motor with a help of various mathematical functions.
Functional Expressions
You can use functional expressions to define magnitudes of input used in:
I Motors
I Forces
Functions can depend on time or other system states, such as
displacement, velocity, and reaction forces and may be composed of any valid combination of simple constants, operators, parameters, and available supported solver functions such as Step (STEP) and
Harmonic (SHF), for example. For a detailed list of functions and its syntax, please refer to the on-line help.
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The following is a list of accepted functions:
Function Definition
ABS Absolute value of (a) ACOS Arc cosine of (a)
AINT Nearest integer whose magnitude is not larger than (a) ANINT Nearest whole number to (a)
ASIN Arc sine of (a) ATAN Arc tangent of (a) ATAN2 Arc tangent of (a1, a2) COS Cosine of (a)
COSH Hyperbolic cosine of (a) DIM Positive difference of a1 and a2 EXP e raised to the power of (a) LOG Natural logarithm of (a) LOG10 Log to base 10 of (a) MAX Maximum of a1 and a2 MIN Minimum of a1 and a2
MOD Remainder when a1 is divided by a2 SIGN Transfer sign of a2 to magnitude of a1
SIN Sine of (a)
SINH Hyperbolic sine of (a) SQRT Square root of a1 STEP Smoothed step function
TAN Tangent of (a)
TANH Hyperbolic tangent of (a)
DTOR Degrees to radians conversion factor
PI Ratio of circumference to diameter of a circle RTOD Radians to degrees conversion factor
TIME Current simulation time IF Defines a function expression
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Force Functions There are five types of force functions that can be used to define the force:
I Constant: Sets a constant value.
I Step: Defines a step by an Initial Value, Start Time, Final Value, Final Time.
I Harmonic: Defines the value by Amplitude, Frequency, Average and Phase Shift.
I Segments: Defines the value by combining segments of the most commonly used functions such as linear, polynomial, half-sine and others.
I Data Points: Takes the values from a table of data points and interpolates a spline between the data points.
I Expression: Defines the value using a formula.
STEP Function A STEP function prescribes the given quantity (displacement, velocity, acceleration or force magnitude, for example) between two values with a smooth transition. Before and after the transition, the displacement, velocity or acceleration magnitude is constant.
For example, consider the illustration at the right where:
d0 = Initial value of displacement d1 = Final value of displacement t0 = Start step time
t1 = Final step time
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8 Create a rotary motor to drive the latch.
Hide the J_Spring.
In the Motion Manager, click Motor . Under Motor Type, select Rotary Motor.
Under either the Motor Location or Components/Direction fields, select Axis1 of the Series Lever as indicated in the figure. This motor will simulate the action of the hand operating the Series Lever to open and close the latch.
Under Motor Type, in the Motion field, select Expression. The command brings up the Function Builder window.
9 Build motor expression.
In the Function Builder, make sure that the Expression button is selected.
Select Mathematical Functions for the input type and double-click STEP(x,x0,h0,x1,h1) to insert the step function.
Modify the functional expression to read STEP(TIME,0,0D,1,90D). Note The TIME variable can be typed in or inserted by chancing the input
type to Variables and Constants and double-clicking TIME. Complete the expression to its final form:
STEP(TIME,0,0D,1,90D)+STEP(TIME,1.5,0D,3,-90D)
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Note The Function Builder graph windows will update the plots for displacement, velocity, acceleration and jerk automatically.
Click OK to complete the definition of the expression and close the Function Builder.
Click OK to complete the definition of the Motor feature.
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Note The above expression is a
combination of two step functions.
The first rotates the SeriesLever component by 90 degrees between 0 and 1 second and then it keeps the vertical position for 0.5 seconds until the time 1.5 seconds.
At time 1.5 seconds, we add the second step function which changes the rotational displacement back to zero between the 1.5 and 3 seconds.
Both functions as well as the
combination (the final motion of the SeriesLever) are shown in the figures.
10 Define Spring and Damper.
We now need to define a spring with a damper which generates tension to keep the latch pulled tight.
In the Motion Manager, click Spring . Choose a Linear Spring with a spring constant of 10 N/mm, and create the spring at the locations shown in the figure below.
Keep the Free Length at its default value.
Turn on the linear Damper and specify a magnitude of 0.10 N/(mm/s).
Notice that the free length of the spring is automatically populated into the Free Length field.
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Contact: Solid Bodies
Contacts are defined between two or more bodies or two curves (a contact pair). During the definition of the contact between solid bodies, whatever feature you pick on the parts, the corresponding body will be selected (and used for the contact analysis). During the solve, the software calculates at each frame the bounding boxes of the parts interfere. As soon as it is the case, a finer interference calculation is done between the two bodies and from the center of gravity of the interference volume, an impact force is computed and applied on both bodies.
This procedure is schematically shown in the figure below.
To understand the contact treatment in the SolidWorks Motion, we first need to reiterate the very original assumption of this modulus: all parts participating in the motion simulation are rigid. Contact conditions are used to simulate impact of the two or more colliding parts (which are not rigid in real life). Nearly without exceptions all impacts feature high relative velocity, which result in elasto-plastic deformations with severe localized strains and significant changes in the local geometry (geometry of the contact region). Approximations are therefore necessary.
SolidWorks Motion allows for the specification of the contact parameters using two distinct approaches: Impact properties (Impact force model) and Restitution coefficient (Poisson model).
1. 2. 3. 4.
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Poisson Model (Restitution Coefficient)
Restitution coefficient (Poisson model): Poisson model is based on the utilization of the restitution coefficient e is defined in the following relationship:
Where v1 and v2 are the velocities of the spheres before the impact and v1’and v2’ are the velocities after the impact. The bounding values of this coefficient are (0;1), where 1 indicates perfectly elastic impact where no
energy is lost, while 0 indicates perfectly plastic impact where the parts adhere after the impact and maximum possible energy is lost.
The restitution coefficient is geometry dependent and spheres in the above illustration are used for the demonstration purposes only.
Poisson model does not require specification of the damping coefficient (as is the case of the Impact force model, discussed below) and does account correctly for the energy dissipation. The use of this model is therefore recommended if energy dissipation is of the great importance in the simulation. Also, determination of the Poisson model parameters, restitution coefficient e, is more straight forward than in the case of the Impact force model; in many instances, the restitution coefficient can be measured using the standardized methods (see ASTM F1887-98 Standard Test Method for Measuring the Coefficient of Restitution (COR) of Baseballs and Softballs, for example) or found in various tables. This model is not suitable for the persistent impacts (impacts, where contact is developed for a prolonged periods of time); Impact force model should be used instead in these situations.
Impact Force Model
Impact properties (Impact force model): Impact properties in
SolidWorks Simulation allow for the calculation of the contact force using the following expression:
where k represent the stiffness of the contact, e is the elastic force exponent, and c is the damping coefficient (cmax) is then the maximum possible damping coefficient). As in the case of the restitution
coefficient, these parameters are both material and geometry dependent and can not be apparently found in the material tables. The following sections describe the Impact force model parameters in more detail.
v′2–v′1 = e v( 1–v2)
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Stiffness k To correctly determine the stiffness, possible solution is to model the configuration of the contact in SolidWorks Simulation finite element software, apply any force in the direction of the impact and solve for the displacements. Stiffness can then be readily obtained from the force magnitude and the resulting displacements. A figure below
demonstrates the impact configuration of two spheres meshed in SolidWorks Simulation software.
In many instances, the elastic solution can be found in various engineering publications. It is apparent that the computation of the contact stiffness k can be a daunting task and simplifications have to be introduced.
Exponent e This parameter controls the degree on nonlinearity in the elastic force;
e=1 then constitutes a linear elastic force.
Damping
Coefficient c and Penetration d
When two objects collide and deform, portion of the kinetic energy is consumed on the plastic deformation, heat and similar phenomena.
Approximately, this value can be obtained from the results of the nonlinear dynamic solution (of the above problem of the two spheres, for example) with advanced material models. Utilizing this procedure is, however, unrealistic and simplifications are necessary. It is assumed that the damping coefficient (a measure of the capacity to dissipate energy) increases from zero (at the beginning of the impact) to its maximum value cmax, when certain specified deformation is achieved;
we call this deformation value penetration d. For any deformation larger than the penetration d, the damping coefficient is constant and equal to cmax. A typical value for the maximum damping coefficient cmax is 0.1% - 1% of the contact stiffness k.
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Closing Remarks It is now apparent that the determination of the above parameters is non-trivial, time consuming and significant simplifications have to be introduced. A corollary of the foregoing is that the solution of the collision characteristics (impact forces, accelerations of the impacting regions and etc.) can only be approximate. Their accurate magnitudes can only be determined by more advanced computational methods, such as nonlinear dynamic solutions using SolidWorks Simulation Premium package, which can be computationally very demanding.
It is important to clarify that for the purpose of this section, impact force and the acceleration of the impacting regions terms represent the contact quantities at the onset of the contact where severe deceleration forces are encountered, i.e. impact or collision. The duration of these collisions is typically very short. After a certain time, when the impacting or colliding components are touching and the dynamics aspects of the solution is less important, contact forces are accurate and can be extracted from SolidWorks Motion. This is demonstrated at the end of this lesson.
In conclusion, if an important objective of the motion simulation is to obtain the impact quantities (impact force, impact region acceleration etc.), time needs to be invested in the determination of the above parameters, or more advanced analysis type must be carried out.
Typically, users are not interested in the accurate impact region results but rather they need to determine the kinematics or dynamics of large systems. Approximate values are then used for the contact
characteristics and accurate solution of the system kinematics and dynamics can be carried out efficiently.
To assist users with the impact characteristics, SolidWorks Motion contact library features approximate values for some contact material configurations (note that the geometry is not clearly defined). You may use these values as a base line if the material composition of your parts participating in the contact is similar. However, if more accurate impact solution is needed, correct impact parameters have to be determined.
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11 Define contact between latch and latch keeper. In the Motion Manager, click Contact .
Under Contact Type select Solid Bodies.
Select the latch arm (J_Spring), the latch lever (Lever), and the latch keeper (keeper).
Select Specify Material to allow us to define the impact parameters.
Select Steel (Dry) from the list for both materials. Keep the Friction on at its default values.
Here we are trying to make the impact more realistic by simulating two hard metals colliding. As discussed above, the elastic properties of the contact are only approximate. More realistic values would be required for a contact region solution (contact reliable force and acceleration of the contact region).
Click OK. 12 Define gravity.
Define gravity in the negative X direction.
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13 Motion analysis Properties.
Verify that Frames per second is set at the default value of 25.
In the Motion Study Properties, set the 3D Contact Resolution slider all the way to the left, to its lowest resolution setting.
Note The contact resolution parameters are explained in the discussion below.
14 Run the simulation for 3.5 seconds.
Notice that the solution was achieved, but is incorrect. The Spring passes through the other components without developing any of the specified contacts. There can be a few reasons for such behavior:
I The time step of the integrator (solver) is too large, in which case the contact is not even detected.
I The accuracy setting is too high or too low.
I The geometrical description of contact is insufficient.
In the present case it is the last one causing the incorrect solution.
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Geometrical Description of Contacts
SolidWorks Simulation treats the geometries of the contacting solid bodies in two distinct ways:
I Tessellated geometry
The surfaces of the contacting bodies are meshed with the triangular elements to simplify the description. The density of the mesh, i.e. the contact geometry resolution, is controlled with the 3D Contact
Resolution parameter in the study properties. Because this description is very efficient, yet typically sufficient to obtain accurate solutions, tessellated geometry is the default choice. Very coarse description may result in inaccurate solution or even failing to develop the contacts.
This is also the cause of the solution failure in the present case.
I Precise geometry
If the tessellated geometry description if not sufficient (solution is not sufficient or can not be obtained), Use Precise Contact option can be used instead. Exact description of the bodies’ surfaces is then used.
While this is the most accurate description, it can be computationally expensive and should be used with caution. Use this option if your contacting bodies feature complex or point like geometries.
Examples of the tessellated geometries at two resolution levels as well as the precise geometry are shown below.
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15 Adjust the Study Properties.
Improve the accuracy of the tessellated data.
In the MotionManager click Motion Study Properties .
Move the 3D Contact Resolution slider to the right to a value of 94.
Click OK.
16 Run the simulation.
Notice that the computation is noticeably slower.
The simulation will fail and display the following message:
The solver failed to converge. Possible causes are:
1. The solver is failing to achieve the specified accuracy.
Relax the Accuracy setting in Motion Analysis Properties.
2. If parts in the model are moving quickly, evaluate the Jacobian more often.
3. The mechanism may be getting locked. Start the
simulation with a different initial configuration or change you motors to get valid motion.
4. If the failure is happening right at the beginning of the simulation, use a smaller Initial Integrator Step Size.
5. Try to use a stiff solver like ‘WSTIFF’.
6. Try to avoid sharp discontinuities in the model like
sudden motion changes, force changes or mate activation/
deactivation.
7. You may have motors with very high speeds. Try to
7. You may have motors with very high speeds. Try to