Ply Placing Operation for Automated Fiber Placement
Ply placing for Automated Fiber Placement (AFP) is a labor-independent task (see
Labor-dependent and Labor-independent Tasks). The cost model assumes that a single operator oversees the automated operation. There is one occurrence of this operation for each ply of the current part.
Layup Time =
(Ply Area / Ply Complexity Layup Rate) +
(Course Changes * Rapid Traverse Time)
Layup time depends on the following:
• Ply area: specified by the geometric property Surface Area. This is the area of one side of the ply.
• Ply complexity layup rate: this is the layup rate (in area per unit time), adjusted for ply complexity. See formula.
• Course changes: this is the number of times the delivery head must break contact with the tool and position itself to start a new course. See formula.
• Rapid traverse time: this is the average time between finishing one course and starting the next. It is specified by the cost model variable averageAFPRapidTraverseTime (5 seconds in starting point VPEs—this assumes unidirectional material, requiring the delivery head to change direction and rapidly traverse the width of the ply between courses).
Course Changes = roundup(Ply Width / (Spool Width * Number of Spools))
This is the number of times the delivery head must break contact with the tool and position itself to start a new course. It depends on the following:
• Ply width: specified by the geometric property Width.
• Spool width: specified by the material property Material Width.
• Number of spools: this is the number of active spools. By default this is determined according to the formula below. Users can override the default with the setup option
Number of Active Spools.
Number of Spools = min(Machine Total Number of Spools,
rounddown(Machine Max Bandwidth / Max Material Width))
By default, the number of active spools is the maximum number of spools that the machine can use, given all the following constraints:
• Number of spools is no greater than the total number of spools that the machine can accommodate.
• Total width of all spools is no greater than the machine’s maximum bandwidth.
• Each spool’s width is the material width for that ply (among all the part’s plies) that has the largest material width.
So the default number of active spools depends on the following:
• Machine total number of spools: specified by the machine property Total Number of Spools. This is the maximum number of spools that can be active.
• Machine max bandwidth: this is the maximum total width of all active spools, specified by the machine property Max Bandwidth.
• Max material width: this is the material width of that ply (among all the part’s plies) that has the largest value for the material property Material Width.
Users can override the default with the setup option
Number of Active Spools.
Ply Complexity Layup Rate =
Linear Complexity Ply Layup Rate * Material Width * Number of Spools
The complexity-adjusted area-based layup rate (in area per unit time) is the product of the following:
• Linear complexity ply layup rate: the complexity-adjusted linear ply layup rate (in distance per unit time). See formula.
• Material width: width of one spool. This is specified by the material property Material Width, for the current ply’s material.
• Number of spools: this is the number of active spools. By default this is determined according to the formula above. Users can override the default with the setup option
Number of Active Spools.
Linear Complexity Ply Layup Rate =
Weighted Flexibility Rate +
Weighted Cutout Rate +
Weighted Deformation Rate +
Weighted Aspect Rate +
This is the complexity-adjusted, linear layup rate in distance per unit time, adjusted for four ply characteristics that affect layup rate:
• Ply material flexibility: a ply made of less flexible materials requires a slower layup rate.
• Ply cutouts: a ply with lots of perimeter and/or interior cutouts requires a slower layup rate.
• Ply deformation: a highly deformed ply requires a slower layup rate.
• Ply aspect ratio: a ply with a smaller length-to-width aspect ratio requires a slower layup rate. (Note that length is the ply bounding box dimension that is aligned with the ply direction, the direction along which each course is laid. With a shorter course, the delivery head can’t achieve as high a speed as with a longer course.)
The adjusted value, linear complexity ply layup rate, is somewhere between the minimum and maximum rates, where the maximum rate (distance per unit time) is specified by the machine property Max Deposition Rate, and the minimum rate is assumed to be 1/6 the maximum rate, in starting point VPEs. Administrators can customize this fraction with the cost model variable minLayupRateFactorAFP (0.16 in starting point VPEs).
Linear complexity ply layup rate is a weighted sum of four different layup rates, each of which takes into account just one of the above ply characteristics (the weights add up to 1). That is, it is the sum of the following:
• Weighted flexibility rate (see formula)
• Weighted cutout rate (see formula)
• Weighted deformation rate (see formula)
• Weighted aspect rate (see formula)
You can generate a layup rate report by selecting Reports > SpreadSheet Reports... > Composites Report.
Weighted Flexibility Rate = Flexibility Weighting * Flexibility Rate
Weighted flexibility rate is the product of the following:
• Flexibility weighting: this reflects the relative importance of material flexibility to layup rate. It is a number between 0 and 1, specified by the cost model variable weightingAFPMaterialFlexibility (0.1 in starting point VPEs). Note that flexibility weighting, cutout weighting, deformation weighting, and aspect weighting must sum to 1.
• Flexibility rate: this is the layup rate, taking into account material flexibility.
Material flexibility is specified by the material property Deformation Average Angle (which is the average of Deformation Limit Angle and Deformation Warning Angle).
Flexibility rate is somewhere between the maximum rate (specified by the machine property Max Deposition Rate) and the minimum rate (1/6 the maximum rate, in starting point VPEs). If material flexibility is some fraction of the way from the easiest-to-handle flexibility to the hardest-to-handle flexibility (for available materials), then flexibility rate is that fraction of the way from the maximum rate to the minimum rate.
For example, if material flexibility is halfway between the easiest-to-handle flexibility and the hardest-to-handle flexibility, then flexibility rate is halfway between the maximum rate and the minimum rate.
Weighted Cutout Rate = Cutout Weighting * Cutout Rate
Weighted cutout rate is the product of the following:
• Cutout weighting: this reflects the relative importance of cutouts to layup rate. It is a number between 0 and 1, specified by the cost model variable weightingAFPPlyCutout (0.4 in starting point VPEs). Note that flexibility weighting, cutout weighting, deformation weighting, and aspect weighting must sum to 1.
• Cutout rate: this is the layup rate, taking into account ply cutouts.
The extent of cutouts is quantified by the cutout ratio, which is a ratio of geometric properties:
Cutout Ratio = Surface Area / Surface Area Filled
Surface Area Filled is the ply’s area plus the estimated area of interior and perimeter cutouts.
Cutout rate is somewhere between the maximum rate (specified by the machine property Max Deposition Rate) and the minimum rate (1/6 the maximum rate, in starting point VPEs). If cutout ratio is some fraction of the way from the easiest-to-handle ratio to the hardest-to-handle ratio, then cutout rate is that fraction of the way from the maximum rate to the minimum rate.
For example, if cutout ratio is halfway between the easiest-to-handle ratio and the hardest-to-handle ratio, then cutout rate is halfway between the maximum rate and the minimum rate.
Weighted Deformation Rate = Deformation Weighting * Deformation Rate
Weighted deformation rate is the product of the following:
• Deformation weighting: this reflects the relative importance of deformation to layup rate. It is a number between 0 and 1, specified by the cost model variable weightingAFPPlyDeformation (0.3 in starting point VPEs). Note that flexibility weighting, cutout weighting, deformation weighting, and aspect weighting must sum to 1.
• Deformation rate: this is the layup rate, taking into account ply deformation.
The degree of deformation is quantified as a level between 1 and 5 (the higher the level, the greater the deformation). The level is determined based on the geometric properties Average Curvature, Curvature Deviation, and Max Curvature, and is intended to reflect a number of aspects of deformation, including the following:
o Degree of curvature: large curvature is harder to handle than mild curvature.
o Uniformity of curvature: varying curvature is harder to handle than overall, uniform curvature.
o Localization of curvature: distributed curvature (with multiple local extrema) is harder to handle than localized curvature.
See
Ply Deformation Level for more information.
Deformation rate is somewhere between the maximum rate (specified by the machine property Max Deposition Rate) and the minimum rate (1/6 the maximum rate, in starting point VPEs). If deformation level is some fraction of the way from the easiest-to-handle level (1) to the hardest-to-handle level (5), then deformation rate is that fraction of the way from the maximum rate to the minimum rate.
For example, if deformation level is halfway between the easiest-to-handle level and the hardest-to-handle level, then deformation rate is halfway between the maximum rate and the minimum rate.
Weighted Aspect Rate = Aspect Weighting * Aspect Rate
Weighted aspect rate is the product of the following:
• Aspect weighting: this reflects the relative importance of aspect ratio to layup rate. It is a number between 0 and 1, specified by the cost model variable weightingAFPAngleVsAspect (0.2 in starting point VPEs). Note that flexibility weighting, cutout weighting, deformation weighting, and aspect weighting must sum to 1.
• Aspect rate: this is the layup rate, taking into account ply aspect ratio.
Aspect ratio, here, is ply Length divided by ply Width. Note that Length is the dimension of the ply bounding box that is aligned with the ply direction. The cost model defines three aspect-ratio levels:
o Level 1 (fastest): aspect ratio >= 1 1/3
o Level 2 (intermediate): ¾ < aspect ratio < 1 1/3
o Level 3 (slowest): aspect ratio <= ¾
Administrators can customize the level thresholds with the cost model variable approxSquareRatio (0.75 in starting point VPEs). The level thresholds are defined in terms of approxSquareRatio as follows:
o Level 1: aspect ratio >= 1 / approxSquareRatio
o Level 2: approxSquareRatio < aspect ratio < 1 / approxSquareRatio
o Level 3: aspect ratio <= approxSquareRatio
Aspect rate is somewhere between the maximum rate (specified by the machine property Max Deposition Rate) and the minimum rate (1/6 the maximum rate, in starting point VPEs). If aspect level is some fraction of the way from the fastest level (1) to the slowest level (3), then cutout rate is that fraction of the way from the maximum rate to the minimum rate.
For example, if aspect ratio level is halfway between the fastest level and the slowest level, then cutout rate is halfway between the maximum rate and the minimum rate.
Ply Material Cost =
(Ply Area / (Material Utilization / 100)) * Material Cost Per Unit Area
Material cost for a ply depends on the following:
• Ply area: specified by the geometric property Surface Area. This is the area of one side of the ply, before cutouts are removed.
• Material utilization: this is the percentage of ply material that is used in parts and is not wasted. It is specified by the material property Material Utilization.
• Material cost per unit area: unit cost of ply material, specified in square meters by the material property Material Cost Per Area. This is converted to cost per square millimeter for use in this formula.