Portable units having high-pressure pumps, which are usable in complicated conditions with abrasive-containing, fast-hardening, corrosive, and other aggressive fluids, are employed as components of specialized mobile complexes of oil and gas field equipment (for cementing and acid treatment of wells, hydraulic strata fracking, hydraulic sand-jet perforating, well killing, and other well plugging-back operations). The quality of technological operations and, consequently, the efficiency of further exploitation of oil and gas wells depend a great deal on the reliability of these equipment, of the pumps in particular. The reliability of these pumps depends to a large extent on the efficiency of their driving systems and especially of the friction units of the cranking (connecting rod-crosshead) mechanism of the plunger drive.

The series-made plunger pumps being used at present [1] (with the exception of the NP-720 and NP-800 pumps) do not match the current technological level and do not meet the oil and gas well service requirements as they have insufficient life and reliability, high mass and size characteristics and specific materials content (mass to useful pump power ratio), significant delivery nonuniformity, low efficiency, narrow range of key operating parameters, etc.

The NP-720 pumps made by Trast-Inzheniring company meet to the maximum extent the current requirements and are standardized with designs of the best world-class prototypes of similar types of pumps (Fig. 1) [1].

Fig. 1
figure 1

NP-720 high-pressure triplex plunger pump.

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The NP-720 pump is a horizontal single-acting pump that includes a hydraulic and a drive section and systems for their forced lubrication. The hydraulic section of the pump is attached to the drive section by coupling stud bolts and incudes a hydraulic block, in the grooves of which are installed interchangeable suction and discharge valve units having compression springs, plungers with rods, and universal sealing packages of plungers with pressing screws. In the lower section of the hydraulic block, a receiving header is attached to the stud bolts via flanges. In the upper section of the hydraulic block, a pump header, which connects all the delivery valve chambers, is placed at the level of the upper edge of the valve seats. The pressure (discharge) manifold and the safety valve of the pump unit are attached to the outlet holes of the discharge header (in the left and right ends of the hydraulic block) by bolts and nuts.

The drive section of the pump (Fig. 2) is a welded nondetachable (single-piece) frame in which three longitudinally placed connecting rod-crosshead groups and a transversely placed crankshaft with three eccentric journals are mounted.

Fig. 2
figure 2

Key components of connecting rod-crosshead mechanism of high-pressure plunger pump drive: 1) casing of drive section of pump; 2) connecting rod; 3) bushing; 4) crankshaft; 5) connecting rod pins; 6) crosshead; 7) guides.

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The connecting rod-crosshead groups include forged steel crossheads and connecting rods, to the small heads of which are pressed antifriction bushings which encircle the crosshead pins. In the large heads of the connecting rods are placed antifriction half-bushings of detachable sliding bearings, which encircle the crankshaft journals. The large heads of the connecting rods are connected with the covers of the coupling bolts. The crankshaft has four supports, which are specially designed roller bearings. There are holes along the crankshaft axis for delivery of lubricant through radial channels to friction surfaces of the crankshaft journals. The pump lubricating system ensures forced lubrication of the moving assemblies of the driving and hydraulic sections of the pump separately.

Connecting rod-crosshead mechanism in high-pressure plunger pump drive creates the most favorable conditions for operation of the main pump mechanism, namely, the plunger pair, because radial loads on the plunger pair are removed completely.

Various modifications of high-pressure plunger pump where this mechanism is used differ in diameter (80–100 mm), crankshaft rotation speed (85–325 rpm), working fluid pressure at the outlet (29.4–105 MPa), and throughput (210.0–1254.5 liters/min) [1]. However, the design and parameters of the parts of the drive of the connecting rod-crosshead mechanism for all modifications of the plunger pump are alike. Such universality of the plunger pump drive is reflected in the operation conditions of its individual mating surfaces moving relative to each other and in their service life under different operation modes, so individual approach is required for determining the parameters of the components of the friction units.

In each connecting rod-crosshead group of the driving mechanism, there are three friction units which differ fundamentally from each other in pattern of movement of mated surfaces and their loading and lubricating conditions. Notwithstanding the fact that fluid lubricant is injected into these units under pressure through specially designed channels and grooves (Fig. 2), fluid friction condition can develop only in rotating bearing assembly on the crankshaft at fixed shaft rotation speeds.

The speeds of motion of the mating surfaces relative to each other and the loads received by them are the governing parameters for assessing the efficiency of the working surfaces of the bearing assemblies and driving mechanism, and for making analytical calculations of their operating conditions. To determine these quantities, we shall carry out kinematic and force studies of the crank-connecting rod mechanism of the driving section of the chosen typical high-pressure oil-gas well service pump.

We shall conduct the kinematic study by the method of kinematic analysis of plain mechanisms [2]. Let us consider a case of assembly of the mechanism where the kinematic loop with the clockwise sequence of kinematic couples ABCA is maintained (Fig. 3).

Fig. 3
figure 3

Schematic diagram of crank-connecting rod mechanism with guide axis passing through the crank rotation axis: 1) support; 2) driving component (crank); 3) connecting rod; 4) crosshead.

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To determine the speeds of the components, we shall present the loop ABCA as a sum of the vectors

$$ {\overrightarrow{l}}_2+{\overrightarrow{l}}_3={\overrightarrow{x}}_c. $$

Projecting this vector equation on the axes AX and AY, we get two equations

$$ \begin{array}{cc}\hfill {l}_2 \cos {\upvarphi}_2+{l}_3 \cos {\upvarphi}_3={x}_c;\hfill & \hfill {l}_2 \sin {\upvarphi}_2+\hfill \end{array}{l}_3 \sin {\upvarphi}_3=0. $$
(1)

From the second equation, we get

$$ \sin {\upvarphi}_3=-{l}_2 \sin {\upvarphi}_2/{l}_3. $$
(2)

The vector l 3 can occur only in the first or fourth quadrants, so cosφ3 is always positive.

From the first equation, we get the distance of travel x c :

$$ {x}_c={l}_2 \cos {\upvarphi}_2+{l}_3\sqrt{1-{\left({l}_2 \sin {\upvarphi}_2/{l}_3\right)}^2}, $$

then

$$ {x}_c=\left({l}_2+{l}_3\right)-{l}_2 \cos {\upvarphi}_2-{l}_3\sqrt{1-{\left({l}_2 \sin {\upvarphi}_2/{l}_3\right)}^2}. $$

The equations for determining angular speeds can be obtained by two-step differentiation of Eqs. (1) with respect to the general coordinate φ2. For determining the angular speed ω3 of the connecting rod 3 and the speed v c of the crosshead 4, we have

$$ \begin{array}{cc}\hfill -{l}_2 \sin {\upvarphi}_2-{u}_{32}{l}_3 \sin {\upvarphi}_3={x}_c^{\hbox{'}};\hfill & \hfill {l}_2\hfill \end{array} \cos {\upvarphi}_2+{u}_{32}{l}_3 \cos {\upvarphi}_3=0, $$
(3)

where u 32 = dφ3/dφ2 and x ' c  = dx c /dφ2 are the respective speed analogs. The speed analog x ' c is determined from the first equation of (3) by putting the analog of the angular speed u 32 of the connecting rod 3 from the second equation of (3), then

$$ {u}_{32}=\begin{array}{cc}\hfill -\frac{l_2 \cos {\upvarphi}_2}{l_3 \cos {\upvarphi}_3};\hfill & \hfill {x}_c^{\hbox{'}}={l}_2\hfill \end{array}\frac{ \sin \left({\upvarphi}_3-{\upvarphi}_2\right)}{ \cos {\upvarphi}_3}. $$
(4)

The true speeds v c and ω3 can be determined by the familiar equations:

$$ \begin{array}{cc}\hfill {v}_c{\upomega}_2{x}_c^{\hbox{'}};\hfill & \hfill {\upomega}_3={\upomega}_2{u}_{32},\hfill \end{array} $$
(5)

where ω2 is the given angular speed of the driving component 2.

Let us consider the calculation of friction unit operation conditions for one of the modifications of the connecting rod-crosshead mechanism of the plunger pump drive (Fig. 2). Pump design NP-720×80, plunger diameter d pl = 90 mm, maximum fluid working pressure p m = 80 MPa, crankshaft rotation speed n = 125 rpm, diameter of the crankshaft journal under the connecting rod d c =190 mm, distance between the connecting rod rotation axes l = 480 mm, pin diameter d 3 = 120 mm, and working length of the upper bushing of the connecting rod l bc = 95 mm.

The full operating load applied to the crosshead when it moves from the left to the right can be determined as a product of the plunger area and the pumped fluid pressure. The magnitude of fluid pressure fluctuations at the triplex plunger pump outlet [3] is negligible and can be taken as roughly constant, in which case the force applied to the crosshead upon its working travel

$$ F=\frac{\uppi {d}_{\mathrm{pl}}^2}{4}{p}_{\mathrm{m}}=\frac{\uppi {90}^2}{4}80=508938\;\mathrm{N}. $$

The driving component 2 of the studied mechanism (Fig. 4) rotates with a constant angular speed

Fig. 4
figure 4

Schematic diagram of forces acting on the components of the pump drive: F is axial load from pump plunger; F r is radial load acting on crosshead; F t is force acting on crank.

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$$ {\upomega}_2=\uppi n/30=\uppi \cdot 125/30=13.09{ \sec}^{-1}. $$

To disclose the regularities of variation of the parameters of the angular speeds of the components and the linear speed of the crosshead, we shall perform kinematic calculation of the driving mechanism for seven positions of the driving component at which the components receive the full working load (Fig. 4).

The results of kinematic calculation of the pump plunger driving mechanism by Eqs. (2), (4), and (5) are adduced in Table 1.

Table 1 ᅟ
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The axial load F applied to the crosshead and dependent on the plunger diameter and fluid pressure at the pump outlet remains practically constant throughout the working process. This load can be divided into radial component F r , which is received by the crosshead guides and is directed perpendicular to the axis of its motion, and tangential component F t transmitted further to the crank. Both these components depend on the angle of tilt of the connecting rod φ3 to the axis of motion of the crosshead and can be determined by the equations

$$ \begin{array}{cc}\hfill {F}_r=F \tan {\upvarphi}_3;\hfill & \hfill {F}_t={F}_t=F/ \cos {\upvarphi}_3.\hfill \end{array} $$

The results of kinematic and force calculations of individual components and units of the connecting rod-crosshead group of the pump plunger driving mechanism and the procedure for their determination allow a more comprehensive evaluation of the distinctions and nature of the friction processes in the moving joints of the drive and determination of the maximally permissible loads and the optimal size of the drive components.

The force F (Fig. 4) that sets into motion the crosshead and the pump plunger, which is rigidly connected to the crosshead (which execute reciprocating rectilinear motion), is transmitted to the crosshead from the upper connecting rod end where the bushing of the sliding bearing is pressed in by a pin secured right in the crosshead body. The force F t varies from the maximum value to F, depends on the rotation angle of the connecting rod φ3, and determines the specific pressure of the pin on the bushing surface in the upper connecting rod end:

$$ {F}_{t \max }=F/ \cos {\upvarphi}_{3 \max };\;p={F}_{t \max }/\left({d}_3{l}_{\mathrm{uc}}\right)=516170/\left(120\cdot 95\right)=45.28\kern0.22em \mathrm{M}\mathrm{P}\mathrm{a}\le \left[p\right], $$

where p is the nominal specific pressure, MPa; F tmax is the maximum force acting on the pin, N; d 3 is the pin diameter, mm; l uc is the working length of the upper bushing of the connecting rod, mm; and [p] is the maximally allowable specific pressure, MPa.

The force F r also depends on the connecting rod rotation angle φ3, varies from zero to the maximum value (Table 1), and is received by the guides of the crosshead as it moves:

$$ {F}_{r \max }=F \tan {\upvarphi}_{3 \max }, $$

where φ3max = 9.594° is the maximum connecting rod rotation angle (Table 1).

The speed of sliding of the bushing surface along the mating surface of the pin can be determined by the equations

$$ \begin{array}{c}\hfill {v}_{\mathrm{sl}}={\upomega}_3{d}_3/\left(2\cdot 1000\right);\hfill \\ {}\hfill {v}_{\mathrm{sl}\kern0.1em \max }={\upomega}_{3 \max }{d}_3/\left(2\cdot 1000\right)=9.594\cdot /\left(2\cdot 1000\right)=0.576m/ \sec .\hfill \end{array} $$

As the driving component moves from position 1 (Fig. 4) to position 4, the angular speed of the connecting rod ω3relative to the pin axis changes from the maximum to zero. The speed of the bushing surface sliding along the pin surface v sl also changes from the maximum (0.576 m/sec) to zero. In this case, static friction, which passes later (at maximum load F max) into semifluid sliding state, will be observed in the bushing and pin surface contact zone (when the driving component is at position 4). Such a state of operation of the studied pair may lead, under specific loads exceeding the permissible and poor lubrication conditions, to seizure of the working surfaces of the bushing and the pin, scoring, rapid wearing, and drastic shortening of drive service life.

In the discussed example, the nominal specific pressure p = 45.28 MPa is much higher than the maximally allowable pressure [p] = 25 MPa as per ISO recommendations for sliding bearings made of BrO10F1 type of tin bronze which operate at low sliding speeds under semifluid lubrication conditions [4]. To improve the efficiency of the studied unit, it is expedient to reduce the nominal specific pressure to the maximally allowable value by increasing the pin and bushing diameters or by decreasing the plunger diameter and simultaneously increasing the angular speed of the driving component (for reducing F max and maintaining the efficiency), in which case the specific pressure on the mated surface will decrease and the speed of sliding between them will increase, which will facilitate transition on a significant path of sliding of the pair to a more favorable friction condition.

The speed of sliding of the working crank surface along the connecting rod bushing surface depends on the angular speed of the connecting rod ω3. It changes from the maximum value at position 1 of the driving component 2 (Fig. 4):

$$ {v}_{23 \max }={\upomega}_3{d}_c/\left(2\cdot 1000\right)=2.1816/\left(2\cdot 1000\right)=0.207262\mathrm{m}/ \sec $$

to zero at position 4 of the driving component 2:

$$ {v}_{23 \min }={\upomega}_3{d}_c/\left(2\cdot 1000\right)=0\cdot 190/\left(2\cdot 1000\right)=0 $$

and then to the maximum negative value at position 7 of the driving component 2:

$$ {v}_{23 \max }={\upomega}_3{d}_c/\left(2\cdot 1000\right)=-2.1816\cdot 190/\left(2\cdot 1000\right)=-0.207262\mathrm{m}/ \sec . $$

When v 23max > v cr (v cr depends on the oil viscosity and the wedge-shaped gap in this region), a sufficiently thick oil film may form to create fluid friction condition; also, in this region in particular occurs severe loading of the noted mate (start of the working stroke), and the oil film formed, because of its damping ability, softens the shock load and facilitates longer life of the contacting surfaces.

Position 4 of the driving component 2 is the most hazardous. At this position, the direction of sliding of the mating surfaces changes under semifluid friction condition and, in the absence of (or in the case of insufficient thickness) of the oil film, seizing of the sliding surfaces may occur, followed by their damage, and the maximum load F tmax is applied particularly at this position. Calculation of this unit also must be performed based on the nominal allowable pressure:

$$ {p}_1={F}_{t \max }/\left({d}_c{l}_c\right)=516170/\left(190\cdot 120\right)=22.64\mathrm{M}\mathrm{P}\mathrm{a}\le \left[p\right]=25\mathrm{M}\mathrm{P}\mathrm{a}, $$

where p 1 is the nominal specific pressure acting on the bushing, MPa; F tmax is the maximum force acting on the crank-connecting rod unit, N; d c is the crank diameter, mm; and l c is the working width of the bushing, mm.

In the noted case, the nominal specific pressure does not exceed the allowable value, and the unit is efficient.

Unlike pin–connecting rod bushing and crank–connecting rod insert sliding bearings, crosshead motion along the guide is translational, which makes it difficult to create the necessary fluid friction conditions that facilitate higher efficiency and longer life of this friction pair. The sliding speed and the radial load acting on the crosshead during its working motion change from zero to the maximum values with further decrease to zero (Fig. 4 and Table 1).

Simultaneous change in sliding speed and radial load in the working cycle process can be used (for finishing the shape of the guide or of the crosshead surface) to create the necessary conditions for transition from semifluid to fluid friction condition in a large section of the sliding path, which will allow drastic reduction of wear of friction pair components.

When the crosshead guides and the crosshead itself are made in accordance with the schematic diagram in Fig. 2, sliding of mated friction pair surfaces occurs in semifluid friction conditions, and the key criterion for evaluation of the friction pair efficiency is comparison of the nominal specific pressure with the permissible pressure for the friction pair materials. In the described example, the guides are made of BrO10F1 type of tin bronze (permissible specific pressure under semifluid lubrication conditions [p] = 25 MPa) and the crossheads are made of 40KhN steel (hardness of working surfaces 52–56 HRC), in which case the nominal specific pressure

$$ p={F}_{r \max }/(bl)=86020/\left(125\cdot 196\right)=3.52\cdot \mathrm{M}\mathrm{P}\mathrm{a}, $$

where F rmax is the maximum radial force on the crosshead guide, N; b is the nominal working breadth of the crosshead contact surface, mm; and l is the length of the working section of the crosshead, mm.

To get more accurate data by analyzing the conditions of operation of the friction units of the connecting rod-crosshead mechanism of the plunger pump drive and the influence of loading conditions on the operation of its components, it is necessary to take account also of the influence of dynamic factors on loading. However, by using the said analytical procedure we can get the initial approximate data on friction unit loading conditions, which are enough for their further structural finishing and designing.