CN106295085A - The modeling method of the overlapping disk spring dummy model of flexible force tactile sense reproduction - Google Patents

Abstract

The invention discloses the modeling method of the overlapping disk spring dummy model of flexible force tactile sense reproduction, it is characterized in that when detecting that virtual protocol collides the arbitrfary point on virtual flexible body surface, under given dummy contact pressure effect, the regional area internal filling overlapping disk spring dummy model that virtual protocol is mutual with virtual flexible body, in interaction, output is fed back to the signal of the power tactile data of the reaction flexible body real-time deformation under pressure emulation using overlapping disk spring dummy model to calculate；In overlapping disk spring dummy model, the superposition of the monolithic disk spring deflection sum of every layer is externally equivalent to the deformation on flexible body surface, and the pressure sum that the overlapping disk spring of every layer consumes when being compressed is equivalent to given dummy contact pressure.Modeling method of the present invention can simulate the deformation process of flexible body the most realistically, and the power tactile data of feedback is truly stable, and practical for virtual teach-in explores a feasible road.

Description

The modeling method of the overlapping disk spring dummy model of flexible force tactile sense reproduction

Technical field

The present invention relates to the modeling method of a kind of haptic feedback, particularly relate to the overlapping dish bullet of flexible force tactile sense reproduction The modeling method of spring dummy model.

Background technology

The purpose of physical modeling is research flexible body produced corresponding deformation, its matter set up when being under pressure effect Amount how, directly determines the accuracy and speed of virtual teach-in.

Flexible body haptic modeling method is the basis of Surgery Simulation, and Chinese scholars has done a lot of work the most Make.Spring-mass has that modeling is simple, computational complexity is low and preferable to the adaptation ability of soft tissue topologies change Etc. advantage, but the shortcoming of this modeling method to be precision and stability limited, and can not accurate description soft tissue when deforming bigger Deformation.Although finite element can construct more accurate model, but calculates complexity, when number of network node is many, cause virtual Operation interactivity is poor.Though boundary element improves the real-time of model to a certain extent, but poor stability.Long unit can construct one Plant highly simplified model, although solve conveniently, but owing to its Model Abstraction degree is higher, thus cause computational accuracy relatively low.Lin Proposing the modeling method that a kind of two stage layereds reproduce, though deforming true to nature, but precondition is object of study is conceptualized as rigidity Object.Though the shape that Kim et al. proposes keeps chain modelling method real-time preferable, but is it is assumed that precision is low based on rigid body.Flat Row rhomboid chain connects, though modeling is simple, but due in this model every layer be all to be made up of an identical rhomboid chain construction unit, At the boundary of emulation deformation, distortion phenomenon easily occurs.

Therefore, research has the flexible body haptic modeling method of good interactivity and sense of reality and will be directly connected to virtual The lifting of surgery systems using value.In view of the above problems, in order to make the mutual mistake of power haptic during virtual teach-in Journey more conforms to the custom of people self, improves mutual feeling of immersion and sense of reality, it is proposed that the overlapping of flexible force tactile sense reproduction The modeling method of disk spring dummy model.

Summary of the invention

The present invention is directed to the deficiencies in the prior art, propose flexible force tactile sense reproduction overlaps building of disk spring dummy model Mould method, and use it in the virtual flexible body real-time deformation simulation process of man-machine interaction；This modeling method calculates simple, energy Calculate deflection quickly and accurately, it is achieved the real-time deformation of flexible body is emulated；Interactive process true nature, feeds back to behaviour The power tactile data of author enriches, and power haptic rendering is true, deforms true to nature.

For solving above-mentioned technical problem, the present invention adopts the following technical scheme that

The modeling method of the overlapping disk spring dummy model of flexible force tactile sense reproduction, its step is as follows:

Step 1, virtual scene initializes；

Step 2, under given dummy contact pressure F effect, when virtual protocol collides appointing on virtual flexible body surface Meaning point time, hang at the point of impingement external diameter be D, internal diameter be d, thickness be l, free height be H₀, maximum change when being driven plain Shape amount is h₀, spring rate be the monolithic disk spring of k, form overlapping disk spring ground floor；Monolithic dish at ground floor Under spring, equidirectional setting and the monolithic disk spring of the monolithic disk spring same specification of ground floor, form overlapping disk spring The second layer；Under the monolithic disk spring of the second layer, the monolithic of the monolithic disk spring same specification of equidirectional setting and ground floor Disk spring, forms overlapping disk spring third layer；The rest may be inferred, under the monolithic disk spring of i-th layer, equidirectional setting with The monolithic disk spring of the monolithic disk spring same specification of ground floor, forms overlapping disk spring i+1 layer；I=1,2,3 ..., N, N are natural number, overlap the external diameter of monolithic disk spring, internal diameter, thickness, free height in each layer of disk spring, be driven plain Time maximum deformation quantity, spring rate the most identical；

Assuming that the position of given dummy contact pressure F is consistent with overlapping disk spring centrage, and giving virtual connecing Under touch pressure F effect, if total M shell monolithic disk spring is deformed in flexible body, then M shell is referred to as deforming cutoff layer；

If the deflection h that given dummy contact pressure F produces when the monolithic disk spring of ground floor can be made to be compressed₁Reach Maximum deformation quantity h when the monolithic disk spring of ground floor is driven plain₀, in this case, it is assumed that the monolithic dish bullet of front M-1 layer Maximum deformation quantity h when the deflection produced when spring is compressed all monolithic disk springs with ground floor are driven plain₀Identical, deformation The monolithic disk spring of the deflection no more than ground floor produced when the monolithic disk spring of cutoff layer M shell is compressed is driven plain Time maximum deformation quantity h₀；

The pressure F that the monolithic disk spring of overlapping disk spring ground floor consumes₁For:

Wherein, k, h₀Represent the spring rate of monolithic disk spring, maximum deformation quantity when being driven plain respectively；

The rigidity k of monolithic disk spring is:

$k=\frac{4E}{1-{\mathrm{\μ}}^2}\frac{l^3}{{\mathrm{\αD}}^2}$

Wherein, E, μ, α are respectively the elastic modelling quantity of monolithic disk spring, Poisson's ratio, design factor, concrete numerical value and monolithic The material of disk spring is relevant；

Design factor α meets:

$\mathrm{\α}=\frac{1}{\mathrm{\π}}\frac{{\left(\frac{C-1}{C}\right)}^2}{\frac{C+1}{C-1}-\frac{2}{\ln C}}$

Wherein, C is the ratio of external diameter and internal diameter:

$C=\frac{D}{d}$

Maximum deformation quantity h when monolithic disk spring is driven plain₀For:

h₀=H₀-l

In addition to overlapping disk spring ground floor and deformation cutoff layer M shell, the monolithic dish of overlapping remaining each layer of disk spring The pressure F that shape spring consumes_jFor:

F_j=k h₀

The span of j is [2, M-1]；

The deflection h of deformation cutoff layer M shell_MFor:

$h_M=\frac{F-\underset{i=1}{\overset{M-1}{\Σ}}{F}_i}{k}$

Step 3, makes given dummy contact pressure F act on virtual flexible body bump point, overlaps i-th layer of correspondence of disk spring Monolithic disk spring compressed, if overlapping disk spring before i layer all of monolithic disk spring consume pressure F_iSum Less than given dummy contact pressure F, and before overlapping disk spring, i layer all of monolithic disk spring generation compression total needs The decay time wanted meets the requirement of more than refreshing frequency 1000Hz, if amounting to through time delay T_iAfter, overlap disk spring i-th layer Monolithic disk spring be compressed to maximum deformation quantity h when being driven plain₀, only when the monolithic dish of overlapping disk spring i-th layer Shape spring is compressed to maximum deformation quantity h when being driven plain₀After, the monolithic disk spring that overlapping disk spring i+1 layer is corresponding Just starting to be compressed, the rest may be inferred, until the pressure sum that before overlapping disk spring, M shell all of monolithic disk spring consumes is not Less than given dummy contact pressure, or the monolithic disk spring of overlapping disk spring M shell produces what compression total needed Decay time is unsatisfactory for the requirement of refreshing frequency；

Use t_i、T_iRepresent that the monolithic disk spring of overlapping disk spring i-th layer produces the time time delay that compression needs respectively Between, before overlapping disk spring, i layer all of monolithic disk spring produces compression and amounts to the decay time needed, and makes interlayer Decay time meet with overlapping disk spring ground floor monolithic disk spring produce compression needs decay time t₁ For first term, Geometric Sequence with q as common ratio it is:

t_i=q^i-1t₁

Count to virtual flexible body surface from virtual protocol making contact, it is assumed that all of list of i layer before overlapping disk spring Sheet disk spring produces compression and amounts to the decay time T needed_iMeet T_i< T, wherein

$\begin{array}{c}{T}_i=t_1+t_2+t_3+...+t_i\\ =\frac{1-q^i}{1-q}\&CenterDot;t_1\end{array}$

T is the inverse of haptic feedback refreshing frequency；

The expression of deflection sum h of each layer in the deflection on described virtual flexible body surface, namely overlapping disk spring Formula is:

Wherein, (M-1) h₀For maximum deformation quantity when M-1 layer is driven plain before overlapping disk spring.

Beneficial effects of the present invention:

(1) compare with the most conventional flexible body deformation simulation haptic modeling method based on physical significance, this modeling In method, if the deflection produced when given dummy contact pressure can make the monolithic disk spring of ground floor be compressed reaches first Maximum deformation quantity when the monolithic disk spring of layer is driven plain, before in this case supposing, the monolithic disk spring of M-1 layer is pressed The maximum deformation quantity when deflection produced during contracting is all driven plain with the monolithic disk spring of ground floor is identical, thus improves and build The calculating speed of mould, it is ensured that the verisimilitude of deformation effect.

(2) due to every layer the external diameter of monolithic disk spring, internal diameter, thickness, free height, be driven plain time maximum distortion Amount, spring rate are the most identical, namely specification is the most identical, therefore in front M-1 layer, when the monolithic disk spring of any i-th layer is compressed The pressure consumed when the pressure consumed is compressed with the monolithic disk spring of ground floor is the most identical, calculates simple.

(3) by changing the external diameter of ground floor monolithic disk spring, internal diameter, thickness, free height in modeling method, being pressed Maximum deformation quantity at ordinary times, spring rate, so that it may different flexible bodies is carried out deformation simulation, so that the making of this modeling method More extensive by scope.

(4) can be applied to virtual surgery emulate, educate, entertain, deep space exploration, the field such as Aero-Space.

Accompanying drawing explanation

Fig. 1 is flexible body deformation simulation flow chart；

Fig. 2 is the modeling method journey figure of the overlapping disk spring dummy model of flexible force tactile sense reproduction；

Fig. 3 be flexible force tactile sense reproduction overlapping disk spring dummy model modeling method in pressure, deformation the number of plies with Decay time relation schematic diagram；

Fig. 4 is the modeling method schematic diagram of the overlapping disk spring dummy model of flexible force tactile sense reproduction, and (a) is original shape State, (b) is the state under compression.

Detailed description of the invention:

The overlapping disk spring of a kind of flexible force tactile sense reproduction that the present invention is proposed by the most shown flow process is empty The modeling method of analog model is described in detail:

The modeling method schematic diagram of the overlapping disk spring dummy model of flexible force tactile sense reproduction as shown in Figure 4.A kind of The modeling method of the overlapping disk spring dummy model of flexible force tactile sense reproduction, it specifically comprises the following steps that

Step 1, virtual scene initializes；

Step 2, under given dummy contact pressure F effect, when virtual protocol collides appointing on virtual flexible body surface Meaning point time, hang at the point of impingement external diameter be D, internal diameter be d, thickness be l, free height be H₀, maximum change when being driven plain Shape amount is h₀, spring rate be the monolithic disk spring of k, form overlapping disk spring ground floor；Monolithic dish at ground floor Under spring, equidirectional setting and the monolithic disk spring of the monolithic disk spring same specification of ground floor, form overlapping disk spring The second layer；Under the monolithic disk spring of the second layer, the monolithic of the monolithic disk spring same specification of equidirectional setting and ground floor Disk spring, forms overlapping disk spring third layer；The rest may be inferred, under the monolithic disk spring of i-th layer, equidirectional setting with The monolithic disk spring of the monolithic disk spring same specification of ground floor, forms overlapping disk spring i+1 layer；I=1,2,3 ..., N, N are natural number, overlap the external diameter of monolithic disk spring, internal diameter, thickness, free height in each layer of disk spring, be driven plain Time maximum deformation quantity, spring rate the most identical；

Assuming that the position of given dummy contact pressure F is consistent with overlapping disk spring centrage, and giving virtual connecing Under touch pressure F effect, if total M shell monolithic disk spring is deformed in flexible body, then M shell is referred to as deforming cutoff layer；

If the deflection h that given dummy contact pressure F produces when the monolithic disk spring of ground floor can be made to be compressed₁Reach Maximum deformation quantity h when the monolithic disk spring of ground floor is driven plain₀, in this case, it is assumed that the monolithic dish bullet of front M-1 layer Maximum deformation quantity h when the deflection produced when spring is compressed all monolithic disk springs with ground floor are driven plain₀Identical, deformation The monolithic disk spring of the deflection no more than ground floor produced when the monolithic disk spring of cutoff layer M shell is compressed is driven plain Time maximum deformation quantity h₀；

The pressure F that the monolithic disk spring of overlapping disk spring ground floor consumes₁For:

Wherein, k, h₀Represent the spring rate of monolithic disk spring, maximum deformation quantity when being driven plain respectively；

The rigidity k of monolithic disk spring is:

$k=\frac{4E}{1-{\mathrm{\&mu;}}^2}\frac{l^3}{{\mathrm{\&alpha;D}}^2}$

Wherein, E, μ, α are respectively the elastic modelling quantity of monolithic disk spring, Poisson's ratio, design factor, concrete numerical value and monolithic The material of disk spring is relevant；

Design factor α meets:

$\mathrm{\&alpha;}=\frac{1}{\mathrm{\&pi;}}\frac{{\left(\frac{C-1}{C}\right)}^2}{\frac{C+1}{C-1}-\frac{2}{\ln C}}$

Wherein, C is the ratio of external diameter and internal diameter:

$C=\frac{D}{d}$

Maximum deformation quantity h when monolithic disk spring is driven plain₀For:

h₀=H₀-l

In addition to overlapping disk spring ground floor and deformation cutoff layer M shell, the monolithic dish of overlapping remaining each layer of disk spring The pressure F that shape spring consumes_jFor:

F_j=k h₀

The span of j is [2, M-1]；

The deflection h of deformation cutoff layer M shell_MFor:

$h_M=\frac{F-\underset{i=1}{\overset{M-1}{\&Sigma;}}{F}_i}{k}$

Step 3, makes given dummy contact pressure F act on virtual flexible body bump point, overlaps i-th layer of correspondence of disk spring Monolithic disk spring compressed, if overlapping disk spring before i layer all of monolithic disk spring consume pressure F_iSum Less than given dummy contact pressure F, and before overlapping disk spring, i layer all of monolithic disk spring generation compression total needs The decay time wanted meets the requirement of more than refreshing frequency 1000Hz, if amounting to through time delay T_iAfter, overlap disk spring i-th layer Monolithic disk spring be compressed to maximum deformation quantity h when being driven plain₀, only when the monolithic dish of overlapping disk spring i-th layer Shape spring is compressed to maximum deformation quantity h when being driven plain₀After, the monolithic disk spring that overlapping disk spring i+1 layer is corresponding Just starting to be compressed, the rest may be inferred, until the pressure sum that before overlapping disk spring, M shell all of monolithic disk spring consumes is not Less than given dummy contact pressure, or the monolithic disk spring of overlapping disk spring M shell produces what compression total needed Decay time is unsatisfactory for the requirement of refreshing frequency；

Use t_i、T_iRepresent that the monolithic disk spring of overlapping disk spring i-th layer produces the time time delay that compression needs respectively Between, before overlapping disk spring, i layer all of monolithic disk spring produces compression and amounts to the decay time needed, and makes interlayer Decay time meet with overlapping disk spring ground floor monolithic disk spring produce compression needs decay time t₁ For first term, Geometric Sequence with q as common ratio it is:

t_i=q^i-1t₁

Count to virtual flexible body surface from virtual protocol making contact, it is assumed that all of list of i layer before overlapping disk spring Sheet disk spring produces compression and amounts to the decay time T needed_iMeet T_i< T, wherein

$\begin{array}{c}{T}_i=t_1+t_2+t_3+...+t_i\\ =\frac{1-q^i}{1-q}\&CenterDot;t_1\end{array}$

T is the inverse of haptic feedback refreshing frequency；

The expression of deflection sum h of each layer in the deflection on described virtual flexible body surface, namely overlapping disk spring Formula is:

Wherein, (M-1) h₀For maximum deformation quantity when M-1 layer is driven plain before overlapping disk spring.

Below as a example by virtual Medical hand and Virtual Cardiac Mode, enumerate the detailed description of the invention of technical solution of the present invention.

In this example, all virtual Medical hands and Virtual Cardiac Mode the most directly use and lead from 3DS MAX 2016 software The OBJ form gone out, with 2865 particles, virtual Medical hand that 5722 triangle griddings are constituted and 10026 particles, 19409 Carrying out deformation simulation as a example by the Virtual Cardiac Mode that triangle gridding is constituted, in experimentation, model obtains and amendment is the most square Just；Operating system is Windows 2010, based on 3DS MAX2016, OpenGL shape library, at Microsoft Visual Emulate on C++2015 Software Development Platform.

Under given dummy contact pressure F=4.0N effect, when detecting that virtual Medical hand collides virtual heart surface On arbitrfary point time, the overlapping dish of the internal filling flexible haptic feedback of the virtual Medical hand regional area mutual with virtual heart Shape spring dummy model, in interaction, output is fed back to use the virtual mould of overlapping disk spring of flexible force tactile sense reproduction The reaction that type calculates is the letter of the power tactile data of virtual heart real-time deformation emulation under given dummy contact pressure effect Number, as shown in Figure 1；

As shown in Figure 2 and Figure 4, hanging external diameter at the point of impingement is D=4 × 10^-4M, internal diameter are d=2.04 × 10^-4M, thickness Degree is l=2.25 × 10^-5M, free height are H₀=3.15 × 10^-5M, maximum deformation quantity when being driven plain are h₀=H₀-l= 3.15×10^-5-2.25×10^-5=9 × 10^-6M, spring rate are the monolithic disk spring of k；

Assuming that the position of given dummy contact pressure F is consistent with overlapping disk spring centrage, and giving virtual connecing Under touch pressure F effect, if total M shell monolithic disk spring is deformed in flexible body, then M shell is referred to as deforming cutoff layer；

The pilot process that calculates, last data equal round off method retain after arithmetic point 3.

If the deflection h that given dummy contact pressure F produces when the monolithic disk spring of ground floor can be made to be compressed₁Reach Maximum deformation quantity h when the monolithic disk spring of ground floor is driven plain₀, the monolithic dish bullet of M-1 layer before in this case supposing Maximum deformation quantity h when the deflection produced when spring is compressed all monolithic disk springs with ground floor are driven plain₀Identical, deformation The monolithic disk spring of the deflection no more than ground floor produced when the monolithic disk spring of cutoff layer M shell is compressed is driven plain Time maximum deformation quantity h₀,

The ratio C of external diameter and internal diameter is:

$C=\frac{D}{d}=1.96$

Design factor α is:

$\mathrm{\&alpha;}=\frac{1}{\mathrm{\&pi;}}\frac{{\left(\frac{C-1}{C}\right)}^2}{\frac{C+1}{C-1}-\frac{2}{\ln C}}=\frac{1}{\mathrm{\&pi;}}\frac{{\left(\frac{1.96-1}{1.96}\right)}^2}{\frac{1.96+1}{1.96-1}-\frac{2}{\ln 1.96}}=0.686$

Elastic modulus E=2.06 × 10 of monolithic disk spring⁵The material of flexible body is depended in MPa, Poisson's ratio μ=0.3；

The rigidity k of monolithic disk spring is:

$k=\frac{4E}{1-{\mathrm{\&mu;}}^2}\frac{l^3}{{\mathrm{\&alpha;D}}^2}=\frac{4\&times;2.06\&times;{10}^5}{1-{0.3}^2}\&times;\frac{{(2.25\&times;{10}^{-5})}^3}{0.686\&times;{(4\&times;{10}^{-4})}^2}=9.397\&times;{10}^{4}N/m$

Use t_i、T_iRepresent that the monolithic disk spring of overlapping disk spring i-th layer produces the time time delay that compression needs respectively Between, before overlapping disk spring, i layer all of monolithic disk spring produces compression and amounts to the decay time needed, and makes interlayer Decay time meet with overlapping disk spring ground floor monolithic disk spring produce compression needs decay time t₁ =10^-5S is first term, Geometric Sequence with q=1.1 as common ratio；

Assuming that haptic feedback refreshing frequency is 1100Hz, then the inverse of haptic feedback refreshing frequency

$T=\frac{1}{1100}s;$

If under given dummy contact pressure F effect, the monolithic disk spring of ground floor can be made to reach when being driven plain Maximum deformation quantity h₀, then the pressure F of the monolithic disk spring consumption of ground floor₁For:

F₁=k h₀=9.397 × 10⁴×9×10^-6=0.846N

F₁< F=4.0N

The monolithic disk spring of ground floor produces the decay time T that compression needs₁=t₁=10^-5S < T, meets and refreshes The requirement of frequency；Only it is compressed to maximum deformation quantity h when ground floor monolithic disk spring₀After, second layer monolithic disk spring Just start to produce compression.

If under given dummy contact pressure F effect, the monolithic disk spring of the second layer can be made to reach when being driven plain Maximum deformation quantity h₀, then the pressure F of the monolithic disk spring consumption of the second layer₂For:

F₂=k h₀=9.397 × 10⁴×9×10^-6=0.846N

The pressure sum that the monolithic disk spring of the first two layer consumes altogether is:

F₁+F₂=0.846+0.846=1.692N < F=4.0N

The monolithic disk spring of the first two layer produces compression and amounts to the decay time T needed₂=t₁+t₂=(1+q) t₁= (1+1.1)×10^-5=2.1 × 10^-5S < T, meets the requirement of refreshing frequency；Only pressed when the monolithic disk spring of the second layer It is reduced to maximum deformation quantity h₀After, the monolithic disk spring of third layer just starts to produce compression.

If under given dummy contact pressure F effect, the monolithic disk spring of third layer can be made to reach when being driven plain Maximum deformation quantity h₀, then the pressure F of the monolithic disk spring consumption of third layer₃For:

F₃=k h₀=9.397 × 10⁴×9×10^-6=0.846N

The pressure sum that the monolithic disk spring of three first layers consumes altogether is:

F₁+F₂+F₃=0.846+0.846+0.846=2.538N < F=4.0N

The monolithic disk spring of three first layers produces compression and amounts to the decay time T needed₃=t₁+t₂+t₃=(1+q+ q²)t₁=(1+1.1+1.1²)×10^-5=3.31 × 10^-5S < T, meets the requirement of refreshing frequency；Only when the monolithic of third layer Disk spring is compressed to maximum deformation quantity h₀After, the monolithic disk spring of the 4th layer just starts to produce compression.

If under given dummy contact pressure F effect, the monolithic disk spring of the 4th layer can be made to reach when being driven plain Maximum deformation quantity h₀, then the pressure F of the monolithic disk spring consumption of the 4th layer₄For:

F₄=k h₀=9.397 × 10⁴×9×10^-6=0.846N

The pressure sum that the monolithic disk spring of first four layers consumes altogether is:

F₁+F₂+F₃+F₄=0.846+0.846+0.846+0.846=3.384N < F=4.0N

The monolithic disk spring of first four layers produces compression and amounts to the decay time T needed₄=t₁+t₂+t₃+t₄=(1+q +q²+q³)t₁=(1+1.1+1.1²+1.1³)×10^-5=4.641 × 10^-5S < T, meets the requirement of refreshing frequency；Only when the 4th The monolithic disk spring of layer is compressed to maximum deformation quantity h₀After, the monolithic disk spring of layer 5 just starts to produce compression and becomes Shape.

If under given dummy contact pressure F effect, the monolithic disk spring of layer 5 can be made to reach when being driven plain Maximum deformation quantity h₀, then the pressure F of the monolithic disk spring consumption of layer 5₅For:

F₅=k h₀=9.397 × 10⁴×9×10^-6=0.846N

The pressure sum that the monolithic disk spring of first five layer consumes altogether is:

F₁+F₂+F₃+F₄+F₅=0.846+0.846+0.846+0.846+0.846=4.23N > F=4.0N

Therefore, the pressure sum that the monolithic disk spring of first five layer consumes altogether not less than given dummy contact pressure F, then the Five layers is deformation cutoff layer, it is not necessary to judge whether to meet the requirement of refreshing frequency again；

The deflection h of deformation cutoff layer layer 5₅For:

$h_5=\frac{F-\underset{i=1}{\overset{5-1}{\&Sigma;}}{F}_i}{k}=\frac{4.0-3.384}{9.397\&times;{10}^4}=6.555\&times;{10}^{-6}m$

In the deflection on described virtual flexible body surface, namely overlapping disk spring, deflection sum h of first five layer is:

H=(5-1) h₀+h₅=4 × 9 × 10^-6+6.555×10^-6=42.555 × 10^-6m

Note: the modeling method at the overlapping disk spring dummy model using flexible force tactile sense reproduction calculates given Under pressure effect flexible body real-time deformation emulation during, if these parameters of C, l choose excessive, then flexible force tactile sense reproduction Overlapping disk spring dummy model modeling method in overlap the deformation cutoff layer numerical value of disk spring just few, amount of calculation is little, Real-time is good, but deformation simulation poor effect；If it is too small that these parameters of C, l are chosen, then the overlapping of flexible force tactile sense reproduction The deformation cutoff layer numerical value overlapping disk spring in the modeling method of disk spring dummy model is the biggest, computationally intensive, real-time The best, but deformation simulation effect is preferable；Additionally t is being set₁And t_iBetween relation time, program to be considered run computer-chronograph The hardware configuration of itself, therefore during debugging whole program, these parameters of selection of compromising, the most repeatedly debug, thus Make deformation effect more life-like.

For verifying the implementation result of the present invention, operator touched by the handle of PHANTOM OMNI hand controller end, The deformation simulation that virtual heart is pressed by perception and the virtual Medical hand of control, and the power sense of touch letter that will produce in interaction Breath Real-time Feedback is to operator.Test result indicate that: this model is effective, in interaction, operator can in real time, truly Perceive deformation simulation during power tactile data between virtual Medical hand and virtual heart, perceived effect is true.

Claims (1)

1. the modeling method of the overlapping disk spring dummy model of flexible force tactile sense reproduction, it is characterised in that its step is as follows:

Step 1, virtual scene initializes；

Step 2, under given dummy contact pressure F effect, when virtual protocol collides the arbitrfary point on virtual flexible body surface Time, hang at the point of impingement external diameter be D, internal diameter be d, thickness be l, free height be H₀, maximum deformation quantity when being driven plain For h₀, spring rate be the monolithic disk spring of k, form overlapping disk spring ground floor；Monolithic disk spring at ground floor Under, equidirectional setting and the monolithic disk spring of the monolithic disk spring same specification of ground floor, form overlapping disk spring second Layer；Under the monolithic disk spring of the second layer, equidirectional setting is dish-shaped with the monolithic of the monolithic disk spring same specification of ground floor Spring, forms overlapping disk spring third layer；The rest may be inferred, under the monolithic disk spring of i-th layer, and equidirectional setting and first The monolithic disk spring of the monolithic disk spring same specification of layer, forms overlapping disk spring i+1 layer；I=1,2,3 ..., N, N For natural number, the external diameter of monolithic disk spring in the overlapping each layer of disk spring, internal diameter, thickness, free height, when being driven plain Maximum deformation quantity, spring rate are the most identical；

Assuming that the position of given dummy contact pressure F is consistent with overlapping disk spring centrage, and in given dummy contact pressure Under the effect of power F, if total M shell monolithic disk spring is deformed in flexible body, then M shell is referred to as deforming cutoff layer；

If the deflection h that given dummy contact pressure F produces when the monolithic disk spring of ground floor can be made to be compressed₁Reach first Maximum deformation quantity h when the monolithic disk spring of layer is driven plain₀, in this case, it is assumed that the monolithic disk spring quilt of front M-1 layer Maximum deformation quantity h when the deflection produced during compression all monolithic disk springs with ground floor are driven plain₀Identical, deformation cut-off When the monolithic disk spring of the deflection no more than ground floor that the monolithic disk spring of layer M shell produces when being compressed is driven plain Maximum deformation quantity h₀；

The pressure F that the monolithic disk spring of overlapping disk spring ground floor consumes₁For:

Wherein, k, h₀Represent the spring rate of monolithic disk spring, maximum deformation quantity when being driven plain respectively；

The rigidity k of monolithic disk spring is:

$k=\frac{4E}{1-{\mathrm{\&mu;}}^2}\frac{l^3}{{\mathrm{\&alpha;D}}^2}$

Wherein, E, μ, α are respectively the elastic modelling quantity of monolithic disk spring, Poisson's ratio, design factor, concrete numerical value and monolithic dish The material of spring is relevant；

Design factor α meets:

$\mathrm{\&alpha;}=\frac{1}{\mathrm{\&pi;}}\frac{{\left(\frac{C-1}{C}\right)}^2}{\frac{C+1}{C-1}-\frac{2}{\ln C}}$

Wherein, C is the ratio of external diameter and internal diameter:

$C=\frac{D}{d}$

Maximum deformation quantity h when monolithic disk spring is driven plain₀For:

h₀=H₀-l

In addition to overlapping disk spring ground floor and deformation cutoff layer M shell, the monolithic dish bullet of overlapping remaining each layer of disk spring The pressure F that spring consumes_jFor:

F_j=k h₀

The span of j is [2, M-1]；

The deflection h of deformation cutoff layer M shell_MFor:

$h_M=\frac{F-\underset{i=1}{\overset{M-1}{\&Sigma;}}{F}_i}{k}$

Step 3, makes given dummy contact pressure F act on virtual flexible body bump point, overlaps i-th layer of corresponding list of disk spring Sheet disk spring is compressed, if the pressure F that before overlapping disk spring, i layer all of monolithic disk spring consumes_iSum is less than Before given dummy contact pressure F, and overlapping disk spring, i layer all of monolithic disk spring produces compression and amounts to needs Decay time meets the requirement of more than refreshing frequency 1000Hz, if amounting to through time delay T_iAfter, the list of overlapping disk spring i-th layer Sheet disk spring is compressed to maximum deformation quantity h when being driven plain₀, only when the monolithic dish bullet of overlapping disk spring i-th layer Spring is compressed to maximum deformation quantity h when being driven plain₀After, the monolithic disk spring that overlapping disk spring i+1 layer is corresponding is just opened Beginning to be compressed, the rest may be inferred, until the pressure sum of M shell all of monolithic disk spring consumption is not less than before overlapping disk spring Given dummy contact pressure, or the time delay that the monolithic disk spring generation compression total of overlapping disk spring M shell needs Time is unsatisfactory for the requirement of refreshing frequency；

Use t_i、T_iRespectively represent overlapping disk spring i-th layer monolithic disk spring produce compression need decay time, Before overlapping disk spring, i layer all of monolithic disk spring produces compression and amounts to the decay time needed, and makes interlayer Decay time meets the decay time t producing compression needs with the monolithic disk spring of overlapping disk spring ground floor₁For First term, Geometric Sequence with q as common ratio be:

t_i=q^i-1t₁

Count to virtual flexible body surface from virtual protocol making contact, it is assumed that i layer all of monolithic dish before overlapping disk spring Shape spring produces compression and amounts to the decay time T needed_iMeet T_i< T, wherein

$\begin{array}{c}{T}_i=t_1+t_2+t_3+...+t_i\\ =\frac{1-q^i}{1-q}\&CenterDot;t_1\end{array}$

T is the inverse of haptic feedback refreshing frequency；

In the deflection on described virtual flexible body surface, namely overlapping disk spring, the expression formula of deflection sum h of each layer is:

Wherein, (M-1) h₀For maximum deformation quantity when M-1 layer is driven plain before overlapping disk spring.