Reconfigurable data driven virtual machine tool: Geometric error modeling and evaluation

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CIRPJ-311; No. of Pages 11 CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx

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Reconfigurable data driven virtual machine tool: Geometric error modeling and evaluation Ronnie R. Fesperman a,*, Shawn P. Moylan b, Gregory W. Vogl b, M. Alkan Donmez b a b

C.R. Onsrud Inc., 120 Technology Drive, Troutman, NC 28166, USA Engineering Laboratory, National Institute of Standards and Technology (NIST), 100 Bureau Drive, Gaithersburg, MD 20899-8220, USA1

A R T I C L E I N F O

A B S T R A C T

Article history: Available online xxx

Standards communities are developing robust machining and instrumented performance tests to evaluate the accuracy of 5-axis machining centers through the direct and indirect measurement of errors affecting the simultaneous motion of all five axes. The combined effect of the numerous geometric errors and servo errors complicates diagnostic analysis of the measurement results and estimation of the individual errors. To better understand the effect of the individual errors on the measurement results, we developed a reconfigurable five-axis data driven virtual machine tool (DDVMT) error simulator. The DDVMT is a generalized model that incorporates machine tool information models, geometric error models, controller models, and (standardized) machine tool metrology test methods and analyses into one modeling scheme. This paper describes the data driven virtual machine tool and demonstrates its ability to simulate the effects of geometric errors on multi-axis performance tests. ß 2015 CIRP.

Keywords: Five-axis machine tool Data driven Virtual machine tool Information modeling Geometric error modeling Standards

Introduction Five-axis machine tools2 provide manufacturers with the capability to efficiently manufacture complex parts. With two rotary and three linear axes, the orientation of the cutting tool can be optimally adjusted with respect to the workpiece. Thus, complex parts and surfaces can be efficiently manufactured with minimal setups and fixtures. Five-axis machine tools have many errors that affect the realized tool path and thus workpiece geometry. These errors can be categorized as thermal errors, errors due to static and dynamic machine compliance, controller errors such as servo mismatch, and geometric errors. Each of these categories can have many contributing errors. As an example, five-axis machine tools can have at least 41 geometric errors, including offsets in the position of the axis average line of rotary axes, errors in the average relative

* Corresponding author. Tel.: +1 +704 508 7000. E-mail address: [email protected] (R.R. Fesperman). 1 Official contribution of the National Institute of Standards and Technology; not subject to copyright in the United States. 2 Disclaimer: Certain commercial equipment, instruments, or materials, some of which are either registered or trademarked, are identified in this paper in order to adequately specify certain procedures In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

alignment of axis motions, and angular and linear deviations in the motion of each axis. Machine tool errors vary between different machine configurations, manufacturers, models, and even machines of the same model. Furthermore, errors may change over time due to wear, crashes, and mishandling. In an agile environment, knowledge of machine tool errors is essential for estimating machine capabilities, error compensation, reducing scrap and rework, and ensuring first part correct manufacturing. National and international standards [1–3] provide procedures for the direct measurement of each individual error. However, application of these procedures to characterize all the errors of 5-axis machine tools can be challenging and time consuming. Periodic checks of machines to ensure optimum performance can benefit manufacturers, but the machine downtime necessary to directly measure the errors can be cost prohibitive. To mitigate this problem, users are employing test procedures designed to measure the simultaneous effects of many errors [4–6] to quickly gage the overall performance of their machines. Selecting the appropriate combination of axis motions and instruments necessary to determine the performance of a machine is challenging. Standards committees have recognized this challenge and are developing standard test methods for evaluating the performance of 5-axis machining centers through direct and indirect measurements of toolpath errors during the simultaneous motion of multiple axes [7,8]. However, the combined effect of errors of multiple axes complicates the diagnostic analysis of the

http://dx.doi.org/10.1016/j.cirpj.2015.03.001 1755-5817/ß 2015 CIRP.

Please cite this article in press as: Fesperman, R.R., et al., Reconfigurable data driven virtual machine tool: Geometric error modeling and evaluation. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.001

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measured data and the estimation of the individual errors. To better understand the effect of the individual geometric and servo control errors on the measurement results for various machines, we developed a data driven virtual machine tool (DDVMT) error simulator [9]. This paper describes the methodology for the DDVMT. A brief survey of machine tool error modeling is provided in second section. Machine tool standards and machine tool information models are briefly discussed in third section. A detailed description of the data driven modeling approach applied to geometric error modeling is provided in fourth section. Core features and modeling modules of the DDVMT are described in fifth section. Results of multi-axis simulations and measurements are provided in sixth section. Discussion of results and closing remarks are provided in last two sections. Generalized machine tool error modeling Machine tool error modeling is not a new concept. Many models have been developed to investigate the effects of machine tools’ geometric errors, static and dynamic compliance, thermal behavior, and servo characteristics on workpiece geometry [10–13]. These models have also been used for the evaluation of test methods, for the evaluation of machine configurations, and for tool path error compensation [12–18]. Furthermore, information models [19] have been developed to facilitate the collection, archiving, use, and exchange of unambiguous machine tool data. Machine tool error modeling is challenging due to the large variety in machine tool classes, configurations, accuracy levels, error sources, and applications. A recent publication suggests that machine tool error modeling is type and topology dependent and that no generic approach for modeling all machine tools exists [16]. We believe that a modular, data driven, modeling approach combining machine tool information models with existing error modeling schemes (e.g., geometric error modeling using homogeneous transformation matrices) is a significant step toward a robust generalized error modeling method. The generalized DDVMT presented in this paper applies information defined in machine tool information models to build error models for a variety of machine configurations using generic, modular, models for geometric errors and servo errors. We believe this is the first demonstration of combining the two model types into one generalized modeling method. The methodology can be extended to include (existing) models for other machine tool errors, such as compliance and thermal errors. Machine tool standards and information models Machine tool standards provide a common infrastructure that improves communication, efficiency, innovation, and interoperability through the standardization of terminology, measurement methods, analyses, and data formats [1,2,7,8,19,20]. Modeling platforms that conform to machine tool standards ensure compatibility between users, machines, and software and minimize modeling errors due to misinterpretation. The DDVMT is designed to be fully compatible with these standards by following their protocols, such as the identification [20] and orientation of coordinate systems [19], the designation for the configuration of machine axes [1,7], the location of measurement functional points [2,19], and the formats for both machine [19] and measurement data [21]. Machine tool information data files [19] are the core feature of the DDVMT, enabling the ability to automatically model multiple configurations and multiple machines. These files are generated following ASME B5.59-2, which defines electronic data formats for properties of machine tools, including machine tool performance

data. Each file contains many data elements (see Example A.1 in Appendix) that describe the machine properties in a systematic structure. Examples of the types of elements defined in [19] and used by the DDVMT include the machine’s identification (), configuration (), work zone (), axis properties (), overall machine performance (), and detailed error data (). Example 1 demonstrates the format (elements and sub-elements) used for representing the mean unidirectional positional deviation of the X-axis, eXX, for a positive approach direction. Example 1. XML sample describing the positioning errors of the X-axis, eXX.

element for a machine tool. Many elements have been removed for simplicity. --> X X0 Y0 Z0 -200 X 0.00 -10.00 -20.00. . . POSITIVE -0.029 -0.027 -0.026 . . . The data defined in the information model is transferred to the DDVMT using the eXtensible Markup Language (XML) [22] where the pertinent data needed for a simulation is loaded into the generalized models. The data is expressed using a standard set of units, specified by ASME B5.59 Parts 1 and 2, to minimize errors in data exchange and to realize a fully generalized virtual machine tool. Any machine tool properly described in its information file can be modeled within seconds using the platform described here. Data driven geometric error modeling Geometric error modeling of a machine tool is normally achieved by building a kinematic model of the machine using homogeneous transformation matrices (HTMs) [13] that describe the rigid body kinematics of the machine tool as a function of axis positions and geometric errors. The model yields the errors in the position and orientation of the tool relative to the workpiece for each tool position of a machining or measurement process. Kinematic models are generated by first dividing the structural loop of the machine tool into two series of machine elements (e.g., base b, positioning axes A, B, C, X, Y, and Z, spindle (C), workpiece w, and tool t) that represent the serial kinematic paths from the machine base to the workpiece and the path from the base to the tool. Coordinate frames are then attached to each machine element

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(see Fig. 1) and HTMs are used to describe the orientation and position of each coordinate frame relative to the preceding coordinate frame in the serial chain. Multiplying the series of HTMs for each kinematic chain results in two HTMs that describe the orientation and position of the tool, bt T, and workpiece, bw T, coordinate frames with respect to the base coordinate frame. A transformation matrix, w t T, describing the position and orientation of the tool coordinate frame with respect to the workpiece coordinate frame can then be expressed as: w t T

¼ ðbw T 1 Þðbt TÞ

(1)

w t T is used to calculate the error in the position of the tool/ workpiece interface (functional point) with respect to the workpiece coordinate frame, we, or with respect to the tool coordinate frame, te. w

e ¼ ½ w eX

t

t

e¼

eX

w

t

w

eY

eY

t

eZ

T t ~ w~ 0  ¼ ðw t TÞð f pa Þ  f pn

eZ 0

T

¼



w 1 t T



w~ f pn



 tf ~ pa

(2) (3)

pa and wf ~ pn are vectors that describe the actual position of where tf ~ the functional point with respect to the tool coordinate frame and the nominal position of the functional point with respect to the workpiece coordinate frame, respectively. If necessary, final orientation errors between the tool and the workpiece may also be calculated using Eq. (1). The need for we or te may vary based on the type of simulation being performed (e.g., metrology versus manufacturing) and the location (tool or workpiece chain) of the sensing element of the metrology instrument. Many axis configurations are possible for 5-axis machine tools [14]. The kinematic model of a machine tool is generally manually constructed, which is a laborious and error-prone process. This challenge can be eliminated with a generalized data-driven modeling approach that uses standardized machine tool information models [19], techniques for automatically constructing the kinematic chains, generic methods for identifying the location of the coordinate frames, generic HTMs, and error data based on standardized measurement techniques [1–3] and formats [21]. Automatic matrix construction of kinematic chains Standardized labeling of machine axes and standardized designations for the configuration (topology) of machine tools

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make automatic matrix construction of the kinematic model possible. This is realized by using the information represented by the configuration designations to automatically order the HTMs for multiplication. As an example, consider the configuration designation for the vertical 5-axis machine tool shown in Fig. 1. Following ISO 10791-6 [7] and ISO 841 [20], the machine designation that serially connects the motion axes of the machine from the workpiece side to the tool side is [wC0 A0 bXYZ(C)t], where w represents the workpiece, C represents the C-axis, A represents the A-axis, b represents the bed or base of the machine, X represents the X-axis, Y represents the Y-axis, Z represents the Z-axis, (C) represents the spindle without numerical control for angular positioning,  t represents the tool, and  0 is used to indicate a workpiece movement by the corresponding axis.        

Stored in the element of the machine’s information model, the designation can be read by software and can be divided into two separate strings representing the two kinematic chains of the machine tool. Chain 1, t(C)ZYXb, represents the sequence of coordinate frames from the tool to the base and Chain 2, wCAb, represents the sequence of coordinate frames from the workpiece to the base. The matrices describing the tool and workpiece coordinate frames with respect to the base coordinate frame are then determined by: ðCÞ

b tT

¼ ðbX TÞðXY TÞðYZ TÞðZðCÞ TÞðt TÞ

(4)

b wT

¼ ðbA TÞðAC TÞðCw TÞ

(5)

Eqs. (4) and (5) are evaluated using a loop to sequentially calculate the HTMs that describe the orientation and position of the tool and/or workpiece coordinate frames with respect to each frame of their respective kinematic chains. The calculation process starts with the tool or workpiece (left side of the chain) and progresses through to the base (right side of the chain): f ðiÞ T f ð1Þ

f ðiÞ

f ði1Þ

¼ ð f ði1Þ TÞð f ð1Þ TÞ

for

N > 2 and i ¼ 3 to N;

(6)

where:  N equals the number of elements in the kinematic chain  f(i) represents the coordinate frame for element i  T is the transformation matrix for the corresponding reference frame (RF). Eqs. (7) through (10) demonstrate the calculation process performed to achieve (4): ðCÞ

Z tT

¼ ðZðCÞ TÞt T;

Y t T

¼ ðYZ TÞZt T;

for i ¼ 4

(8)

X t T

¼ ðXY TÞYt T;

for i ¼ 5

(9)

b tT

¼ ðbX TÞXt T;

for i ¼ 6

(10)

for i ¼ 3

(7)

Eqs. (11) and (12) demonstrate the calculation process performed to achieve (5): Fig. 1. Machine configuration wC0 A0 bXYZ(C)t.

A wT

¼ ðAC TÞCw T;

for i ¼ 3

(11)

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b wT

¼ ðbA TÞAw T

for i ¼ 4

(12)

All geometric error calculations are performed for each discretized point on the tool path. Coordinate frame and error measurement locations Machine tool errors can be directly characterized using various standardized measurement methods [1–3]. For simplicity and efficiency, the errors of each axis are traditionally measured at target points along a line in the machine axis space instead of every possible position throughout the machine’s work volume. The results of the linear error measurements (i.e., linear positioning and straightness) are only valid along the reference straight line that passes through the functional point of the measurement. This is because the errors in tool position are directly affected by the angular errors of the axes. Any deviation from the functional point will change the errors in tool position as a function of angular error(s) and offset distance [23]. The linear errors of an axis are defined at positions where the functional point coincides with the axis’s coordinate frame origin. However, it is not always possible to measure all the errors of an axis at the location where they are defined. Accurate geometric error modeling of machine tools requires detailed knowledge of the location where (linear) errors are measured. This meta data is recorded in the and elements of the machine tool information model. and are sub-elements of the element and represent the positions of the machine axes and the tool offset, respectively, at the location where the errors were measured. With this detailed information, the measured linear errors can be transformed by software to represent the magnitude of the linear errors at the locations of the coordinate frame origins of the kinematic model. This transformation corresponds to a compensation for the effect of observed angular errors. For generalized modeling, the location of the coordinate frames must be clearly understood and the method used to specify coordinate frame locations must be consistent between machine types. ASME B5.59-2 provides information that can be used to automatically define the position and orientation of coordinate frames with the and elements, respectively. In our generalized modeling method, coordinate frame positions and orientations are established by first assuming that the linear machine axes (X, Y, and Z) are aligned with the machine coordinate system (MCS) of the machine tool. In addition, the orientations of

the linear axes are assumed to be nominally orthogonal to each other. The coordinate frame for the base, b, is identical with the MCS, and the coordinate frame for the tool, t, is identical to the spindle coordinate frame, (C), which has its origin at the intersection of the spindle gauge plane and the spindle axis of rotation. Five-axis configurations are categorized as tilting rotary table, tilting spindle, or gimballing spindle. The locations of the frames representing the axes of the machine tools are based on these categories, as described in the following three examples. Example 2. Coordinate frame locations for Tilting Rotary Table type configurations. With tilting rotary table type configurations, the two rotary axes reside in the workpiece kinematic chain (Fig. 2).  X, Y, Z, (C), t, and b are nominally coincident when all axes are at their (machine) zero positions.  The origins of the two rotary axes (A, B, or C) coordinate frames are nominally located at the intersection of the respective axis average lines. Their positions with respect to the base coordinate frame, {x, y, z}b, are defined by the sub-elements , , , and of the machine tool information model.

Example 3. Coordinate frame locations for Tilting Spindle type configurations. With tilting spindle type configurations, one rotary axis resides in the tool kinematic chain and the other rotary axis resides in the workpiece kinematic chain, as shown in Fig. 3.  X, Y, Z, and b are nominally coincident and located at the B-axis origin when all axes are at their (machine) zero positions.  The coordinate frame for the rotary axis used for changing the orientation of the spindle (e.g., B in Fig. 3a) is located on its axis average line at the intersection with the spindle axis (C). The respective distance from the origin of B to origin of (C) is defined by the element of the machine tool information model.  The rotary axis used for positioning the workpiece, (e.g., C in Fig. 3a) is located on its axis average line. The origin of the axis is in near proximity of or located with the table surface or gauge line of the workpiece collet. Its location, {x, y, z}b, is defined by the , , and elements of the machine tool information model.

Fig. 2. Coordinate frame locations for tilting rotary table type configurations: (a) configuration wC0 A0 bXYZ(C)t, (b) configuration wC0 B0 bXYZ(C)t.

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Fig. 3. Coordinate frame locations for tilting spindle type configurations: (a) configuration wC0 bZYXB(C)t, (b) configuration wC0 Y0 bXZB(C)t.

Example 4. Coordinate frame locations for Gimballing Spindle type configurations. With gimballing spindle type configurations, the two rotary axes reside in the tool kinematic chain and are used for positioning and orienting the tool with respect to the workpiece. See Fig. 4.  A, C, X, Y, Z, and b are nominally coincidental and located at the intersection of the axis average lines of A and C when all axes are at their (machine) zero positions.  The axis average line of (C) nominally passes through the origin of the rotary axis used to position the (C). Its respective position is defined by the element of the machine tool information model. The nominal orientations of the rotary axes for all machine categories are defined by unit vectors stored in the elements (sub-element of ) of the machine tool information model. Homogeneous transformation matrices for linear axes Linear axes (X, Y, and Z) are modeled by HTMs that describe the nominal translation of the axis, three linear errors, three angular

Fig. 4. Coordinate frame locations for gimballing spindle type configuration, wY0 bXZCA(C)t, when all axes are at their home positions.

errors, and the alignment of the axis with respect to the machine coordinate system [12,13]. A schematic indicating the errors of an X-axis is shown in Fig. 5 and the transformation matrix representing the X-axis is described by Eq. (13). 2

1 6 eCX RF 6 X T ¼ 4 e BX 0

eCX 1 eAX 0

eBX eAX 1 0

3 x þ eXX eYX þ x  ECOX 7 7 eZX  x  EBOX 5 1

(13)

The linear (eXX, eYX, eZX) and angular (eAX, eBX, eCX) errors are a function of the position of the axis in machine (absolute) coordinates. The alignment (squareness or parallelism) errors (EBOX, ECOX) are position invariant errors. Transformation matrices for the Y- and Z-axes are similar and only differ by the location of the alignment errors in the matrices. In general, nine axis alignment errors are necessary to fully characterize all errors in the average relative axis orientations of a five-axis machine tool (e.g., three squareness errors for the linear axes and two alignment errors each for the rotary axes and spindle). To eliminate redundant alignment errors (i.e., redundant measurements), the machine coordinate system is aligned to a primary axis of motion which can be any of the three linear axes or two rotary axes [2]. The machine coordinate system is then rotated around the primary axis to align it with a secondary axis, which will have one alignment error (with respect to the primary axis).

Fig. 5. A schematic indicating the errors of an X-axis.

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All other axes will have two alignment errors. Each element defines the alignment error in the orientation of an axis relative to an arbitrary reference axis (see Example 5). The alignment errors may differ between machine information models. The DDVMT examines the data stored in the alignment elements of each information model and converts the respective errors to the appropriate alignment errors in the geometric error model. Example 5. XML sample describing the parallelism error of the C-axis to the Z-axis in the YZ plane indicating 90 arc-seconds of parallelism error (according to ASME B5.59 specifications).

REF loc C T

describes the nominal location (XOC, YOC, ZOC), and location (offset) errors (EXOC, EYOC, EZOC). ori  REF describes the nominal (alignment) orientation (AOC, BOC) C T and the orientation errors (EAOC, EBOC). lin dev  REF describes the linear deviation errors (eXC, eYC, eZC). C T rot  REF T describes the nominal angular position, c, angular position C error (eCC), and the angular deviation errors (eAC, eBC). 

The offset and alignment errors are constant, whereas the linear and angular deviations are functions of angular position. Transformation matrices for the A- and B-axes are similar to (13). The individual errors for each axis are defined in [2]. Geometric error data

C Z A X-389.9 Y0 Z-512 90

During simulation, the HTMs representing each axis are populated with error values, pertinent to the position and direction of motion of the axis, and then multiplied. The error data used is stored in the element of the machine tool information model. Alignment and offset error values are constant values (see Example 5) that do not change with axis position. Angular and linear axis deviations depend on axis position and direction of motion. They are stored as tables representing mean error values observed at discrete axis (target) positions for positive and negative approach directions (see Example 1) The DDVMT identifies the simulated direction of motion of the axis and selects

Homogeneous transformation matrices for rotary axes Rotary axes, typically, are nominally parallel to an axis of the machine coordinate system when all axes are at their zero position, see Fig. 1. In a few designs, the rotary axes are inclined, as shown in Figs. 2b and 3b. Rotary axes are modeled using a series of HTMs that describe the nominal position and orientation of the axis, alignment and offset errors in the average axis location, linear and angular errors in axis motion, and the nominal axis motion. Fig. 6 provides a schematic indicating the errors of a C-axis. Rotary axis errors are modeled using four sets of HTMs: REF C T

loc REF ori REF lin dev REF rot ¼ ðREF ÞðC T ÞðC T ÞðC T Þ; C T

(14)

where

Fig. 6. A schematic indicating the errors of a C-axis.

Fig. 7. A flowchart of the DDVMT. The acronyms are defined throughout this document.

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the appropriate error table. The target positions generally do not correspond to the axes’ positions used in simulations. Therefore, the error data is linearly interpolated before being entered into the HTMs. Reconfigurable data driven virtual machine tool Developed using Matlab1 [24] and the Simulink1 Toolbox [25], the DDVMT is designed to be a generalized versatile model that can be used to simulate and analyze the combined or independent effect of the geometric and servo errors on (standard) 5-axis performance test results [7]. Simulations of machining tests [27] and multi-axis kinematic tests [4,26] can be performed for many machine tool configurations. In addition, the DDVMT may be used to predict the errors of machined workpieces, to correct cutter location data [28,29], or as a tool for removing the effects of machine errors from on-machine measurement data [30]. The DDVMT is a software application that is the combination of five generalized computational modules (see Fig. 7): ideal trajectory generation (ITG), tool path animation (TPA), control error modeling (CEM), geometric error modeling (GEM), and workpiece feature analysis (WFA). Versatility is achieved by populating the parameters of the generalized modules with data described by machine tool information models [19] transferred using the XML. The DDVMT is driven by simulation data files in an XML format [22] with a general structure similar to ASME B5.59 [19]. These files contain information used to identify the machine (manufacturer, model, and serial number), the workpiece, the workpiece location and orientation, the tool(s), the tool path relative to the workpiece (e.g., numerical control program), simulation and analysis

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parameters, and simulation results. The analysis parameters provide information pertaining to the analysis to be performed on the results (e.g., analyses prescribed by machine tool metrology standards), simulation speed, and machine errors considered. The information pertaining to the machine, workpiece, and cutting tool are used as pointers for automatically acquiring data files and algorithms from various data repositories affiliated with the DDVMT. The DDVMT’s simulation files provide a mechanism for storing information about the simulation and simulation results. Additionally, the DDVMT can be controlled through the graphical user interface (GUI) shown in Fig. 8. The GUI can be divided into five sections: the menu bar, simulation description panel, simulation status panel, animation panel, and axis position panel. During simulation, the panels display information about the simulation to the user. The menu bar is used to load and save simulation files, reset default values, and view and set up various features of the simulation. One important feature that the GUI provides is the ability to activate and deactivate the machine errors through an error control menu. The computational modules of the DDVMT are described below. Ideal trajectory generation (ITG) module The numerical control (NC) program describes the cutting tool’s nominal motion relative to the workpiece. The machine controller interpolates between the programmed points for each axis and moves the cutting tool and the workpiece along a smooth trajectory. Similarly, the DDVMT has a trajectory generation module with the capability of selecting a suitable trajectory generation method, such as jerk limited federate modulation [31],

Fig. 8. An image of the graphical user interface (GUI).

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from the control model repository (CMR). The ideal trajectory generation module uses the selected trajectory method to generate the cutter location (CL) data, which describes the position of each axis as a function of time along an ideal trajectory. If the user does not wish to calculate an ideal trajectory based on an NC program and a formal trajectory generation method, then a CL data file can be identified in the simulation file or selected through the GUI. With this type of simulation, the ITG and CEM modules are bypassed and the servo control errors are not analyzed. Tool path animation (TPA) module To visualize the tool path, the CL data is processed by the TPA module. In this module, pointers identifying the machine tool (manufacturer and model number) are used to retrieve the appropriate three-dimensional (3D) computer-aided design (CAD) models representing the machine tool components from the CAD repository. The CAD models, stored using the STereoLithography (STL) file format, include models of the machine base and positioning axes. A total of six CAD files are used to animate the movements of a five-axis machine tool. Similarly, CAD models representing the workpiece (part or instrument) and tool (cutter or artifact) are identified by the simulation data file and retrieved from the CAD repository. Once the models are retrieved, they are animated on the screen according to the CL position data using HTMs that include only the nominal orientation and position of each CAD model. Additionally, the CL values are simultaneously shown on the Axis Position Panel. The result is a 3D animation of the machine axes, workpiece, and tool traversing along the prescribed path (Fig. 8).

the functional point with respect to the tool coordinate system (TCS) is also generated. Workpiece feature analysis (WFA) module The workpiece data file is analyzed using algorithms from the feature analysis repository (FAR). These algorithms evaluate workpiece data and compare it to feature tolerances by first fitting circles, cylinders, planes, or spheres to the data points [4,32,33] and then calculating errors in dimension or form using methods outlined by geometric dimensioning and tolerancing (GD&T) standards [34]. Machine tool performance parameters are calculated using methods described in national and international machine tool metrology standards [1,7,8,35]. The results from the analysis are then added to the simulation data file for further evaluation by additional software applications. Simulations The combined analyses and results from the computation modules represent a complete simulation by the DDVMT. An exhaustive error simulation for a defined tool path uses all modules and includes all servo and geometric errors. A partial simulation may include only one or a few machine errors. The DDVMT is intended to be used as an evaluation tool for studying the individual effects of the different servo and geometric errors. During simulations, single to multiple errors are activated and their effect on the multi-axis measurement result or machining result is studied. Testing and evaluation

Control error modeling (CEM) module In the CEM module, the CL data generated by the ITG module is modified to account for the effects of the machine tool servo characteristics and machine dynamics. This may include, but is not limited to, the effects due to mass, damping, friction, filters, and electrical gains. These effects can be simulated for each machine axis in the DDVMT’s CEM module, which uses general control schemes assembled using building blocks provided by the dynamic systems simulation software Simulink1 [25]. An example of such a control scheme is a nested closed-loop control of the drive motor current controller, velocity controller, and position controller. Information identifying the machine is used to retrieve machine specific control parameters (e.g., mass, damping, gains, and control scheme) from the machine information model repository (IMR). The data elements used for specifying these parameters are not described by ASME B5.59-2 [19], but were added to the information model element to support the DDVMT. This data is used to select, populate, and run the appropriate Simulink1 block(s). The output of this module is a modified axis motion trajectory (MT) that includes the errors due to the control parameters. Geometric error modeling (GEM) module The tool trajectory defined by the CL data, optional MT data, and machine kinematics can be modified for the effects of the geometric errors of the machine tool in the GEM module. This is achieved by implementing the methodology described in section ‘‘Data driven geometric error modeling’’. The output from this module is a workpiece data file that contains for each CL data point the nominal position and actual orientation of the tool in the workpiece coordinate system (WCS) and the respective errors, {eX, eY, eZ}WCS, in the position of the functional point in the WCS. A similar file that contains the errors, {eX, eY, eZ}TCS, in the position of

Validation of the DDVMT is carried out by comparing measured and simulated coordinated multi-axis motions on a mill/turn machine similar to the configuration of Fig. 3a. Prior to performing the simulations and measurements, the individual geometric errors of the machine tool are directly measured following test methods outlined by both national and international machine tool standards. To enhance the accuracy of simulation, the errors are bidirectionally measured at target positions evenly spaced along the (full) travel of the axis at intervals much less than the maximum allowable interval (e.g., 1/10 of the axis length) recommended by existing standards [1–3]. The interval for linear axes is 10 mm and the interval for rotary axes is 58. Exceptional care is also taken to identify and document the location, within the machine work volume, where each individual error is measured with respect to the axis coordinate frame. Before recording the error values in the machine tool information model, all linear errors (i.e., positioning and straightness) are transformed to represent the error at the origin of the respective axis coordinate frame. In the validation experiments, the errors of the tool with respect to the workpiece, we, are evaluated for coordinated motions involving several linear and rotary axes. The measurements and axes motions are based on standard performance tests described in ISO 10791-6 [7] and ISO 230-4 [35]. Commercially available telescoping ballbar and R-test devices with standard measurement uncertainties of 0.5 mm and 0.7 mm, respectively, are used to measure we at static target positions. Figs. 9, 10, 12 and 13 provide plots comparing simulated (SIM) test results with measured (MEAS) test results. Fig. 9 shows a polar plot comparing simulated and measured results for a partial circular test involving the X- and Z-axes and a telescoping ballbar [1,7,35]. The ballbar length (i.e., radius) is approximately 100 mm and the ballbar travel is clockwise (CW) from 08 to 908 in 58 increments and counter-clockwise (CCW) from

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908 to 08 in 58 increments. For presentation, a 0.005 mm radial offset was added to the data in Fig. 9. Fig. 10 shows a plot comparing simulated and measured R-test device output for a CK2 test [7] involving the X-, Y-, and C-axes. Measurements are performed using a commercially available Rtest device (sensor nest) mounted to the C-axis approximately 9.4 mm from the C-axis average line and a tool with a spherical artifact (ball) mounted to and aligned with the milling spindle axis

average line. C-axis motions are CW from 08 to 3608 in 108 increments and CCW from 3608 to 08 in 108 increments. The Xand Y-axes are programmed to follow the C-axis. Fig. 11 shows a schematic of a partial CK1 test [7] involving the X-, Z-, and B-axes and a commercially available R-test device. Measurements are performed with the R-test device mounted to the C-axis and held stationary (i.e., C = 0) and the spherical artifact (tool) mounted to and aligned with the milling spindle axis average line. B-axis motions are CW from 08 to 908 in 58 increments and CCW from 908 to 08 in 58 increments. The X- and Z-axes are programmed to hold the sphere center stationary as the B-axis rotates. The pivot radius (distance from the B-axis average line to the sphere center) is 283.141 mm and includes a tool length (distance from the spindle gage line to the sphere center) of 134.122 mm. Fig. 12 shows a plot comparing simulated and measured R-test device output for the partial CK1 test. A similar

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Fig. 12. A plot comparing simulated and measured R-test device output (standard measurement uncertainty equals 0.7 mm) for a partial CK1 test involving the X-, Z-, and B-axes.

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the respective measurement uncertainty can have a significant effect on the simulation results as well as the numerical compensation of the machine. For example, the simulated and measured error profiles in Fig. 12 have similar trends, yet the differences are as large as 32 mm. Furthermore, errors in some instances have a one-to-one effect on the result of a multi-axis performance test. In the CK1 test of Fig. 13, a 0.040 mm error in the measured tool length (i.e., a controller parameter) was simulated by the DDVMT and emulated by entering a false tool length into the machine controller. As a result, the simulated and measured R-test output in the z-direction increased by 0.040 mm, as seen by comparing Figs. 12 and 13. The accurate measurement and separation of some geometric errors and errors in some controller parameters presented a challenge while characterizing the machine tool used in this evaluation. During the initial software validation phase of the DDVMT, discrepancies between simulated and multi-axis measurements were found. The DDVMT was used to help identify the cause of such discrepancies (e.g., an error in the specified distance between the B-axis average line and the spindle face) by activating specific errors and evaluating their contribution to the overall measurement and simulation results. These exercises led to the design of additional measurements that were performed to more accurately characterize the errors causing the discrepancies.

Concluding remarks

plot demonstrating the effects of a -0.040 mm tool length error on a CK1 test is shown in Fig. 13. In this evaluation a tool length error is emulated by changing the programmed tool length in the machine controller. The resulting programmed pivot radius is 283.101 mm. Discussion of results As can be seen in Figs. 9, 10, 12 and 13 the simulated results correlate with the measured results. In Fig. 9, the shape of the error profiles are similar and, except for certain outliers, the difference in magnitudes are within 0.5 mm, which is the measurement uncertainty (k = 1) for the telescoping ballbar. However, while the measured data in the CW and CCW directions generally match very well, the simulated error profiles deviate more due to directional differences in the X- and Z-axis errors used for the simulated results. The amplitude of the CK2 measurement presented in Fig. 10 is mostly due to an error (approximately 0.15 mm) in the controller parameter specifying the location of the C-axis in the x-direction. This offset error was verified following an alternate measurement method described by ISO 230-1 [2]. The results of the CK2 evaluation suggest that the CK2 test is a valuable test for identifying offsets in the position of the axis average line of rotary axes. Predicting the true results of multi-axis instrumented performance test using the methodology described herein relies on the careful measurement and characterization of the individual error sources. The characterization of some errors can be difficult and

In this paper, we described a methodology for a generalized reconfigurable data driven virtual machine tool error simulator. The DDVMT is compliant with existing machine tool performance standards and machine tool data specifications. In addition to describing the methodology, we demonstrated its ability to simulate multi-axis performance tests. Future work will involve modeling and simulating multiple machine tool configurations and testing and evaluating proposed 5-axis performance tests. Further development may include integrating the DDVMT with a commercially available computer aided manufacturing (CAM) software package and evaluating the capability of the system to predict workpiece errors. Acknowledgements The authors would like to acknowledge:  Jeff Gorniak of the University of Waterloo, Canada, for his service in the development of servo error models used by the DDVMT.  Mikael Hedlind and Andreas Archenti of the KTH Royal Institute of Technology, Sweden, for their participation in demonstrating the capability of this methodology.  Clive Warren of Renishaw Inc., USA, for his collaboration on rotary axis measurements.  ASME B5 TC 56 committee members for their efforts in the development of standardized information models for machine tools and machine tool performance tests (ASME B5.59).  Johannes Soons of the National Institute of Standards and Technology, USA, for his thorough review of this paper.

Please cite this article in press as: Fesperman, R.R., et al., Reconfigurable data driven virtual machine tool: Geometric error modeling and evaluation. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.001

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Appendix A

Example A.1. High level elements used to describe and store properties of machine tools, as defined by ASME B5.59-2:2013 [19].

Identification information of the specified machine tool Local date and time when the current list of machine properties was generated Classification of the listed information Location and ownership information of the machine within a company Classification of the machine's recondition status Classification of the machine tool according to its main function Classification of the machine tool according to the configuration of its components Orientation of the work spindle Configuration of the major machine components Properties of the machine work zone available for cutting operations Maximum workpiece size that can be accommodated by the machine Properties of the machine axes Properties of the machine spindle(s) Properties of devices used to handle cutting tools Properties of device used to handle workpieces Properties of the machine controller Properties of additional sensing devices Properties of cutting fluid delivery system Properties of a machine tool subsystem Properties of the machine environment Installation and facility planning information Information on the method used to stabilize the temperature of the machine Performance data Summary of the machine errors URL to drawings or images of the machine References [1] ASME B5.54. 2005, Methods for Performance Evaluation of Computer Numerically Controlled Machining Centers, ASME. [2] ISO 230-1. 2012, Test Code for Machine Tools – Part 1: Geometric Accuracy of Machines Operating Under No-Load or Quasi-Static Conditions, ISO. [3] ISO 230-2. 2006, Test Code for Machine Tools – Part 2: Determination of Accuracy and Repeatability of Positioning Numerically Controlled Axes, ISO. [4] Kakino, Y., Ihara, Y., Shinohara, A., 1993, Accuracy Inspection of NC Machine Tools by Double Ball Bar Method, Hanser/Gardner Publications. [5] Weikert, S., 2004, R-Test, A New Device for Accuracy Measurements on Five Axis Machine Tools, CIRP Annals, 53/1: 429–432. [6] Spaan, H., Florussen, G., 2012, Determining the 5-Axes Machine Tool Contouring Performance with Dynamic R-Test Measurements, in: Proceedings of the 12th Euspen International Conference, . [7] ISO/DIS 10791-6. 2011, Machine Tools – Test conditions for Machining Centres – Part 6: Accuracy of Speeds and Interpolations, ISO. [8] ISO/DIS 10791-7. 2011, Test Conditions for Machining Centres – Part 7: Accuracy of Finished Test Piece, ISO. [9] Fesperman, R., Moylan, S., Donmez, A., 2012, A Virtual Machine Tool for the Evaluation of Standardized 5-Axis Performance Tests, in: Proceedings of the 27th ASPE Annual Meeting, vol. 54, pp.484–487. [10] Soons, J.A., Theuws, F.C., Schellekens, P.H., 1992, Modeling the Errors of Multiaxis Machines: A General Methodology, Precision Engineering, 14/1: 5–19. [11] Tsutsumi, M., Yumiza, D., Utsumi, K., Sato, R., 2007, Evaluation of Synchronous Motion in Five-Axis Machining Centers with a Tilting Rotary Table, Journal of Advanced Mechanical Design Systems and Manufacturing, 1/1: 24–35. [12] Donmez, M.A., Yee, K.W., Damazo, B., 1993, Some guidelines for implementing error compensation on machine tools. NIST Interagency Report 5236, . [13] Donmez, M.A., Blomquist, D.S., Hocken, R.J., Liu, C.R., Barash, M.M., 1986, A General Methodology for Machine Tool Accuracy Enhancement by Error Compensation, Precision Engineering, 8/4: 187–196. [14] Chen, F.-C., 2001, On the Structural Configuration Synthesis and Geometry of Machining Centres, Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 215/6: 641–652. [15] Lei, W.T., Paung, I.M., Yu, C.-C., 2009, Total Ballbar Dynamic Tests for Five-Axis CNC Machine Tools, International Journal of Machine Tools & Manufacture, 49:488–499. [16] Khan, A.W., Chen, C., 2011, A Methodology for Systematic Geometric Error Compensation in Five-Axis Machine Tools, The International Journal of Advanced Manufacturing Technology, 53/5–8: 615–628. [17] Slamani, M., Mayer, R., Balazinski, M., Zargarbashi, S.H.H., Engin, S., Lartigue, C., 2010, Dynamic and Geometric Error Assessment of an XYC Axis Subset on Five-Axis High-Speed Machine Tools Using Programmed End Point Constraint

[18]

[19]

[20] [21]

[22] [23] [24] [25] [26]

[27]

[28]

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[31]

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Please cite this article in press as: Fesperman, R.R., et al., Reconfigurable data driven virtual machine tool: Geometric error modeling and evaluation. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.001