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SAE TECHNICAL
PAPER SERIES
Development of an Optimum
Design Program for Wiper Linkages
Jin-Ho Choi and Dong-Hoon Choi
Hanyang Univ.
Myung-Won Suh and Jin-Won Suh
Kia Motors
@*
and
=For
The Engineering Society
Advancing Mobility
Sea Air and Space,
International Congress & Exposition
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I N T E R N A T I O N A L February 28-March 3,1994
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Development of an Optimum
Design Program for Wiper Linkages
Jin-Ho Choi and Dong-Hoon Choi
Hanyang Univ.
Myung-Won Suh and Jin-Won Suh
Kia Motors
ABSTRACT authors' knowledge, however, there exists little litera-
ture on effective design methods for the wiper linkage
An optimization program for the design of wiper satisfying all t*liedesign requirements within the lead
linkages is developed to minimize jerky motion while time allowed.
satisfying design constraints on kinematic and torque In this study, an optimization program is devel-
performances, mobility condition, and packa.ging. The oped to effectively design the wiper linkage satisfying
lengths/orientations of links and the position of a driv- all the design constraints.
ing motor are selected as design variables. In our op-
timum design program for wiper linkages, an optimiza- DESIGN CONSTRAINTS
tion module interacts with an analysis module which
calculates kinematic and force/torque properties, until pivot 2
pivot 1 1
convergence.
The optimization results of a. particular wiper link-
age are presented to illustrate the effectiveness of the
program developed.
INTRODUCTION
The design process of a wiper syst,em comprises
the stage of deciding wiping area and wiping pattern,
the positions and orientations of pivots, and the stage
of deciding the wiper mechanism which can generate
the desired motion. Particulary, the latt,er is iinportant
since it greatly influences the performance characteris-
tics of wiper systems.
A typical wiper mecllanism consists of two basic
RSSR linkages driven by one motor. Even though the
wiper system which employs an individual motor for Figure 1: Wiper linkage
each wiper is recently being used for some models, it
seems not as popular as that utilizing two basic RSSR Figure 1 shows a wiper linkage composed of one
linkages due to its expensive cost. This study focuses RSSR linkage a0 - a1 - bl - bo and the other RSSR
on the wiper mechanism comprising two basic RSSR linkage a; - a; - b; - bb. Such wiper linkage should
linkages, and refers to it as a wiper linkage hereafter. be designed for wipers to wipe sufficient area smoothly
The conventional approach to generating an ac- without any sta,ll. This design requirement for the wiper
ceptable design of a wiper linkage has been the lengthy linkage ca.n be represented by four groups of design con-
procedure of design, test and redesign, which heavily de- straints.
pends on designers' intuition and experience. An anal- KINEMATIC CONSTRAINTS - When any
ysis procedure and a simplified approach to evaluating wiper cannot wipe the desired wiping area or there ex-
a particular wiper linkage design has been presented to ists high phase lag between wipers, it can cause dis-
alleviate the burden of difficult design task[']. To the taction to the driver. Since the maximum wiping an-
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gles at pivots 1 and 2 determine wiping area, their val- forward stroke and return stroke, respectively, and Tdl
ues should be within an adequate tolerance from the denotes the corresponding upper bound.
desired values. This requirement can be presented as
EQS (1) and (2). In these equations, P1 and /32 repre-
sent output angles at pivots 1 and 2, respectively. To
prevent high phase lag between wipers, the driving m e
tor should convert wipers from forward stroke to return If the torque available at any wiper is insufficient
stroke near 180° of its rotation. This consideration can and/or the torque distributions between strokes and be-
be expressed as EQS (3) and (4). In these equations, tween wipers are poor, wipers can also be stalled. For
01 and 0 2 represent the rotation angles of the motor any wiper not to stall, the torques available at wipers
converting wipers 1 and 2 from forward stroke to re- 1 and 2 should be properly constrained. EQS (13) and
turn stroke, respectively. In EQ (1) through EQ (4), (14) present the condition that the minimum magni-
at,
Pf, 3,/; P$, P;, a ? , cry, and C Y denote
~ the bound tudes of torques available at wipers 1 and 2 must be
values specified by the designer. greater than or equal to the lower bounds specified by
the designer. EQ (15) expresses the condition that the
difference of minimum magnitudes of torques available
between wipers should be constrained to be below an
adequate upper bound. EQS (16) and (17) present the
differences of minimum magnitudes of torques available
between strokes for wipers 1 and 2 must be less than or
equal to the upper bounds specified by the disigner. In
EQ (13) through EQ (17), TI and T2 respectively r e p
If the angular velocities of wipers 1 and 2 are very resent the torque available at wipers 1 and 2, and TS1,
high, it can cause high load at the motor. When the an- Ts2,Td2,Td3, and Tdbdenote the limit values assigned.
gular accelerations of wipers 1 and 2 is very high, it can Also, the subscripts f and r mean forward stroke and
cause high dynamic load at the motor. Also, if the an- return stroke, respectively.
gular jerks of wipers 1 and 2 are very high, wipers may
have jerky motion. Hence, the maximum magnitudes
of angular velocities, angular accelerations and angu-
lar jerks of wipers 1 and 2 should be constrained below
adequate upper bounds. These constraints can be pre-
sented as EQ (5) through EQ (10). In these equations,
the dots above pl and p2 denote time derivatives, and
Vl, V2, Al, A2, J1, and J2represent the corresponding
upper bounds specified by the designer.
MOBILITY CONDITION - Wiper linkages
must satisfy the mobility conditions that the crank con-
nected to the motor should have a complete revolution
of 360° and that the lengths of the remaining links
should be adequate for assemblage. In this study, the
mobility condition for a RSSR linkagei2] is exploited.
For the S S R linkage a0 - a1 - b1 - bo shown in Fig-
ure 1, the condition that the crank should have a com-
plete revolution can be presented as EQ (18). In EQ
(18), lC1 denotes the length of the coupler a1 - bl , and
Lmin(a) and L,,,(a) represent the minimum and max-
TORQUE CONSTRAINTS - When the motor imum coupler length for ,a giv7n vafue o: a , respectively.
is overloaded, and/or the load distribution at the mc+ For the RSSR linkage a. - a l - bl - bo shown in Fig-
tor between strokes is poor, wipers can be stalled. To ure 1, the condition that this linkage should be movable
avoid this undesirable problem, it is necessary that the can be expressed as EQ (19). In EQ (19), lC2 denotes
maximum load at the motor and the difference of the the length of the coupler al - b;, and Lmin(P1) and
maximum load between strokes should be constrained Lm,,(P1) represent the minimum and maximum cou-
to be below appropriate upper bounds. These require- pler length for a given value of &, respectively.
ments are mathematically expressed as EQS (11) and
(12). In EQ ( l l ) , To represents load at the motor and
T, denotes the corresponding upper bound. In EQ
(12), Tof and Tor represent load at the motor during
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STRUCTURE OF AN OPTIMUM DESIGN
PROGRAM FOR WIPER LINKAGES
PACKAGING CONSTRAINTS - One can:
The skeleton structure of an optimum design pro-
not arbitrarily assign the position of the motor and the
gram developed is briefly drawn in Figure 2. At first,
lengths/orientations of links selected as design variables
since the motor and the linkage must fit into restricted
available space. These packaging constraints can be
presented as EQ (20). In EQ (20), x, denotes it11 design I Preprocessor I
variable, n the number of design variables, and xk and
x y represent the lower bound and the upper bound
for ith design variable, respectively. The length of ld
between bl and a, shown in Figure 1 should also be
constrained as expressed in EQ (21), where If; and 1:
represent the lower bound and the upper bound for I d ,
respectively.
Postprocessor
Figure 2: Skeleton structure of an optimum design pro-
OPTIMUM DESIGN PROBLEM FORMULA-
gram for wiper linkages
TION
A design satisfying all the constraints described the input data are given through an interactive prepro-
above is called an adequate design. Among many ad- cessor. Then, kinematic and force/torque properties of
equate designs, it would be benefical if the optimum the wiper linkage of the specified configuration are cal-
design can be obtained which minimizes or maximizes culated by the analysis module. These properties are
an important performance index. In this study, the per- fed into the optimization module, and the optimization
formance index is chosen as the integral of the angular module is activated to obtain a better design. Note that
jerks at wipers 1 and 2 during one cycle of motor ro- we resort t o the analysis module t o calculate the corre-
tation, to make wiper motions as smooth as possible. sponding kinematic and force/torque properties when-
This performance index can be presented as EQ (22), ever design variables are modified during optimization
where PI(,) and ,&(a) represent the angular jerks of process. This procedure is repeated until convergence.
wipers 1 and 2 as a funtion of crank angle a. After the optimum design is obtained, the postprocessor
produces the summary of optimization results in a ta-
ble format, and the graphs which compare the various
performances of the wiper linkage optimally designed
with those of the wiper linkage initially designed.
According to the design situation, design variables As for force/torque analysis, we obtained the
can be selected at the designer's disposal. A particular torque properties by using both the static analysis
set of design variables (x) chosen in this study is pre- method and the inverse dynamic analysis method. Both
sented in EQ (23). In EQ (23), ao, and ao, denote the results showed little difference for the speed range of
position of the motor in y-z plane, and (11, d l ) , (12,192)~ the current wiper linkages. Therefore the static analysis
(13, 7J3), and (14, ~ 9 represent
~ ) the lerfgths/orientatio:s method is adopted. Moreover, we accomplish kinematic
oflink a,-all link bl-ao, link a,-a,, and link b;-bO, and static force/torque analysis in closed form in this
respectively, as shown in Figure 1. study.
The optimization module employs the augmented
Lagrange multiplier method in which the BFGS method
is used for finding vector search directions and the poly-
Now, an optimization problem for the design of no~nialopproximation method is used for line searches.
wiper linkages can be formulated as follows :
find the design variables of EQ (23)
to minimize the performance index of EQ (22) APPLICATION
satisfying the co~lstraintsof EQ (1) through EQ
The optimum design program developed in this
(21)
study is applied to design the wiper linkage for a paticu-
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lar future model of a company. An initial design and the
limit values on kinematic, torque, and packa,ging con-
straints are provided by the company. The opti~num
design is optained in 11 iterations with the cost value
-
- optimum design
iniM design
reduction of 38%. The CPU time for convergence on
IBM PC 486 elapses around 10 minutes to obtain the
results.
Figure 3 through Figure 8 show the comparisons
of performance characteristics of the wiper linkage ini-
tially designed and that optimally designed. Only the
performance characteristics of wiper 2 are depicted in
the figures since those of wiper 1 have not been changed
significantly. The dotted lines in the figures present the
limt values on various performances.
Figure 3 shows that the excessive wiping range gen-
-2.Ooi,,,,~ , 8 l4 ~4 ,
~ ,l m ~ ~
a ~ l 8 t O L 2 4 8 t ~ I
erated by the initial design is adjusted t o the desired 0.d0 ~ . b 0120100 180100 240100 300100 360.00
wiping range of 85' with the optimum design. The opti- motor r o t a h ( d e g )
mum design slightly reduces angular velocity in compar- Figure 4: Comparison of angular velocities with the
ison with that produced by the initial design as shown in initial design and with the optimum design for wiper 2
Figure 4. Figure 5, however, exhibits that the angular
acceleration generated by the optimum design decreases
appreciably compared with that using the initial design, CONCLUDING REMARKS
which means lowering the dynamic 1oa.d on the motor. An optimum design program is developed to auto-
As for angular jerk, the initial design does not meet the matically design the wiper linkage comprising two basic
acceptance criterion as shown in Figure 6. By contast, RSSR linkages, once an initial design and the perfor-
the optimum design significantly reduces the magnitude mance criteria are provided. The program is composed
of angular jerk, which means preventing the wiper from of an interactive preprocessor, an analysis module, an
jerky motion. optilnization module, and a postprocessor. The opti-
mum solution efficiently gives the lengths/orientations
of the links and the position of a driving motor, which
generate the smoothest wiper motion satisfying kine-
matic constraints, torque requirements for no stall, mo-
bility condition, and packaging constraints.
A particular wiper linkage is optimally designed in
about 10 CPU minutes on IBM PC 486, t o demonstrate
the validity of the program developed in this study.
ACKNOWLEDGMENTS
This work was supported by Kia Motors and
KOSEF, Turbo and Power Machinery Research Center.
REFERENCES
X I 1 1 1 1 1 I I I I I I I I I I I I I I I I I I
60.b0 120100 180100 240100 300100
nzo t o r ~ o t a t w n ( d e ~ ) [I] H. Singh, Ford Co., "Windshield Wiper Linkage
Analysis", SAE Pap. 710254, 1971
Figure 3: Comparison of wiping ranges with the initial
design and with the optimum design for wiper 2 [2] C. H. Shu and C. W. Radcliffe, Kinematics and
Mechanism Design, John Wiely and Sons, 1978
Figure 7 shows that the optimum design result,s in
higher torque available a.nd better torque distributions
within one stroke and between strokes than are gener-
ated by the initial design, which means reducing stalling
possibility. As far as the load at the motor is concerned,
both designs give satisfactory results as shown in Figure
8.
Downloaded from SAE International by North Carolina State Univ, Saturday, September 15, 2018
-
- optimum
initial, design
design
-
- aptimum design
initial design
-2.co1cat4L ~ l L 4 ~ l t 1~ l ~~ l 1 1 ~1 4 L 1 ~ 3 1 r r 11 1 o . o o l l ~ ~ r r l ~ ~ ~ ~ ~ , ~ ~ ~ ~ ~ l ~ ~ ~ ~
0.b 60.b0 120.00 180100 240100 300.00 360.00 0.00 60.00 120.00 180.00 240.00 300.00 360.00
m o t o r rotation(deg) m o t o r rotation(deg)
Figure 5: Comparison of angular accelerations with the Figure 7: Comparison of torques available with the ini-
initial design and with the optimum design for wiper 2 tial design and with the optimum design for wiper 2
---------- - - ------
-
-optimum dssign
initiaZ design
----------
0.00 60.00 120.00 180.00 240.00 300.00 360.00
m o t o r rotation(deg)
Figure 6: Comparison of angular jerks with the initial Figure 8: Comparison of loads at the motor with the
design and with the optimum design for wiper 2 initial design and with the optimum design
