Output Speed and Torque of Differential Double-Stator Swing Hydraulic Multi-motors

WEN De-sheng(),CAI Qiu-xiong()(),GAO Jun-feng()

College of Mechanical Engineering,Yanshan University,Qinhuangdao 066004,China

Introduction

Hydraulic motors convert hydraulic energy into mechanical energy.They are used as part of a hydraulic system with fluid reservoir and pumps to supply the fluid.The fluid,supplied via a pump from the reservoir,forces the movable components of the motor into motion,which in turn rotate the attached output shaft[1].Hydraulic motors are usually divided into two groups: low-speed high-torque ones and high-speed low-torque ones.In recent years,higher demands for the rotational speed and torque of motors were required.It is difficult to obtain a wide range of rotation velocity regulation for the current fixed-displacement motors[2].To improve the performances and the shortages mentioned above,significant amounts of study on hydraulic motors have been performed[3-5].

The main research performed on hydraulic motors concentrates on pressure distribution,friction analysis,advanced materials application,manufacturing process,tightness methods,and lubrication.Growing concern about environmental issues and dynamic characteristics of components has led to interest in functional materials,such as water hydraulics and magnetic fluids[6-8].In addition,research on reducing noise level is a hot topic today,and much research work has been performed[9].Moreover,there is a considerable amount of work regarding optimal design method.For example,with rapid response speed and high control precision,a motor tracking the periodic signal with high accuracy was put forward[10].To acquire large unit volume displacement,the characteristics of the motor with three planet gears were researched[11].However,little attention is paid to the operating

principles of the existing components to improve their characteristics[12].

The design of differential double-stator swing hydraulic multi-motors offers a lower-cost alternative in comparison to other fluid-transfer mechanisms over broad application prospects.Designers of engines,compressors,machine tools,tractors,and other equipments requiring hydraulic systems can use an integrally designed differential double-stator swing hydraulic multi-motor for a more compact and lower weight unit.In most cases,it will also run more quietly for no variable mechanisms are required.

It is a challenging and significant issue to study the structure and operating principles of hydraulic components.For this reason,we made an innovation in the field of structure and operating principles of components and developed a series of novel ones.

1 Structure and Operating Principles

Generally,the traditional swing hydraulic motors require the use of one rotator corresponding to one stator in a single shell[13].Different from the common ones,there are two stators corresponding to one rotator for this novel double-stator structure.The basic structure includes a rotator,inner and outer stators.The inner and outer stators are stationary.Two groups of the inlet and outlet ports,used for suction and delivery action,are installed on the shell.It comes into being two groups of inner and outer motors,whose displacements are fixed.There is a proportional relationship between each of the rotational speed and the displacement ratio of the inner motors to the outer one.Each of these sub-motors can work alone or be combined depending on the actual requirements.

Using the single-acting differential double-stator swing hydraulic multi-motor as an example to introduce operating principle,the specific configuration is shown in Fig.1.The variable volume of the outer motor is formed by the outer stator,the rotator,the outer moving blade,the outer static blade,and two side plates.Likewise,the variable volume of the inner motor is composed of the inner stator,the rotator,the inner static blade,the inner moving blade,and two side plates.There are one inner motor and one outer motor.A certain number of different rotational speed and torque can be provided by one differential double-stator swing hydraulic multi-motor,and it can work under various kinds of hydraulic system pressure at the same time.Furthermore,if we change the shape of the rotator,the inner and outer stators,the double-acting,triple-acting,and even the multiple-acting differential double-stator swing hydraulic multi-motors can be acquired.Obviously,if the acting number of the differential swing hydraulic multi-motors isN,there will be 2Nsub-motors in one shell,which includesNinner motors andNouter motors with equal displacement,respectively.The prototype of a double-acting differential double-stator swing hydraulic motor is shown in Fig.2.

Fig.2 The prototype of a double-acting differential double-stator swing hydraulic motor

2 Graphic Symbols

In order to describe this new industry innovation clearly and research conveniently,it is needed to design the graphic symbols of these novel hydraulic components.Considering the existing rules[14]of graphic symbol,three rules are established as follows.

Rule 1: as several motors exist in one shell using the same stators and rotors and output through the same axis,we adopt the coaxial graphic symbol.

Rule 2: one semicircle stands for the outer motors and two concentric semicircles represent the inner motors.

Rule 3: the number of triangles located by the side of semi-circle is the same as the number of sub-motors.

For example,the graphic symbol of the single-acting differential double-stator swing hydraulic multi-motors is shown in Fig.3(a),and Fig.3(b) illuminates the double-acting differential double-stator swing hydraulic multi-motors.The graphic symbols of other multi-motors can be drawn in the same way.

Fig.3 The symbols of single-acting and double-acting differential double-stator swing hydraulic multi-motors

3ConnectionModesinSingle-ActingDifferentialDouble-StatorSwingHydraulicMulti-motors

Two groups of sub-motors,whose displacements are different,exist in differential double-stator swing hydraulic multi-motors,and different rotational speed and torque characters can be acquired through changing the connection modes.

The single-acting swing hydraulic multi-motors is used as an example here.Let Δpbe the differential pressure,qbe the flow rate of hydraulic transmission system,andV1andV2be the displacements of the inner and outer motors.Here,the relationship betweenV1andV2can be described as:

(1)

whereCis a constant,depending on the displacement ratio of the inner and outer motors.

There are two kinds of connection modes: one is common connection and the other is differential connection.The rotational speed and torque of single-acting differential double-stator swing hydraulic multi-motors in different connection modes can be discussed as follows.

3.1 Common connection of single-acting

In Fig.4,there are three connection ways under common connection mode.The connection way of the inner motor working alone is shown in Fig.4(a),and the theoretical rotational speed[15]can be expressed as

(2)

wherer1andr2are the radii of the outside circle in inner stator and the inside circle in rotator,respectively,andbis the width of the blade.

The theoretical torque under this condition can be expressed as

(3)

Equations (2)-(3) are the basic expressions of rotational speed and torque provided by differential double-stator swing hydraulic multi-motors.The calculation method of rotational speed and torque under the other conditions is similar with Eqs.(2)-(3).The results are listed in Table 1.It is obvious that the rotational speed and torque characters have a certain proportional relationship withn1andT1.LetCWbe the connection way,Noutbe the number of outer working motors,andNinbe the number of inner working motors.

(a) The inner working motor

(b) The outer working motor

(c) Both the inner and outer working motor

Table 1 Common connections of single-acting differential double-stator swing hydraulic multi-motors

3.2 Differential connection of single-acting

3.2.1Operatingprincipleofdifferentialconnection

In order to accomplish swinging motion,the input and output volumes of traditional swing hydraulic motors must be symmetrical,and the working areas must be equal[16].The output axis will keep still if high pressure oil is put into both volumes,because the torque is equal.

With the special structure,the differential double-stator swing hydraulic multi-motors can accomplish differential connection.When high pressure oil is put into both of the inner and outer motors,the torque is unequal because of different working areas.The multi-motors accomplish swinging motion[17].

Using the single-acting differential swing hydraulic multi-motors as an example,there is one pair of inner and outer motors.Both of them use the same rotator,and the displacement of the inner motor is larger than that of the outer motor.When high pressure oil is put into the two sub-motors from the entrance port A of the outer motor and the exit port b of the inner motor,as shown in Fig.5(a),the high pressure oil in the outer motor makes the rotator have a trend of clockwise rotation,while the high pressure oil in the inner motor makes the rotator have a trend of counterclockwise rotation.The arms of force and displacement in the outer motor are larger than those of the inner motor,so the clockwise torque is larger than the counterclockwise torque,and then the rotator will rotate clockwise.In other words,the rotation direction is determined by the outer motor.Then the inner motor is used as a pump in differential connection to provide hydraulic oil to the outer motor.Therefore,the total input flow of the differential double-stator swing hydraulic multi-motors is enlarged.The differential function is suitable for high-speed working system.The graphic symbol of differential connection is shown in Fig.5(b).

Fig.5 Differential connection mode and graphic symbol of single-acting differential double-stator swing hydraulic multi-motors

3.2.2Rotationalspeedandtorque

There is only one differential connection way in single-acting differential double-stator swing hydraulic multi-motors,as shown in Fig.4.The theoretical rotational speed under this condition can be expressed as

(4)

The mathematical expression of the theoretical torque in single-acting differential double-stator swing hydraulic multi-motors is

(5)

The description above shows that the single-acting differential double-stator swing hydraulic multi-motors,without a complex variable displacement mechanism,can output four kinds of rotational speeds and torques under the same conditions of input flow rate and pressure.

4 Connection Modes in Multi-acting Differential Double-Stator Swing Hydraulic Multi-motors

One fixed-displacement differential double-stator swing multi-motor driven by a constant flow rate and pressure can output a certain number of rotational speeds and torques,and work under diverse system pressure.There are two groups of inner and outer motors in multi-motors.Many kinds of rotational speeds and torques can be acquired if the connection modes are changed reasonably.In order to know the performance,it is possible to research the rotational speed and torque provided by differential double-stator swing hydraulic multi-motors.The conditions in double-acting and triple-acting differential double-stator swing hydraulic multi-motors will be researched as follows,and the results should be promoted to multi-acting swing multi-motors.

4.1 Common connection of double-acting and triple-acting

Many different connection ways of differential double-stator swing hydraulic multi-motors can be acquired under common connection mode.The rotational speeds and torques of double-acting and triple-acting differential double-stator swing hydraulic multi-motors under common connection mode are listed in Tables 2-3.The calculation method is similar with Eqs.(2)-(3).

Table 2 Common connections of double-acting differential double-stator swing hydraulic multi-motors

Table 3 Common connections of triple-acting differential double-stator swing hydraulic multi-motors

4.2 Differential connection of double-acting and triple-acting

There are four kinds of differential connection ways in double-acting differential double-stator swing multi-motors and nine kinds in triple-acting swing multi-motors.Regardless of the influence of the displacement ratio,four kinds of rotational speeds and torques can be acquired in double-acting differential double-stator swing multi-motors under differential connection mode and nine kinds in triple-acting swing multi-motors.The mathematical expressions are listed in Tables 4-5.

Table 4 Differential connections of double-acting differential double-stator swing hydraulic multi-motors

Table 5 Differential connections of triple-acting differential double-stator swing hydraulic multi-motors

Through the description above and observing the data in Tables 1-3,it is obvious that three,eight,and fifteen kinds of connection ways can be acquired under common connection mode in single-acting,double-acting,and triple-acting multi-motors.Furthermore,through changing the connection way of the differential double-stator swing hydraulic multi-motors under common modes,the number of rotational speed and torque should be (N+1)2-1.Here,Nis the acting number of differential double-stator swing hydraulic multi-motors.

By analyzing the data in Tables 4-5,one,four,and nine kinds of connection ways,regardless of the influence of displacement ratio,can be acquired under differential connection mode in single-acting,double-acting,and triple-acting differential double-stator swing hydraulic multi-motors.Furthermore,through changing the connection way of the differential double-stator swing hydraulic multi-motors under differential modes,the number of rotational speed and torque should beN2.

In all,regardless of the influence of displacement ratio,differential double-stator swing hydraulic multi-motors can provideN2+(N+1)2-1 kinds of rotational speeds and torques.

4.3 Experimental analysis

In order to verify the correctness of the theory analysis above,an experiment based on double-acting differential double-stator swing hydraulic multi-motors was done.The connection ways were changed through the controlling of electromagnetic reversing valves[18].The experiment proofs that double-acting differential double-stator swing hydraulic multi-motors can provide twelve kinds of rotational speeds and torques under the conditions of the same input flow and pressure.The theory analysis of differential connection was proved to be reasonable.The picture of experimental site is shown in Fig.6.

Fig.6 The experimental site of double-acting differential double-stator swinging hydraulic multi-motors

Due to its many connection ways,we choose four kinds of typical connection ways to test,which are shown in Table 6.The experimental and theoretical (in the brackets) data are shown in Table 7.LetWoutbe the working style of outer working motors,andWinbe the working style of inner working motors.

Table 6 Four kinds of typical connection

Table 7 The torque of swing hydraulic motor

Fig.7 The torque of different connection ways

By analyzing the curves in Fig.7,on the whole,the torque of swing hydraulic motor increased with rising differential pressure under four connection modes.Although there were certain differences between theoretical and experimental data,in consideration of volumetric and mechanical efficiencies,the error of measuring instruments and so on,they were in conformity to the theoretical data.

Discovered through four experimental curves,the torque of swing hydraulic motor was different from one differential pressure and another,which was consistent with the theoretical,it demonstrated fully that double-stator swing hydraulic motor can output multiple torques by changing connection way,not by turning differential pressure.Also,the four torques had a proportional relation with the same differential pressure,which is associated with the ratio of displacement.

Table 8 is the data of efficiency when the output volume of swing hydraulic motor is the largest (CW-3),and Fig.8 is the curve based on Table 8.The volumetric efficiency decreases with rising differential pressure.As the differential pressure rises,the internal leakage of the motor aggravates.As a result,the volume efficiency decreases.Besides,the mechanical efficiency increases with rising differential pressure.Through the analysis of the motor’s structure,there are no dynamic seals’ components.So the loss of torque is small and it can gain a high mechanical efficiency.

Table 8 The efficiency of swing hydraulic motor

Fig.8 The efficiency of CW-3

5 The Ratio of Displacement

The rotational speed and torque characters provided by differential double-stator swing hydraulic multi-motors have a close relationship with the ratio of displacement[19].Practically,it is important to select the reasonable ratio of displacement so that the designed multi-motors are suitable for the working conditions.Making a deep research on the ratio of displacement and finding the relationship between the ratio of displacement and output performance are necessary.Because the interaction between rotational speed and torque is one-to-one correspondence,and the analysis method of single-acting differential double-stator swing hydraulic multi-motors is similar with multi-acting differential double-stator swing hydraulic multi-motors,as shown in Table 9,only the torque characters of single-acting differential double-stator swing hydraulic multi-motors is researched[20].

There are four kinds of output torques in single-acting differential double-stator swing hydraulic multi-motors.The first three kinds of torques can be acquired through common connection mode,and the last one through differential connection mode.

Table 9 The output torque of single-acting double-stator swing hydraulic multi-motors

When the ratio of displacement changes from 0 to 0.5,the relationship among the torque characters above provided by single-acting differential double-stator swing hydraulic multi-motors can be described as:

CT1<(1-C)T1

(6)

Under this condition,(C+1)T1is the maximum torque character,andCT1is the minimum torque character.The ratio of maximum and minimum is (C+1)/C.The torque characters under different displacement ratio are listed in Table 10 from the smallest to the largest.

Table 10 Output torque characters of single-acting differential swing hydraulic multi-motors under different ratio of displacement

With the changing of displacement ratio,output torque characters of single-acting differential swing hydraulic multi-motors are different.Both of the maximum and minimum torque characters change with the displacement ratio,and it is necessary to select the reasonable ratio of displacement depending on the working condition when the multi-motors are designed.

6 Conclusions

In this paper,some conclusions can be drawn based on the analyses above.

(1) As a novel swing hydraulic motors,differential swing hydraulic multi-motors have two groups of sub-motors which can work separately in one shell.The same rotor is used by the inner and outer motors.The fixed displacement of the inner and outer motors is different,so differential connection mode can be accomplished.

(2) Different rotational speed and torque characters can be acquired through changing the connection way under the constant conditions of input flow rate and pressure in differential double-stator swing hydraulic multi-motors.

(3) The output rotational speed and torque characters have a close relationship with the ratio of displacement.Selecting the suitable ratio of displacement depending on working conditions is important when designing differential double-stator swing hydraulic multi-motors.

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