Danfoss Selection of Driveline Components User guide

Applications Manual

Selection of Driveline Components

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Applications Manual

Selection of Driveline Components

Revision history	Table of revisions
	Date	Changed	Rev
	July 2015	Minor edits	0304
	April 2015	Minor edits	CC
	December 2014	Corrections to the equations	CB
	November 2013	Major rewrite - Danfoss layout	CA
	July 1997	Second edition	B

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Applications Manual
Selection of Driveline Components
Contents
Introduction
Applications Manuals......................................................................................................................................................................	4
Selection of Driveline Components
Introduction........................................................................................................................................................................................	5
Design Goal.........................................................................................................................................................................................	5
Sizing Procedure...............................................................................................................................................................................	5
Machine Corner Power (CP)..........................................................................................................................................................	6
Variable or Fixed Motor..................................................................................................................................................................	8
Motor Selection.................................................................................................................................................................................	9
Final Drive Selection.....................................................................................................................................................................	11
Input Gearing...................................................................................................................................................................................	13
Pump Selection...............................................................................................................................................................................	14
Continuous Pressure.....................................................................................................................................................................	16
System Sizing Flow Chart............................................................................................................................................................	17
Sizing Flow Chart......................................................................................................................................................................	19
Equations..........................................................................................................................................................................................	23
Definition of Terms........................................................................................................................................................................	25
Tractive Effort
Tractive Effort..................................................................................................................................................................................	26
Acceleration
Acceleration.....................................................................................................................................................................................	30
Charge Pump Sizing
Introduction.....................................................................................................................................................................................	33
Charge Pump Considerations....................................................................................................................................................	33
Charge Pump Sizing Worksheet...............................................................................................................................................	36

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Introduction

Applications Manuals

Content included in these manuals

These applications manuals provide design theory and detailed calculations for building hydraulically powered machines.

The original document was written as one manual with four sections.

The current set of manuals includes the four documents listed below. The section numbers from the original document are listed in parenthesis after the current document title.

•Selection of Driveline Components BLN-9885 (originally Section 1)

•Pressure and Speed Limits for Hydrostatic Units BLN-9884 (originally Section 2)

•Transmission Circuit Recommendations BLN-9886 (originally Section 4)

•Fluids and Lubricants 520L0463 (originally Section 3)

Other Reference Manuals

•Hydraulic Fan Drive Systems Technical Information 520L0824

•Hydraulic Fan Drive Systems Design Guidelines 520L0926

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Applications Manual

Selection of Driveline Components

Selection of Driveline Components

Introduction

This section presents a method of sizing driveline components for typical closed loop hydrostatic transmissions. Although the method was developed for propel systems, it may be used for winch, or reel, applications, or other circuits with very slight modifications. The terminology used in this procedure also tends to reflect off-highway mobile applications.

It is assumed that the specific functional requirements of the application have been defined, and that the fundamental design parameters have been established for each mode of operation. These typically include vehicle speed, gradability, useful life, vehicle weight, and drive configuration. It is also assumed that required engine power has been established.

Design Goal

The goal of this design method is to optimize the performance and cost of the driveline system by selecting appropriate driveline components. Smaller hydraulic components cost less than larger components, but they have lower torque capability.

Hydraulic unit life is highly dependent on system pressure. Establish maximum and continuous pressure based on the required life of the driveline. Danfoss document Pressure and Speed Limits for Hydrostatic Units BLN-9884 covers this subject in detail.

The figure below Driveline Element Selection shows the components typically found in a closed loop hydrostatic drive system as well as the design parameters and degree of design flexibility associated with each component. Because driveline design includes so many variables (each dependent on the others), and because final component selection is ultimately limited by product availability, several iterations of this procedure may be required before arriving at the optimum system.

Sizing Procedure

The sizing procedure starts with values for the machine maximum torque and required speed. From these values, a hydraulic motor size can be selected. This motor selection is then made compatible with ratings of available output gear drives. From a motor size, a pump size can be established. The pump must be capable of accepting the required input power, and it must be compatible with the pump drive mechanisms. It must also be large enough to provide sufficient flow to the drive motor to attain the required speed.

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Selection of Driveline Components

Selection of Driveline Components

Driveline Element Selection

	Driving		Design	Design
	Element		Parameter	Flexibility
			Power
	Engine			No
			Speed
	Gearing		Ratio	Sometimes
			Size
	Pump
			Pressure	Yes
			Speed
			Size
	Motor
			Pressure	Yes
			Speed
	Gearing		Ratio	Usually
			Speed
	Load			No
			Weight

Optimizing the size of the hydraulic units depends on selecting the correct gear ratios. By matching machine corner power with motor corner power, the required unit sizes can be quickly determined. The gear ratios can usually be adjusted to provide some optimization of hydraulic unit component size.

Along with the equations presented throughout this document, a sizing flowchart is included to assist with sizing. The flowchart details the sizing procedure and includes numerous design check steps to validate the calculated sizing values.

Design limits for associated mechanical components are not identified.

Machine designers should verify that the design parameters are met for all driveline components.

The steps outlined in this manual are designed to guide you in component selection. For further assistance, contact your Danfoss representative for help interpreting and verifying your results.

Machine Corner Power (CP)

The first step in the sizing process is to determine the value referred to as Machine Corner Power (CP). The concept of Corner Power is abstract and is normally not an attainable value of transmission power. It is useful in the design process because it provides an indication of transmission component size and ratio requirements. Corner Power is representative of the maximum torque and the maximum speed (at full load) that the machine is required to have. These two values of maximum speed and maximum torque (or Tractive Effort) never happen at the same time, but the purpose of Corner Power is to capture both values to define an operating envelope for the machine and to aid in the selection of the hydraulic motor. Refer to the Machine Corner Power graph below for an illustration of the concept.

The concept of Corner Power also applies to hydraulic motors. As demonstrated in the topic Motor Selection on page 9, the maximum corner power of a hydraulic motor represents the maximum torque and maximum continuous speed capabilities of that product. Equations are provided in the Motor Selection topic that allow you to select the appropriate motor based on the machine’s corner power.

The equations for calculating Corner Power are provided below. For rotary drives (work function), the input values to the equation are the required maximum output torque and the maximum output speed

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Applications Manual

Selection of Driveline Components

Selection of Driveline Components

(at full load) of the machine. For propel drives, the input values are maximum tractive effort and maximum vehicle speed (at full load).

For multi-speed drives (e.g. work mode and travel mode), corner power must be calculated for all ranges.

Tractive Effort

Tractive Effort refers to the amount of force available at the wheel or wheels of the vehicle and represents the maximum possible pull a vehicle could exert, if it had no resistance to movement.

Ideally, tractive effort or output torque requirements should be derived from actual tests of the machine. However, for establishing tractive effort design values, an analytical approach based on machine parameters and functional modes of operation has been used successfully.

The topic Tractive Effort on page 26 describes tractive effort in more detail.

Machine Corner Power

Max System Pressure

		CP
		Full Load Speed
<![if ! IE]> <![endif]>Output Torque	HP Out	Part Load Speed
	(Approx. 0.70 HP In)
	Rated Speed	No Load, High
		Idle Speed (NLHI)
	Output Speed	BLN-9885-4

Machine Corner Power (CP) is determined by estimating the maximum torque and maximum output speed required. It is normally greater than actual transmission output power. Maximum output speed is assumed to be at engine rated speed. However, under part load conditions slightly higher speed may be obtained.

W Warning

Protect yourself from injury. Use proper safety equipment, including safety glasses, at all times.

W Warning

Check to ensure that maximum motor speed is NOT exceeded under dynamic braking conditions, when engine speed can exceed No Load High Idle (NLHI) ratings.

	SI System			US System					Description
		TQ • ND		Rotary Drives					CP = machine corner power	kW (hp)
	1) Machine CP =			Machine CP =	TQ • ND
									TQ = maximum drive output torque	Nm (in lbf)
		9549
					63 025
									ND= maximum drive output design speed rpm
		TE • S		Propel Drives
	Machine CP =			Machine CP =			TE • S		TE = maximum vehicle tractive effort	N (lbf)
		3600			375				S = maximum vehicle design speed	kph (mph)

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Selection of Driveline Components

Variable or Fixed Motor

Because the machine corner power is an expression of maximum torque (tractive effort) and maximum vehicle speed, it can be used to establish the effective Transmission Ratio (TR) required to satisfy system demands.

The effective Transmission Ratio (TR) is the ratio of the required vehicle corner power divided by the available power from the machine’s prime mover (engine). This ratio is similar to the ratio spread of a similarly sized mechanical transmission and indicates the amount of hydrostatic ratio which is required.

Systems with high transmission ratios normally benefit from variable, or two-position, drive motors.

For drives with variable load cycles, determine the normal input power (available power) to the transmission by deducting the average power dedicated to other functions from the maximum engine power available to the drive.

A Transmission Ratio (TR) greater than 1.0 means that there is not enough engine power available to meet all of the operating requirements at the same time.

•Typically, machines with high transmission ratios have high torque (Tractive Effort) requirements at low speed and high speed requirements at low torque (Tractive Effort). In this case, a large fixed motor would satisfy the high torque requirements, but operating the same motor to meet the maximum speed requirement could exceed the speed limit of the motor and require a large displacement pump. For high transmission ratios, use a variable displacement motor; it can be used at high displacement to satisfy the maximum torque requirement and then shifted to a smaller displacement to satisfy the machine’s maximum speed requirement. A fixed motor could be used with a multi-ratio gearbox for machines with a high transmission ratio, but usually a variable motor will be the most cost effective solution.

•If the transmission ratio is low, that means that there is probably enough engine power available to achieve the maximum torque and speed requirements simultaneously. In those cases, a fixed motor is suitable for the task.

•In cases of extremely high transmission ratio, a variable motor may not satisfy the need. In these cases, a multi-speed gearbox may also be required. Some applications use 2-speed, 3-speed, or 4- speed gearboxes to meet the vehicle requirements; but a 2-speed gearbox is most common.

The rule for selecting a fixed or variable drive motor is as follows:

•If TR is greater than 4, use a variable motor,

•If TR is less than 2, use a fixed motor,

•If TR is between 2 and 4, evaluate both variable and fixed motors for suitability,

•If TR is greater than 14, use a multi-ratio gear box between the motor and the final drive.

There is no direct relationship between transmission ratio and final drive ratio. The final drive ratio is calculated based on the displacement of the motor that has been chosen, the maximum pressure, the loaded radius of the wheels, and the required maximum tractive effort.

The transmission ratio is only used to help determine the motor type, not the motor size. Refer to the topic Final Drive Selection on page 11 to calculate the Final Drive Ratio (FD).]

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Selection of Driveline Components

Selection of Driveline Components

	SI / US System		Description
	2) TR =	Machine CP	TR = effective transmission ratio
		HP	HP = normal input power	kW (hp)

HP = 0.7 * Available prime mover power

TR < 2, use fixed displacement motor

TR > 4, use variable displacement motor

TR > 14, use multi-ratio gearbox

Motor Selection

Calculate the required motor corner power from machine corner power and driveline efficiency using equation (3) Required Motor CP. This establishes the minimum motor size capable of meeting the power requirement of the machine. For multi-speed drives, use the largest corner power for each of the operating ranges.

For transmission circuits using multiple drive motors, the required motor corner power should be interpreted as the required corner power at each motor.

Use equation (4) Maximum Motor CP to calculate the maximum motor corner power based on the design maximum pressure and the design maximum speed and the desired life of the motor.

Design maximum pressure is the maximum pressure at which the motor is intended to operate to meet the required life. The design maximum pressure may or may not be the same as the maximum pressure rating published in the product literature. Published ratings for maximum pressure assume the pressure will occur for only a small percentage of the operating time, usually less than 2% of the total, and will result in “normal” life. For applications in which the maximum pressure will occur over a significant portion of the duty cycle, or applications in which additional life is required, the design maximum pressure should be assigned a value less than the published rating for maximum pressure.

Design maximum speed is the maximum speed at which the motor is intended to operate to meet the required life. Although speed has less effect on life than pressure, lower operating speeds will have the effect of increasing life. The value for the design maximum speed must never exceed the maximum speed rating published in the product literature; and will usually be less, to allow for motor speed increases as a result of reduced-load, or no-load, conditions (see Machine Corner Power graph).

Danfoss document Pressure and Speed Limits for Hydrostatic Units BLN-9884, provides additional information concerning pressure and speed limits with respect to component life.

Ideally, values for the design maximum pressure and design maximum speed would be used in Equation

(4) Maximum Motor CP to determine motor CP capability. However, this is difficult at this stage of the sizing process because both the motor displacement and final drive ratio are unknown. Despite this limitation, the next step is to choose a logical motor displacement based on the required motor CP. The table Hydrostatic Motor Corner Power Chart can be used as an aid in preliminary motor selection. You should choose a motor with a motor CP at least as large as the required motor CP calculated using Equation (3) Required Motor CP.

Equation (A) Design Check serves as a design check to ensure that a motor with sufficient corner power capability is selected. Motor selection based on corner power results in the smallest motor capable of transmitting the required machine power while achieving system life requirements.

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Selection of Driveline Components

SI System

US System

Description

Machine CP

Required Motor CP =

Machine CP

CP = corner power

kW [hp]

3)

Required Motor CP =

E = final drive efficiency

(%/100)

E • #

E • #

# = number of motors

4)

Maximum Motor CP =

DM • NM • PM

Maximum Motor CP =

DM • NM • PM

600 000

396 000

DM = maximum motor displacement

cc [in3 ]/rev

NM = design maximum speed

rpm

A)

Design Check: Maximum Motor CP ≥ Required Motor CP

PM = design maximum pressure

bar [psi]

For variable motor systems, the transmission CP is determined only by the motor. For various pump sizes, actual applied motor CP may be varied by adjusting the minimum motor angle.

For fixed motor systems, the transmission CP is ultimately determined by the pump speed and displacement. Although the fixed motor CP must be large enough to accommodate the maximum load and speed, the pump must be large enough to drive the motor at the required design speed.

An additional sizing exercise may be required for fixed motor systems after pump selection has been made.

For either variable or fixed motor systems, it may be necessary to increase the motor size if proper output gearing is not available. Gearing must accommodate both the desired transmission ratio and maximum motor speed, in addition to meeting the torque requirements.

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Selection of Driveline Components

Hydrostatic Motor Corner Power Chart

							Fixed		Variable
			Max
		Max	Speed
	Max	Working at Max		Cont Speed a	Max Speed at	Cont Speed	Corner	Corner	Corner	Corner
	Pressure	Pressure	Angle	Max Angle	Min Angle	at Min Angle	Power	Power	Power	Power
Motor	(psid)	(psid)	(rpm)	(rpm)	(rpm)	(rpm)	(HP)	(kW)	(HP)	(kW)
Series 15	4500	4350	----	4000	----	----	42	31	----	----
Series 40M25	5000	4350	----	4000	----	----	77	57	----	----
Series 40M35	5000	4350	----	3600	5300	4200	97	72	113	84
Series 40M44	5000	4350	----	3300	4850	3900	112	83	132	99
Series 40M46	5000	4350	----	3600	5000	4500	128	95	160	119
LV/LC25	6000		----	----	5000	4400	----	----	102	76
LV/LC30	5000		----	----	5150	4450	----	----	103	77
LV/LC35	4350		----	----	5300	4500	----	----	106	79
KV/KC38	6000		----	----	5200	4650	----	----	163	122
KV/KC45	5000		----	----	5050	4500	----	----	156	116
Series 9055cc	7000		4250	3900	5100	4600	231	173	273	204
Series 9075cc	7000		3950	3600	4700	4250	291	217	344	256
Series 90100cc	7000		3650	3300			356	266	----	----
Series 90130cc	7000		3400	3100			435	324	----	----
H1B060	7000	6525		----	7250	5900	----	----	382	285
H1B080	7000	6525		----	6600	5300	----	----	457	341
H1B110	7000	6525		----	5950	4800	----	----	570	425
H1B160	7000	6525		----	5250	4250	----	----	734	547
H1B250	7000	6525		----	4500	3650	----	----	985	734
51V060	7000				7000	5600	----	----	363	270
51V080	7000				6250	5000	----	----	432	322
51V110	7000				5600	4500	----	----	534	398
51V160	7000				5000	4000	----	----	691	515
51V250	7000				4250	3400	----	----	917	684

These values for corner power capability are based on maximum pressure and maximum speed ratings.

Refer to Pressure and Speed Limits for Hydrostatic Units BLN-9884 for detailed information on ratings of units and expected life.

Final Drive Selection

After the motor is initially sized, calculate the required final drive ratio. One of two approaches can be taken to determine this ratio. Both take into account the design maximum and continuous pressures allowed to meet the life requirements of the machine (see Pressure and Speed Limits for Hydrostatic Units BLN-9884).

The two methods are as follows:

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Selection of Driveline Components

1.Using the Sizing Flow Chart on page 19, size the final drive ratio using the design maximum pressure and the maximum torque requirement. Use equation (5) Required FD on the following page for this calculation. After the pump is sized and all speed conditions have been met, estimate the continuous pressure, using the Sizing Flow Chart on page 19, and compare it with the maximum design continuous pressure.

2.As an alternate method, calculate the final drive ratio required for all modes of operation (travel mode, work mode, etc.). Calculate the final drive ratio from the assumed pressure and torque requirements for each operating mode. For worst case or intermittent modes of operation, use the design maximum pressure along with the tractive effort or torque requirement to obtain a value for the final drive ratio. Use the design continuous pressure for typical or continuous modes of operation, and calculate required final drive ratios for these modes as well. Select the largest final drive ratio from the values calculated for the various operating modes.

For variable or two-position motors, only final drive ratios from those modes utilizing maximum motor displacement can be calculated, since the motor minimum displacement is not yet known.

The next step is to check motor speed limits using the limits obtained from Pressure and Speed Limits for Hydrostatic Units BLN-9884, or the respective Technical Information manual.

Motor speed will usually be satisfactory unless the final drive ratio is significantly higher than required (Gearbox limits must also be met). Equation (6) NMR=FD•NMD is used to determine the required motor speed at maximum motor displacement based on the final drive ratio calculated in equation (5) Required FD. For fixed displacement motors, the maximum motor displacement referred to in the equation is simply the displacement of the motor. For variable motors, use the displacement at the maximum swashplate angle. Use design check (C) NMR ≤ NML to ensure that the speed limit of the motor is not exceeded. If a variable motor is specified, use equation (7) NVR=FD•NMD and design check (D) NVR ≤ NVL to determine if the speed required at the minimum motor displacement exceeds the maximum reduced angle speed limit. As explained in Pressure and Speed Limits for Hydrostatic Units BLN-9884, the maximum speed limit of a variable motor increases with decreasing angle, up to a certain value (the maximum reduced angle speed limit or cutoff point on the speed/angle curve). At low swashplate angles (i.e., below the angle cutoff point), a decrease in angle does not result in a greater maximum speed limit.

Note that reduced angle speed limits cannot be checked until the pump displacement and minimum motor displacement have been established. (This will be done in subsequent steps of this procedure.) However, if the speed exceeds the limit associated with the smallest possible swashplate angle (i.e., at the cutoff point of the speed/angle curve), then increase the motor’s maximum displacement and recalculate the final drive ratio.

Refer to Pressure and Speed Limits for Hydrostatic Units BLN-9884 for more information concerning speed limits.

Both SM (vehicle speed required at max angle) and SV (vehicle speed required at min angle) are customer defined conditions

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Selection of Driveline Components

SI System

US System

Rotary Drives

5)

Required FD =

Torque • 20π

Required FD

=

Torque • 2

π

DM • PM • E • EM

DM • PM • E • EM

Propel Drives

Required FD =

TE • LR • 20 π

Required FD =

Torque • 2

π

DM • PM • E • EM • #

DM • PM • E • EM • #

B)

Design Check:

FD ≥ Required FD

Rotary Drives

6)

NMR = FD • NMD

NMR = FD • NMD

Propel Drives

NMR = FD • SM • 2650

NMR =

FD • SM • 168

LR

LR

C)

Design Check:

NMR ≤ NML

Rotary Drives

7)

NVR = FD • NVD

NVR = FD • NVD

Propel Drives

Description

DM	=	max motor displacement	cc (in3)/rev
E	=	final drive efficiency	(%)/100
FD	=	final drive ratio	d’less
E M	=	motor mechanical efficiency	(%)/100
LR	=	wheel loaded radius	mm (in)
NMD =		non-propel design speed at max angle	rpm
NML =		motor speed limit at max angle	rpm
NMR =		req'd motor speed at max angle	rpm
NVD =		non-propel design speed at min angle	rpm
NVR =		req'd motor speed at min angle	rpm
NVL	=	motor speed limit at min angle	rpm
PM	=	maximum pressure	bar (psid)
SM	=	vehicle speed req'd at max angle	kph (mph)
SV	=	vehicle speed req'd at min angle	kph (mph)
TE	=	vehicle tractive effort	N (lbf)
TQ	=	max drive output torque	Nm (in•lbf)

#= number of motors

	NVR =	FD • SV • 2650			NVR =	FD • SV • 168
		LR				LR
D)	Design Check:		NVR		≤ NVL

Input Gearing

The use of input gearing is usually customer defined and determined by the machine configuration. For vehicles with multiple hydraulic systems, use of an input splitter box is common. Splitter boxes are usually available with various ratios to accommodate pump speed requirements. For machines with only a single hydrostatic system (or machines utilizing tandem pumps) a direct drive pump may be appropriate, in which case the pump speed is the same as the prime mover speed.

Use equation (8) NP = NE•IR to determine the relationship between the prime mover speed, pump speed, and input gear ratio.

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SI / US System		Description
8) NP = NE • IR	NP	= maximum pump design speed	rpm
	NE	= prime mover design speed	rpm
	IR	= pump input ratio

Pump Selection

Pump sizing consists of selecting a pump that will meet the flow (speed) requirements of the motor, or motors, in the system.

Use equation (9) to determine the required pump displacement. This calculation is based on an assumed pump input speed. Select a pump displacement at least as large as the calculated displacement. Also, check that the desired pump speed does not exceed the rated maximum speed for the pump. If the rated speed limit is exceeded, choose a different pump and calculate the input speed required and the corresponding input ratio using equations (10) and (11).

With a pump displacement selected, calculate the actual motor speed. The actual speed will usually be slightly higher than the required motor speed because the pump that is selected will usually have a displacement slightly greater than the calculated displacement.

Fixed Motor

For a fixed motor, determine the actual motor speed and compare with its rated maximum speed using equation (12) and design check (G). Note that equation (12) includes a calculation for an overrunning condition. An overrunning condition is characterized by a speed increase at the pump (and consequently the motors), typically by as much as 15%. The condition is especially common during downhill operation. Not only is there an increase in pump speed, but during either downhill operation or vehicle deceleration using hydrostatic braking; the motor becomes the pump and the pump becomes the motor. The net result is that the motor will turn faster for any given pump speed than what would be experienced during normal propel operation.

A 15% increase in engine speed is just an estimate; check with the engine manufacturer for specific details concerning the engine’s ability to provide dynamic braking and its maximum, or [not-to-exceed] operating speed.

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