undercut feature recognition ina an injection mould design sysetm
Undercut feature recognition in an injection mould design system
M.W.Fu a,J.Y.H.Fuh b,A.Y.C.Nee b,*
a PROM Group,Manufacturing IT Division,Gintic Institute of Manufacturing Technology,Singapore,Singapore638075
b Department of Mechanical and Production Engineering,National University of Singapore,Singapore,Singapore119260
Received6April1999;received in revised form30June1999;accepted7July1999
Abstract
In the design of plastic injection moulds,the presence of undercut features would affect mould cost and structure.In this paper,the de?nition,classi?cation of undercut features and the related notions to identify them are presented.Based on the proposed undercut feature de?nition and taxonomy,the relationships between the undercut features and their mouldability are described.The de?nition of undercut feature parameters and the computational methodologies to determine them are proposed.The undercut feature draw range and directions are introduced based on the V-maps of undercut features.The recognition criteria from which the undercut features can be identi?ed are presented.In consideration of blending surfaces,two pairs of notions,viz.actual and virtual?rst adjacent surfaces,actual and virtual edges are proposed.As undercut features can be consistently recognized,the identi?cation criteria for undercut features are given.The industrial case studies show that the methodologies developed are ef?cient in recognition and extraction of undercut features in complex injection moulded parts.?1999Elsevier Science Ltd.All rights reserved.
Keywords:Undercut feature recognition;Computer-aided design;Injection mould design
1.Introduction
Mould and die making is an important supporting indus-try since their related products represent more than70%of the non-standard components in consumer products.The production runs,however,are typically of small lot-size and with great varieties.The high demand for shorter design and manufacturing lead times,good dimensional and overall quality,and rapid design changes has become the bottle-necks in die and mould industries.For mould-making companies wishing to maintain the competitive edge, there is the urgent need to shorten the design and manufac-turing lead times by automating the design process using advanced manufacturing equipment,processes and improv-ing the skill level of their employees.Currently,some of the mould-making companies use3-D commercial CAD soft-ware tools to design moulds,however,many companies are still designing moulds manually,which is time-consuming and error-prone.The development of a Computer-Aided Injection Mould Design System(CAIMDS)has become the focus of research in both industry and academia.
In CAIMDS,the recognition and extraction of undercut features is one of the prime issues as it affects the determi-nation of parting direction,parting lines and surfaces,generation of the core and cavity,and creation of the local tools and their actuating mechanisms.The determination of optimal parting direction depends on the types,number, volumes,directions and locations of undercut features[1]. The optimal parting direction should ideally be in the direc-tion where the number of undercut features and their corre-sponding volumes are maximal.The rest of the undercut features not considered would need side-cores,side-cavities or other local tools.In automatic determination of parting lines and surfaces,the parting lines and surfaces should include as many undercut features as possible such that the number of the side-cores or side-cavities needed is mini-mal[2].In generating the core and cavity,some undercut hole features should be identi?ed and extracted such that they can be“patched”for the Boolean Regularized Differ-ence Operation(BRDO)between the core/cavity box and the moulded part.The core/cavity box contains the moulded part and is separated into core/cavity blocks.In creating local tools(side-cores,side-cavities,form pins and split cores),the“heads”of these local tools are generated based on the geometric entities of the related undercut features.Consequently,all the undercut features in a mould-ing should be identi?ed?rst before the other design activ-ities can be carried out.
Although the determination of undercut features is impor-tant in CAIMDS,there are relatively few published works because of the complexity of injection-moulded parts.Most
0010-4485/99/$-see front matter?1999Elsevier Science Ltd.All rights reserved. PII:S0010-4485(99)https://www.wendangku.net/doc/5b4105816.html,/locate/cad
*Corresponding author.Tel.:?65-874-2892;fax:?65-779-1459. E-mail address:mpeneeyc@https://www.wendangku.net/doc/5b4105816.html,.sg(A.Y.C.Nee)
of the previous work in this area addresses the determination of parting direction,rather than providing a complete solu-tion for CAIMDS.The representative work has been presented by Chen et al.[3,4]and Mochizuki et al.[5], where BRDO is used to recognize and extract the undercut features in a moulding by obtaining the regularized differ-ence between the part to be moulded and its convex hull.In Mochizuki’s work,the given moulding Q is denoted as a concave polyhedron.The convex polyhedron is generated by“clay-?lling”into the concavities of Q to make it the smallest convex polyhedron,which can just fully contain the original concave polyhedron.After subtracting the convex polyhedron by the given concave polyhedron,the remaining parts are the potential undercut features,which are called“sealed pockets”in Chen’s work[3].From the viewpoint of solid modeling,the above process is the same as generating the convex hull CH(Q)for a given3-D concave polyhedron Q and?nding the regularized differ-ence between the convex hull CH(Q)and Q.The regularized difference CH Q ??Q(??denotes a regularized differ-ence operation)represents the potential undercut features. The dif?cult task in BRDO is the extraction of the potential undercut feature and feature geometric entities from CH Q ??Q.Since CH Q ??Q also represents a3-D solid and all its undercut features are linked together,its decomposition into many single undercut features is equiva-lent to the recognition and extraction of the features from a 3-D solid model.
Besides the above methodology,Ganter and Skolgund[6] also reported an approach in recognizing and extracting three classes of concave undercut features,viz.internal voids,single-and multi-surface holes and boundary pertur-bations from a B-Rep model for the development of casting core in casting mould design.The features recognized are limited to concave features.The recognition of convex features is not mentioned in their work.The convex portions of the moulding may also be possible undercut features,and hence the method is not suitable for recognizing and extract-ing all the undercut features in a moulding.Rosen et al.[7] classi?ed undercut features into external undercut features, accessible laterally with respect to the mould closure direc-tion,and internal undercut features,accessible only through the mould core.For a given parting direction,the?rst step is to ignore all the surfaces with a positive or zero dot product between the surface’s normal vector and the parting direc-tion,and all the other surfaces are then projected onto the plane perpendicular to the parting direction.If the projected surfaces overlap,then the surfaces form an undercut feature. This method can be used to design side-cores and side-cavities.Hui[8]presented a mouldability analysis based on the geometry of moulded parts.The notions of the inter-nal and external undercuts are de?ned and the mouldability is studied based on these notions.However,the recognition of these undercut features and the undercut feature para-meters,which greatly in?uence mouldability,are not discussed.
In this paper,the de?nition and classi?cation of undercut features are presented.Based on the undercut feature char-acteristics,the relationship of mouldabilty and undercut features is described.The de?nition of undercut feature parameters and their determination are also presented.For the different undercut features,the recognition criteria of these features are also proposed.
2.De?nition and classi?cation of undercut features
2.1.De?nition of undercut features
In a moulding,concave regions such as local recesses, slots,pockets and holes are potential undercut features; while convex regions such as cylinders,bosses,cones and spheres can also be undercut features.If the main core and cavity and their inserts cannot mould the undercut features, side-cores or side-cavities or other local tools are required to be incorporated in the mould structure.In Fig.1,there are three undercut features A,B,C in the moulded part.If the parting direction is selected as shown in the?gure,then undercut feature A can be moulded in by the main core, but undercut features B and C cannot be moulded in by the main core,cavity and inserts,and would need side-cores and side-cavities for moulding.Consequently,they are the real undercuts.It is noted that whether A,B or C would become the real undercut is dependent on the parti-cular parting direction.
2.2.Classi?cation of undercut features
Based on the mould structure and the local tools(e.g. side-cores,side-cavities,form pins,and split cores)required for a moulding,the undercut features could be classi?ed into two types:External Undercut Features(EU)and Internal Undercut Features(IU).EUs are moulded in by the side-cores or side-cavities;while the IUs are moulded by form pins or split cores inside the core and cavity.Side-cores and side-cavities are withdrawn outwards from the moulded part before injection;while form pins or split cores are with-drawn inwards from the moulded part.EU is the restriction region,which prevents the moulding from being withdrawn from the cavity;while IU prevents the moulding from being ejected from the core.On the contrary,according to the geometric characteristics of the EU and IU features,EU
M.W.Fu et al./Computer-Aided Design31(1999)777–790
778
Fig.1.Undercut features.
features can be further classi?ed into Inside External Under-cut features (IEU)and Outside External Undercut features (OEU).In order to de?ne IEUs as shown in Fig.2,the target surface,which is de?ned as the surface in which there are undercut features to be identi?ed,is investigated.It is found that the edges of the target surface form different edge-loops in which the edges are linked together.In a target surface,the largest edge-loop is its outside boundary and is desig-nated as the external edge-loop (an external edge-loop 1is shown in Fig.2(b)).The other edge-loops lying inside the largest edge-loop are known as the internal edge-loop (e.g.internal edge-loops 2and 3as illustrated in Fig.2(b)).On the contrary,from the viewpoint of surface features,the adjacent surfaces of a target surface are classi?ed into exter-nal and internal adjacent surfaces.The internal adjacent surfaces can be divided into different groups in which the adjacent surfaces are linked together and form an undercut feature.In Fig.2(a),the target surface is the top surface of the block and the external adjacent surfaces are the four-sided surfaces.Its internal adjacent surfaces lying inside the target surface form the two undercut features.Based on these de?nitions,the internal and external edge-loops are the intersection boundaries of the internal and external adja-cent surfaces with the target surface respectively.The IEU is composed of the inside adjacent surfaces,and its intersec-tion boundary with the target surface is the internal edge-loop;while the OEU is a boundary perturbation made up by the whole target surface and its ?rst adjacent surfaces.If the target surface has only one edge-loop and some connecting edges between the target surface and the ?rst adjacent surfaces (S AF )are concave,the target surface and its S AF s will form an OEU.In other words,the OEU is composed of target surface and the S AF s,which connecting edges between target surface and S AF are concave.In Fig.3,(a)is an OEU (it can also be an OIU).Fig.3(b)and (c)show the concave and convex edges,the ?rst adjacent surfaces and the second adjacent surfaces (S AS )of the target surface respectively.The target surface F i and its S AF s form an OEU or OIU.The undercut features are classi?ed in such a way that it is easy to set up the recognition criteria.Similarly,the
internal undercut features can also be classi?ed into inside internal undercut feature (IIU)and outside internal undercut feature (OIU).The de?nitions and classi?cation are similar to the above.Fig.4shows an IIU which consists of internal adjacent surfaces and the second adjacent surface (S AS ).The classi?cation of undercut features is summarized in Fig.5.Fig.6shows a moulding with different undercut features.In the moulding,undercut feature A is an EU since it prevents the moulding from being withdrawn from the cavity.It can also be further classi?ed into an IEU because it consists of internal adjacent surfaces of the target surface.Similarly,undercut feature B is also an IEU.Undercut feature C is an IU because it hinders the moulding from being withdrawn from the core.It can further be classi?ed into IIU since it consists of the internal adjacent surfaces of the target surface.Undercut feature D is an OEU because it consists of the whole target surface and its ?rst adjacent surfaces.
3.Undercut feature parameters
Undercut feature parameters are undercut feature volume
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(a) A moulding (b) Its top view
Inside external undercut features consisting
Fig.2.De?nition of inside external undercut features.
(a) Undercut feature
(b) First adjacent surfaces (S AF )
(c) Second adjacent surfaces (S AS )
AF
Fig.3.Outside external undercut feature.
and undercut feature direction.The undercut feature volume
can be determined based on the geometric entities of the undercut feature,while the undercut directions can be deter-mined by the visibility map(V-map)of the undercut feature surfaces.The V-map of a surface is a notion to describe the surface visibility and is formed by the points on the unit sphere from which the surface is completely visible from in?nity[9].The surface V-map is a twin notion of Gauss map,which is introduced by Gauss through mapping the surface normal of a given point in a surface onto a unit sphere to describe the surface property[10].
3.1.Undercut feature volume
Undercut feature volume U V refers to the3-D space enclosed by the geometric entities of undercut feature.It is also equal to the volume of the concave portions of the core,cavity or local tools,or the volume of the mould insert or local tool that inserts into the concave portions of the moulding.U V can be determined based on the geometric entities of undercut features.For the IEU,U V can be made up by the internal adjacent surfaces and the common second adjacent surface as shown in Fig.7(a)and can be approxi-mately calculated based on the area of the internal edge-loop,area of the common second adjacent surface(S AS)and the length of undercut feature edges.The method to calcu-late the area of edge-loop and a surface is presented in Ref.
[2].If the undercut feature consists of only one curved surface,U V is the volume formed by the curved surface as shown in Fig.7(b).For the OEU in Fig.8(a),U V is made up by the target surface and its positive undercut feature edges as shown in Fig.8(b).The undercut feature edges(UE)are the wire frame of undercut features.If one of the vertices of undercut feature edge lies in the target surface,it is neces-sary to de?ne the vector of these edges.The vector is de?ned as the ray away from the target surface.If the vector of undercut feature edge V UE i meets Eq.(1),the undercut
feature edge is positive,otherwise,it is negative.
V UE i?L i?0 1 where L i is the central normal vector of the target surface.
Consequently,the undercut volume shown in Figs.8and9
can be calculated based on the target surface and its positive
undercut feature edges.The equation is as follows:
U V A T?A UE ?UE 2 where A T is the area of the target surface,A UE is the area
bounded by the vertices of the positive undercut edges(not
in the target surface,if the number of positive undercut
edges is equal to2,A UE 0)and UE is the average length of the positive undercut edges projected onto the central
normal vector of the target surface.
3.2.V-map and draw-range of undercut feature
The V-map of undercut feature V-map(U)is the intersec-
tion of all V-maps of the surfaces of which the undercut
feature is composed.V-map(U)can be de?ned as
V-map U
n
i
V-map F i 3
where n is the number of surfaces belonging to the undercut feature.V-map(F i)is the V-map of the undercut surface F i. For the undercut feature shown in Fig.10(a),the corre-sponding V-map(U)is illustrated in Fig.10(b).In the?gure, F j1and F j2are one group of the?rst adjacent surfaces,and H j1and H j2are another group of the?rst adjacent surfaces. The draw-range of undercut features refers to the range in which the local tools can be withdrawn from the moulding. In V-map(U),the boundary of V-map constitutes the draw-range of the undercut features.In practice,not all withdra-wal directions in the draw-range are preferred withdrawal directions,only the directions in which the local tools can be effectively withdrawn are considered.These preferred with-drawal directions are called undercut feature directions in this paper.
3.3.Undercut feature directions
The direction of undercut feature can be de?ned as the directions in which the local tool can be withdrawn most
M.W.Fu et al./Computer-Aided Design31(1999)777–790 780
Fig.4.Inside internal undercut feature.
Undercut features IU s
Inside internal undercut features (IIU)
Outside internal undercut features (OIU)
Inside external undercut features (IEU) EU s
Outside external undercut features (OEU)
Fig.5.Undercut feature classi?cation.
A: D:OEU Fig.6.Different undercut features in a moulding.
effectively from the undercut features to avoid the warpage of the moulding.Based on the V-maps of undercut features,it is found that any point in the V-map(U )can be a feasible withdrawal direction of the local tool.For any given under-cut feature,there exist the most preferred withdrawal direc-tions,which are different from case to case.For inside external or inside internal undercut features,the undercut direction can be determined uniquely.For the outside exter-nal or outside internal undercut features,there is more than
one preferred withdrawal direction and thus more than one undercut direction.For the case shown in Fig.10,the preferred direction is in the intersectional line of two bi-sectional planes between the ?rst adjacent surfaces F j 1and F j 2,and F h 1and F h 2.
4.Outside external undercut features
Based on the edge characteristics of target surface F i with its adjacent surfaces,there are three types of cases,viz.three edges,four edges and more than four edges.They may form three-edge-OEU (3-OEU),four-edge-OEU (4-OEU)and more than four-edge-OEU (?4-OEU).The undercut criteria,which are the proposed basis to identify the under-cut features and undercut directions can be determined according to the geometrical and topological information of the target surface and the undercut feature surfaces.4.1.Three-edge-OEU (3-OEU)
In this case,the edges of the target surface are three and at least one of the edges is concave,the target surface and its ?rst adjacent surfaces will form an undercut feature.Supposing that the target surface F i has three edges.Let L i be the normal vector of F i at the surface centre and L ji j 1;2;3;the ?rst subscript refers to the adjacent surface and the second subscript refers to the coordinate axis)be the normal vector of the ?rst adjacent surfaces.Ecave(F i )and Evex(F i )are the concave and convex edges number of the target surface respectively.The undercut features,V-map and its undercut directions are summarized in Table 1.
4.2.Four-edge-OEU (4-OEU)
In this case,the target surface has four edges and four adjacent surfaces.Let the ?rst adjacent surfaces be divided into two groups (i.e.groups j and h )in which the two oppo-site surfaces are in the same group.The normal vectors at the surface centre of the two groups are L ji and L hi j j 1;j 2;h h 1;h 2 :The undercut criteria,V-maps and
M.W.Fu et al./Computer-Aided Design 31(1999)777–790
781
(a) Undercut feature (b) Undercut Feature Volume
Internal edge-loops
Undercut edges(UE
)
S
AS
Fig.7.IEU volume.
(a)
(b)
(c)
1
i
UE
Fig.8.Undercut feature volume of OEU (Case 1).
undercut directions can be determined based on the geome-trical information and topological relationships of F i with its adjacent surfaces and are summarized in Table 2.4.3.More than four-edge-OEU (?4-OEU)
If the edges of the target surface are more than four,there are more than four ?rst adjacent surfaces.The target surface and its adjacent surfaces can constitute the different convex and concave portions in the moulded part,which can become undercut features.All the possible cases are listed as follows:
4.3.1.All edges are concave edges i :e :E F i Ecave F i and Evex F i 0
In this case,all the edges of the target surface are concave edges,the target surface and its ?rst adjacent surfaces will form a depression in the moulded part.A particular case E F i 5 is shown in Fig.11.In this case,the target surface is a ?ve-edge surface.The target surface and its ?rst adjacent surfaces form the concave portion in the moulding.It can be an OEU or OIU since it consists of
the target surface and its ?rst adjacent surfaces.The under-cut criteria and directions can be determined based on the undercut geometric entities and their properties.For the case,they can be de?ned as:
Criteria of ?4-edge-OEU (1):(1)E F i ?4;and Evex F i 0:Directions of ?4-edge-OEU (1):
(1)L i ,if L i ?L ji ?0 j 1;2;…n ;where n is the number of ?rst adjacent surface),or
(2) L j 1;i ×L j 2;i ?L j 2;i ×L j 3;i ?…… =2;if L i ?L j ;i ?0 j j 1;j 2or j 3……n
4.3.2.All edges are convex edges E F i Evex F i and Ecave F i 0
In this case,all the edges of the target surface are convex edges.From the 2-D viewpoint of the target surface,however,there may exist some “concave edges”in the target surface.These concave edges are de?ned as the ones inside the convex hull of the target surface.These concave edges and their corresponding adjacent surfaces can form undercut features in the moulding.Fig.12(a)shows the undercut feature of this case,(b)shows that all the edges in the target surface are convex edges,and (c)shows the concave edges in the convex hull CH(F i )of the target surface F i .Three edges are concave in the convex hull CH (F i )and their corresponding ?rst adjacent surfaces form a concave undercut feature.In order to judge these concave edges in the target surface based on convex hull CH (F i ),the
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(a) Undercut feature
(b) Undercut edges
(c) Undercut volume
4
Fig.9.Undercut feature volume of OEU (Case 2).
(a) Undercut feature
(b) Corresponding V-map
Feasible withdrawal directions
Draw-range of Fig.10.V-map of undercut features.
following algorithms are proposed.The original coordinate system X–Y–Z is?rstly transformed into X H–Y H–Z H with the origin at the target surface centre O H and Z H in the direction of the surface central normal,as shown in Fig.13.The procedures to determine the convexity and concavity of the edges in the target surfaces are as follows:
(a)Extract all the vertices of the target surface and arrange the vertices in a CCW order.
(b)Extract all the edges and determine the line type of Edge V i?13V i?1 :Edge V i?13V i?1 links vertices V i?1and V i?1(Fig.13).If the directional cosine L ei i 1;2 of Edge V i?13V i?1 in X H–Y H coordinate system satis?es?L ei??0:707;it is a Y-type line,otherwise,an X-type line.
(c)Determine the convexity and concavity of vertices V i?1;V i;V i?1:Y-type Edge V i?13V i?1 :
x H i?f V i?13V i?1 ?Y H Y H
i
when y H i?1?y H i?1
x H i?f V i?13V i?1 ?Y H Y H
i when y H i?1?y H i?1
W
a
Y 4
where f V i?13V i?1 is the line equation of the
Edge V i?13V i?1 :If x H i and y H i coordinates of vertex V i
satisfy Eq.(4),then vertices V i?1,V i and V i?1will consti-
tute a convex portion of the target surface,otherwise,it is
concave.If it is concave,the edges between vertices V i?1,
V i and V i?1will be the concave edge in the convex hull
CH(F i).
If Eq.(5)is satis?ed,vertices V i?1,V i and V i?1will consti-
tute a convex portion of the moulded part,otherwise,it is
concave.Similarly,the rule can be used to determine the
concavity of edges between vertices V i?1,V i and V i?1in the
concave hull CH(F i).
X-type Edge V i?13V i?1 :
y H i?f V i?13V i?1 ?X X H
i
when X H i?1?X H i?1
y H i?f V i?13V i?1 ?X X H
i
when X H i?1?X H i?1
W
a
Y 5
In this case,the concave edge related adjacent surfaces can
form undercut features and undercut criteria,and undercut M.W.Fu et al./Computer-Aided Design31(1999)777–790783
Table1
The undercut features of three-edge target surface and its directions
Undercut cases Undercut V-map Undercut criteria Undercut
directions
(1)E F i 3;
(2)Ecave F i 3 and Evex F I 0:(1)L i,if L i?L ji?0(j 1;2and3);
(2) L1i×L2i?L2i×L3i?L3i×L1i =3; if L i?L ji?0;(j 1;2or
3).
(1)E F i 3;
(2)Ecave F i 2
and Evex F i 1:
(1)L i?0;if L i?L1i?0and L i?L2i?0;
(2) L i×L1i?L i×L2i =?L i×L1i?L i×
L2i?;if L i?L1i?0or L i?L2i?0
:
(1)E F i 3;
(2)Ecave F i 1
and Evex F i 2:
(1)L i?0;if L i?L1i?0;
(2) L i?L1i =2;if L i?L1i?0:
parameters can be determined based on the undercut geometric entities.
4.3.3.Some edges are convex and others are concave
Evex F i 0and Ecave F i 0
There are two possible cases in this category.The ?rst is that the concave edges in the moulding are linked together and their corresponding?rst adjacent surfaces form the convex undercut feature in the moulding as shown in Fig.14(a).Another case is that the concave edges are not linked together,but their corresponding adjacent surfaces form an undercut feature in the moulding(Fig.14(b)).In these two cases,the undercut parameters and criteria can be
M.W.Fu et al./Computer-Aided Design31(1999)777–790 784
Table2
Undercut features of four-edge target surface and its directions
Undercut cases Undercut V-map Undercut Criteria and Directions(U D
)
Criteria:
E F i 4;and Ecave F i 4:
Directions:
(a) L j1;i?L j2;i?L h1;i?L h2;i =?L j1;i?L j2;i?L h1;i?L h2;i?;If L i?L ji?0
and L i?L hi?0; j j1;j2;h h1;h2 ;
(b)L I;If L i?L ji 0and L i?L hi 0; j j1;j2;h h1;h2 ;
(c)L i L j1;i×L h1;i?L j2;i×L h2;i =2;If L i?L ji?0 j j1;j2;h1or h
2).
h1
F
1
)
h2
)
Criteria:
E F i 4;Ecave F i 3;and Evex F i 1:
Directions:(a) L h2;i×L j1;i?L j1;i×L h1;i =?L h2;i×L j1;i?L j1;i×L h1;i?;
when L i?L j;i?0 j j1;h1;h2 ;or L i×L h1;i?L i×L h2;i =?L i×L h1;i?L i×L h2;i?;
when L j?L j1;i?0 j i;h1;h2 ;
(b) L i×L h1;i?L i×L h2;i =?L i×L h1;i?L i×L h2;i?;when L i?L j;i?0 j j1;h1or h2),
or L h2;i×L j1;i?L j1;i×L h
1;i
=?L h2;i×L j1;i?L j1;i×L h1;i?;
when L j?L j1;i?0 j i;h1;h2 :
j2
)
(F
i
)
Criteria:
E F i 4;Ecave F i 2;and Evex F i 2:
Directions:
(a) L j1;i?2L i?L j2;i =?L j1;i?2L i?L j2;i?;if L j1;i?L i?0and L j2;i?L i?0;
(b) L i×L
j1;i
?L j2;i×L i =?L i×L j1;i?L j2;i×L i?;if L j1;i?L i?0or L j2;i?L i?0:
)
Criteria:E F i 4;Ecave F
i
2;and Evex F i 2:
Directions:
(a)L i,if L j;i?L i?0 j j1;j2 ;
(b)L j1,i,if L j1;i?L i?0or L j2,i,if L j1;i?L i?0:
Criteria:
E F i 4;Ecave F i 1;and Evex F i 3:
Directions:(a)L i,L j1,i,or L i?L j1;i =?L i?L j1;i?,if L j1;i?L i?0;
(b) L i?L j1;i =?L i?L j1;i?;if L j1;i?L i?0:
determined based on the concave edges,the central normal of the concave edge related adjacent surfaces.
5.Inside external undercut features
If the edge-loops of the target surface are more than two,there are more than one IEU in the target surface consisting of edge-loop related adjacent surfaces.Fig.15shows that IEUs,edge-loops,and edge-loop related adjacent surfaces.In Fig.15,(a)shows two IEUs,one is a convex and the other is concave IEU,(b)is the edge-loops of undercut features with target surface,and (c)shows the edge-loop related surfaces of which the IEUs are composed.The main procedures to identify the IEU are as follows:
(a)Determine the internal and external edge-loops of the target surface.
(b)Identify the convexity and concavity of internal edge-loops.
(c)Extract the edge-loop-related surfaces.If the
edge-loop is concave,the common second adjacent surface of the edge-loop-related surfaces needs to be extracted.The common second adjacent surfaces are shown in Fig.15(c).
6.Internal undercut features
Fig.16shows the internal undercut features.There are also two types of internal undercuts,namely inside internal undercut (IIU)and outside internal undercut (OIU).The de?nitions and criteria of IIU and OIU are similar to those of IEU and OEU.The following rule is used to determine if the undercut feature is an internal or external undercut feature.If the undercut feature is an IU,the rays in the undercut direction and its opposite direction will have more than one intersection point with the moulding besides the point in which the rays are cast.If the undercut feature is an EU,there will be no intersection point of the ray in the undercut direction with the moulding besides the point in which the ray is cast.As can be seen in Fig.16,if Ray 1is in the undercut direction,there are two intersection points P 1?1and P 1?2between the ray and moulding excluding the point from which the ray is cast.Similarly,Ray 2has at least one intersection point P 2?1excluding the casting point.7.Identi?cation criteria
Based on the undercut feature classi?cation,there are four types,viz.IIU,IEU,OIU and OEU.From different target surfaces,an undercut feature may be recognized as
M.W.Fu et al./Computer-Aided Design 31(1999)777–790
785
Fig.11.?4-edge-OEU undercut feature (?4-OEU (1)).
(a) Concave undercut feature (b) Convex edges in target surface
(c) Convex hull of F i (CH (F i )) and concave edges in CH (F i )
Concave undercut
Concave edge
F i
Fig.12.Concave undercut feature,convex edges in F i and concave edges in CH (F i )(?4-edge-OEU (2)).
one of the several types of undercut features and a large undercut feature may cover two or several smaller undercut features.Fig.17shows an undercut feature recognized as two different undercut features.If target surface 1is referred,the undercut feature will be recognized as IIU or IEU,and OIU or OEU while target surface 2is considered.Actually,these two are the same undercut feature due to the same geometrical entities and undercut volumes.Fig.18shows another undercut feature.From target surface 1,it is recognized as undercut feature 1and belongs to IIU or IEU as shown in Fig.18(b).From target surfaces 2and 3,the undercut feature is recognized as different undercut features,namely,undercut features 2and 3(Fig.18(c)and (d)).As the compound undercut feature 1consists of undercut features 2and 3,it is necessary to derive a criterion for the identi?cation of undercut features.
In order to describe the criterion,it is necessary to inves-tigate the undercut feature parameters.There are three undercut feature parameters,viz.undercut geometrical enti-ties,which constitute the undercut features,undercut direc-tion and undercut volume.The undercut geometrical entities are the surfaces,edges and vertices.If the undercut features meet the following requirements,they are considered as the same undercut feature in the moulding,i.e.
1.Same undercut feature geometrical entities;and
2.Same undercut volume,but the undercut directions can be different.If a compound undercut feature covers other small undercut features,they should meet the following conditions:
(1)Geometrical entities condition:U k GE
U i
GE ?U j GE ;and
(2)Undercut volume condition:U k V
U i
V ?U j V :If an undercut feature k meets the above conditions,it will
cover undercut features i and j .In Fig.18,as undercut feature 1meets the above conditions,it includes undercut features 2and 3.Undercut features 2and 3must therefore be removed from the undercut feature sets.
M.W.Fu et al./Computer-Aided Design 31(1999)777–790
786Fig.13.Concave edges in the target surface.
(a)(b)
Fig.14.Undercut features made up by concave edges in CH (F i )(?4-edge-OEU (3)).
Fig.15.IEUs,edge-loops and edge-loop related adjacent surfaces.
Fig.16.Internal undercut feature.
8.Blending surfaces in moulding
In the moulding,the blending surfaces are often used in smoothing the junction of two surfaces.This is done for the reasons of good stress distribution,good mouldability and for certain special functions of the moulded parts.The blending surfaces are usually cylindrical surfaces with four edges.Two of them are straight edges and the other two are curved edges.When the blending surfaces are the ?rst adjacent surfaces of the target surface,the following two pairs of notions are proposed to recognize the undercut features consisting of these blending surfaces.
8.1.Actual and virtual?rst adjacent surfaces
If the blending surfaces are the?rst adjacent surfaces of the target surface,the undercut feature recognized may not represent the real undercut features.Fig.19(a)shows an undercut feature consisting of the target surface,blending surfaces(?rst adjacent surfaces)and2-s adjacent surfaces. From previously de?ned criteria,the undercut feature usually consists of the target surface and its?rst adjacent surfaces.In this case,the target surface and its?rst adjacent surfaces(blending surfaces)forming the undercut feature as
shown in Fig.19(b)cannot represent the real undercut
feature.The notion of virtual?rst adjacent surface S H AF is
hence proposed.
The actual?rst adjacent surfaces S AF are those which are
directly adjacent to the target surface;while virtual?rst
adjacent surfaces S H AF are the second adjacent surfaces
when the?rst adjacent surfaces are the blending surfaces.
Fig.19(c)shows two?rst adjacent surfaces S AF which are
also blending surfaces.Fig.19(d)shows the second adjacent
surfaces of the target surface.In recognition of this undercut
feature,the two second adjacent surfaces are considered as
the?rst adjacent surfaces,they are called virtual?rst adja-
cent surfaces S H AF as shown in Fig.19(e).In this case,the
undercut feature parameters are determined based on the
target surface and S H AF.
8.2.Actual and virtual edges
The actual edges of the target surface form the external
edge-loop of the target surface;while the virtual edges of
the target surface constitute the external edge-loop of the
target surface and its blending surfaces.Fig.19(f)shows the
actual edges E(F i)and the virtual edges E H F i of the target surface.When the?rst adjacent surfaces are the blending
surfaces,the actual edges E(F i)are substituted by the virtual
edges E H F i :Since the concavity and convexity of the edges in the actual edges are the same as the virtual edges,the virtual edges of the target surface can be used in the recog-nition of undercut features and determination of undercut feature parameters.
In summary,the notions of actual?rst adjacent surfaces
and virtual?rst adjacent surface are important in recogniz-
ing undercut features consisting of the blending surface.If
M.W.Fu et al./Computer-Aided Design31(1999)777–790787
Fig.17.Recognition of undercut features based on target surfaces.
(b) Undercut feature 1(c) Undercut feature 2(d) Undercut feature 3
https://www.wendangku.net/doc/5b4105816.html,pound undercut features.
there is no blending surface,S H AF is the same as S AF .Simi-larly,actual edges E H F i are the same as virtual edges E (F i ).
9.Case studies
The undercut feature de?nitions,classi?cation and criteria have been implemented in a software program.The following cases are used to validate the robustness of the above methodologies and algorithms.
For a given injection moulded part shown in Fig.20,all the undercut features can be recognized and extracted based on the proposed methodology.The thin-wall plastic moulded part is made up of various types of surfaces.In order to investigate the robustness of the program,the part is split into ?ve sections and only four of them are investi-gated,as one of the sections is similar.In Fig.20(a),there
are four undercut features.Undercut feature 1consists of a cylindrical surface.It is an IEU since it lies in another curved surface.The undercut direction is in the axis direc-tion of the cylindrical surface as shown by arrow 1in the ?gure.From the different target surfaces,different undercut features can be identi?ed.Undercut feature 2is an OEU consisting of the entire target surface and its ?rst adjacent surfaces.The undercut direction is shown by arrow 2in the ?gure.Undercut feature 3is also an OEU.If the side surface is taken as the target surface,the target surface and its ?rst adjacent surfaces form a concave feature 3H .Actually,undercut features 3and 3H are the same concave portion in the moulded part and should be the same OEU based on the identi?cation criterion.Therefore,undercut features 3and 3H must be combined together to form undercut feature 3as shown in Fig.20(e).Undercut features 4and 5are OEUs and their directions are shown by arrows (Fig.20(b)and
M.W.Fu et al./Computer-Aided Design 31(1999)777–790
788(a) Moulding
(b) Undercut features consisting of S AF and S’AF
(c) First adjacent surfaces S AF (d) Second adjacent surfaces S AS
(e) Actual S AF and Virtual S’AF (f) Actual edges E(F i ) and Virtual edges E’(F i )
i )
Target surface F
i
Blending surfaces and S AF of the target
Undercut feature consisting of blending surface and
Real undercut
Actual first adjacent surfaces S AF of the
i
Virtual first adjacent surfaces S’AF of the
Fig.19.Geometry of blending surfaces.
(c)).In Fig.20(d),undercut features7and8are also OEUs, but undercut feature10is an IEU consisting of?ve surfaces. Like undercut feature1,undercut feature10can also be identi?ed as two undercut features from two different target surfaces.These two undercut features are exactly the same as shown.Fig.20(e)shows all the undercut features recog-nized and extracted based on the above recognition metho-dology and identi?cation criterion.
Fig.21shows another plastic part made up of several types of surfaces.Undercut features1,3and8are IEUs consisting of cylindrical surfaces.The undercut directions are in the axis direction of the cylindrical surfaces.Undercut feature4is an OEU consists of the bottom surface,four?rst adjacent surfaces(cylindrical blending surfaces),and eight second adjacent surfaces(four cylindrical blending surfaces and four planar surfaces).The undercut direction is deter-mined based on the geometrical information of the second adjacent surfaces.Undercut features2and6are the bosses on the bottom surfaces.They are IEUs and the undercut directions are in the axis directions of the cylindrical surfaces.Undercut feature7is the boss at the back of the surface.Like undercut features2and6,its undercut direc-tion is in the cylindrical axis.Undercut features5and9are IIUs.Form pins or split cores are needed to mould these undercut features no matter which parting direction is chosen.Besides undercut features5and9,side-cores and side-cavities are also needed to mould undercut features1, 3,7since their undercut directions are not in the parting direction.
10.Conclusions
An ef?cient methodology which systematically presents the undercut feature de?nition,classi?cation,undercut feature parameters,and the recognition criteria of all types of undercut features is proposed in this paper.Based on the undercut feature taxonomy,characteristics and geometric entities,the algorithms related to feature parameter deter-mination,classi?cation and recognition criteria are
M.W.Fu et al./Computer-Aided Design31(1999)777–790
789
Fig.20.Case
1.
Fig.21.Cases2.
presented and implemented.The methodology and algo-rithms consider different types of cases and different geometric entities such as curved and free-formed surfaces.In considering blending surfaces,two pairs of notions,viz.actual and virtual ?rst adjacent surfaces,actual and virtual edges are used in the recognition of undercut features.This pioneering work provides a complete solution for the further design activities in CAIMDS,such as the determination of optimal parting direction,parting lines and surfaces,genera-tion of core and cavity blocks and the creation of local tools.To validate the robustness of the methodology and algo-rithms,several industrial cases have been tested and shown to be ef?cient in providing feasible solutions for a CAIMDS.
References
[1]Nee AYC,Fu MW,Fuh JYH,Lee KS,Zhang YF.Determination of
optimal parting direction in plastic injection mould design.Annals of the CIRP 1997;46/1:429–32.
[2]Nee AYC,Fu MW,Fuh JYH,Lee KS,Zhang YF.Automatic deter-mination of 3-D parting lines and surfaces in plastic injection mould design.Annals of the CIRP 1998;47/1:95–98.
[3]Chen LL,Chou SY,Woo TC.Parting directions for mould and die
https://www.wendangku.net/doc/5b4105816.html,puter-Aided Design 1993;25:762–8.
[4]Chen LL,Chou SY,Woo TC.Partial visibility for selecting a parting
direction in mould and die design.Journal of Manufacturing Systems 1995;14:319–30.
[5]Mochizuki T,Yuhara N.Method of extracting potential undercut and
determining optimum withdrawal direction for mould designing.International Journal of Japanese Society of Precision Engineering 1992;26:68–73.
[6]Ganter MA,Skoglund PA.Feature extraction for casting core devel-opment.ASME,Journal of Mechanical Design 1993;115:744–9.[7]Rosen DW.Towards automatic construction of moulded and dies.
Computers in Engineering,ASME 1994;1:317–26.
[8]Hui KC.Geometric aspects of the mouldability of https://www.wendangku.net/doc/5b4105816.html,puter-Aided Design 1997;29:197–208.
[9]Gan JG,Woo TC,Tang K.Spherical maps:their construction,proper-ties,and approximation.ASME,Journal of Mechanical Design 1994;116:357–63.
[10]Hilbert D,Cohn-Vossen S.Geometry and the imagination,New York:
Chelsea,1983Translated by P.Nementi.
M.W.Fu et al./Computer-Aided Design 31(1999)777–790
790Professor A.Y.C.Nee received his PhD from the Institute of Science and Technology,University of Manchester (UMIST)in 1973.He joined the then University of Singapore in 1974.He had held several appointments including Director of CAE/CAD/CAM Centre,Head of the Department of Mechanical and Production Engineering,Vice Dean and Dean of Engineering Faculty,Directors of the Of?ce of University Relations and the Of?ce of Qual-ity Management,etc.in the university.In 1982,he became the ?rst recipient outside USA to
receive the Outstanding Young Manufacturing Engineer’s Award from the Society of Manufacturing Engineers.In 1990,he was elected an Active Member of CIRP and a Fellow of the Society of Manufacturing Engineers.Professor Nee has over 300technical publications in refereed journals and conferences.He is the editorial board member and associate editor of twelve international journals.His research interests include Computer-aided Design of Metal Stamping Dies and Plastic Injection Moulds,Rapid Prototyping,Computer-aided Process and Fixture Planning,and Application of AI Techniques in
Manufacturing.
Dr Jerry Fuh Y.H.received his PhD (Mech Eng)from University of California at Los Angeles (UCLA)in 1992.After graduation he worked with the CAM development group at the Unigraphics Division of EDS in US and then joined the National University of Singa-pore in 1993as a Lecturer and is currently an Associate Professor.He obtained his BS (Mech Eng)from National Chia-Tung University and MS from National Taiwan University.He left Taiwan to USA to pursue advanced study in 1984.After obtaining the MS (Mfg Eng)
from UCLA in 1985,he worked for four years for Menasco Aerosystems Corp.and Micropolis Corp.in Southern California as CIM and Automation Engineer,respectively.His research interests include Fixture Design &Analysis,Integrated CAD/CAM,Rapid Prototyping Technique,and Injec-tion Mould
Design.
Dr Fu Mingwang received his B.Eng and M.Eng from Northwestern Polytechnical Univer-sity,P.R.China and PhD from National University of Singapore.He is currently a Research Fellow at Gintic Institute of Manu-facturing Technology,Singapore.His research interests include Metal Forming Technology,CAE,CAD,Computer-aided Design of Metal Stamping Dies and Plastic Injection Moulds,and Integrated
CAD/CAPP/CAM.
高考物理电路的基本规律及其应用单元测试题(含答案)
2019高考物理电路的基本规律及其应用单 元测试题(含答案) 由查字典物理网为您提供的电路的基本规律及其应用单元测试题，大家一定要在平时的练习中不断积累，希望给您带来帮助! 一、选择题 1. 关于电源的电动势，下列说法正确的是( ) A.电源的电动势等于电源两端的电压 B.电源不接入电路时，电源两极间的电压大小等于电动势 C.电动势的国际单位是安培 D.常见的铅蓄电池电动势为1.5V 【答案】选B. 【详解】电源电动势等于电源路端电压与内电压之和，只有外电路是断路时，电源两端的电压等于电源电动势，A错，B对；电动势的国际单位是伏特，C错；常见铅蓄电池的电动势为2 V，D错. 2.下列关于电源电动势的说法中正确的是( ) A.在某电池的电路中，每通过2 C的电荷量，电池提供的电能是4 J，那么这个电池的电动势是0.5 V B.电源的路端电压增大时，其电源的电动势一定也增大 C.无论内电压和外电压如何变化，其电源的电动势一定不变 D.电源的电动势越大，电源所能提供的电能就越多
【答案】选C. 【详解】由E= 得E=2 V，则A错误；电源的电动势与外电路无关，只由电源自身的性质决定，则B错C对；电源的电动势大，所提供的能量不一定大，电源的电动势取决于通过电源的电量与电动势的乘积，D错误. 3.某实验小组用三只相同的小灯泡连接成如图所示的电路，研究串并联电路的特点.实验中观察到的现象是( ) A.K2断开，K1与a连接，三只灯泡都熄灭 B.K2断开，K1与b连接，三只灯泡亮度相同 C.K2闭合，K1与a连接，三只灯泡都发光，L1、L2亮度相同 D.K2闭合，K1与b连接，三只灯泡都发光，L3的亮度小于L2的亮度 【答案】选D. 【详解】K2断开，K1与a连接时三只灯泡串联，三只灯泡应该亮度相同，A错误；K2断开，K1与b连接时，L1、L2两只灯泡串联，L3被断开没有接入电路，B错误；K2闭合，K1与a连接时只有L2亮，L1和L3被短路，C错误；K2闭合，K1与b连接时，L1和L3并联，然后与L2串联，此时三只灯泡都发光，L3的亮度与L1的亮度相同，都小于L2的亮度，D正确. 4.如图所示，水平放置的平行板电容器中有一个带电液滴正
最常用轴承型号尺寸
6000系列深沟球轴承型号规格表 轴承代码 内径 d 毫米 英寸 外径 D 毫米 英寸 宽度 W 毫米 英寸 倒角 r 毫米 英寸 基本额定负荷 KN 极限转速 重量 Kg/pc 动负荷 C 静负荷 C 0 脂 r/min 油 r/min 6000 6001 6002 6003 6004 6005 6006 6007 6008 6009 6010 6011 6012 6013 6014 6015 6016 6017 6018 10 .3937 12 .4724 15 .5906 17 .6693 20 .7874 25 .9843 30 1.1811 35 1.3780 40 1.5748 45 1.7717 50 1.9685 55 2.1654 60 2.3622 65 2.9551 70 2.7559 75 2.9528 80 3.1496 85 3.3465 90 3.5433 26 1.0236 28 1.1024 32 1.2598 35 1.3780 42 1.6535 47 1.8504 55 2.1654 62 2.4409 68 2.6772 75 2.9528 80 3.1496 90 3.5433 95 3.7402 100 3.9370 110 4.3307 115 4.5276 125 4.9213 130 5.1181 140 5.5118 8 .3150 8 .3150 9 .3543 10 .3937 12 .4724 12 .4724 13 .5118 14 .5512 15 .5906 16 .6299 16 .6299 18 .7087 18 .7087 18 .7087 20 .7874 20 .7874 22 .8681 22 .8681 24 .9449 0.3 .012 0.3 .012 0.3 .012 0.3 .012 0.6 .024 0.6 .024 1.0 .039 1.0 .039 1.0 .039 1.0 .039 1.0 .039 1.1 .043 1.1 .043 1.1 .043 1.1 .043 1.1 .043 1.1 .043 1.1 .043 1.5 .059 4.55 5.10 5.60 6.80 9.40 10.10 13.20 16.00 16.80 21.00 21.80 28.30 29.50 31.90 39.70 41.60 47.50 49.50 58.00 1.96 2.39 2.84 3.35 5.05 5.85 8.30 10.30 11.50 15.10 16.60 21.20 23.20 25.00 31.00 33.50 40.00 43.00 49.50 20000 19000 18000 17000 15000 13000 12000 10000 8000 7200 6400 5700 5000 4800 4600 4400 4300 4200 4000 28000 26000 24000 22000 19000 17000 15000 13000 11000 9000 7800 7000 6300 6100 5800 5600 5500 5300 5100 0.019 0.021 0.030 0.039 0.069 0.080 0.116 0.155 0.185 0.231 0.250 0.362 0.385 0.440 0.600 0.6400 0.8540 0.8900 1.0200 6200系列深沟球轴承规格型号表
呼和浩特市高考物理一轮专题： 第32讲 电路的基本规律及应用B卷
呼和浩特市高考物理一轮专题：第32讲电路的基本规律及应用B卷 姓名:________ 班级:________ 成绩:________ 一、单选题 (共9题；共18分) 1. （2分）电阻R1 与R2并联在电路中，通过R1与R2的电流之比为1∶2，则当R1 与R2串联后接入电路中时，R1和R2两端电压之比U1∶U2为（） A . 1∶2 B . 2∶1 C . 1∶4 D . 4∶1 2. （2分）下列用电器正常工作时，在相同的时间内产生热量最多的是（） A . “220V，60W”的电风扇 B . “220V，60W”日光灯 C . “220V，60W”的电热器 D . 一样多 3. （2分） (2019高二上·宝山期中) 在如图所示的电路中，输入电压U=8V，灯泡L标有“3V 6W”字样，M 为电动机．若灯泡恰能正常发光时，电动机的输入电压是（） A . 3V B . 5V C . 8V
D . 11V 4. （2分） (2017高二上·九江期末) 在如图所示的电路中，电源的电动势为E，内阻为r，平行板电容器C 的两金属板水平放置，R1和R2为定值电阻，P为滑动变阻器R的滑动触头，G为灵敏电流表，A为理想电流表．开关S闭合后，C的两板间恰好有一质量为m、电荷量为q的油滴处于静止状态．在P向上移动的过程中，下列说法正确的是（） A . A表的示数变大 B . 油滴向下加速运动 C . G中有由b至a的电流 D . 电源的输出功率一定变大 5. （2分） (2017高二上·黑龙江期中) 如图所示，电源电动势大小为E，内阻大小为r，闭合开关S，当滑动变阻器的滑片P向左滑动的过程中（） A . 灯泡L变亮 B . 电流表读数变大，电压表读数变小 C . 电源的总功率先变大后变小 D . 处于电容器C两板间某固定的正点电荷的电势能变大 6. （2分）在如图所示电路中，当滑动变阻器滑片P向下移动时，则（）
【物理文档】2019届高中物理二轮复习热点题型专练专题7.2电路的基本规律及应用及答案(1).doc
专题7.2 电路的基本规律及应用 1.如图所示，E为内阻不能忽略的电池，R1、R2、R3为定值电阻，S0、S为开关， 与分别为电压表和电流表。初始时S 与S均闭合，现将 S断开，则 ( ) A．的读数变大，的读数变小 B．的读数变小，的读数变大 C．的读数变小，的读数变小 D．的读数变大，的读数变大 答案：D 解析：将S断开后，闭合电路的总电阻增大，根据闭合电路的欧姆定律可得：I ＝E R＋r ，干路电流I减小，路端电压U＝E－Ir变大，电阻R3两端的电压U3＝E－I(R1 ＋r)增大，通过电阻R3的电流I3＝U 3 R 3 变大，选项D正确，A、B、C错误。 2.如图所示电路中，4个电阻阻值均为R，开关S闭合时，有质量为m、带电量为q的小球静止于水平放置的平行板电容器的正中间。现断开开关S，则下列说法不正确的是 ( ) A．小球带负电 B．断开开关后电容器的带电量减小 C．断开开关后带电小球向下运动 D．断开开关后带电小球向上运动 答案：D 3．在测量电珠伏安特性实验中，同学们连接的电路中有两个错误电路，如图所示。电源内阻不计，导线连接良好，若将滑动变阻器的触头置于左端，闭合S，在向右端滑动触头过程中，会分别出现如下四种现象：
a．电珠L不亮；电流表示数几乎为零 b．电珠L亮度增加；电流表示数增大 c．电珠L开始不亮；后来忽然发光；电流表从示数不为零到线圈烧断 d．电珠L不亮；电流表从示数增大到线圈烧断 与上述a b c d 四种现象对应的电路序号为 ( ) A．③①②④B．③④②① C．③①④②D．②①④③ 答案：A 4．电池甲和乙的电动势分别为E1和E2，内电阻分别为r1和r2，已知E1 轴承型号含义对照表, 轴承类型代号 进口轴承常用类型代号（指型号的开头的数字或者字母，比如6200，6开头就是深沟球轴承，NU,NJ为圆柱滚子轴承）： 调心球轴承—1; 调心滚子轴承—2； 圆锥滚子轴承—3； 推力球轴承—5 深沟球轴承—6； 角接触球轴承—7； 圆柱滚子轴承—N； 滚针轴承—NA; 如何去看懂一个轴承，6200轴承 最右边两位数字表示轴承的公称内经尺寸当内径在20~480MM范围的时候，内径乘以五就是内径尺寸 10~17。 右起第三位是直径系列代号：直径系列代号有7，8，9，0，1，2，3，4，5等外径尺寸依次递增。 右起第四位是宽度系列代号，用8，0，1，2，3，4，5，6表示宽度尺寸递增。相同内径的同类轴承，外廓尺寸大（外径，宽度）则承载能力强。 轴承类型对照 轴承型号含义------轴承有0-9类（没有5类） 0类：双列角接触球轴承（通常省略）例：（0）3204 A 1类：自调心球轴承例：1201 ETN9 2类：球面滚子轴承、球面滚子推力轴承例：22209 E 29328 E 3类：圆锥滚子轴承例：32016 X/Q 4类：双列深沟球轴承例：4206 ATN9 深沟球轴承尺寸 5类：推力球轴承例：51100 6类：深沟球轴承例：6213-2Z 7类：角接触球轴承例：7305 BECBM 8类：圆柱滚子推力轴承例：81111 TN N类：圆柱滚子轴承第二个字母，有时候第三个字母，用来确定法兰结构，例如：NJ，NU，NUP; 双列或多列圆柱滚子轴承的型号总是以NN开头。 例：NU 2317 ECJ C类：CARB轴承C 2205 QJ类：四点接触球轴承例：QJ 217 MA。 轴承类型特点作用型号对照 双列角接触球轴承：能承受较大的径向和轴向联合负荷和力矩负荷，用于限制轴和外壳双向轴向位移的部件中。常见的双列角接触球轴承型号：3200ATN轴承、3203A-ZTN轴承、3205ATN轴承、3207ATN轴承等 推力滚子轴承：推力圆锥滚子轴承，推力圆柱滚子轴承用于承受轴向载荷为主的轴、径向联合载荷，但径向载荷不得超过轴向载荷的55% 。与其他推力滚子轴承相比，此种轴承摩擦因数较低，转速较高，并具有调心性能。常见的推力滚子轴承型号：81120轴承、81209 轴承、81217轴承等 圆锥滚子轴承：圆锥滚子轴承可以承受大的径向载荷和轴向载荷。由于圆锥滚子轴承只能传递单向轴向载荷，因此，为传递相反方向的轴向载荷就需要另一个与之对称安装的圆锥滚子轴承。常见圆锥滚子轴承型号：52375/52637轴承、30312JR轴承、H913849轴承等 深沟球轴承：深沟球轴承主要承受径向载荷，也可同时承受径向载荷和轴向载荷。当其仅承受径向载荷时，接触角为零。常见的深沟球轴承型号：6200轴承，6308轴承，6201轴承，6000轴承，6309轴承等深沟球 一滚动轴承 1、滚动轴承的结构、分类及特点 结构 滚动轴承（以下简称轴承）一般由内圈、外圈、滚动体和保持架组成。（如图） 内圈与外圈之间装有若干个滚动体，由保持架使其保持一定的间隔避免相互接触和碰撞，从而进行圆滑的滚动。 轴承按照滚动体的列数，可以分为单列、双列和多列。 1）、内圈、外圈 内圈、外圈上滚动体滚动的部分称作滚道面。球轴承套圈的滚道面又称作沟道。 一般来说，内圈的内径、外圈的外径在安装时分别与轴和外壳有适当的配合。 推力轴承的内圈、外圈分别称作轴圈和座圈。 2）、滚动体 滚动体分为球和滚子两大类，滚子根据其形状又分为圆柱滚子、圆锥滚子、球面滚子和滚针。 3）、保持架 保持架将滚动体部分包围，使其在圆周方向保持一定的间隔。 保持架按工艺不同可分为冲压保持架、车制保持架、成形保持架和销式保持架。 按照材料不同可分为钢保持架、铜保持架、尼龙保持架及酚醛树脂保持架。 分类 轴承受负荷时作用于滚动面与滚动体之间的负荷方向与垂直于轴承中心线的平面内所形成的角度称作接触角，接触角小于45°主要承受径向负荷称为向心轴承，在45°~90°之间主要承受轴向负荷称为推力轴承，根据接触角和滚动体的不同，通用轴承分类如下： 深沟球轴承（单、双列） 向心球轴承角接触球轴承（单、双列） 四点接触球轴承 调心球轴承 向 心圆柱滚子轴承（单、双、四列） 轴向心滚子轴承圆锥滚子轴承（单、双、四列）滚承滚针轴承（单、双列） 动调心滚子轴承 轴 承推力球轴承推力球轴承（单、双列） 推力角接触球轴承（单、双向） 推 力推力圆柱滚子轴承 轴推力滚子轴承推力圆锥滚子轴承 承推力滚针轴承 推力调心滚子轴承 特点 1.3.1滚动轴承的优点 滚动轴承虽有许多类型和品种，并拥有各自固定的特征，但是，它们与滑动轴承相比较，却具有下述共同的优点： （1）、起动摩擦系数小，与动摩擦系数之差少。 （2）、国际性标准和规格统一，容易得到有互换性的产品。 §7.3 电路的基本规律及其应用（复习学案） 【复习目标】 1． 理解闭合电路的欧姆定律并能应用。 2． 掌握串，并联电路的特点。 3． 能够对电表进行改装并知道其原理。 4．能够分析电路的动态问题。 【自主复习】 一 闭合电路的欧姆定律 1．闭合电路 (1)组成 ①内电路： 的电路，内电阻所降落的电压称为 . ②外电路： 的用电器和导线组成的电路，其两端电压称为外电压或路端电压. （2）在外电路中，沿电流方向电势 ． 在内电路中，沿电流方向电势 ． （3）内外电压的关系：E ＝_________． 2．闭合电路欧姆定律 （1)内容：闭合电路里的电流跟电源的电动势成_____，跟内、外电路的电阻之和成_____． (2)公式????? I ＝_____ (只适用于纯电阻电路).E ＝______ (适用于任何电路). 3．路端电压与外电阻的关系 (1)一般情况：根据U ＝IR ＝E R ＋r R ＝E 1＋r R 可知，当R 增大时，U______． (2)特殊情况 外电路断路时，R 为无穷大，I ＝0，U ＝ . 电源两端短路时，R ＝0，U ＝0，I ＝ . 4．路端电压跟电流的关系 (1)关系式：U ＝______. (2)用图象表示如下图所示． 图象 物理意义 图线与纵轴交点 表示______ 提示：若—图象中的纵坐标()不是从零开始时，此时图线与横坐标的交点小于短路电流，但图线的斜率仍然等于电源的内阻． 二串、并联电路 1．串、并联电路特点 2.几个有用的结论 (1)串联电路的总电阻____电路中任意一个电阻，电路中任意一个电阻变大时，串联总电 阻____． (2)并联电路的总电阻_____电路中任意一个电阻，任意一个电阻变大时，总电阻_____． (3)无论电阻怎样连接，每一段电路消耗的电功率P总等于各个电阻消耗的电功率之和． 三与电学实验有关的基本仪器 1．小量程电流表(表头) 主要由磁场和放入其中可转动的_____组成，当线圈中有电流通过时，线圈在______作用下带动指针一起偏转，电流越大，指针偏转的角度越大，从表盘上可直接读出电流值． 三个参数：满偏电流I g，表头内阻R g，满偏电压U g，它们的关系：U g＝_____. 2．电压表、电流表的改装 教案 第一章电路的基本概念与基本定律 单元教案首页 三、电路的基本定律 1.有关电路结构的名词 （1）支路：由单个或几个电路元件串联而成的电路分支。 （2）节点：三条或三条以上支路的连接点。 （3）回路：电路中任意一个由若干支路组成的闭合路径。 （4）网孔：电路中的回路内部不含有支路的回路叫做网孔。 2.基尔霍夫电流定律（KCL） （1）任何时刻，流出（或流入）一个节点的所有支路电流的代数和恒等于零。ΣI=0（2）任何时刻流入节点的电流之和等于流出节点的电流之和。ΣI i=ΣI o 3.基尔霍夫电压定律（KVL） （1）任何时刻沿着一个回路的所有支路电压的代数和恒等于零。ΣU=0 （2）任何时刻沿任意闭合路径的全部电压升之和等于电压降之和。ΣU升= ΣU降 四、例题讲解 【例1-1】如图1-5所示，用方框代表某一电路元件，其电压、电流如图中所示。求图中各元件功率，并说明该元件实际上是吸收还是释放功率? 解 :(a)电压、电流的参考方向关联， 元件的功率为P=UI=5×3=15 W >0，元件吸收功率。 (b)电压、电流的参考方向非关联， 元件的功率为P=-UI=-5×3=-15 W <0，元件释放功率。 (c)电压、电流的参考方向非关联， 元件的功率为P=-UI=-5×3=-15 W <0，元件释放功率。 (d)电压、电流的参考方向关联， 元件的功率为P=UI=5×3=15 W >0，元件吸收功率。 【例1-2】如图1-8所示电路，已知U S1=2V，U S2=6V，U S3=4V，R1=1.5Ω， R2=1.6Ω，R3=1.2Ω。按图示电流参考方向，若I1=1A，I2=-3A。 试求:(1)电流I3;(2)电压U AC和U CD。 解（略）见教材Ｐ5 【巩固小结】1．电压和电流的参考方向 2．基尔霍夫定律的应用 【课后练习】Ｐ9 Ｔ3、Ｔ6、Ｔ7、Ｔ9、 南京市高考物理一轮专题：第32讲电路的基本规律及应用（I）卷 姓名:________ 班级:________ 成绩:________ 一、单选题 (共9题；共18分) 1. （2分）三个电阻的阻值之比为R1∶R2∶R3＝1∶2∶5，并联后接入电路，则通过三个支路电流的比值为（） A . 1∶2∶5 B . 5∶2∶1 C . 10∶5∶2 D . 2∶5∶10 2. （2分）磁电式电流表(表头)最基本的组成部分是磁铁和放在磁铁两极之间的线圈，由于线圈的导线很细，允许通过的电流很弱，所以在使用时还要扩大量程．已知某一表头G ，内阻Rg＝30 Ω，满偏电流Ig＝5 mA，要将它改装为量程为0～3 A的电流表，所做的操作是（） A . 串联一个570 Ω的电阻 B . 并联一个570 Ω的电阻 C . 串联一个0.05 Ω的电阻 D . 并联一个0.05 Ω的电阻 3. （2分）如图所示为某一电路的局部，已知I=3A，I1=2A，R1=10Ω，R2=5Ω，R3=10Ω，则通过电流表的电流大小和方向分别为（） A . 1.5A，向右 B . 1.5A，向左 C . 0.5A，向右 D . 0.5A，向左 4. （2分） (2017高二上·淄川期末) 如图所示的电路中，电源的电动势E和内电阻r恒定不变，电灯L恰能正常发光，如果滑动变阻器的滑片向b端滑动，则（） A . 电灯L更亮，电流表的示数减小 B . 电灯L更亮，电流表的示数增大 C . 电灯L变暗，电流表的示数减小 D . 电灯L变暗，电流表的示数增大 5. （2分） (2017高二上·珠海期末) 在如图所示的电路中，R1、R2、R3和R4皆为定值阻，R5为可变电阻，电源的电动势为ε，内阻为r．设电流表A的读数为I，电压表V的读数为U．当R5的滑动触点向图中a端移动时（） A . I变大，U变大 B . I变大，U变小 C . I变小，U变大 第一章电路基本概念和基本定律 知识要点 ·了解电路和电路模型的概念； ·理解电流、电压和电功率；理解和掌握电路基本元件的特性； ·掌握电位和电功率的计算；会应用基尓霍夫定律分析电路。 随着科学技术的飞速发展，现代电工电子设备种类日益繁多，规模和结构更是日新月异，但无论怎样设计和制造，几乎都是由各种基本电路组成的。所以，学习电路的基础知识，掌握分析电路的规律与方法，是学习电工学的重要内容，也是进一步学习电机、电器和电子技术的基础。本章的重点阐明有关电路的基本概念、基本元件特性和电路基本定律。 1.1电路和电路模型 1.1.1 电路的概念 1. 电路及其组成 简单地讲，电路是电流通过的路径。实际电路通常由各种电路实体部件（如电源、电阻器、电感线圈、电容器、变压器、仪表、二极管、三极管等）组成。每一种电路实体部件具有各自不同的电磁特性和功能，按照人们的需要，把相关电路实体部件按一定方式进行组合，就构成了一个个电路。如果某个电路元器件数很多且电路结构较为复杂时，通常又把这些电路称为电网络。 手电筒电路、单个照明灯电路是实际应用中的较为简单的电路，而电动机电路、雷达导航设备电路、计算机电路，电视机电路是较为复杂的电路，但不管简单还是复杂，电路的基本组成部分都离不开三个基本环节：电源、 负载和中间环节。 电源是向电路提供电能的装置。它可以将其他形式的能量，如化学能、热能、机械能、原子能等转换为电能。在电路中，电源是激励，是激发和产生电流的因素。负载是取用电能的装置，其作用是把电能转换为其他形式的能（如：机械能、热能、光能等）。通常在生产与生活中经常用到的电灯、电动机、电炉、扬声器等用电设备，都是电路中的负载。中间环节在电路中起着传递电能、分配电能和控制整个电路的作用。最简单的中间环节即开关和联接导线；一个实用电路的中间环节通常还有一些保护和检测装置。复杂的中间环节可以是由许多电路元件组成的网络系统。 图1-1所示的手电筒照明电路中，电池作电源，灯作负载，导线和开关作为中间环节将灯和电池连接起来。 图1-1手电筒照明实际电路 2. 电路的种类及功能 工程应用中的实际电路，按照功能的不同可概括为两大类：一是完成能量的传输、分配和转换的电路。如图1-1中，电池通过导线将电能传递给灯，灯将电能转化为光能和热能。这类电路的特点是大功率、大电流；二是实现对电信号的传递，变换、储存和处理的电路，如图1-2是一个扩音机的工作过程。话筒将声音的振动信号转换为电信号即相应的电压和电流，经过放大处理后，通过电路传递给扬声器，再由扬声器还原为声音。这类电路特点是小功率、小电流。 各类轴承大全 一、圆锥滚子轴承主要承受以径向为主的径、轴向联合载荷。轴承承载能力取决于外圈的滚道角度，角度越大承载能力越大。该类轴承属分离型轴承，根据轴承中滚动体的列数分为单列、双列和四列圆锥滚子轴承。单列圆锥滚子轴承游隙需用户在安装时调整；双列和四列圆锥滚子轴承游隙已 在产品出厂时依据用户要求给定，不须用户调整。 圆锥滚子轴承有圆锥形内圈和外圈滚道，圆锥滚子排列在两者之间。所有圆锥表面的投影线都在轴承轴线的同一点相聚。这种设计使圆锥滚子轴承特别适合承受复合（径向与轴向）负荷。轴承的轴向负荷能力大部分是由接触角α决定的；α角度越大，轴向负荷能力就越高。角度大小用计算系数e来表示；e值越大，接触角度越大，轴承承受轴向负荷的适用性就越大。 圆锥滚子轴承通常是分离型的，即由带滚子与保持架组件的内圈组成的圆锥内圈组件可以与圆锥外圈（外 圈）分开安装。 单列圆锥滚子轴承 此种轴承只能限制轴或外壳的一个方向的轴向位移，承受一个方向的轴向载荷。当轴承承受径向负荷时，将会产生一个轴向分力，所以常需要用另一个可承受反方向轴向力的轴承来加以平衡。 双列圆锥滚子轴承 此种轴承在承受径向负荷的同时可承受双向轴向负荷。可在轴承的轴向游隙范围内限制轴或外壳的双向轴向位移。该种轴承一般用于中、低转速场合。我公司还可为用户提供特殊轴向游隙的圆锥滚子轴承。 四列圆锥滚子轴承 此种轴承的性能与双列圆锥滚子轴承基本相同，但比双列圆锥滚子轴承承受的载荷更大，极限转速稍低， 主要用于重型机械，如轧钢机等。 圆锥滚子轴承型号: 一、深沟球轴承是最常用的滚动轴承。它结构简单，使用方便。主要用来承受径向载荷，但当增大轴承径向游隙时，具有一定角接触球轴承的性能，可以承受径、轴向联合载荷。在转速较高又不宜采用推力球轴承时，也可用来承受纯轴向载荷。与尺寸相同的其它类型轴承比较，此类轴承摩擦系数小，极限转速高。但不耐冲击不适宜承受重载荷。 深沟球轴承装在轴上后，在轴承的轴向游隙范围内，可限制轴或外壳两个方向的轴向位移，因此可在双向作轴向定位。此外，该类轴承还具有一定的调心能力，当相对于外壳孔倾斜2′～10′时，仍能正常工作， 但对轴承寿命有一定影响。 电工技术A 上网教案 课程编号：1950510；课程名称：电工技术A ； 学时：54；学分：3；考试类型：统考、笔试；课程分类：必修课； 课内总学时：59；实验总学时：10；讲课总学时：49； 基本面向：非电类专业二年级学生；教学方式：课堂讲授、实验； 教材：秦曾煌，《电工学》上册，高等教育出版社，1999； 参考书：姚海彬《电工技术》（电工学I ），高等教育出版社。 唐介，《电工学》，高等教育出版社。 叶挺秀《电工电子学》，高等教育出版社。 第1章 电路的基本概念与基本定律 本章基本要求： 1.了解电路模型及理想电路元件的意义； 2.理解电路变量（电压、电流及电动势）参考方向（及参考极性）的意义 ； 3.理解电路的基本定律（“Ω”、KCL 及KVL ）并能正确地应用； 4.了解电源的不同工作状态（有载、开路 及短路）及其特征； 5.理解电气设备（或元件）额定值的意义； 6.能分析计算简单的直流电路及电路中各点的电位。 本章重点内容： 电路变量参考方向（及参考极性）及基本定律（“Ω”、KCL 及KVL ）的正确应用。 本章学习时间：4学时 第1节 电路的的基本概念 1.电路的的组成及其模型 1）电路及其组成 （1）电路：电流的通路称为电路。连续电流的通路必须是闭合的。 （2）电路组成：电路由电源、负载及中间环节三部分组成。 （3）电路的作用∶实现电能的传输和转换（或信号的传递及转换）。 2）电路的模型——有理想元件组成的电路。 (1)电源元件：电压源(E ,O R ),电流源(S I ,O R ),受控电源。 (2)负载元件：电阻元件R ，电感元件L ，电容元件C 。 (3)中间环节：导线、开关等。电压表，电流表等等 2．电路的的基本概念 1)电流 (1) 电流强度定义：单位时间内通过某导线横界面的电荷的多少。大小及方向都不随时间而变化的电流称为直流电流（这里指的是恒稳直流电流）；大小及方向随时间而变化的电流称为交流电流。 (2)电流的方向 ①实际方向：规定正电荷移动的方向（或者与负电荷移动方向相反的方向）。 ②参考方向：任意标定。一经标定就的依次为准，对电路进行分析和计算。若计算结果为正，则说明电流的实际方向与参考方向一致；若为负，则说明电流的实际方向与参考方向相反。只有标有参考方向才有正负之分，没有参考方向的正负是没有意义的。 (3)电路中电流的表示 ① ② ③ 2)电压 电路的基本规律及应用 一、电阻的串联与并联 U ＝U ＋U ＋U U ＝U ＝U ＝U 二、电动势和内阻 1．电动势 (1)定义：电源在内部移动电荷过程中，非静电力对电荷做的功与移动电荷的电荷量的比值． (2)定义式：E ＝W q ，单位为V . (3)大小：电动势在数值上等于在电源内部非静电力把1 C 正电荷从负极移送到正极所做的功． 2．内阻：电源内部导体的电阻． 三、闭合电路的欧姆定律 1．闭合电路的欧姆定律 (1)内容：闭合电路的电流跟电源的电动势成正比，跟内、外电阻之和成反比． (2)公式 ①I ＝E R ＋r (只适用于纯电阻电路)； ②E ＝U 外＋Ir (适用于所有电路)． 2．路端电压与外电阻的关系 ■判一判 记一记 易错易混 判一判 (1)闭合电路中的电流跟电源电动势成正比，跟整个电路的电阻成反比．( ) (2)当外电阻增大时，路端电压也增大．( ) (3)闭合电路中的短路电流无限大．( ) (4)电动势的单位跟电压的单位一致，所以电动势就是电源两极间的电压．( ) (5)非静电力做的功越多，电动势就越大．( ) (6)在闭合电路中，外电阻越大，电源的输出功率越大．( ) (7)电源的输出功率越大，电源的效率越高．( ) (1)当n 个等值电阻R 0串联或并联时，R 串＝nR 0，R 并＝R 0 n . (2)外电路任一处的一个电阻增大，总电阻增大，总电流减小，路端电压增大；外电路任一处的一个电阻减小，总电阻减小，总电流增大，路端电压减小． (3)纯电阻电路，内、外电路阻值相等时输出功率最大，P m ＝E 2 4r ；R 1R 2＝r 2时输出功率相等． (4)含电容器电路中，电容器是断路，电容器不是电路的组成部分，仅借用与之并联部分的电压，稳定时，与它串联的电阻是虚设，相当于导线，在电路变化时电容器有充、放电电流． 题型I 电路的动态分析 1．判定总电阻变化情况的规律 (1)当外电路的任何一个电阻增大(或减小)时，电路的总电阻一定增大(或减小)． (2)若开关的通、断使串联的用电器增多时，电路的总电阻增大；若开关的通、断使并联的支路增多时，电路的总电阻减小． (3)在如图所示分压电路中，滑动变阻器可视为由两段电阻构成，其中一段R 并与用电器并联，另一段R 串与并联部分串联．A 、B 两端的总电阻与R 串的变化趋势一致． 2．电路动态分析的两种常用方两法 (1)程序判断法：遵循“局部→整体→局部”的思路，按以下步骤分析： (2)极限法：即因滑动变阻器滑片滑动引起的电路变化问题，可将滑动变阻器的滑片分别滑至两个极端去讨论． 1．[电阻变化引起的动态分析问题] 如图所示，接通开关S ，在滑动触头由a 端滑向b 端的过程中，下列表述正确的是( ) A ．路端电压变小 B ．电流表的示数变大 C ．电源内阻消耗的功率变小 D ．电路的总电阻变大 答案：A 2．[开关变化引起的动态分析问题] 在如图所示的电路中，电源内阻不可忽略，开关S 闭合前灯泡A 、B 、C 最常用轴承型号尺寸 案场各岗位服务流程 销售大厅服务岗： 1、销售大厅服务岗岗位职责： 1)为来访客户提供全程的休息区域及饮品; 2)保持销售区域台面整洁; 3)及时补足销售大厅物资,如糖果或杂志等; 4)收集客户意见、建议及现场问题点； 2、销售大厅服务岗工作及服务流程 阶段工作及服务流程 班前阶段1）自检仪容仪表以饱满的精神面貌进入工作区域 2）检查使用工具及销售大厅物资情况，异常情况及时登记并报告上级。 班中工作程序服务 流程 行为 规范 迎接 指引 递阅 资料 上饮品 （糕点） 添加茶水 工作 要求 1）眼神关注客人，当客人距3米距离 时，应主动跨出自己的位置迎宾，然后 侯客迎询问客户送客户 注意事项 15度鞠躬微笑问候：“您好！欢迎光临！”2）在客人前方1-2米距离领位，指引请客人向休息区，在客人入座后问客人对座位是否满意：“您好！请问坐这儿可以吗？”得到同意后为客人拉椅入座“好的，请入座！” 3）若客人无置业顾问陪同，可询问：请问您有专属的置业顾问吗？，为客人取阅项目资料，并礼貌的告知请客人稍等，置业顾问会很快过来介绍，同时请置业顾问关注该客人； 4）问候的起始语应为“先生-小姐-女士早上好，这里是XX销售中心，这边请”5）问候时间段为8:30-11:30 早上好11:30-14:30 中午好 14:30-18:00下午好 6）关注客人物品，如物品较多，则主动询问是否需要帮助（如拾到物品须两名人员在场方能打开，提示客人注意贵重物品）； 7）在满座位的情况下，须先向客人致歉，在请其到沙盘区进行观摩稍作等 待； 阶段工作及服务流程 班中工作程序工作 要求 注意 事项 饮料（糕点服务） 1）在所有饮料（糕点）服务中必须使用 托盘； 2）所有饮料服务均已“对不起，打扰一 下，请问您需要什么饮品”为起始； 3）服务方向：从客人的右面服务； 4）当客人的饮料杯中只剩三分之一时， 必须询问客人是否需要再添一杯，在二 次服务中特别注意瓶口绝对不可以与 客人使用的杯子接触； 5）在客人再次需要饮料时必须更换杯 子； 下班程 序1）检查使用的工具及销售案场物资情况，异常情况及时记录并报告上级领导； 2）填写物资领用申请表并整理客户意见；3）参加班后总结会； 4）积极配合销售人员的接待工作，如果下班时间已经到，必须待客人离开后下班； 第2讲 电路的基本规律及应用 [课时作业] 单独成册 方便使用 [基础题组] 一、单项选择题 1．电源电动势反映了电源把其他形式的能量转化为电能的能力，因此( ) A ．电动势是一种非静电力 B ．电动势越大，表明电源储存的电能越多 C ．电动势的大小是非静电力做功能力的反映 D ．电动势就是闭合电路中电源两端的电压 解析：电动势是反映电源通过非静电力做功将其他形式的能转化为电势能本领的物理量，电动势越大说明这种转化本领越强，但不能说明储存的电能越多，故选项A 、B 错误，C 正确；闭合电路中电源两端电压大小等于外电压大小，故选项D 错误． 答案：C 2.如图所示，直线A 为某电源的U-I 图线，曲线B 为某小灯泡的U-I 图线，用该电源和小灯泡组成闭合电路时，电源的输出功率和电源的总功率分别是( ) A ．4 W,8 W B ．2 W,4 W C ．2 W,3 W D ．4 W,6 W 解析：电源的U-I 图线A 在纵轴上的截距表示电源电动势为E ＝3 V ，图线A 、B 的交点表示电路工作点，对应的工作电压为U ＝2 V ，工作电流为I ＝2 A ．用该电源和小灯泡组成闭合电路时，电源的输出功率P 出＝UI ＝4 W ，电源的总功率 P 总＝EI ＝6 W ，选项D 正确． 答案：D 3.(2018·陕西西安名校联考)某电路如图所示，已知电池组的总内阻r ＝1 Ω，外电路电阻R ＝5 Ω，理想电压表的示数U ＝3.0 V ，则电池组的电动势E 等于( ) A ．3.0 V B ．3.6 V C ． 4.0 V D ．4.2 V 解析：由于电压表的示数为路端电压，而U ＝IR ，则I ＝U R ＝0.6 A ，由闭合电路欧姆定律可得E ＝I (R ＋r )＝0.6×(5＋1)V ＝3.6 V ，故选项B 正确． 答案：B 4.如图所示电路，电源内阻不可忽略．开关S 闭合后，在滑动变阻器R 0的滑片向下滑动的过程中( ) 1.1 引言 1．电路理论 电路理论起源于物理学中电磁学的一个分支。若从欧姆定律（1827年）和基尔霍夫定律（1845年）的发表算起，至今已有170多年的历史。电路理论融合了物理学、数学和工程技术等多方面的成果。物理学，尤其是其中的电磁学为研制各种电路器件提供了原理依据，对各种电路现象做出理论上的阐述；数学中的许多理论在电路理论中得到广泛的应用，成为分析、设计电路的重要方法；工程技术的进展不断向电路理论提出新课题，推动电路理论的发展。 电路理论是研究电路的基本规律及基本分析方法的工程学科。它通常包括电路分析和网络综合两个分支。电路分析指根据已知的电路结构和元件参数，求解电路的特性；网络综合是根据对电路性能的要求，确定合适的电路结构和元件参数，实现所需要的电路性能。另外，由于电子元件与设备的规模扩大，促进了故障诊断理论的发展，因而故障诊断理论被人们视为继电路分析和网络综合之后电路理论的又一个新的分支。 2．课程地位和任务 “电路分析基础”课程是电子信息类专业的第一门专业基础课，它与先修课程“高等数学”、“电磁学”等密切相关，又是学习后续课程“信号与系统”、“电子电路”的基础。 电路理论的各个分支中，网络综合、故障诊断都以电路分析为基础，本课程“电路分析基础”即指电路分析这一分支，并且是最基本的内容。本书主要讨论电路分析的基本规律和电路的各种分析方法。电路分析基础课程理论严密、逻辑性强，有广阔的工程背景。通过本课程的学习，使学生掌握电路的基本理论知识、电路的基本分析方法和初步的实验技能，为进一步学习电路理论打下初步的基础，为学习后续课程准备必要的电 电路分析基础教程 2 路知识。同时对培养学生严肃认真的科学作风和理论联系实际的工程观点，对培养学生的科学思维能力、分析计算能力、实验研究能力和科学归纳能力都有重要的作用。 3．课程的结构体系 课程的基本结构是以模型为基础，以电阻电路分析、动态电路时域分析和正弦稳态电路分析为序的课程体系。其中第1章电路的基本概念与定律是后面几个部分内容的基础，起着至关重要的作用。 本章从电路模型概念出发，主要介绍电路分析中的基本概念与定律、电路的基本变量、基本元件、简单电路分析、等效概念及其应用等。 1.2 知 识 结 构 集总假设 电路模型 电流 电路的基本变量 电压 功率 电阻元件 电路的基本概念 两类约束 电路等效 电路的基本定律 利用基本概念与定律分析电路 电压源 电流源 VCVS VCCS CCVS CCCS 元件约束 结构约束 电路等效的定义 等效分析方法应用 欧姆定律 基尔霍夫定律（KCL 、KVL ） 两类约束的初步运用 等效分析法 独立源 受控源 电路的基本元件 1.3 教学要求及时间分配 1．教学要求 （1）掌握电路模型的概念，理解集总假设。 （2）理解电流、电压、功率的定义，理解电流、电压参考方向的概念，掌握功率的计算方法。 （3）理解电阻元件、独立源、受控源的定义及其端口伏安关系。 （4）理解基尔霍夫电流定律（KCL ）和电压定律（KVL ）及其实质，掌握KCL 和KVL 方程的列写方法。 （5）理解两类约束是电路分析的基本依据。 专题电路的基本规律和应用 【知识点一】电路的动态分析 1．判定总电阻变化情况的规律 (1)当外电路的任何一个电阻增大(或减小)时，电路的总电阻一定增大(或减小)． (2)若开关的通、断使串联的用电器增多时，电路的总电阻增大；若开关的通、断使并联的支路增多时，电路的总电阻减小． (3)在如图所示分压电路中，滑动变阻器可视为由两段电阻 构成，其中一段R并与用电器并联，另一段R串与并联部分串联．A、 B两端的总电阻与R串的变化趋势一致． 2．电路动态分析的两种常用方法 (1)程序判断法：遵循“局部→整体→局部”的思路，按以下步骤分析： (2)口诀：串反并同 【例1】[电阻变化引起的动态分析问题]如图所示，接通开关S，在滑动触头由a端滑向b 端的过程中，下列表述正确的是() A．路端电压变小B．电流表的示数变大 C．电源内阻消耗的功率变小D．电路的总电阻变大 【例2】[开关变化引起的动态分析问题]在如图所示的电路中，电源内阻不可忽略，开关S闭合前灯泡A、B、C均已发光．那么，当开关S闭合时，A、B、C三个灯泡的亮度变化情况是() A．A亮度不变，B变亮，C变暗 B．A变暗，B变亮，C变暗 C．A变亮，B变暗，C变亮 D．A变暗，B变亮，C亮度不变 【例3】[含容电路动态分析问题]在如图所示的电路中，当开关S闭合后，若将滑动变阻器的滑片P向下调节，下列说法正确的是() A．电压表和电流表的示数都增大 B．灯L2变暗，电流表的示数减小 C．灯L1变亮，电压表的示数减小 D．灯L2变亮，电容器的带电荷量增加【知识点二】电源和电阻的U-I图像 图像上的特征 物理意义 电源U-I图像电阻U-I图像 图形 图像表述的物理量变化关系电源的路端电压随电路电流 的变化关系 电阻两端电压随电阻中的电 流的变化关系 图线与坐标轴交点与纵轴交点表示电源电动势 E，与横轴交点表示短路电流 E r 过坐标轴原点，表示没有电压 时电流为0 图线上每一点坐标的乘积UI 表示电源的输出功率表示电阻消耗的功率 图线上每一点对应的U、I比值表示外电阻的大小，不同点对 应的外电阻大小不同 每一点对应的比值均等大，表 示此电阻的大小不变 图线斜率的绝对值大小内阻r 电阻大小 则() A．电源的电动势为6.0 V B．电源的内阻为12 Ω C．电源的短路电流为0.5 A D．电流为0.3 A时的外电阻是18 Ω 【例4】[对电阻U-I图像的理解](2019·浙江杭州五校联盟诊断)如图所示为A、B两电阻的伏安特性曲线，关于两电阻的描述正确的是() A．电阻A的电阻随电流的增大而减小，电阻B的阻值不变 B．在两图线交点处，电阻A的阻值等于电阻B的阻值 [课时作业·巩固提升]精选名校试题考点全面覆盖 一、选择题 1．(2019·高考江苏卷)如图所示的电路中，电阻R＝2 Ω.断开S后，电压表的读数为3 V；闭合S后，电压表的读数为2 V，则电源的内阻r为() A．1 ΩB．2 Ω C．3 ΩD．4 Ω 解析：当断开S时，电压表的读数等于电源的电动势，即E＝3 V；当闭合S时，有U ＝IR，又由闭合电路欧姆定律可知，I＝E R＋r ，联立解得r＝1 Ω，A正确，B、C、D错误．答案：A 2．(2020·湖南株洲上学期质检)如图为某控制电路的一部分，已知AA′的输入电压为24 V，如果电阻R＝6 kΩ，R1＝6 kΩ，R2＝3 kΩ，则BB′不可能输出的电压是() A．12 V B．8 V C．6 V D．3 V 解析：若两开关都闭合，则电阻R1和R2并联，再和R串联，U BB′为并联电路两端电压，U BB′＝ R1R2 R1＋R2 R1R2 R1＋R2 ＋R U AA′＝6 V；若S1闭合S2断开，则R1和R串联，U BB′＝ R1 R1＋R U AA′＝12 V； 若S2闭合S1断开，则R2和R串联，U BB′＝R2 R2＋R U AA′＝8 V；若两者都断开，则电路断路，U BB′＝0.故D项不可能． 答案：D 3．(2020·湖南十校联考)如图所示为某闭合电路电源的输出功率随电流变化的图象，由 此图象可以判断() A．电源的内耗功率最大为9 W B．电源的效率最大为50% C．输出功率最大时，外电路的总电阻为4 Ω D．电源的电动势为12 V 解析：由题图可知，当电流为1.5 A时电源的输出功率最大，这时内耗功率等于输出功率，为9 W，电源的效率为50%，这时电源的总功率为18 W，根据P＝IE，可求得电源的电动势为12 V，D项正确；由P r＝I2r可知，电源的内阻为4 Ω，由于不确定外电路是不是纯电阻电路，因此C项错误；随着电流的增大，内耗功率增大，A项错误；随着电流的减小，电源的效率增大，B项错误． 答案：D 4．(2020·湖北六校期中联考)硅光电池是一种太阳能电池，具有低碳环保的优点．如图所示，图线a是该电池在某光照强度下路端电压U和电流I的关系图象(电池内阻不是常量)，图线b是某电阻R的U-I图象．在该光照强度下将它们组成闭合回路时，硅光电池的内阻为() A．5.5 ΩB．7.0 Ω C．12.0 ΩD．12.5 Ω 解析：由欧姆定律得U＝E－Ir，当r＝0时，E＝U，由图线a与纵轴的交点读出电源的电动势为E＝3.6 V，根据两图线交点处的状态可知，电阻的电压为U＝2.5 V，电流为I＝0.2 A，则硅光电池的内阻为r＝E－U I ＝ 3.6－2.5 0.2Ω＝5.5 Ω，故选项A正确． 答案：A 5.(2020·河北定州中学承智班检测)阻值相等的四个电阻R、电容器C及电池E(内阻可忽略)接成如图所示的电路．保持S1闭合，开关S2断开且电流稳定时，C所带的电荷量为Q1；轴承型号含义对照表
轴承分类型号及尺寸
高中物理 7.3电路的基本规律及其应用教案 新人教版
电路的基本概念和基本定律
南京市高考物理一轮专题： 第32讲 电路的基本规律及应用(I)卷
第1章电路基本概念和基本定律
各类轴承型号尺寸
电路的基本念与基本定律
电路的基本规律及应用
最常用轴承型号尺寸
2019届高考物理一轮复习第八章恒定电流第2讲电路的基本规律及应用作业新人教版
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