30.1.1. Contact Characteristic Page

This page defines characteristic values to contact between two geometry entities. Roller, Roller Sprocket, Multiplex Sprocket, Silent Sprocket, Guide, Group Guide Arc, and Lateral Guard. supported in RecurDyn are using this page.

Figure 30.3 Sprocket property page [Contact Characteristic page]

Contact Normal Force

The contact normal force is obtained by

\(\mathbf{f}_\mathrm{n} = \mathbf{k}\delta^\mathrm{m1}+\mathbf{c}\frac{\dot{\delta}}{\left| \dot{\delta} \right|}\left| \dot{\delta} \right|^\mathrm{m2}\delta^\mathrm{m3}\)

where, \(\mathbf{k}\) and \(\mathbf{c}\) are the stiffness and damping coefficients which are determined by an experimental method, respectively. \(\delta\) and \(\dot{\delta}\) are a penetration and time differentiation of the penetration, respectively. The exponents \(^\mathrm{m1}\) and \(^\mathrm{m2}\) generates a non-linear contact force and the exponent \(^\mathrm{m3}\) yields an indentation damping effect.

• Characteristic: Defines the contact properties such as the stiffness coefficient, damping coefficient, and friction coefficients. Also, these coefficients can be given as user-defined spline curves.

• Stiffness Coefficient: Specifies a stiffness coefficient for the contact normal force.

• Stiffness Spline: The spline shows the contact normal force for the penetration. For more information, click here.

• Damping Coefficient: Specifies a damping coefficient for the contact normal force.

• Damping Spline: The spline shows the contact normal force for the velocity of penetration. For more information, click here.

• Dynamic Friction Coefficient: Specifies a dynamic friction coefficient for the contact friction force. It has three options.

• Dynamic Friction Coefficient: The constant friction coefficient is applied.

• Friction Force Spline: The spline shows the fiction force for the relative velocity. It is recommended to use the spline that x and y values are defined as positive.

• Friction Coefficient Spline: The spline shows the friction coefficient for the relative velocity.

• More: Specifies some friction coefficients for the contact friction force.

• Stiffness and Damping Exponent: Generates a non-linear contact normal force.

• Indentation Exponent: Yields an indentation damping effect. When the penetration is very small, the contact force may be negative due to a negative damping force, which is not realistic. This situation can be overcome by using the indentation exponent greater than one.

• No. of Max Contact Point: Defines the number of max contact point for output. User can define this value from 0 to 1000. This value only affects Force Display and RPLT data about contact points.

• Force Display: Graphically displays the all contact force vectors (the sum of the normal and tangential contact force) at each contact point up to the No. of Max Contact Point as shown in the below figure. The contact force display vectors about internal 2D contact logic is graphically showed on center plane of base entities (Sprocket, Guide).

  

  Figure 30.4 Example of Contact Force Display

• Contact Output File: When this function is checked, RecurDyn creates the contact output file for contact information between sprocket and chain links as follows. (Please refer to this option only output the results for chain links, they checked at Output tab in assembly information). The name of output file is ‘ModelName_bodyName.out’.

Table 30.1 Contact Output File Contents

Col.	Variables	Descriptions
1	Time (sec)	Simulation Time
2	amount of contact point	Total number of calculated contact points
3	Pos_TX of Sprocket CM	Position X of sprocket’s center marker
4	Pos_TY of Sprocket CM	Position Y of sprocket’s center marker
5	Pos_TZ of Sprocket CM	Position Z of sprocket’s center marker
6	Pos_PSI of Sprocket CM	Orientation Psi of sprocket’s center marker
7	Pos_THETA of Sprocket CM	Orientation Theta of sprocket’s center marker
8	Pos_PHI of Sprocket CM	Orientation Phi of sprocket’s center marker
9		The index of contact points
10	Chain Link ID	Contacted chain link’s ID
11	Pos_TX of Chain Link CM	Position X of contacted chain link’s center marker
12	Pos_TY of Chain Link CM	Position Y of contacted chain link’s center marker
13	Pos_TZ of Chain Link CM	Position Z of contacted chain link’s center marker
14	Pos_PSI of Chain Link CM	Orientation Psi of contacted chain link’s center marker
15	Pos_THETA of Chain Link CM	Orientation Theta of contacted chain link’s center marker
16	Pos_PHI of Chain Link CM	Orientation Phi of contacted chain link’s center marker
17	Global contact position	Global contact position
18	Contact position based on Sprocket	Contact position based on Sprocket
19	Contact position base on Chain Link	Contact position base on Chain Link
20	Contact force based on Sprocket	Contact force based on Sprocket
21	Friction force based on Sprocket	Friction force based on Sprocket
22	Contact force based on Chain Link	Contact force based on Chain Link
23	Friction force based on Chain Link	Friction force based on Chain Link

30.1.1.1. Friction

• Dynamic Friction Coefficient: Specifies a dynamic friction coefficient for the contact friction force.

  

  Figure 30.5 Relationship between relative velocity and friction coefficient

• More: Specifies some friction coefficients for the contact friction force.

  

  Figure 30.6 Friction Definition dialog box

• Static Threshold Velocity: If the relative velocity between a contact pair is less than this value, the friction coefficient is defined as following.

  \(\mu =\text{step5}(\nu ,\,\,-{{\nu }_{s}},\,\,{{\mu }_{s}},\,\,{{\nu }_{s}},\,\,-{{\mu }_{s}}\,)\)

• Dynamic Threshold Velocity: If the relative velocity between a contact pair is greater than this value, the friction coefficient is same as the specified dynamic friction coefficient. If the relative velocity between a contact pair is greater than “Static Threshold Velocity” and less than this value, the friction coefficient is defined as following.

  \(\mu =\text{step5}\,(\nu ,\,\,{{\nu }_{s}},\,\,-{{\mu }_{s}},\,\,{{\nu }_{d}},\,\,-{{\mu }_{d}}\,)\)

• Static Friction Coefficient: Specifies a static friction coefficient.

Figure 30.7 Relationship between relative velocity and friction coefficient

The friction force of contact elements is determined by the following equations.

\({{f}_{f}}=-\,\text{sign}\,(v)\,\,\left| \mu (v) \right|\,\,\left| {{f}_{n}} \right|\)

where, \({f}_{n}\), \({\mu }_{s}\) and \({f}_{max}\) are the contact normal force, the friction coefficient and the maximum friction force, respectively. The friction coefficient of \({f}_{f}\) is determined by a relative and tangential velocity on the contact point as shown in Figure 30.7.