Page 1
Technical Information PVG 16 Proportional Valve Group www.danfoss.com...
Page 2
Technical Information PVG 16 Proportional Valve Group Revision history Table of revisions Date Changed December 2018 Major rework of document: new sections added, data corrected. 0901 October 2018 'PVBS Main Spools' section reworked. 'Safety in Systems' and 'PVB Basic Modules 0801 Accessories' sections added.
Technical Information PVG 16 Proportional Valve Group Contents General Information General Description..................................5 PVG 16 Features....................................5 Safety in Systems....................................6 PVG 16 Modules Overview................................8 PVP Inlet Modules Open Center PVP....................................10 Open Center PVP with PPRV..............................13 Open center PVP with HPCO and PVE PPRV.........................17 Closed Center PVP..................................
The PVG 16 is a member of the PVG product platform and interfaces to other valve families enabling all machine functions being controlled from one single valve stack. PVG 16 controls work port flow up to 65 l/min [17 US gal/min] l/min and up to 420 bar [6090 psi] bar work port pressure.
This example breaks down the control system into smaller bits explaining the architecture in depth. Even though many Danfoss components are used in the PVG control system. The function of the control system is to use the output from the PVE together other external sensors to ensure the PLUS+1 main controllers correct function of the aerial lift.
Page 7
A mix of electrical actuation and hydraulic actuation on the same valve stack is not safe. PVE and PVH are designed for different pilot pressure. Cost-free repairs, as mentioned in Danfoss General Conditions of Sale, are carried out only at Danfoss or at service shops authorized by Danfoss.
Technical Information PVG 16 Proportional Valve Group General Information PVG 16 Modules Overview PVG proportional valve group shown in the exploded view illustration for a quick modules navigation. PVG 16 Modules Assembly Overview PVBS PVH/Covers PVHC PVAS PVG Modules Navigation:...
PVG 16 Proportional Valve Group PVP Inlet Modules The PVG 16 PVP inlet modules, also referred to as pump side modules, act as an interface between the PVG 16 proportional valve group and the hydraulic pump and tank reservoir. PVP Inlet Module PVP inlet module dimensions 23 [0.9]...
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Open Center PVP The basic Open Center PVP inlet module is intended for use with fixed displacement pumps in applications, where a valve group with mechanically controlled work sections is desired, or where the pilot pressure to the valve group is supplied externally.
Page 11
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Theoretical Performance Graphs Integrated LS pressure relief valve characteristics [psi] (bar) 4000 3000 2000 1000 [l/min] [US gal/min] Neutral by-pass pressure drop characteristics [psi] (bar) (l/min) [US gal/min] Part numbers for Open Center PVP...
Page 12
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Part numbers for Open Center PVP (continued) Part number P-port T-port LS-, M-port (LS1 T0-port Mounting PVPX JIS 1/2 JIS 3/4 JIS 1/4 157B5925 G1/2 G3/4 G1/4 157B5945 1 1/16-12 UNF...
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Open Center PVP with PPRV The Open Center PVP inlet with integrated pilot pressure reduction valve (PPRV) is intended for use with fixed displacement pumps in applications, where a valve group with electro-hydraulically or hydraulically controlled work sections is desired (PVE or PVH/PVHC).
Page 14
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Theoretical Performance Graphs Integrated LS pressure relief valve characteristics [psi] (bar) 4000 3000 2000 1000 [l/min] [US gal/min] Neutral by-pass pressure drop characteristics [psi] (bar) (l/min) [US gal/min] Pilot pressure reduction valve characteristics...
Page 15
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Part numbers for Open Center PVP with PPRV Part number Actuation P-port T-port LS-port M-port Pp-port T0-port Mounting PVPX G1/2” G3/4” G1/4” G1/4” 157B5010 G1/2” G3/4” G1/4” G1/4” 157B5012 G3/4”...
Page 16
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Part numbers for Open Center PVP with PPRV (continued) Part number Actuation P-port T-port LS-port M-port Pp-port T0-port Mounting PVPX G3/4 G3/4 G1/4 G1/4 157B5977 M22 x 1.5 M22 x 1.5 M12 x 1.5...
The integrated HPCO functionality guides the excess flow of the PVG 16 valve group to the external hydraulic subsystem(s), giving priority to the PVG 16 work functions.
Page 18
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Theoretical Performance Graphs Integrated LS pressure relief valve characteristics [psi] (bar) 4000 3000 2000 1000 [l/min] [US gal/min] Neutral by-pass pressure drop characteristics [psi] (bar) (l/min) [US gal/min] Pilot pressure reduction valve characteristics...
Page 19
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Part numbers for OC PVP (HPCO and PPRV) Part number P-port HPCO- LS-port M-port Pp-port T0-port Mounting PVPX port G3/4” G3/4" G1/4” G1/4” G1/4” G1/4” 157B5140 G3/4” G3/4" G1/4” G1/4”...
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Closed Center PVP The basic Closed Center PVP inlet is intended for use with variable displacement pumps in applications where a valve group with mechanically controlled work sections is desired, or where the pilot pressure to the valve group is supplied externally.
Page 21
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Theoretical Performance Graphs Integrated LS pressure relief valve characteristics [psi] (bar) 4000 3000 2000 1000 [l/min] [US gal/min] Part numbers for Closed Center PVP Part P-port T-port LS-port M-port T0-port...
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Closed Center PVP with PPRV The Closed Center PVP inlet with integrated pilot pressure reduction valve (PPRV) is intended for use with variable displacement pumps in applications where a valve group with electro-hydraulic or hydraulically controlled work sections is desired.
Page 23
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Theoretical Performance Graphs Integrated LS pressure relief valve characteristics [psi] (bar) 4000 3000 2000 1000 [l/min] [US gal/min] Pilot pressure reduction valve characteristics [psi] (bar) (l/min) [US gal/min] Part numbers for Closed Center PVP with PPRV...
Page 24
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Part numbers for Closed Center PVP with PPRV (continued) Part number Actuation P-port T-port LS-port M-port Pp-port T0-port Mounting PVPX (LS1 1 1/16-12 UNF 1 1/16-12 UNF 9/16-18 UNF 9/16-18 UNF...
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Closed center PVPV with PPRV The Closed Center PVPV inlet with integrated pilot pressure reduction valve (PPRV) is intended for use with variable displacement pumps in applications where a valve group with electro-hydraulic or hydraulically controlled work sections is desired.
Page 26
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Part numbers for Closed Center PVPV with PPRV Part number Actuation P-, T-port LS-, M-port Mounting TO-port PVPX G1” G1/4” – 11008856 PVH/PVHC 1 5/16-12 UN 9/16-18 UNF 5/16-18 UNC –...
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Closed center PVPVM with PPRV The Closed Center PVPVM mid-inlet module with integrated pilot pressure reduction valve (PPRV) is intended for use with variable displacement pumps in applications where a valve group with electro- hydraulic or hydraulically controlled work sections is desired.
Page 28
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Part numbers for Closed Center PVPVM with PPRV Part number Actuation P-, T-port LS-, M-port Mounting PVLP PVH/PVHC 11083156 157B5912 1 5/16-12 UN 9/16-18 UNF 5/16-18 UNC 157B5914 157B5937 G1”...
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Open/Closed center PVP with PPRV The Open Center/Closed Center PVP with integrated pilot pressure reduction valve (PPRV) is intended for use with fixed or variable displacement pumps in applications where the application manufacturer does not determine the pump type.
Page 30
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Theoretical Performance Graphs Integrated LS pressure relief valve characteristics [psi] (bar) 4000 3000 2000 1000 [l/min] [US gal/min] Neutral by-pass pressure drop characteristics [psi] (bar) (l/min) [US gal/min] Pilot pressure reduction valve characteristics...
Page 31
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Part numbers for Open/Closed Center PVP with PPRV Part number Actuation P-port T-port LS-port (LS1 ) M-port T0-port Mounting LS Boost 11093273 G3/4 G3/4 G1/4 11119094 G3/4 G3/4 G1/4 11119095...
Technical Information PVG 16 Proportional Valve Group PVP Inlet Modules Open/Closed center PVPM The Open Center/Closed Center PVPM mid-inlet acts as a simple manifold and is intended for use with fixed or variable displacement pumps. The PVPM features no logic other than a PVLP shock/anti- cavitation valve facility for pressure peak protection and anti-cavitation prevention.
Technical Information PVG 16 Proportional Valve Group PVP Inlet Module Accessories The generic PVP inlet module accessory platform includes the PVPX Electrical LS pressure unloading valve, External pilot pressure adapters PVPC with or without check valve for all Open Center PVP with PPRV.
Technical Information PVG 16 Proportional Valve Group PVP Inlet Module Accessories PVPX technical data (continued) 155°C [311°F] Max. coil surface temperature 3/4-16 UNF Thread size Technical specification Parameter Minimum Recommended range Maximum -30°C [-22°F] 30 to 60°C [86 to 140°F] 90°...
Page 35
Technical Information PVG 16 Proportional Valve Group PVP Inlet Module Accessories Part numbers for PVPX, NOMO configuration (continued) Part number Manual Override Voltage Supply Connector IP Rating PUSH 12 V 11193839 PUSH 24 V 11193836 1x2 DEUTSCH IP 67 PUSH...
Technical Information PVG 16 Proportional Valve Group PVP Inlet Module Accessories PVPC without Check Valve The PVPC external pilot pressure adapter without check valve is an accessory in the M-port available for PVP inlet modules with integrated pilot pressure reduction valve (PPRV).
Technical Information PVG 16 Proportional Valve Group PVP Inlet Module Accessories PVPC with Check Valve The PVPC external pilot pressure adapter with check valve is an accessory in the M-port available for PVP inlet modules with integrated pilot pressure reduction valve (PPRV).
PVG 16 Proportional Valve Group PVB Basic Modules The PVG 16 PVB basic modules, also referred to as work sections, are the interface between the PVG 16 proportional valve group and the work function such as a cylinder or a motor.
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Compensated PVB The compensated PVB is intended for controlling a work function where the function behavior in terms of flow and pressures requires independence on the load pressure of other functions used simultaneously.
Page 40
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Performance graphs (Theoretical) Fluid flow as a function of spool travel Spool types: AA = 5/min A = 10 l/min B = 15 l/min C = 25 l/min D = 40 l/min...
Page 41
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Load Independent Fluid Flow – Pressure Compensated PVB (l/min) [US gal/min] AA = 5/min A = 10 l/min B = 15 l/min C = 25 l/min D = 40 l/min...
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Compensated PVB with PVLP/PVLA The compensated PVB featuring an optional PVLP/PVLA shock and anti-cavitation valves on each work port for pressure peak protection and anti-cavitation prevention. The compensated PVB is intended for controlling a work function where the function behavior in terms of flow and pressures requires independence on the load pressure of other functions used simultaneously.
Page 43
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Performance graphs (Theoretical) Fluid flow as a function of spool travel Spool types: AA = 5/min A = 10 l/min B = 15 l/min C = 25 l/min D = 40 l/min...
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Compensated PVB with LS A/B The compensated PVB is intended for controlling a work function where the function behavior in terms of flow and pressures requires independency on the load pressure of other functions used simultaneously.
Page 47
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Performance graphs (Theoretical) Fluid flow as a function of spool travel Spool types: AA = 5/min A = 10 l/min B = 15 l/min C = 25 l/min D = 40 l/min...
Page 49
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules PVB pressure compensated P-line and T-line characteristics [psi] (bar) Port A/B T-line P-line (l/min) [US gal/min] Part numbers for Compensated PVB with LS A/B Part number A/B-port 3/8” BSP 11130982 3/4”...
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Uncompensated PVB The uncompensated PVB is intended for controlling a work function where the function behavior in terms of flow and pressures requires independence on the load pressure of other functions used simultaneously.
Page 51
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Performance graphs (Theoretical) Fluid flow as a function of spool travel Spool types: AA = 5/min A = 10 l/min B = 15 l/min C = 25 l/min D = 40 l/min...
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Uncompensated PVB with PVLP The uncompensated PVB featuring an optional PVLP shock valve on each work port for pressure peak protection and anti-cavitation prevention, is intended for controlling a work function where the function behavior in terms of flow and pressures requires independence on the load pressure of other functions used simultaneously.
Page 54
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Performance graphs (Theoretical) Fluid flow as a function of spool travel Spool types: AA = 5/min A = 10 l/min B = 15 l/min C = 25 l/min D = 40 l/min...
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules PVLP Shock and Anti-Cavitation Valve The PVLP shock and anti-cavitation valve will relieve a pressure peak to the internal tank galleries and will furthermore suck oil from the tank to the work port to prevent cavitation. Pressure settings range: 32–400 bar [460–5801 psi].
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Accessories The generic PVB module accessory platform include the PVLP shock and anti-cavitation valve and PVLA suction valve. • PVLP Shock and Anti-Cavitation Valve on page 56 • PVLA Suction Valve...
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Accessories PVLP Shock and Anti-Cavitation Valve The PVLP shock and anti-cavitation valve will relieve a pressure peak to the internal tank galleries and will furthermore suck oil from the tank to the work port to prevent cavitation. Pressure settings range: 32–400 bar [460–5801 psi].
Technical Information PVG 16 Proportional Valve Group PVB Basic Modules Accessories PVLA Suction Valve The PVLA valve is an accessory available for PVB basic modules. The PVLA will suck fluid from the tank to the work port to prevent cavitation by the 0.5 bar spring. The plug will ensure that when using a single acting spool, all flow returning through the work port is led to tank.
Technical Information PVG 16 Proportional Valve Group PVBS Main Spools The main spools (PVBS) determine the flow out of the work section or the pressure build up and are based on a generic platform with a wide selection of additional features, enabling you to tailor the PVBS to suit the demands of any hydraulic system and any function.
Technical Information PVG 16 Proportional Valve Group PVBS Main Spools PVBS Fluid Flow Characteristics - Theoretical Performance Fluid flow as a function of spool travel Spool types: AA = 5/min A = 10 l/min B = 25 l/min C = 40 l/min...
Page 64
Technical Information PVG 16 Proportional Valve Group PVBS Main Spools Fluid flow as a function of spool travel (asymmetrical spools) Spool types: AA = 5/min A = 10 l/min B = 15 l/min C = 25 l/min D = 40 l/min E = 65 l/min 0.25...
Technical Information PVG 16 Proportional Valve Group PVBS Main Spools Part Numbers Flow Control Spools - Closed Neutral Position Schematic for PVBS - 4-way, 3 positions Schematic for PVBS - 4-way, 4 positions Symmetrical spools Part number Actuation Flow – l/min [US gal/min] A →...
Technical Information PVG 16 Proportional Valve Group PVBS Main Spools Part Numbers Flow Control Spools - Throttled Open Neutral Position Schematic for PVBS - 4-way, 3 positions Schematic for PVBS - 4-way, 4 positions Part number Actuation Flow – l/min [US gal/min] A →...
Technical Information PVG 16 Proportional Valve Group PVBS Main Spools Part Numbers Flow Control Spools - Open/Closed Neutral Position Schematic for PVBS - 4-way, 3 positions Schematic for PVBS - 4-way, 4 positions Asymmetrical spools Part number Actuation* Flow – l/min [US gal/min] A →...
Technical Information PVG 16 Proportional Valve Group PVG 16 Actuation PVH Hydraulic Actuation The PVH hydraulic actuation is intended for use on any work section where the operator wants to have a possibility to interact with the main spool via a hydraulic joystick. The spool spring package must match with this activation method.
Page 72
Technical Information PVG 16 Proportional Valve Group PVG 16 Actuation Technical data 5 – 15 bar [73 – 218 psi] Main spool spring control pressure range 30 bar [435 psi] Maximum pilot oil pressure 10 bar [145 psi] Maximum pressure on port T...
Technical Information PVG 16 Proportional Valve Group PVG 16 Actuation PVHC Electro-Hydraulic Actuation The PVHC is an electrical actuator module for main spool control. The PVHC control is done by dual Pulse Width Modulated, high current supply 100-400 Hz PWM control signals. The spool position will shift when conditions are changed such as temperature change.
Page 74
Technical Information PVG 16 Proportional Valve Group PVG 16 Actuation PVHC spool stroke vs current characteristics PVHC characteristics – Spool stroke vs current Spool stroke, mm Ideal curve Hysteresis [Current in mA] [Current in mA] 1600 @12V 1600 1400 1200...
All proportional actuators feature a closed- loop spool control and continuous fault monitoring. The analog PVE Series 6 actuator program for PVG 16 features two different main hydraulic principle variants (PVEO and PVEA).
Page 76
Technical Information PVG 16 Proportional Valve Group PVG 16 Actuation PVG 16 with PVEA sectional view PVE Series 6 Overview ON/OFF voltage control, non-proportional functions Proportional spool control for work functions PVEO Series 6 PVEA Series 6 For more information please see PVEO on page 77.
Technical Information PVG 16 Proportional Valve Group PVG 16 Actuation PVEO The PVEO actuator is a non-proportional ON/OFF control actuator with open-loop spool control primarily used to control simple ON/OFF work functions where a proportional control of speed or oil flow is not a requirement.
Technical Information PVG 16 Proportional Valve Group PVG 16 Actuation PVEO Technical Data Control Specifications Description Type 12 V ± 10% 24 V ± 10% Supply Voltage (U Range 11 to 15 V 12 to 30 V Max. ripple Current Consumption...
Technical Information PVG 16 Proportional Valve Group PVG 16 Actuation PVEA Series 6 Proportional Control Actuator The PVEA actuator is a proportional control actuator with a closed-loop spool control primarily used to control work functions with above medium performance requirements PVEA Series 6 The PVEA functionality includes an electric circuit with a closed-loop logic.
Technical Information PVG 16 Proportional Valve Group PVG 16 Actuation PVEA (-F) Series 6 schematic PVEA (-F) Series 6 dimensions 78.5 [3.09] 39 [1.54] Weight: 0.7 kg [1.54 lb] PVEA Technical Data PVEA/PVEA-CI/PVEA-F actuator technical specification and part numbers. Control specification...
Page 82
Technical Information PVG 16 Proportional Valve Group PVG 16 Actuation Technical data (continued) Fluid consumption Neutral 0.04 l/min [0.01 US gal/min] Locked position 0.04 l/min [0.01 US gal/min] Actuating 0.6 l/min [0.16 US gal/min] Fluid temperature Ambient Storage -50 to +90°C [-58 to +194°F] Ambient Operating -40 to +90°C [-40 to +194°F]...
Technical Information PVG 16 Proportional Valve Group Fault Monitoring and Reaction All proportional control PVG 16 actuators feature: • Integrated fault monitoring • Detecting spool stroke inconsistencies • Detecting internal hardware defects • Detecting demand signal inconsistencies • Fault reaction depending on the type of fault monitoring Generic ‒...
Technical Information PVG 16 Proportional Valve Group Fault Monitoring and Reaction Fault Reaction Overview Description Monitoring Solenoid valves Error pin output Reaction time (ms) Spool not at setpoint Passive — High Unable to reach float position Passive — High > max.
PVS End Plates The PVG 16 PVS end plates close off the valve stack section placed between them by placing them at the end. Furthermore, the end plate is ensuring Load Sense (LS) is relieved to tank pressure when the valve is not operated.
Technical Information PVG 16 Proportional Valve Group PVS End Plates PVS/PVSI The PVS/PVSI are made of either aluminum or cast iron material and works as an end plate. The PVSI Start Plates features: • Integrated LS pressure relief valve to tank •...
PVS/PVSI with LX-connection The PVG 16 PVS end plates are placed at the end the valve stack section. Furthermore, the end plate is ensuring Load Sense (LS) is relieved to tank pressure when the valve is not operated. The LX port enables other remote valves to be connected onto the Load Sense shuttle network.
Page 89
Technical Information PVG 16 Proportional Valve Group PVS End Plates Part numbers for PVS/PVSI with LX-port connection (continued) Part number Max. pressure Material Weight kg [lb] LX port Mounting G1/8” 157B2011 300 bar [4351 psi] Aluminum 0.495 [1.09] 3/8-24 UNF...
PVSI is made of cast iron and works as an end plate. The PVSI with LX connection enables another valves LS pressure to be shuttled to the pump when needed. The additional P- and T-port connections enables an additional pump flow to a PVG 16 valve. The PVSI with P-, T-, LX- and M-connection features: •...
Technical Information PVG 16 Proportional Valve Group PVS End Plates PVST with T-connection The PVST end plate closes off the valve stack section placed between them by placing it at the end. Furthermore, the end plate is ensuring Load Sense (LS) is relieved to tank pressure when the valve is not operated.
The tie rods are inserted through the entire length of the PVG valve stack. The nuts are tightened at the pump side and at the end plate. To find the PVAS kit that fits your PVG 16 valve stack, you need to go to the table PVG 16 modules total length and weight on page 93 and find the length.
Technical Information PVG 16 Proportional Valve Group PVAS Stay Bolts PVG 32/16 Combinations The table of PVB 32 and PVB 16 modules combination, the total length depending on the amount of valve groups. PVB 16 Modules in mm [in] [6.26] [7.83]...
Technical Information PVG 16 Proportional Valve Group PVAS Stay Bolts PVG 256/128/32/16 Combinations The tables of PVB 256/128, 32/16 modules, total length depending on the amount of valve groups. Stay bolts for PVG 128/256/32/16 combinations consist of 2 different kits: 1.
Technical Information PVG 16 Proportional Valve Group PVG 16 Combinations Valve Stack Dimensions PVG 256/16 Dimensions The table of PVB 256 and PVB 16 combination valve stack dimensions overview table with accompanying drawing. 95 [3.74] 132 [5.20] PVB 256/16 combination valve stack dimensions, mm [in]...
Page 107
Technical Information PVG 16 Proportional Valve Group PVG 16 Combinations Valve Stack Dimensions Weight for a PVG 256/16 valve stack The combined weight of a PVG 256/16 valve stack can be defined like this: (Numbers of PVB 256 x 20.9) + (numbers of PVB 16 x 3,67) + 17.5 = Weight in kg (Numbers of PVB 256 x 40.08) + (numbers of PVB 16 x 8.09) + 38.6 = Weight in lb...
Page 112
Phone: +86 21 3418 5200 Danfoss can accept no responsibility for possible errors in catalogues, brochures and other printed material. Danfoss reserves the right to alter its products without notice. This also applies to products already on order provided that such alterations can be made without subsequent changes being necessary in specifications already agreed.
Need help?
Do you have a question about the PVG 16 and is the answer not in the manual?
Questions and answers