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Procedia Manufacturing
Volume XXX, 2015, Pages 1–12
43rd Proceedings of the North American Manufacturing Research
Institution of SME http://www.sme.org/namrc
Development of a Dynamic Substructuring Framework
to Facilitate in Situ Machining Solutions Using Mobile
Machine Tools
Mohit Law1,a*, Hendrik Rentzsch1,b and Steffen Ihlenfeldt1,c
1
Fraunhofer Institute for Machine Tools and Forming Technology IWU, Chemnitz, Germany
b
[email protected],
[email protected],
c
[email protected]
a
Abstract
In situ machining of large parts using mobile machines that are moved to part
location(s) allows these parts to be machined, repaired and maintained directly on the
site of operation. However, every new part and location that the machine is moved to
results in different boundary conditions for the machine-part system which singularly
influences the dynamics of the combined system and makes for difficult planning of
first-time right machining solutions. To facilitate the planning of in situ machining
solutions, this paper presents a dynamic substructuring framework that can predict
assembled system dynamics by combining measured and/or modelled substructural
response of the individual components under varying base/part/contact/configuration
characteristics. Substructural coupling is formulated in the frequency and the
continuous-time domains for representative examples of the mobile machine being
connected to two different part/base models. The frequency based substructuring
approach is used to predict tool point dynamics, results of which are instructive for
designing of machining strategies to ensure stable productive cutting conditions. Statespace substructural coupling predicts the changing nature of the plant model under the
varying influences, which provides guidelines for designing appropriate control
strategies and selection of appropriate CNC control parameters. Methods presented aid
establishment of experimental guidelines for planning of first-time right in situ
machining solutions.
Keywords: Dynamic substructuring, mobile machine tool, in situ machining, varying boundary conditions,
receptances, state-space coupling, modular synthesis, mutability
*
Corresponding author
Selection and peer-review under responsibility of the Scientific Programme Committee of NAMRI/SME
c The Authors. Published by Elsevier B.V.
1
Development of a Dynamic Substructuring Framework to Facilitate in Situ Machining Solutions
Using Mobile Machine Tools
Mohit Law, Hendrik Rentzsch and Steffen Ihlenfeldt
1 Introduction
Consistent growth in the transport, energy, aircraft and naval sectors has resulted in an increase in
demand for the manufacturing and maintenance of large parts used in these industries (Uriarte, et al.,
2013; Allen, et al., 2010). Traditionally, machining and maintenance of these large parts has been
carried out by disassembling these components from the system and shipping the parts to specialized
workshops for processing before they are returned to be reassembled. These complex and timeconsuming processes result in prolonged down times for systems and are associated with high
transportation and energy usage costs, making these processes economically unviable. In this context,
innovative solutions that instead move small versatile mobile machine(s) to the part location allow
these parts to be manufactured, machined and repaired directly on the site of operation. An example of
one such versatile machine, a novel patented five-strut parallel kinematic machine was developed at
the Fraunhofer IWU together with Metrom GmbH (Neugebauer, et al., 2011; Schwaar, et al., 2010).
Figure 1 shows two examples of this mobile machine being effectively utilized for in situ machining
of a turbine rotor and a large water turbine housing.
Figure 1: Examples of in situ machining with mobile machines for (a) turbine rotor (Schwaar, et al.,
2010), and (b) water turbine housing (Neugebauer, et al., 2011)
Every new part and location that the mobile machine is moved to results in different boundary
conditions for the machine-part system. Changing boundary conditions are due to different ways in
which the machine is mounted onto the base/part and changes in interface characteristics at the points
of coupling. All these factors contribute to and influence the dynamics of the combined system.
Furthermore, if in situ machining has to be carried out at different places on the same part, as shown in
Figure 2, the configuration of the mobile machine further influences the overall system behaviour.
In situ machining solutions are essentially turn-key. Hence, changing characteristics under varying
influences should be addressed in the planning phase to ensure first-time right solutions. This includes:
i.
Determining beforehand how to mount and position the machine on the part or base,
ii.
Selection of appropriate mounting/interface components and their characteristics,
iii.
Designing appropriate CNC control strategies that account for changing plant models, and
iv.
Pre-process tool and machining parameter selection to design effective in situ machining
strategies that account for changing tool point dynamics.
Given the huge number of parts and industries that need to be serviced, the effort required to obtain
all the relevant data for effective planning is overwhelming. Hence there is an urgent need to develop
virtual models and frameworks that predict system behaviour to help advance first-time right
solutions. The main objective of this paper is to formulate and present a dynamic substructuring
framework that will allow efficient investigation of mobile machine tool dynamics under varying
base/part/contact/configuration characteristics. This characterization will help establish experimental
guidelines for part/machine referencing and for planning of first-time right in situ machining solutions.
2
Development of a Dynamic Substructuring Framework to Facilitate in Situ Machining Solutions
Using Mobile Machine Tools
Mohit Law, Hendrik Rentzsch and Steffen Ihlenfeldt
Figure 2: Schematic of in situ machining with mobile machine tools under different configurations
A dynamic substructuring approach is a way to obtain the structural dynamics of large and/or
complex structures by combining measurements and/or models of individual components for which
the dynamic behavior is generally easier to determine. Substructural components can be represented
by their spatial mass, stiffness and damping data, modal data, or receptances.
Spatial and modal representation of individual substructures forms part of the family of the
generalized component mode synthesis approaches (Craig Jr & Bampton, 1968). Such spatial level
substructuring has found much use in the design and analysis of machine tool concepts and has proven
effective for facilitating modularity and reconfigurability (Zatarian, et al., 1998; Law, et. al., 2013).
The receptance coupling substructure analysis (RCSA) approach combines receptances, i.e.
frequency response functions (FRFs) of individual components to predict assembled system dynamics.
The RCSA approach has extensively and very successfully been applied in machine tool applications
to model and predict assembled tool point receptances by combining measured and/or modelled
response of tools, tool holders and spindles (Schmitz & Donaldson, 2000; Park, et al., 2003; Schmitz,
& Duncan, 2005; Movahhedy & Gerami, 2006; Albertelli, et al., 2013; Mancisidor, et al., 2014). The
RCSA method has also been used quite effectively to model and identify joint characteristics in
machine tools (Yigit & Ulsoy 2002; Dhupia, et al., 2007; Mehrpouya, et al., 2013). Earlier use of
RCSA methods that reported on the simple case of substructures in end-to-end contact was also
extended to multiple point coupling for concentric assemblies (Schmitz & Duncan, 2006). Those
formulations were further extended by the authors to model machine tool substructures simultaneously
in contact with and moving over each other to realize tool motion (Law & Ihlenfeldt, 2014).
The RCSA method is preferred in the present case since it can synthesize response of parts/base
measured at location with model predicted or measured machine response as desired. This facilitates
rapid and efficient investigations of assembled system dynamics under varying
base/part/contact/configuration characteristics. The dynamic substructuring approach is demonstrated
herein for representative examples of the mobile machine being connected to two different part/base
models, as described in Sect. 2. Since the mobile machine tool is in contact with a different part/base
at multiple points, previous work on the multiple point frequency based substructuring approach
(Schmitz & Duncan, 2006; Law & Ihlenfeldt, 2014) is built on to obtain the assembled system
dynamics, as described in Sect. 2.1. Frequency domain substructuring predicts the assembled tool
point dynamics required for pre-process tool and machining parameter selection. To account for the
changing nature of plant models under varying influences, substructural modal models are also
decomposed into a state-space form for ease of combining it with controllers. Previous analysis for
substructural coupling in the state-space domain (Hoher & Röck, 2011) is extended in Sect. 2.2 to
account for the substructures being in contact at multiple points. Methods described in this paper are
thought to be novel extensions and applications of otherwise well-developed theories and ideas.
Even though the proposed approach can combine measured and/or modelled response, discussions
herein are limited to demonstrating the approach using virtual model response only. Individual
substructural characteristics are discussed in Sect. 3, followed by investigation under assembled
configurations in Sect 4. This is followed by discussions addressing challenges with and limitations of
the approach in Sect. 5 and the main conclusions in Sect. 6
3
Development of a Dynamic Substructuring Framework to Facilitate in Situ Machining Solutions
Using Mobile Machine Tools
Mohit Law, Hendrik Rentzsch and Steffen Ihlenfeldt
2 Development of the Dynamic Substructuring Framework
Dynamic substructuring is demonstrated for the mobile machine (substructure I) connected to two
different base models (substructure II) shown schematically in Figure 3. The first base model is a
simple steel frame enveloping a workpiece and demonstrates how the mobile machine may be
mounted on a structure smaller than itself. The second base model represents the case wherein the
mobile machine is smaller than the base it is mounted on. The second base model is made of concrete
and has very different physical and dynamic characteristics than the first base model. The mobile
machine is connected to base type 2 using an intermediate frame. There are three connections between
the machine and the intermediate frame and four connections between the machine-frame combination
and the base type 2. In the case of the base type 1, the machine is connected to the base at three
different points. Finite element (FE) models for the machine and each of the base models were
generated from their respective CAD models (Tuchscherer, 2014), and modal analysis results for each
of the models were exported to the MATLAB environment for subsequent processing and synthesis.
Substructural formulations in the frequency and continuous-time domains (Sect. 2.1-2.2) though
generalizable, are described for the specific case of the mobile unit in contact with base model type 1.
Figure 3: Schematic of the mobile machine tool connected to two different base models
2.1 Frequency Based Substructuring
Response after assembly is desired at location 1 within Figure 3, i.e. the free-end of substructure I
that corresponds to the tool centre point of the mobile machine tool. Locations 2-4 correspond to the
mounting locations of the mobile platform. These locations (i.e. locations 2-4) are connected to
locations 5-7 on substructure II that belong to the base type 1. Each of the contacting interfaces on
each of the coupling surfaces is approximated by a single node in the FE environment to ease the
process of dynamic substructuring. Each of these interface nodes has three translational degrees of
freedom (DOFs), making the component receptances for any node in compact form to be:
4
Development of a Dynamic Substructuring Framework to Facilitate in Situ Machining Solutions
Using Mobile Machine Tools
Mohit Law, Hendrik Rentzsch and Steffen Ihlenfeldt
‫ݑ‬௜ = ℎ௜௝ ݂௝
(1)
wherein ‫ ݑ‬represents the displacement in each of the principal ‫ݔ‬, ‫ݕ‬, ‫ ݖ‬directions; ݂ represents the force
in these principal directions; ℎ represents the displacement-to-force receptance constructed using the
mass normalized eigenvectors output from a modal analysis run carried out in the FE environment, as:
ℎ௜௝ ሺ߱ሻ = ෍
ே೘
௥
−߱ ଶ
ߔ௜ ௥ ߔ௝ ௥
+ ݅௠ 2ߞ௥ ߱߱௡ ௥ + ߱௡ ଶ௥
(2)
wherein ߱௡ is the undamped eigenvalue for ‫ ݎ‬modes of interest for a total of ܰ௠ modes; ߔ௜,௝ is the
eigenvector at the location of interest (݅ and ݆ are the respective response and excitation locations); ߞ௥
is the modal damping ratio; ߱ is the frequency vector and ݅௠ is the imaginary operator.
Component level receptances for substructure I are (Schmitz & Duncan, 2006; Law, et al., 2014):
࢛ଵ = ࡾଵଵ ࢌଵ + ࡾଵଶ ࢌଶ + ࡾଵଷ ࢌଷ + ࡾଵସ ࢌସ
࢛ଶ = ࡾଶଶ ࢌଶ + ࡾଶଵ ࢌଵ + ࡾଶଷ ࢌଷ + ࡾଶସ ࢌସ
࢛ଷ = ࡾଷଷ ࢌଷ + ࡾଷଵ ࢌଵ + ࡾଷଶ ࢌଶ + ࡾଷସ ࢌସ
࢛ସ = ࡾସସ ࢌସ + ࡾସଵ ࢌଵ + ࡾସଶ ࢌଶ + ࡾସଷ ࢌଷ
(3)
wherein ࡾ௜௝ is the generalized receptance matrix describing translational component behaviour and ࢛௜
and ࢌ௝ are the corresponding generalized displacement and force vectors. Similarly, the component
level receptances for substructure II are:
࢛ହ = ࡾହହ ࢌହ + ࡾହ଺ ࢌ଺ + ࡾହ଻ ࢌ଻
࢛଺ = ࡾ଺଺ ࢌ଺ + ࡾ଺଻ ࢌ଻ + ࡾ଺ହ ࢌହ
࢛଻ = ࡾ଻଻ ࢌ଻ + ࡾ଻଺ ࢌ଺ + ࡾ଻ହ ࢌହ .
(4)
ࡲଵ = ࢌଵ ; ࢌଶ + ࢌହ = 0; ࢌଷ + ࢌ଺ = 0 ܽ݊݀ ࢌସ + ࢌ଻ = 0.
(5)
ࡷሺ࢛ହ − ࢛ଶ ሻ = ࢌହ ; ࡷሺ࢛଺ − ࢛ଷ ሻ = ࢌ଺ ܽ݊݀ ࡷሺ࢛଻ − ࢛ସ ሻ = ࢌ଻ ,
(6)
Equilibrium conditions for a force ࡲଵ applied at location 1 in the assembled configuration are:
Interface compatibility conditions for a flexible contact with a viscous damping model are:
wherein the complex stiffness matrix for constant levels of stiffness, ݇௫,௬,௭ and damping, ܿ௫,௬,௭ is
(Schmitz & Duncan, 2006):
݇௫ + ݅߱ܿ௫
0
ࡷ=቎
0
0
݇௬ + ݅߱ܿ௬
0
0
0
቏.
݇௭ + ݅߱ܿ௭
(7)
Although a single ࡷ matrix is employed in Eq. 6, each coupling location and/or direction could
have a different stiffness and/or damping.
5
Development of a Dynamic Substructuring Framework to Facilitate in Situ Machining Solutions
Using Mobile Machine Tools
Mohit Law, Hendrik Rentzsch and Steffen Ihlenfeldt
With brevity the desired assembled tool centre point response matrix ࡳଵଵ , which is synthesized
from the individual substructural receptances, can be shown to be (Law, et al., 2014):
ࡳଵଵ = ࡾଵଵ + ࡾଵଶ
ࢌଶ
ࢌଷ
ࢌସ
+ ࡾଵଷ
+ ࡾଵସ
ࡲଵ
ࡲଵ
ࡲଵ
(8)
wherein the three terms of ࢌଶ /ࡲଵ , ࢌଷ /ࡲଵ and ࢌସ /ࡲଵ are obtained by first substituting the component
receptances of Eq. 3-4 into the compatibility of Eq. 6 and eliminating ࢌହ , ࢌ଺ , ܽ݊݀ ࢌ଻ from the resultant
expressions by substituting relations from the equilibrium conditions of Eq. 5. For additional details,
the reader is directed elsewhere (Schmitz & Duncan, 2006; Law, et al., 2014; Law & Ihlenfeldt, 2014).
Each time the mobile machine is mounted on a different base/part with unique interface
characteristics, a new set of component receptances are constructed from measured and/or virtual
models of the new base/part. These receptances are combined with already available receptances of
the machine with relevant changes to contact characteristics, allowing for efficient investigations. The
single-stage substructuring approach formulated above can also be extended to a multiple-point-andstage approach as is necessary for coupling the mobile machine to base model type 2. The general idea
is to first combine two substructures to obtain their synthesized response, followed by combining this
synthesized response with additional substructures as desired to obtain the global synthesized tool
point response (Zatarian, et al., 1998; Schmitz & Duncan, 2005; Law & Ihlenfeldt, 2014).
2.2 State-space Substructural Coupling
Variability in the base/part/contact/configuration characteristics results in the closed loop
controllability of the mobile machine connected to the part/base to also vary. To accommodate the
varying nature of the plant models, transfer function between axis drives and tool positions necessarily
need to be evaluated for appropriate control parameter selection and controller design. To facilitate
evaluation of the closed loop dynamics, modal models for the each of the substructural components
are decomposed into a state-space form for ease of combining it with controllers in the MATLAB –
SIMULINK environment. Figure 4 shows the schematic of such as closed loop system.
The substructural state-space model(s) in Figure 4 can be represented as:
࢞ሶ = ࡭࢞ + ࡮࢛ௌௌ ;
࢟ = ࡯࢞
(9)
0
‫ܫ‬
0
࡭ = ൤−઩ −࡯ ൨
; ࡮ = ൤ࢂ் ‫ܨ‬
൨; ࡯ = ሾ ࢂ 0ሿ
௤ ଶ௡×ଶ௡
௣௛௬௦௜௖௔௟
(10)
wherein ࢞, ࢛ௌௌ , and ࢟ are the state, input and the output vectors of the system. The system matrix ࡭,
input matrix ࡮, and the output matrix ࡯ are described as:
߱௡ ଵଶ
wherein:઩ = ቎ 0
0
ࢂ = ሾܸଵ
…
0
⋱
0
0
0 ቏
߱௡ ଶ௡
௡×௡
2ߞ߱௡ ଵ
; ࡯௤ = ቎ 0
0
ܸ௠ ሿ௡×௠ ; ܽ݊݀ ‫ܨ‬௣௛௬௦௜௖௔௟ = ሾࡵሿ
0
⋱
0
0
0 ቏
2ߞ߱௡ ௡
;
௡×௡
(11)
wherein n represents the number of DOFs associated with the connection points; m the number of
modes to consider; ߱௡ and ࢂ represent the eigenvalues and the eigenvectors output from the FE
environment. Since the substructures are in contact at multiple points simultaneously, ‫ܨ‬௣௛௬௦௜௖௔௟ takes
the form of an identity matrix to represent the multiple-input-multiple-output (MIMO) system.
6
Development of a Dynamic Substructuring Framework to Facilitate in Situ Machining Solutions
Using Mobile Machine Tools
Mohit Law, Hendrik Rentzsch and Steffen Ihlenfeldt
Feedback
Reference axis
commands
Motor
input
CNC
Controller
SI
State-space model
Tool
point
Controlled axis/tool
position(s)
Plant Model
S II
State-space model
Mobile machine
Base/part
Figure 4: Schematic of controlled axis/tool point response obtained by state-space substructural
coupling procedure to couple the mobile machine to arbitrary part/base models
Dynamically, the model expressed in Eq. (9-11) can be viewed as a state-space block, having input
ports into which forces are fed, and output ports describing states of the system, as shown in Figure 4.
Substructures are synthesized by ensuring compatibility and equilibrium conditions with introduction
of springs, ݇ and dampers, ܿ. ݇ and ܿ are scalar constants which are adjusted for each contact pair and
direction independently. Construction of transfer functions between motor torque and tool point
displacement requires the input to the motor in its local coordinate frame (see Figure 3) and output at
the tool point in the global frame. Interactions between the substructures will result in the closed loop
controllability to vary under varying influences. The state-space coupling also facilitates modularity,
since individual substructural models can be replaced quite easily by other measured and/or virtual
models which can be coupled with contact characteristics as desired.
3 Substructural Response Characteristics
For better understanding the substructural characteristics and their interactions, direct and cross
responses (simulated) of the mobile machine and the two base models are compared in this section. A
uniform damping of the level of ߞ = 0.02 is assumed for all structural modes. Direct response
comparisons at the tool point and at coupling locations of either of the substructures, cross response
comparisons between the tool and mounting locations (for substructure I) and between different
mounting locations on either of the substructures are limited up to 400 Hz, i.e. the range corresponding
to global substructural modes. Cross response comparisons between the motor input and tool position
for substructure I are limited up to 150 Hz, i.e. the range corresponding to the bandwidth of typical
feed drives.
3.1 Mobile Machine Tool Response
Figure 5 compares the direct response of the mobile machine for all directions at the tool centre
point (Figure 5(a)) and at a representative coupling location (Figure 5(b)). Since the mobile machine is
evaluated in its unassembled free-free configuration, its receptances contain rigid body modes. In the
case of the direct tool point response, the Z directional response appears stiffer than the X and Y
directions, whereas response at the representative coupling location 2 (see Figure 3) appears to be
symmetric in all directions and is almost as flexible as the direct tool point response.
7
Development of a Dynamic Substructuring Framework to Facilitate in Situ Machining Solutions
Using Mobile Machine Tools
Mohit Law, Hendrik Rentzsch and Steffen Ihlenfeldt
Figure 5: (a) Direct response at tool centre point; (b) Direct response at location 2, substructure I
Figure 6 compares the cross FRFs between the tool and the coupling location 2 (Figure 6(a)) as
well as between coupling locations 2 and 4 (Figure 6(b)). In either case it appears that different modes
for different directions become dominant at different frequencies. There also appears some significant
cross-talk between the two locations and this is expected to influence the overall assembled response.
Figure 6: Response for substructure I. (a) Cross response between tool and coupling location 2; (b)
Cross response between between locations 2 and 4
Figure 7 compares the response between torque input to the motor and tool point displacement for
only one of the representative parallel struts under consideration (see Figure 3). Motor input was
transformed to align the global coordinate system with the local reference frame. Cross excitations in
all principal directions resulting from torque input along the drive axis suggests strong cross coupling
between the axes, which may need to be considered during the design of feed drive control strategies.
Figure 7: Cross response between the motor torque input and the tool displacements, substructure I
8
Development of a Dynamic Substructuring Framework to Facilitate in Situ Machining Solutions
Using Mobile Machine Tools
Mohit Law, Hendrik Rentzsch and Steffen Ihlenfeldt
3.2 Base Response
Figure 8 shows the direct response at coupling location 5 (Figure 8(a)) and cross response between
locations 5 and 7 (Figure 8(b)) for base type 1 (see Figure 3). These results are obtained after having
constrained the base as rigidly fixed to ground. The Y directional response is more flexible than the X
directional response and the Z directional response is stiffer than the other principal directions.
Direct responses at the location 14 (see Figure 3) for base model 2 is shown in Figure 9(a) and
response between two representative coupling locations 12 and 14 is shown in Figure 9(b). In this
case, differently from the earlier case of base model type 1, the X directional response is significantly
more flexible than the other directions due to the geometry of this base type. Furthermore, since base
type 2 is made of concrete and is much larger than type 1, its response is also dynamically stiffer than
base type 1. As was observed for the machine response in Figures 5-6, there appears significant crosstalk between base coupling locations and this is also expected to influence the assembled response.
Figure 8: Responses for substructure II – base model 1. (a) Direct response at coupling location 5; (b)
Cross response between locations 5 and 7
Figure 9: Responses for substructure II – base model 2. (a) Direct response at coupling location 14;
(b) Cross response between locations 12 and 14
4 Assembled System Dynamics
Assembled direct tool point dynamics and cross response between the motor input and the tool
point are shown in Figures 10-11. Response comparisons are reported for machine rigidly connected
to both base models as well as for the case of connecting the mobile machine directly and rigidly to
the ground. Investigations under variable contact characteristics and numerical verification of the
proposed approach were carried out elsewhere (Law, et al., 2014) and are not discussed again herein.
9
Development of a Dynamic Substructuring Framework to Facilitate in Situ Machining Solutions
Using Mobile Machine Tools
Mohit Law, Hendrik Rentzsch and Steffen Ihlenfeldt
Figure 10: Assembled tool point response with different base types. (a) X direction (b) Y direction
Direct assembled tool point response shown in Figure 10 is limited to the X and Y directions only.
Interestingly, despite substructural response of base type 2 being dynamically stiffer than type 1 (see
Figures 8-9), assembled system response with base type 2 is as flexible as with the nimbler base type 1
or with the machine being directly connected to the ground. The intermediate frame between the
machine unit and base type 2 is thought to be the source of this increased flexibility. Furthermore,
lower stiffness of the intermediate frame combined with the large mass of the base type 2 results in
lower eigenfrequencies of the combined machine-base system. Connecting the machine rigidly to the
ground naturally results in stiffening of system, as can be seen in the response for this case being
dominated by higher frequency modes than with either of the base models. Effects of mode
interactions between substructures are also evident in assembled tool point results of Figure 10, which
are significantly different than the individual substructural responses in Figures 5-9. These
investigations clearly demonstrate how the assembled system response is a strong function of
changing base/part/contact characteristics. Such investigations can also be instructive on how to
design intermediate frames to couple the mobile machine unit to arbitrary base/part/frame models such
that assembled system response is not adversely influenced by the nature of coupling.
Response between the motor input and tool point response in the Y direction under changing
boundary conditions is shown in Figure 11. Response is characterized by rigid body motion of the
spindle housing connected to and driven by the torque input to the axis drive of the strut. As evident,
changing base types and boundary conditions result in significantly different plant models that have
different vibration modes dominating the response spectrum. Characterizing these changing dynamics
early in the planning phase is instructive for appropriate controller design and parameter selection.
Figure 11: Comparison of transfer functions between motor and tool point for different base models
10
Development of a Dynamic Substructuring Framework to Facilitate in Situ Machining Solutions
Using Mobile Machine Tools
Mohit Law, Hendrik Rentzsch and Steffen Ihlenfeldt
5 Discussions
Efficacy of point to point substructuring is a function of dynamic characteristics (observability and
controllability) at the point of coupling, as well as of how well a coupling point is able to approximate
the substructural interface surface it is meant to represent (Schmitz & Duncan 2006; Law & Ihlenfeldt
2014). If the coupling point does not entirely capture substructural behavior, this will translate to
errors in the assembled response and this remains a limitation of the proposed approach.
Though the framework was demonstrated using virtual models, it is ideally suited for experimental
substructuring. Since, models of parts to which the machine is to be moved may not be available a
priori, response of these parts can be measured at location and synthesized with model predicted or
measured machine response as desired for further planning. Experimental substructuring requires
measurements on the machine in unsupported configuration, something that is non-trivial (Brecher et.
al 2014). Furthermore, synthesizing measured FRFs corrupted with measurement noise and
uncertainties is difficult. Further difficulties with inverting ill-conditioned matrices corrupted with
measurement noise (that is necessary for synthesis) are also well known (Yigit & Ulsoy 2002;
Mehrpouya, et al., 2013) and will need to be appropriately addressed.
6 Conclusions and Outlook
Mobile machine tools when transported to part location(s) allow these parts to be easily machined,
repaired and maintained. However, since every new part and location results in different machine-part
system dynamics, these dynamics need to be evaluated beforehand to guide first-time right planning of
in situ machining solutions. First-time right solutions are facilitated by the dynamic substructuring
framework presented in this paper. The framework helps rapidly predict assembled system dynamics
by combining substructural response of the individual components under varying influences.
Preliminary investigations clearly demonstrate the effect that individual substructural response
characteristics have on the overall assembled response. Knowledge of the changing tool point
dynamics under the varying influences is necessary for designing of machining strategies to ensure
stable productive cutting conditions. Given the tool point response, algorithms for stability and part
surface characterization can be applied to guide first-time right solutions for in situ machining of large
high-value parts. Furthermore, these simulation models can further aid the optimization of control
programs as well as guide appropriate control parameter selection to account for how the plant model
continuously changes with any change of part and contact characteristics.
To appropriately service the huge variety of parts and industries, methods presented are planned to
be used to develop modular connection elements to help mount the machine on different parts as may
be required. As part of the planned future work and experimental validation, receptances for different
base/part are planned to be measured at location and combined with the validated machine response,
thus establishing the real strength of the proposed approach in facilitating mutability and modularity.
Acknowledgements
This research was supported by the Fraunhofer Gesellschaft’s ICON Project for Strategic Research
Co-Operation on Sustainable Energy Technologies.
11
Development of a Dynamic Substructuring Framework to Facilitate in Situ Machining Solutions
Using Mobile Machine Tools
Mohit Law, Hendrik Rentzsch and Steffen Ihlenfeldt
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